LANDOLT-BORNSTEIN Numerical Data and Functional Relationships in Scienceand Technology
Nau Series Editor in Chief: 0. Madelung Group III: Crystal and Solid StatePhysics
Volume 26 Diffusion in Solid Metals and Alloys H. Bakker - H.P. Bonzel - C.M. Bruff * M.A. Dayananda W. Gust - J. Horvath * I. Kaur - G.V. Kidson - A.D. Le Claire H. Mehrer - G.E. Murch * G. Neumann - N. Stolica - N.A. Stolwijk
Editor: H. Mehrer
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ISBN 3-540-50886-4 ISBN o-387-50886-4
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technology. - N.S. teilw. Gesamthrsg.: K.-H. Hellwege; 0. Madelung. - N.S. Gesamthrsg.: 0. Madelung. Gruppe 3, Kristall- und Festk6rperphysik. NE: Landolt, Hans [Begr.]; Hellwege, Karl-Heinz IHrsg.1; Madelung. Otfried [Hrsg.]; PT Ed. 26. Diffusion in festen Metallen und Legierungen/H. Bakker... Hrsg.: H. Mehrer. - 1990
ISBN 3-540-50886-4(Berlin . . .) ISBN o-387-50886-4 (New York.. .) NE: Bakker, H. IMitverf.1; Mehrer, Helmut B-Ins.1
This work is subjectto copyright, All rights are reserved,whether the whole or part of the material is concerned,specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its current version, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. 0 Springer-Verlag Berlin Heidelberg 1990 Printed in Germany The useof registerednames,trademarks, etc. in this publication doesnot imply, even in the absenceof a specific statement, that such namesare exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: K. Triltsch, Wiirzburg Printing: Druckhaus Langenscheidt KG, Berlin Bookbinding: Liiderita & Bauer-GmbH, Berlin 2163/302&543210- Printed on acid-free paper
Editor H. Mehrer
Institut fur Metallforschung, Universitit Miinster, W-4400 Miinster, FRG
Contributors H. Bakker
Natuurkundig Laboratorium der Universiteit van Amsterdam, 1018 XE Amsterdam, The Netherlands H. P. Bonzel Institut fur Grenzfllchenforschung und Vakuumphysik, KFA Jiilich, W-5170 Jiilich, FRG C. M. Bruff Department of Chemical and Materials Engineering, The University of Newcastle, Newcastle, NSW 2308, Australia M. A. Dayananda School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA W. Gust Max-Planck-Institut fur Metallforschung, Institut fur Werkstoffwissenschaften, W-7000 Stuttgart 1, FRG J. Horveth W-7000 Stuttgart 1, FRG I. Kaur Max-Planck-Institut fur Metallforschung, Institut fur Werkstoffwissenschaften, W-7000 Stuttgart 1, FRG %. V. Kidson Deep River, Ontario, KOJ IPO, Canada A. D. Le Claire Oxford Research Unit, The Open University, Boars Hill, Oxford OX1 RDY, United Kingdom H. Mehrer Institut fur Metallforschung, Universitat Miinster, W-4400 Miinster, FRG G. E. Murch Department of Chemical and Materials Engineering, The University of Newcastle, Newcastle, NSW 2308, Australia G. Neumann Institut fur Physikalische Chemie, FU Berlin, 1000Berlin 33, FRG N. Stolica Institut fiir Metallforschung, Universitat Miinster, W-4400 Mtinster, FRG N. A. Stolwijk Institut fur Metallforschung, Universitlt Miinster, W-4400 Mtinster, FRG
VIII
Preface
high precision became possible. Since then considerable experimental efforts have been devoted to a systematic study of diffusion in all types of metals and alloys using radioactive tracers. In addition during the recent decades, the scientific development of other techniques applicable in diffusion studies like electron microprobe analysis, secondary ion mass spectroscopy, ion beam backscattering profiling, nuclear magnetic relaxation, MEiBbauer spectroscopy, after effect measurements, etc., has been extraordinary. Because of the historical development and the strict desire for a critical evaluation of the available data, the reference lists in the various chapters start in general with references from the 50’s. The critical compilation of data was done in collaboration with 13 experts from the ‘diffusion community’ and has resulted in tables and series of diagrams which present in 12 chapters data for the following properties: self- and impurity-diffusion in metallic elements, self-diffusion in homogeneous binary alloys, chemical diffusion in binary and ternary alloys, diffusion in amorphous alloys, diffusion of interstitial foreign atoms like hydrogen, carbon, oxygen and nitrogen in metallic elements, mass and pressure * dependence of diffusion, diffusion along dislocations, grain and interphase boundary diffusion, and diffusion on metal surfaces. A general introductory chapter acquaints the user of this volume of the basic concepts and experimental methods in the field. The efforts of many people were involved in the preparation of this volume: It was a great experience for me at the beginning, that most colleagues whom I asked were indeed ready to make a contribution. The collaboration with coauthors continued to be excellent. I am also grateful to them for many suggestions to the general introductory chapter. The collaboration with the editor-in-chief, Professor O.Madelung, and with the editorial staff of Landolt-Bernstein, in particular with Dr. W. Polzin, Mrs. I. Lenhart and Mrs. R. Lettmann, was always encouraging. I also have benefited greatly over the years from discussions with my colleagues in Miinster, Dr. N. A. Stolwijk, Dr. N. Stolica, Professor Chr. Herzig, em. Professor Th. Heumann, Professor E. Nembach, with many students who worked for their diploma or doctoral thesis and with the guest scientists Dr. G. Erdelyi and Dr. J. Cermak. In the preparation of this volume during several years, I have been helped by my secretary Mrs. Niehues-Korouma, by Dipl. Phys. W. Lerch and Dip!. Phys. H. G. Hettwer, Mrs. G. Todt and Mr. M. Mevenkamp. I expressmy gratitude to all these persons. I am also grateful to Professor W. L. Johnson who invited me to spend several months in 1990 as a visiting professor at California Institute of Technology in Pasadena during a sabattical leave from Mtinster. The accomplishment of the volume has benelitted from this visit in many respects. Last, but not least, I express my deep gratitude to my wife, Karin, and to my children, Tobias, Julia, Simon and Lisa, for their moral support and their patience during many weekends over several years. Miinster, October 1990
Helmut Mehrer
Ref. p. 301
I
1.1 Fick’s laws, flux of particles, isotropic and anisotropic diffusion
1 General introduction 1.1 Fick’s laws, flux of particles, isotropic and anisotropic diffusion The law governing diffusion processesand hence the redistribution of concentrations is Fick’s first law, which for an isotropic medium or a cubic crystal can be written as J= -D grade.
(1.1)
J is the instantaneous flux of particles of a certain speciesand c is the concentration of the same species.The negative sign in (1.1) indicates the opposite direction of the flux compared to the concentration gradient. The factor of proportionality D is denoted as diffusion coeficient or as diffusivity. Jis expressedin number of particles or moles per unit area and unit time and c in particles or moles per unit volume. Consequently D has the dimension length2 time- l. In the international system of units (SIU) used in this volume, diffusion coefficients are expressedin m 2s- ’ . In the cgs-systemwhich is still used in the literature, too, they are expressedin cm’ s-I . D depends on temperature, pressure and in general also on concentration. Many metallic elements and alloys are cubic. Therefore, in many casesD is indeed a scalar quantity. For anisotropic media and non-cubic crystals Fick’s first law generalizes to J= - BVc,
(I.3
where 9 is a symmetric second rank tensor denoted as the diffusion coefficient tensor. Equation (1.2)meansthat the diffusion coefficient varies with direction. The diffusion flux is parallel to grade only along the three orthogonal principal axes of diffusion. If x1, x2, xj denote these principal axes and J1, J, and J3 the pertaining components of the diffusion flux, (1.2) may still be written as JI=-D,; J=-D 2
i 2 ax,
J,=-D,&. 3 D,, D,, D, denote the principal diffusion coefficients. In general the diffusion flux and grad c are not parallel.
However, if yl, yZ, y3 denote the direction cosines of grad c a diffusion coefficient for the direction (rl, yZ, y3)may be defined as (1.4) D(Y,,Yz,Y~)=Y:.D~+Y~Dz+Y~D~. Therefore, anisotropic diffusion is completely described by the three principal diffusion coefficients. For crystals with orthorhombic and higher symmetry the principal axes of diffusion coincide with the axes of crystallographic symmetry. In uniaxial (tetragonal, hexagonal, trigonal) crystals with the unique axis parallel to the x, axis, we have D, = D, =l=D,. The diffusion coefficients for both directions perpendicular to the unique axis are the sameand are usually denoted as D,. The diffusion coefficient parallel to the unique axis is denoted as D,,. For uniaxial crystals (1.4) reduces to D(0) = D,, cos2 0 + D, sin2 8, (I.3 where ~9is the angle between diffusion direction and crystal axis. For cubic crystals we have D, = D, = D, = D and (1.2) reduces to (1.1). Equation (1.1) and its three dimensional generalizations provide a formal definition of the diffusion coefhcient as the ratio of the flux and the concentration gradient. The steady state methods for measuring diffusion are based directly on Fick’s first law.
Land&-BBmstein New Series III/26
Mehrer
2
1.2.1 Sandwich solution and thin layer solution
[Ref. p. 30
In non-steady state situations the diffusion flux and the concentration vary with time t. In such situations in addition to Fick’s first law ‘a balance equation is necessary.For particles which undergo no reactions this is the equation of continuity
Combining (1.2) and (1.6) yields 8C
ar = div (3 Vc)
(1.7)
which is denoted as Fick’s second law. When the concentration varies only along a certain direction denoted by x (1.7) becomes
If furthermore D is independent of concentration and hence of position x in the sample (1.8) reduces to (1.9) For most diffusion experiments either (1.1) or its generalization to the anisotropic case(1.2),and in non-steady state situations either (1.8) or (1.9), respectively provide appropriate descriptions of the diffusion process.
1.2 Solutions of diffusion equations for constant diffusivity The diffusion coefficient is independent of concentration and position when diffusion occurs in chemically homogeneoussystems.Such measurementsare possible e.g.through the use of radioactive tracer elements.Since these measurementsrequire extremely small amounts of tracers, the system remains essentially homogeneous during the diffusion. The diffusion of an interstitial solute in a metal or alloy solvent may be also described by a constant D as long as the concentration differences are small. In section 1.2 some simple analytical solutions of the equation (1.8) for various initial and boundary conditions are described. For more comprehensive collections of solutions we refer to several textbooks [55H, 59C, 63S, 645,66A, 7X, 85P, 89Sl].
1.2.1 Sandwich solution and thin layer solution A very thin layer of the diffusing speciesof total amount M per unit area is deposited at the boundary x = 0 between two identical samples. After diffusion for time t the concentration is described by M
exp (1.10) 2&E provided that the thickness of the deposited layer is much smaller than 2(D t) *‘2. (1.10)is often also called either instantaneous sowce solution or Gaussian concentration profile. A plot of (1.10)in linear scalesis shown in Fig. 1 for 4 different values of 2 fi. The quantity 2(0 t)‘12 is a measurefor the penetration depth and occurs in most diffusion problems. It is often denoted as d@sion length. Instantaneous source diffusion also occurs when a quantity M per unit area is placed as a source on the surface of a sample and if the diffusing speciesis consumed only by diffusion into the sample.The concentration profile is then given by c(x, t) = ~
-- * c(x, t)=-& exp ( 4Xdt >
(1.11)
The thin layer solution is often used in radiotracer experiments for the determination of D from the concentration profile (seesubsection 1.6.1.2.1).The thin layer solution differs by a factor 2 from the sandwich solution since in (1.11) diffusion occurs into a half-space. Casesin which the thin film condition is violated becauseof low solubility of the diffusing speciesare not uncommon in impurity diffusion. In such casesoften (1.14)can be used instead of(l.11). For a detailed discussion of solubility-limited diffusion the reader is referred to [63 M].
Mehrer
Land&-B6mstein New Series 111126
Ref. p. 301
3
1.2.2 Constant surface concentration and semi-infinite sample
0.6
Fig. 1. Instantaneous source (Gaussian) diffusion profiles. The concentration normalized to the total amount Mis plotted versus penetration distance x for four different values of the diffusion length 2 @.
0
0.5
1.0
1.5
x-
2.0
2.5
:
1.2.2 Constant surface concentration and semi-infinite sample If at t = 0 the concentration in a semi-infinite sample was c(x, 0) = c0 and if at t > 0 the surface concentration is maintained at ~(0, t) = c, the appropriate solution is c - c,
In (1.12)
(1.12)
= erf(x/2 J&) co - c,
erfz = -?- 5 e-“‘du (1.13) fro denotes the error function. A sample may be considered as semi-infinite as long as (D t)l” is very much smaller than the sample dimension in diffusion direction. For co = 0 (1.12) leads to , (1.14) cfc, = erfc(x/2 JiYt) where the complementary error function is defined by erfcz = 1 - erfz.
(1.15)
Equation (1.14) describes the in-diffusion of a certain speciesfrom a surface concentration maintained at c,. A plot of (1.14) in linear scales is shown in Fig. 2 for 4 different values of 2(Dt)‘/2. Figure 3a and 3b show comparisons between the instantaneous source concentration profile (1.11)and the constant surface concentration profile (1.14) in logarithmic scales either as a function of the penetration distance or as a function of the penetration distance squared. For c, = 0 (1.12) leads to c/co = erf(x@ @) . (1.16) (1.16)is the appropriate solution e.g.for the evaporation of a volatile solute element of initial concentration co from a non-volatile solvent, or for the decarburization of a metal in an oxidizing atmosphere. The diffusion flux per unit area which penetrates the surface is D cJ~ in the caseof (1.14)and - D co/ ,/&% in the case of (1.16).The total amount of diffusing substance M(t) which penetrates into the sample is &f(t) = 2c, JzJi
(1.17)
in case of (1.14) and the amount escaping from the sample in the case of (1.16) is M(t) = 2c, JEqi
.
(1.18)
Equations (1.17)or (1.18)may be used in in- and out-diffusion experiments to determine D either from the total amount of material taken up by or lost from a sample. The solutions given in subsections 1.2.1and 1.2.2are applicable as long as (D t)1/2is very much smaller than the sample dimensions in diffusion direction. Under such conditions the samplesmay be considered as infinite or semi-infinite. Land&-Bibstein New Series III/26
4
1.2.3 Diffusion in a membrane
[Ref. p. 30
0.8 0.6 I L.7 :
0.4
0.2 2.5 i0 1.5 2.0 xFig. 2. Constant surface concentration (erfc) diffusion proIiles. The concentration normalized to the constant surface conccntraction r/c, is plotted versusdistance from the surface for four different values of the diffusion length 2 fi. 0.5
1.0-
1 10 ;;I 10-2 II ; 10-s u lo-’ 10.5 0
0 1.5 3.0 k.5 6.0 15 9.0 0.5 1.0 1.5 2.0 2.5 30 b a I’= x2/1,Lit z=x/zyzFig. 3. Instantaneous source (Gaussian) and constant surface concentration source (erfc) diffusion profiles in a semilogarithmic plot. The concentration normalized to the surface concentration is plotted in (a) versus the distance from the surface normalized to the diffusion length z = x/2 ,/% and in (b) versus z*.
1.2.3 Diffusion in a membrane In this subsection we consider two casesof one dimensional diffusion in a membrane of thickness L bounded by two parallel planes. If the surfaces of the membrane at x = 0 and x = L are maintained at constant concentrations c, and c2 as illustrated in Fig. 4a, after some delay time of the order of L2/6D(seebelow) a stead~~ sr~te is reached which is described by
c-c, c,=c,=
x
(1.19)
According to (1.19)the concentration changeslinearly from c1 to c2 through the membrane.The flux acrossthe membrane is given by
J = D(c, -Q/L.
(1.20)
Provided that c,, c2 and L are known, D can be determined from (1.20) by measuring .I. If the region of the membrane - L/2 < x < L/2 is initially at uniform concentration c0 and the surfacesare kept at constant concentration c, either desorption (c, < c,J or ahsorption (c, > cO)can occur as illustrated in Fig. 4 b. The ~~ort-srca~~~ srnre solution of (1.9) is described by c - co -,1-T! cs - co
C-1) n 2=. 2n ”
cos[(2n + 1)
Mehrer
nx/L] exp[-(2n
+ l)2n2Dt/L2].
(1.21 a)
land&BBmstcin New Series III,‘26
Ref. p. 301
1.2.3 Diffusion
in a membrane
Solution (1.21 a) is particularly useful for large timessince then only few terms in the sum contribute significantly. The appropriate solution for small times is
c - co
F (- 1y erfcW + 1) WI - x + 2 (- 1y erfcIOn + 1) WI + x
cs- co
n=O
n=O
2JDt
(1.21 b)
2JDt
Equations (1.21 a) and (1.21 b) can be written in terms of the dimensionless parameters D t/L’ and x/L. Graphs of (c - co)/(c, - co) versus x/(L/2) are shown in Fig. 4c for various values of 4 D tJL2. The total amount M(t) of the diffusing species which has entered the membrane at time t with respect to the corresponding quantity M(co) after infinite time obtained by integration of (1.21 a) is
M(t)
M(a) and by integration
= 1
8 m 1 “FO exp[- 2 (2n + 1)27?
(2n + 1)2x2Dt/LZ]
(1.22a)
of (1.21 b) is I/&
+ 2 jJ (- I)” ierfc nL n=O 2JDt
where ierfc z = 7 erfc u du I
1
(1.22b)
(1.22c)
denotes the integral of the complementaryerror function. For c, = 0 the expressions (1.21) and (1.22) can be used to describe the outgassing of a gaseous or volatile solute from a membrane. The case co = 0 describes the uptake of a gas or a solute by a thin slab of solvent material.
in.
a
0
L
x-
l
-L/2
b
0
L/2
X-
Fig. 4. Concentration distributions in “plane sheet” membranes of thickness L. (a) Steady state distribution with constant surface concentrations c1 and c2 according to (1.19). (b) Schematic non-steady state distribution according to (1.21a) for the casesof absorption c, > c,, and desorption cs < cO. (c) Concentration distribution at various times in a membrane -L/2 < x < L/2 with an initial uniform concentration c0 and surface concentration c, from (1.21) according to [75C]. The numbers on the curves are values of the dimensionless quantity 4 D t/L'.
Land&-Bhmstein New Series III/26
Mehrer
1.2.4 Diffusion in a cylinder; 1.2.5 Diffusion in a sphere
6
[Ref. p. 30
1.2.4 Diffusion in a cylinder We consider a long circular cylinder of radius R in which diffusion occurs everywhere radially. Concentraion is then a function of distance r from the cylinder axis and of time t. If the concentration is initially uniform and equal to c0 throughout the cylinder and if the surface concentration at r = R is maintained at c, for t 2 0, :he solution of (1.9) . , is c - co m exp(- D~,2t) JO(cl,r) -= (1.23a) + n 1 a, Jl 6%RI . cs - co In (1.23)J,(z) and J,(z) are the Besselfunctions of the first kind with orders zero and one, respectively. The r, are roots of J,(cc,R) = 0
which are tabulated in tables of Besselfunctions. Solutions for small times can be found in [75C]. The solution ‘or a cylinder can be written in terms of the dimensionless parameters Dt/R* and r/R. The corresponding graphical representation is given in Fig. 5. The quantity M(t) of the diffusing specieswhich has entered or left the cylinder in time t with respect to the :orresponding quantity M(co) at infinite time is obtained from (1.23) as
-=M(t) M(a)
(1.24) $ -$exp(-Daft). n’ n Equations (1.23) and (1.24) can be used for cylindrical samples to describe the outgassing or the uptake of Ysolute.
I
/I
Y
A
1 -f
//n/llrr
Fig. 5. Concentration distribution at various times in a cylinder of radius R with an initial uniform concentration cOand constant surface concentration c, according to [7X3 The numbers on curves are values of the dimensionless quantity DrjR’.
0.4
0.6
0.8
1.0
r/R -
1.2.5 Diffusion in a sphere We consider a sphere of radius R and restrict ourselves to a case where diffusion is radial. If the surface concentration for t 2 0 is maintained at c, and if the sphere is initially loaded with a uniform concentration co the solution is c - co =,+E cs - co
2 iI....? n xr “=I
sin y
exp[- n*rr* Dt/R*]
(1.25)
where r denotes the distance from the centre of the sphere.The total amount of the diffusing speciesM(t) at time t entering or leaving the sphere obtained by integration of (1.25) is given by
MO) -= M(a)
1 - -$ “el -$ exp(- n27c2Dt/R2)
(1.26)
where M(m) denotes the total amount at infinite time. Curves showing the solution of (1.25) as a function oi r/R for different values of the dimensionless parameter Dt/R* are reproduced in Fig. 6. Equation (1.25)and (1.26) can be used to describe the outgassing or the uptake of a solute from or by a sphere. Mehrer
la”ooll-Bomslel” New Series III/26
Ref. p. 301
1.3 Diff. eq. for cont.-dependent diffusivity;
Fig. 6. Concentration distribution at various times in a sphere of radius R with an initial uniform concentration cO and constant surfaceconcentration c, according to [75C]. The numbers on curves are values of the dimensionless quantity
1.4.1 Self-diff. coefficient
0.2
Dt/R2.
0
0.2
OA
0.6
0.8
'
r/R -
1.3 Diffusion equation for concentration-dependent diffusivity In general the diffusion coefficient will depend on the concentration of the species,which also means that the diffusion coefficient changes with position in the sample. In this case according to (1.8) Fick’s second law must be written as (1.27) In (1.27) we have used d for the chemical diffusion coef$cient (seesection 1.4). The solution of (1.27) in closed form is (apart from special casesof b(c)) usually not possible and numeric or graphic integrations of (1.27) are necessary.The most frequently used method of analysis is the Boltzmann-Matano method which was proposed by Matano [33M] and is based on a transformation of (1.27)which is due to Boltzmann [1894B]. This method is described in subsection 1.6.1.2.2.
1.4 The various diffusion coefficients In this section various experimental situations and the various diffusion coefficients which they entail are described. In order to permit a clear distinction between the various diffusion coefficients in the present chapter the symbol "D" is used for the diffusion coefficient in combination with lower and upper indices. However, the indices are dropped again in the following sections of chapter 1 and in the data chapters of the whole volume whenever it is clear which diffusion coefficient is considered.
1.4.1 Self-diffusion coefficient 1.4.1.1 Pure elements If in a solid of element A the diffusion of A atoms is studied, one speaks about self-diffusion. Studies of self-diffusion usually utilize tracer atoms A* of the same element. In most experiments tracers are marked by their radioactivity. A typical situation for a radiotracer experiment is shown in Fig. 7a. The isotopic mass or the nuclear spin is sometimes used as tag for tracer atoms as well. The tracer self-&&ion coefficient DF is in a microscopic picture according to
DA’ =fI” A
62
related to the jump length 1of atomic jumps and to the mean residence time of atoms r on a certain site in a ,crystalline solid. The correlation factor f is in the caseof self-diffusion often only a numeric factor which depends on the crystal structure and on the diffusion mechanism [7OLl]. Tracer self-diffusion data in pure metallic elements are listed in chapter 2. Land&Biimstein New Series III/26
Mehrer
1.4.1 Self-diffusion coefficient
8
a Fig. sion (a) (b) (c) (d)
b
C
[Ref. p. 30
d
7. Various situations for diffusion experiments which entail different diffucocflicients: thin layer of A* on A: tracer self-diffusion in pure elements thin layer of B* on A: impurity diGsion in pure elements thin layer of A* or B* on AB alloy: tracer self-diffusion in homogeneous alloys diffusion couple of metals A and B: interdiffusion of two metals A and B.
1.4.1.2 Homogeneous alloys In a homogeneous binary AB alloy two tracer self-diffusion coefficients for both A* and B* tracer atoms can be measured.They are denoted as Dii and DAB;),respectively. A typical experimental situation is illustrated in Fig. 7c. Since in a radiotracer experiment the concentration of A* or B* is usually negligible the alloy composition is not modified by the diffusing species.In general the tracer self-diffusion coeflicients depend on the alloy composition. Results on self-diffusion in &/tlte binary alloys containing small atomic fractions X, are frequently represented in terms of (1.29a) 0;; = D,^;(X,) = D,^‘[l + b,X, + b2X; . ..I. Then D:rf is denoted as the sol~~t seljrdtj%oa coeffjcient and DIi as the solute diJiusion coeflcienf. Experimenare usually well represented by (1.29a) and b,, b, etc. are denoted as solvent tal measurements of Dii(X,) enhnrtcet~lcnrfictors. D,A’(O) is the tracer self-diffusion coefficient in the pure solvent. b, is largely determined by perturbations due to isolated solute atoms, b, by pairs of solute atoms, and so on. For similar reasons,the soltrt~ dijirsion coej’kient DrR at low concentrations, can be representedby a power seriesdependence D:f Dy is then also denoted as impurity solute enhnncement factors.
= D,“;(X,)
=
Dr[l
+ B, X, + B,X; . ..I.
(1.29b)
diffusion coefficient of speciesB in solvent A. B,, B, etc. are denoted as
Depending on the specific alloy system, the one component is more or less soluble in the other component, i.e. the primary and terminal phases extend over wider or smaller composition ranges. A primary phase of an alloy AB is the solution of element B in A and thus has the same crystal structure as element A, whereas the terminal phase crystallizes in the crystal structure of element B. For higher concentrations these alloys exhibit usually short-range or even long-range atomic order, which may cause substantial deviations from the behaviour represented by the equations (1.29a, b). Attempts to describe the diffusion coefficients in these concentrared alloys as a function of composition theoretically or even empirically are less successful than for dilute alloys [84Bl]. For a limited number of alloy systems the primary/terminal phase extends over the whole composition range, sometimes with a tendency of atomic long-range order at higher concentrations and lower temperatures. This ordering has a profound influence on the diffusion coefficients of both components. An example is the Fe-Co system. In contrast, many alloy systemsexhibit intermediate phases. In the phase diagram these phasesare separated from the primary or terminal phases or from each other by two-phase regions. They usually crystallize in ordered structures. These may be completely different from the crystal structures of the pure components. Therefore the self-diffusion coeilicients in these materials can not be related to those in the pure constituents at all. A scarcenumber of theseintermediate phasesshow an order-disorder transition at higher temperatures with a considerable influence on the diffusion characteristics. Ordered intermediate phasesare also called intermetallit compods. The number of measurementsof self-diffusion coefficients in intermetallic compounds is relatively small. but it is clear already that the detailed atomic defect structure of these materials is essential to their self-diffusion behaviour. Tracer self-diffusion data in binary alloys and in intermediate phases are listed in chapter 4. Land&BBmstein New Series III,/26
Ref. p. 301
1.4.2, 3, 4 Impurity, chemical, intrinsic diffusion coefficients
9
1.4.2 Impurity diffusion coefficient When the diffusion of a solute B in a solvent A is measured at extremely small concentration of B, which e.g. radiotracers permit (by diffusion of tracer B* into pure metal A (see Fig. 7 b), the impurity diffusion coefficient 0: is observed. Apart from their practical importance impurity diffusion coefficients are also of special theoretical interest becausethey describe the diffusion of an isolated impurity atom in an otherwise pure solvent. Impurity diffusion of metallic elementsin metals is covered in chapter 3 and the diffusion of C, N, and 0 diffusing in metals in chapter 8.
1.4.3 Chemical diffusion coefficient A diffusion coefficient which is measured in a chemical concentration gradient is denoted as chemical coefficient 6 (seealso section 1.3).Any chemical diffusion coefficient describesdiffusion referred to fixed axes in the sample. d can be deduced from the concentration-depth-profile (see section 1.6) and in general depends on concentration. Measurements which entail diffusion in a chemical diffusion gradient are:
difision
(1) Diffusion of interstitial solutes (e.g. hydrogen) in metals (2) Interdiffusion of two metals A and B which form substitutional solid solutions or interdiffusion between two alloys of the metals. An interdiffusion experiment between two pure metals is schematically illustrated in Figs. 76 and 17(a). Obviously diffusion is measured in a chemical gradient. In the case of interdiffusion d is also denoted as interdiffusion coefjcient. For many practical purposes the chemical interdiffusion coefficient is an adequate measure of the diffusion behaviour of an alloy. Data for chemical diffusion are compiled for binary alloys in chapter 5 and for ternary alloys in chapter 6. Chapter 6 also contains an introduction to ternary diffusion, which is beyond the scopeof the general introduction. Diffusion of interstitial solutes except hydrogen is covered in chapter 8 and hydrogen diffusion in chapter 9.
1.4.4 Intrinsic diffusion coefficients The intrinsic diffusion coeficients (or component diffusion coefficients) DA and D, of an AB alloy, which are primarily of interest for more fundamental physical reasons, describe the diffusion of the two speciesA and B relative to the lattice planes. The diffusion rates of A and B are usually not equal. Therefore, in an interdiffusion experiment a net flux of atoms acrossany lattice plane’exists. If the number of lattice sites is conserved the lattice planes in the diffusion zone move with respect to the sample-fixed axes to compensate for the unequal fluxes across it. At the same time lattice sites are created on the one side of the diffusion zone and annihilated on the other side. This can be achieved by creation and annihilation of point defects(vacancies,self-interstitials). The shift of lattice planes with respect to sample-fixed axes is denoted as Kirkendall effect. The Kirkendall effect is illustrated schematically in Fig. 17(b). Inert markers (e.g. fine insoluble wires, oxide particles, etc.) have been incorporated at the initial interface between the two interdiffusing metals A and B or between two interdiffusing AB alloys of different composition. During the diffusion process a shift of the markers takes place. This Kirkendall shift was for the first time observed in [47S].It can be used to determine the velocity u of the markers. u is also denoted as Kirkendall velocity. A more complete description of diffusion in substitutional binary alloys is based on the intrinsic diffusion coefficients. DA and D, can be determined from the chemical diffusion coefficient d and the marker shift: It is possible to show [48D, 49D, 63S, 66A, 85P, 89Sl] that the chemical and intrinsic diffusion coefficients are related by the equation 0” =X,0,
+ X,0,
(1.30)
where X, and X, are the molar fractions of speciesA and B. The velocity u of an inert marker is given by v = (D, - DB) ax&
(1.31)
with aX,/ax denoting the concentration gradient at the marker position. u is also denoted as Kirkendall velocity. Using (1.30) and (1.31) DA and D, can be calculated separately when B and 2)have been measured. An alternative method permits the measurement of the ratio DA/DB instead of v. Such a method which is based on the marker shift in a sandwich arrangement of alloy samples with two different compositions is described in [77Hl]. Land&-Biimstein New Series III/26
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10
1.5.1 Direct interstitial mechanism
[Ref. p. 30
Equation (1.30) assumesno net volume change which is only correct for ideal solutions. For non-ideal mixtures (1.30) must be replaced by [7OL2, 85P] (1.32) where t’ and vBdenote the partial molar volumes of speciesA and B, respectively. c, and cs are the concentrations of speciesA and B. Equations (1.31)and (1.32)also require complete flux compensation along the diffusion direction. In practice this is sometimes not the caseas can be seenfor example, from the occurrence of pores [53B] on the side of the diffusion couple suffering a net loss of atoms and from the occurrence of changes in lateral dimensions [52S, 59R]. These “side effects” of the Kirkendall effect are also illustrated in Fig. 17(b). The intrinsic diffusion coefficients DA and D, and the tracer diffusion coefficients Dfi and Dz”;, in an AB alloy differ fundamentally. The latter pertain to a homogeneous alloy whereas the intrinsic diffusion coefficients are measured in the presenceof a chemical composition gradient. This gradient imposes on the otherwise random motion of atoms a bias, which makesatoms preferentially jump in one direction along the composition gradient. It is possible to show [48D, 83B, 85P] that the intrinsic diffusion coefficients and the tracer self-diffusion coefficients in the alloy are related via DA=
D;;d,
(1.33)
D,=
D,“;$
(1.34)
and where 4 is denoted as thcrn~od~man~ic factor. The relations (1.30),(1.31),(1.33) and (1.34) were first established by Darken [48D, 49D]. They are sometimes denoted as Darken’s equations. The thermodynamic factor is given by
+=1+$$
x. ap. z-L.1 kT
I
(1.35)
aXi’
where yi is the activity coejlicient of the species i in the alloy and pi its chemical potential. Because of the Gibbs-Duhem relation Q,is the samefor both speciesof binary alloys. The thermodynamic factor is larger than unity for alloys with negative enthalpy of mixing and smaller than unity in the opposite case.Sometimesit may be even negative which leads to the phenomenon of “uphill’‘-diffusion. Equations (1.33) and (1.34) are approximate forms of the more elaborate expressions DA = Dti4rA
(1.36)
D, = Dik+rB
(1.37)
and where r, and r, denote the so-called vacancy wind factors. For a detailed discussion of these factors the reader is referred to [68M, 83B, 85P]. Often (1.33) and (1.34) are reasonably well obeyed experimentally.
1.5 Atomistic mechanisms of diffusion For a given temperature the diffusion coefticients of different atoms in a metal or an alloy may differ by many orders of magnitude. The diffusivity of an atom depends strongly on the mechanism by which it moves. In this section we describe briefly the most important atomic mechanisms of diffusion. For further details seee.g.[63S, 66A, 85P, 89Sl].
1.5.1 Direct interstitial mechanism Foreign atoms that are located exclusively in interstitial sites of an otherwise perfect crystal may diffuse simply by jumping from interstitial site to interstitial site as indicated in Fig. 8a. This mechanism is denoted as the interstitial (or even more specifically the direct interstitial) mechanism. The movement of interstitially dissolved atoms does not involve intrinsic point defects(vacancies,divacancies, self-interstitials . . .) as diffusion vehicles. Therefore, direct interstitial diffusion is usually much faster than the diffusion of substitutionally incorporated atoms. The direct interstitial mechanism is responsible e.g.for diffusion of hydrogen (seechapter 9) and for the diffusion of other small impurity atoms like C, N and 0 (seechapter 8) in metals. Mehrer
l..andolt-Bornstem New Series III!26
Ref. p. 301
11
1.5.2,3,4 Direct exchange and ring, vacancy, divacancy mechanisms
Fig. 8. Illustration of various direct diffusion mechanismsin zrystals according to [84F]: [a) direct interstitial mechanism (foreign atom [full circle] jumping from interstice 1 to interstice 2, from 2 to 3, etc.); [b) direct exchange mechanism of two neighbouring atoms on regular lattice sites; cc) ring mechanism of 4 neighbouring atoms.
a
b
1.5.2 Direct exchange and ring mechanisms The direct diffusion of substitutionally incorporated foreign atoms or of host atoms on regular lattice sites would involve the exchange of two atoms on neighbouring lattice sites (seeFig. 8 b) or of a ring of atoms (see Fig. SC).So far, no examples of these kinds of direct diffusion have been found presumably because these mechanismsare energetically unfavourable. Usually the diffusion of self-atoms or of foreign atoms on substitutional sites requires intrinsic point defects 1sdzfision vehicles (seethe following subsections 1.5.3to 1.5.6).The fact that the Kirkendall-effect (seesubsection 1.4.4)is observed in substitutional alloys is strong evidence in favour of diffusion mechanismswith diffusion vehicles.
1.5.3 Vacancy mechanism In the vacancy mechanism vacant lattice sites act as diffusion vehicles. A substitutional foreign atom or a self-atom diffuses by jumping into a neighbouring vacancy (seeFig. 9). Self-diffusion in most metals and alloys and diffusion of foreign atoms (impurity diffusion) exclusively dissolved on substitutional sites occur mainly by the vacancy mechanism. Attractive or repulsive interactions between the vacancy and substitutionally dissolved foreign atoms may lead to higher or lower diffusivities of foreign atoms compared with self-diffusion of the solvent.
Fig. 9. Illustration of the vacancy mechanism according to 34F]: the tagged self-atom in tracer self-diffusion or the forAgn atom in substitutional-solute diffusion (full circle) moves, by jumping into the vacancy on its right-hand side (a), to the right (b) by one nearest-neighbour distance of the regular lattice atoms.
a
b
1.5.4 Divacancy mechanism In this casebound pairs of vacancies on neighbouring lattice sites act as diffusion vehicles. A host atom or a substitutional foreign atom on a regular site diffuses by jumping into one vacancy of the neighbouring pair (seeFig. 10).The divacancy mechanism has been proposed to contribute to self-diffusion in face-centeredcubic metals above 2/3 T, (7’,‘,= melting temperature) besidesthe vacancy mechanism [7OS].The temperature dependence of self-diffusion of fee metals has been sometimes analysed in terms of a sum of two Arrhenius terms (see section 1.8).If this is the casethe term with the lower activation enthalpy is attributed to diffusion via monovacancies and the term with the higher activation enthalpy to diffusion via divacancies.
Fig. 10. Illustration of the divacancy mechanism: The tagged self-atom in tracer self-diffusion or the foreign atom in substitutional-solute diffusion (full circle) moves, by exchanging its site with one vacancy of the divacancy on its right-hand side (a), to the right (b) by one nearest-neighbour distance of the regular lattice atoms. Land&Biirnstein New Series III/26
Mehrer
a
b
12
1S.5 Interstitialcy
mechanism; 1.5.6 Interstitial-substitutional
1.5.5 Interstitialcy
mechanisms
[Ref. p. 30
mechanism
In the intersfitinlcy (or indirect irrrerstitinl) mechanism self-b~terstitials act as diffusion vehicles. A self-interstitial replaces a substitutional atom which then in turn replaces a neighbouring lattice atom (Fig. 11). This mechanismis the counterpart of the vacancy mechanism since the self-interstitial is the antidefect ofthe vacancy. In silicon. this mechanism dominates self-diffusion and presumably plays a prominent role in the diffusion of some substitutional solutes [84F]. In metals it is presumably not of importance under thermal equilibrium conditions. However, it is important if self-interstitials are created by irradiation of a crystal with energetic particles. DitTusion in an irradiation environment is not treated in this volume.
a
c
b
Fig. 11. Illustration of the interstitialcy mechanism according to [84F]. In (a) a self-interstitial (open circle in the center of the lattice cell) has approached a tagged self-atom or a substitutional foreign atom (full circle), rcspcctively; in (b) the tagged atom has exchanged its original position with the self-interstitial. In this way the tagged atom has temporarily become an interstitial, whereas the original self-interstitial has disappcarcd by occupying a regular lattice site. In (c) the tagged atom has jumped into a regular site by pushing a self-atom into an interstitial site.
1.5.6 Interstitial-substitutional
mechanisms
Some foreign atoms A may be dissolved on interstitial (Ai) and also on substitutional sites (A,). Such atoms may diffuse via the dissociotire n~~rhnnisntor via the kick-out nwchanism. The two mechanismshave in common that the diffusivity of foreign atoms is much higher when they are located in interstitial sites than when they are located in substitutional positions. Under such circumstances the incorporation of A atoms can occur by fast diffusion as Ai interstitials and their subsequent change-over to the substitutional positions [89Sl]. The difference between the two mechanismslies in the type of the intrinsic point defect which mediates this change-over: In the dissociative mechanism illustrated in Fig. 12a (sometimesalso denoted as the Frank-7imbull or as the Longini mechnnism) the interchange involves vacancies (V) according to the reaction A,+VF-?A,.
(1.38)
The.rapid diffusion of some foreign elements in some polyvalent metals has been attributed to the dissociative mechanism (seechapter 3). For further details seee.g. [84F, 89Sl]. In the kick-out mechanism illustrated in Fig. 12b the interchange involves self-interstitials (I) according to the reaction (1.39) Ai+AA,+I. Examples for the kick-out mechanism have been established for some rapidly diffusing foreign atoms in silicon. So far no examples for kick-out diffusion in metals have been found. For details seee.g. [84F]. Mehrer
Landok-Bkimstein New Series III:26
Ref. p. 301
13
1.6.1.1 Steady-state methods
a
AS
Ai
1
AS Ai b Fig. 12. Illustration of interstitial-substitutional mechanisms: (a) dissociative mechanism (also known as Frank-Turnbull mechanism or as Longini mechanism) (b) kick-out mechanism.
1.6 Methods of measuring diffusion coefficients The experimental methods of measuring diffusion coefficients can be grouped into two categories: Direct methods which are directly based on Fick’s laws and indirect methods. The latter take advantage of the fact that many physical phenomena in solids depend on the occurrence of thermally activated motion of atoms. From suitable measurements of such phenomena it is also possible to determine a diffusion coefficient.
1.6.1 Direct methods Since in methods based on Fick’s laws diffusion always occurs over distances which are large compared to the interatomic distance direct methods are sometimes also referred to as macroscopic methods. One measures a diffusion flux, an integral over a diffusion flux, a concentration profiles or an integral over a concentration profile.
1.6.1.1 Steady-state methods These methods are based directly on Fick’s first law. The usual procedure is to perform a permeation experiment through a “membrane” which e.g.can be a thin plane sheet or a cylindrical tube. The concentrations of the diffusant are maintained at c1 and c2 on the opposite sides of the sample. The diffusion flux J is measured. After a certain delay time of the order of L2/6 D (seesubsections 1.2.3 or 1.2.4)the steady-state concentration distribution.is established in the sample. Then the diffusion coefficient can be deduced according to L
D=Jp Cl
-
(1.40) c2
from measurementsperformed on a plane sheet of thickness L (seeFig. 4a), or according to
D= _
J WW,) 2nR,
c1 -c2
(1.41)
from measurements of e.g. outward diffusion performed on a cylindrical tube with inner and outer radii R, and R,. As an alternative to (1.40), the diffusion coefficient can be determined from D = - J/(&/ax)
(1.42)
if the steady state concentration distribution across the plane sheet is measured. Permeation measurements are applicable when the diffusing speciesis either a gas (e.g.hydrogen, . . .) or if it can’be supplied to and removed from the sample through a gas or vapour phase. Land&-B6mstein New Series III/26
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14
1.6.1.2 Non-steady-state methods
[Ref. p. 30
1.6.1.2 Non-steady-state methods These methods are based on Fick’s second law for concentration-dependent (1.8)or concentration-independent diffusivities (1.9).Most frequently the concentration distribution in a sample is measured and the diffusion :oeffrcient is deduced from a comparison with the solution of Fick’s second law appropriate to the conditions >f the experiment. 1.6.1.2.1 Thin layer methods A very thin layer of the diffusant is deposited on a plane surface of the sample (seeFig. 7a, b, c). Vacuum :vaporation, electrochemical or chemical deposition and ion implantation are used as deposition techniques. After the diffusion anneal the concentration profile is given by (1.11)provided that the deposited thickness was very much smaller than (D t) ‘1’. This condition is usually easy to satisfy in radiotracer experiments of self- and impurity diffusion. Many details about the thin layer methods can be found in [84R, 89S2].Several procedures are in use to determine the redistribution of the diffusant: a) Direct profile measurements After diffusion the profile c(x) is usually determined by sectioning the diffusion zone and measuring the concentration (activity) in each section. The tracer diffusion coefficient D (in section 1.4 denoted as Dy in the caseof self-diffusion, as Dr in the caseof impurity diffusion and as 0:; in the caseof self-diffusion of A tracer in a homogeneous AB alloy) may be determined from a plot of logarithm of concentration in each section against the penetration distance squared. According to (1.11)in such a plot bulk diffusion leads to a straight line with slope - l/(4 Dt). Examples for the experimental standard of penetration profiles that can be achieved with this method are shown in Figs. 13 and 14 [87G, 84H]. The excellent linearity of these profiles permits a determination of diffusion coefficient within an accuracy of the order of a few percent. For serial sectioning several techniques are in use: Mechanical sectioning with a precision lathe (10 urn, 5 . lo-r6 m2s-‘), a microtome (1 urn, 5 * lo-‘* m* s- ‘) or a precision grinder (0.5 pm, IO- l8 m2s- ‘). Available microsectioning techniques are chemical or electrochemical attack (5 nm, lo-** m*s-‘) and sputtering by bombardment with ions (2 nm, 5 . 1O-24 m* s- ‘). The numbers in parentheses indicate the minimum section thicknessesand the minimum diffusion coefficients which can be obtained in practice. The section thicknesses and from these the penetration distance can be measured by weighing. For very thin sections weighing may be too inaccurate and optical methods (interference microscopy, . . .) or surface profile methods are to be preferred. For the determination of concentration activity counting is used in radio-tracer experiments. Becauseof the high sensitivity of counting facilities for radioactive substancesextremely small quantities of tracer atoms suffice to study diffusion. Mass spectrometry is sometimes also used for concentration measurements. Ionic sputtering for sectioning is associatedwith secondary ion massspectrometry (SIMS), secondary neutral mass spectrometry (SNMS), or Auger electron spectroscopy (AES) in commercial SIMS, SNMS, or AES analyzers. A schematic illustration of the SIMS technique is shown in Fig. 15. For details seee.g. the review [84P]. Sputtering for sectioning associated with activity counting has been combined in some laboratory devices (see,e.g.,[75Gl, 85M]). An example is shown in Fig. 16. Occasionally electronmicroprobe analysis (EMPA) has been used to measureimpurity diffusion coeflicients. A high sensitivity of the microprobe is necessaryto monitor diffusion from deposited layers of diffusants thin enough to meet the conditions for the use of equation (1.11). b) Residual activity measurement The residual activity emanating from each newly exposed sample surface at depth x in a radiotracer-sectioning experiment can be used to calculate the diffusion coefficient. This method is denoted as Gruzin-Seibel or as residual activity method. c) Surface activity decreasemeasurement The diffusion coefficient may be determined from the total activity emanating from the sample surface at x = 0 after various diffusion anneals. This procedure is denoted as the surface decreasemethod. Both the residual activity and the surface decreasemethod require an integration of (1.11).They should be regarded as less reliable than the sectioning method because they necessitate a knowledge of the absorption characteristics of the radiation concerned and an assumption about the concentration profile. In addition the surface decreasemethod is particularly susceptible to errors arising from sample oxidation, tracer losses and short circuiting diffusion. Mehrer
Land&-B6mst.h New Series Ill/26
1.6.1.2 Non-steady-state methods
Ref. p. 301
.YZ-
IO9 orb. units
105
8
12
16
20.10bnm2 :
arb. units
1OS
104
I x c .P z 0 IO3 .u .z E LA
10’
10
10
0
1 0
5
10
15
20
-Km4cm2 30
x2. Fig. 13. Examples for penetration profiles obtained with the radiotracer method and microtome sectioning according to [87G]. The isotope “‘Te was implanted to a depth of about 30 nm into silver single crystals. Afterwards diffusion anneals were performed at four different temperatures and times resulting in average diffusion lengths much larger than 30 nm. Under such conditions the implants may be considered as thin film sources.The specific activities are plotted as functions of the penetration distances squared. The slopes of these curves correspond to the quantity - 1/(4Dt).
(secondary ions, neutrals 1
Fig. 15. Schematic illustration of the SIMS technique for direct measurements of diffusion profiles. Landolt-Bibstein New Series III/26
Fig. 14. Examples for profiles obtained with the radiotracer method using sputter sectioning accordjng to [84H]. The isotope Q5Zrwas electrodeposited on the surface of a-Zr single crystals. Diffusion anneals were performed at eight temperatures for different times. The specific activities are plotted as functions of the penetration distances squared. The slopes of these curves correspond to the quantity - 1/(4Di). 1 ,
I 2 3 6
Tungsten filament Anode Catcher foil camera Ar’ ions (500 to 1500eV)
2 /
3 Sputtered moteriol (neutral) I
4 Specimen 5 Specimen holder with motor for specimen rototion
Fig. 16. Schematic view of a sputtering device which is used for radioactive diffusants according to [85M]. The penetration profiles shown in Fig. 14 have been obtained with this device.
Mehrer
1.6.1.2 Non-steady-state methods
16
[Ref. p. 30
1.6.1.2.2 Diffusion couple methods with profile measurement Two homogeneous metals or alloys of concentrations c, and c2 are brought into intimate contact across a plane interface and are then allowed to interdiffuse to provide a concentration profile c(x). If the profile is determined in some convenient manner (seea) to d)) b(c) is obtained from b(c*) = -
j xdc (2tac/ax). (1.43) ( L-1 >I Equation (1.43) is the basis of the Bo/tz,tlnnr~-Mntnno method which is illustrated in Fig. 17(a). The chemical Wusion coeficient B (seesubsection 1.4.3)can be determined from an integral over a part of the measured profile and from its slope in P. The origin of the abscissax, which is denoted as the Matano plane, is defined by the condition (1.44)
Ixdc=O.
A graphic interpretation of (1.43) and (1.44) is also given in Fig. 17(a). For concentration independent B the Matano plane coincides with the initial position of the interface. For concentration dependent d this is usually not the case (SWsubsection 1.4.4).
I
F’
n’
Shifted position of markers
Cl
-
lniliol position of morkers
X-
Fig. 17(a). Illustration of the Boltzmann-Matano method for the calculation of d from equation (1.43). The Matano plane is defined by the equality of the two hatched arcas FOhl and F’O’M. Jx-dr is equal to the doubly hatched area FOHP. a@.~ is the slope of the tangent of the concentration profile in P.
Fig. 17(b).. Schematic illustration of the Kirkendall-effect and its side effects: Jn and Ja denote the diffusion fluxes of species A and B; Jhl is the net flux of matter causing the Kirkcndall shift I which is indicated by a fat arrow. The formation of pores on the side of the faster diffusing species (D,, > 0,) and lateral changes of sample dimensions are frequently observed “side effects” of the Kirkendall effect.
Sauer and Freise [62S] have deduced an expression which does not require a knowledge of the position of the Matano plane. Using the expression 7 (1 - Y) dx + (1 - y(x*)) 1 ydx -m where
1
(1.45) (1.45a)
denotes a normalized concentration, the interdiffusion coefficient can be deduced from two integrals over the observed concentration profile and from one slope. Expressions (1.43) to (1.45) are applicable if the molar volume does not change upon interdiffusion. If the molar volume V, = V,(y) depends on concentration, which is the casefor non-idea! systems,instead of (1.45) the expression (1.46) D(y(x*)) = uY*) dx + (1 - y(x*)) 1 + dx 2t (aJl/ax),. m must bc used.
1
Mehrer
Land&-BBmstein New Series 111’26
1.6.1.2 Non-steady-state methods
Ref. p. 301
17
If 0” varies little in the concentration range c1 to c2, which is often the caseif the range c1 to c2 is sufficiently restricted, the appropriate solution for concentration independent D c-q c2-Cl
1 X = - erfc ~ 2 2JE
(1.47)
may be used instead of (1.43),(1.45) or (1.46). It should be pointed out that it is the chemical or interdiffusion coefjcient (see subsection 1.4.3) which is measured with the diffusion couple method. As already mentioned in 1.4.4markers inserted at the interface can be used to locate its final position after diffusion. From this the Kirkendall velocity can be determined. If the chemical diffusion coefficient and the Kirkendall velocity or the ratio DA/DBare known the intrinsic difision coefficients can be calculated according to subsection 1.4.4. The determination of the chemical diffusion coefficient by the diffusion couple method usually requires a measurement of the concentration profile c(x) (seehowever subsection 1.6.1.2.3).Several methods are in use for this purpose: a) Sample sectioning
The profile can be obtained by sectioning the diffusion zone and measuring the quantity of the diffusing speciesin each section with an appropriate method of analysis (seesubsection 1.6.1.2.1).Sample sectioning is of course a destructive technique. It is often indispensible in thin layer experiments, especially when radiotracers are used (seea) in subsection 1.6.1.2.1).For thin film diffusion couples nowadays several non-destructive techniques are available which allow the profile determination without sectioning (seec) and d)) below. b) Electron microprobe analysis (EMPA)
In an electron microprobe analyzer a thin electron beam (diameter about 1 urn) stimulates X-ray emission of the elements to be studied. The profile can be obtained by analysing the intensity of characteristic radiation from the sample along the diffusion direction. The sensitivity in concentration is about 10e3 to 10m4depending on the element. Becauseof the finite thickness of the electron beam and the finite size of the excited volume only diffusion coefficients d 2 10-l’ m2 s- ’ can be measured.EMPA is used for interdiffusion studies in macroscopic diffusion samples.An example for an interdiffusion profile obtained by EMPA is shown in Fig. 18. Interdiffusion coefficients determined from such profiles according to equation (1.45)are shown in Fig. 19 [86H, 89Hl].
-I”000-800 -600
-400
-200 x-
0
200
400
600 pm 800
Fig. 18. Example for an interdiffusion profile obtained with electron microprobe analysis according to [86H, 89Hl]. In this experiment a diffusion couple consisting of an Ag - Sb alloy (3.92 at% Sb) and ofpure Ag was formed and annealed for 35 h at 1048K. Land&-Biimstein New Series III/26
Mehrer
[Ref. p. 30
1.6.1.2 Non-steady-state methods
18
I 0
I 1
I
I
I
I
2
3
4 ot %
5
xSb -
Fig. 19. Interdiffusion coefficients in dilute Ag-Sb alloy as a function of the Sb concentration according to [86H, 89Hl].
c) Rutherford backscattering (RBS) Rutherford backscattering uses an ion beam (usually 4He ions, typical energies several MeV) from an accelerator. A schematic illustration of a backscattering device is shown in Fig. 20. The sample is bombarded along the diffusion direction with monoenergetic ions and one studies the number of elastically backscattered ions as a function of their energy. From this energy spectrum the profile can be determined. The element itrformntion is contained in the kinematic factor of Rutherford scattering which depends on the mass of the scattering atom. The deptlt injbrmation comesfrom the continuous energy loss of the analyzing ions. The yield of backscattered ions is proportional to the concentration of backscattering atoms. This is illustrated schematically in Fig. 21(a). An example for an RBS diffusion study is shown in Figs. 21(b) to 21(d). Becauseof the limited penetration range of the ions (several urn) in a solid sample RBS is applicable when one species is deposited at t = 0 as a fairly thin film. Diffusion coefficients between lo-r6 mzsV1 and 10mz3m2s-’ are accessible.RBS is mainly applicable for the analysis of a heavy element in a light matrix. For details see,e.g., the review [84M3]. m
M
MeV Heions
000000.. 000000.. 000000*a
I
Sample
Preamplifier
1
I
m M
2
jr
Energy
Fig. 20. Schematic representation of a Rutherford backscattering device. The ion beam. the sample and the detector are indicated.
Amplifier
4
c
MCA
Fig. 21(a). Schematic illustration of Rutherford backscattering: A sample consisting of two layers of heavy and light atoms (massesM and m) is shown. Yield and energy of the backscattered ions are monitored with an appropriate detector and a multichannel analyzer (MCA). The energy spectrum is also shown. The high energy end of the spectrum (M-signal) corresponds to the ions backscattered from heavy atoms near the sample surface. The low energy end of the M-signal corresponds to the ions backscattered from heavy atoms near the interface. The signals from heavy and light atoms are separated in the energy spectrum because of the different kinematic factors.
Mehrer
Landolt-Kmstein New Series III!26
1.6.1.2 Non-steady-state methods
Ref. p. 301
x012 I
0.14 pm I 4 nt%
1.0
1.2
1x
1.6 E-
1.8
2.0
2.2 MeV 2.1,
Fig. 21 (b). RBS back scattering spectrum resulting from 2.5 MeV 4He ions incident upon Sn implanted Fe according to [84M3]. The half width of the implanted Sn profile is 25.5 nm. Y,: backscattering yield.
6.0 6.51 0
I 0.5
I 1.0
-
Y 1.5
I -Joe2pm2
2.5
Fig. 21 (c). Depth profiles of Sn in Fe measured during a sequenceof anneals at 823 K with RBS according to [84M3]. The profile at t = 0 corresponds to the as-implanted profile shown in Fig. 21(b).
lo-l7 m2/s 104'8 IP
~I lo-l9
1o-zo
10-2' 10-2'1 1.05
1.10
1.15 l/T-
1.20
1.25&' 1.2540-3K' 1.30
Fig. 21 (d). Diffusion coefficients of Sn in Fe measured by RBS according to [84M3].
d) Nuclear reaction analysis (NRA) In a nuclear reaction analysis experiment a monoenergetic ion beam (protons, 4He, . . .) is used as in RBS. The sample is bombarded in the diffusion direction and the ions induce with the element to be studied a nuclear reaction with a narrow resonance. The yield of the out-going particles created by this reaction is measured as a function of the energy of the incident beam. From the yield versus energy curve the c(x) profile can be determined. As in the caseof RBS, NRA is also applicable to diffusion couples where one speciesis deposited as a thin film. Diffusivities between lo-l6 m2 s-l and 10ez3 m2sM1 are accessible. The NRA technique is convenient for some light nuclei. For details seee.g. the review [84L].
Landolt-BGmstein New Series III/26
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1.6.1.2 Non-steady-state methods
[Ref. p. 30
1.6.1.2.3 Diffusion couple methods without profile measurement Methods for the determination of chemical diffusion coefficients without profile measurementbut restricted to low solute concentrations - i.e. close to the impurity dijiision cocjkient - are the resistometric analysis developed by Ceresara et al. [66C] and the X-ray dij’k-tion analysis developed by Fogelson [68F, 71Fj: In the resistonwtrir method a thin wire (diameter about 0.1 cm) is plated with a layer (about low4 cm) of the solute metal. The time dependenceof the resistance R of the wire at constant annealing temperature can be used to determine the diffusion coeflicient. The measured quantity usually is
R(t) - R(O) a0 = R(a) - R(0) ’
(1.48)
where R(f) denotes the resistance of the wire at time t. A theoretical expression for 4 is given in [66c]. This expression is based on the solution of Fick’s second law for diffusion into a cylinder given in subsection 1.2.4 and on the approximation that the resistivity is proportional to the solute concentration. From a comparison between the experimental values for 4 and the pertaining theoretical expression D-values can be determined. Accurate D-values are obtained for solute concentration of not more than some 0.1% provided that the solute is sufficiently soluble, that surface hold-up does not occur and that D is not strongly dependent on the concentration. The principle of the X-ray diffr,action annl~~is consists in the measurement of the surface concentration decreaseof the diffusant. A layer of about 10e5 cm is deposited on a foil of about 2. 10m2cm thickness. In a surface layer of about 10m3cm the concentration of the diffusant is determined by analyzing the diffraction line profile. The shift of the line edge is used to find the concentration, which changes upon diffusion by about 1 . ..3%. This method leads to diffusion coefficients very close to the impurity diffusion coef!icient, if the solubility is large enough to ensure the validity of the thin-film solution (1.11) and if a surface hold-up of the diffusant can bc exluded. It is obvious that both methods should be regarded as lessreliable than diffusion couple methods with profile measurement. 1.6.1.2.4 In- and out-diffusion methods Material is allowed to diffuse into, or out of, an initially homogeneous sample of concentration c0 under condition where the surface concentration is maintained at c,. The diffusion coefficient may be deduced from a measurement of the concentration distribution within the sample. For a concentration-dependent b the Boltzmann-Matano method can be used to give a a(c). Concentration-independent diffusion coefficients are determined by comparison with an appropriate analytical solution. For some simple sample geometries(plane sheet,cylinder, sphere) the analytical solutions to Fick’s second law are described in subsections 1.2.3, 1.2.4 and 1.2.5. The diffusion coefficient may also bc calculated from the total amount of material picked up or lost from the sample. For constant diffusivities appropriate expressions for the total amount of material have been given for the above mentioned geometries in subsections 1.2.3, 1.2.4and 1.2.5 as we!!. For concentration-dependent diffusivities this method gives an average diffusivity over the range c0 to c,. 1.6.1.2.5 Other macroscopic methods There are a number of phenomena in solids which for their occurrence depend on diffusion over distances large compared to the interactomic distance. From suitable measurement made on such phenomena it is possible to deduce with some limited accuracy a diffusion coefficient. The more important methods are: - Measurements of the growth rate of a new phase [74S]. A prerequisite of this method is that the growth rate is controlled by diffusion. - Measurements of the sintering kinetics, which under appropriate conditions can be controlled by bulk diffusion. For a recent review see,e.g., [89Gl]. - Measurements of the creep rate of a crystal, when it is controlled by bulk diffusion, which is the case in the so-called Nabarro-Herring creep regime. For a recent review see[8962]. By contrast in the so-called Cable creep regime the creep rate is dominated by grain boundary diffusion (seechapter 12).
Ref. p. 301
1.6.2.1 Relaxation methods; 1.6.2.2 Nuclear methods
21
1.6.2 Indirect methods These methods are not based directly on Fick’s laws. One studies phenomena which are influenced by the occurrence of the thermally activated motion of atoms. These methods are often sensitive to only one or to a few atomic jumps. A relaxation time, a relaxation frequency, a relaxation rate or a line-width is measured.With the help of a microscopic model of the underlying jump processthe mean residencetime z of the diffusing species is deduced. According to D =f d=r/6 (1.49a) a diffusion coefficient can be determined provided that the jump length d and the correlation factor f are known. d is usually obvious from the lattice geometry. f depends on the crystal structure and the diffusion mechanism. The quantity r= l/2 (1.49b) is often denoted as the mean jump frequency of the diffusing atoms. The indirect methods can be grouped into two categories - relaxation methods and nuclear methods:
1.6.2.1 Relaxation methods In the relaxation methods the atomic motion is induced by external influences like mechanical stresses, magnetic fields or temperature jumps. Anelastic or magnetic after-effects or internal jiktion are monitored. A great variety of experimental devices has been used (seee.g. [72N]). The more important relaxation phenomena related to diffusion are: a) Snoek effect
In body-centered cubic metals the interstitial (octahedral or tetrahedral) sites have a tetragonal symmetry. Due to this lower symmetry atoms in interstitial solution like C, N, 0 can give rise to a relaxation phenomenon, the so-called Snoek effect.The Snoek effect can be studied in anelastic after-effect and internal friction measurements. In addition in ferromagnetic material magnetic after-effect measurementscan be used to study the Snoek effect. b) Got-ski effect
Any foreign atom solute in a solvent which produces a lattice dilatation can give rise to an anelastic relaxation which is due to the diffusion in a macroscopic strain gradient. In practice the Gorski effect is detectable only if the diffusion coefficient is high enough. Therefore, Gorski effect measurementshave been used so far only for the study of hydrogen diffusion in metals. For details see e.g., the reviews [72V, 84B2] and chapter 9 of this volume. c) Zener effect
In substitutional AB alloys the reorientation of solute-solvent atom pairs under the influence of an applied stresscan give rise to an anelastic relaxation denoted as Zener effect. From the reorientation kinetics the jump frequencies can be determined for a given pair model.
1.6.2.2 Nuclear methods Examples are nuclear magnetic relaxation (NMR), Miissbauer spectroscopy (MBS) and quasi-elastic neutron scattering (QENS). Like other indirect methods these methods are sensitive to one or a few atomic jumps. a) Nuclear magnetic relaxation
(NMR)
The width of the resonance line and the spin-lattice relaxation time 7” have contributions which are due to the thermally activated motion of atoms. Measurements of the “diffusional narrowing” of the linewidth or of T1as functions of temperature permit a determination of diffusion coefficients (seee.g.[82K, 84S]).A prerequisite for NMR measurementsis a non-vanishing nuclear moment of the diffusing species.An example for a NMR study of diffusion is shown in Fig. 22(a) and (b). NMR methods are particularly appropriate for self-diffusion measurements of solid or liquid metals. In favourable cases(Li, Al, . ..) di ffusion coefficients between lo-l8 m*s-’ and 10-l’ m’s-’ are accessible(see Fig. 25). In the case of foreign atom diffusion NMR studies are handicapped by the fact that a signal from a minority of nuclear spins must be detected.However, in favourable casesNMR studies are possible. For details seee.g. [88G]. Land&-Bhnstein New Series III/26
Mehrer
22
[Ref. p. 30
1.6.2.2 Nuclear methods lo-'0 lo-'0 I.
I
d/S
10-l’ 10-12 lo-”
11
0
4
0 0
16
8
lo-16
0.45 MH; 1.8 4.8 8
x v,= ' . . .
15.5
.
35
.
I Q 10-15 10-1’6 10-n
I3K-’ 10-18
IL1
8 *lo-
Fig. 22(a). Nuclear magnetic relaxation times ‘& and T1pin’Li as a function of reciprocal temperature according to (78MJ. The spin-lattice relaxation time TI has been measured for several Larmor frequencies. In the caseof the spin-lattice relaxation time T,, the magnetic field is given instead of the Larmor frequency. The minima in T, and T,, are caused by the diffusional motion of Li atoms.
10-19 lo-‘91 2
3
4 l/T -
5 40JK-’ 40JK-' 6
Fig. 22 (b). Self-diffusion coeflicient of ‘Li as a function of reciprocal temperature deduced from the NMR data of Fig. 22(a) according to [78M].
b) Miissbauer spectroscopy(MBS) and quasielastic neutron scattering (QENS) The linewidth in Mhshauer spectroscopy and in quasielastic scattering of monoenergetic neutrons both have a contribution Ar which is due to the diffusional motion of atoms. This diffusional broadening can be observed only in systemswith fairly high diffusivities (seeFig. 25) since Ar must be comparable to or exceed the natural linewidth in MBS measurementsand the energy resolution of the neutron spectrometer in QENS experiments. Appropriate probes for MBS are “Fe, ‘19Sn, “‘Eu and 16’Dy. QENS is applicable to a few fast diffusing elementswith a large enough, quasielastic scattering cross section for neutrons. Examples are Na self-diffusion and hydrogen diffusion in metals. Further nuclei with large enough quasielastic scattering cross sections for thermal neutrons are Co, Ni, V, Ti and Cr. Fig. 23(a), (b) shows examples for MBS spectra together with the deduced diffusion coefficients. Fig. 24 illustrates typical effects of diffusive motion on a QENS spectrum. Neither MBS nor QENS are routine methods for diffusion measurements.An interesting aspect of both methods is that they can provide some microscopic information on the elementary jump process. If single crystals are used in MBS or QENS measurementsAr depends on orientation. This anisotropy can be used to deduce the jump direction and the jump length (see e.g. [84M2, 842, SSV]) of the diffusing atoms.
Mehrer
Land&BBmslein New Series III/26
Ref. p. 301
1.6.2.2 Nuclear
Fe
T=1767K
23
methods
FWHM=25.1mm/s
96 100
I c E ,; E 6 z
98 96 100 98 96 100
0.56
2 98 c) 2
701
lii2JK
I -40
,f
I
I -20
I
0.830mm/s 1
I 0
I
I 20
I I mm/s 40
0.60
I
vFig. 23 (a). Mijssbauer spectra for self-diffusion in y-iron (bottom) and S-iron in polycrystalline samples according to [85v]. The Miissbauer source was s7Co in Rh at room temperature. The linewidth increases with increasing temperature due to the diffusional motion of the Fe atoms. For each temperature the full width of half maximum of the Mossbauer line is given in mm s- r .
-6
-4
-2
0
2
4
Fig. 24. Quasi-elastic neutron scattering (QENS) spectrum (number of scattered neutrons N as a function of the energy transfer ho for a fixed scattering vector Q = 1.3 IO-r0 m-r) measured at 365.7 K on a sodium single-crystal according to [80G]. The dashed line represents the resolution function of the neutron spectrometer. The observed line is broadened due to the diffusional motion of sodium atoms. Land&-BBmstein New Series III/26
0.62
0.64
.lO"K“
0.68
Fig. 23 (b). Self-diffusion coefficient of iron as a function of reciprocal temperature deduced from the Miissbauer data of Fig. 23 (a) according to [85v]. Circles represent Mijssbauer results. For reasons of comparison tracer data are shown as solid lines.
96
,!I
0.58
Mehrer
1.6.3 Comparison of diffusivity
24
f D(l,)
t t Lll2/31~1 D(l,)
sputtering
Tracer
SIMS.AES
RBS
----------___--------
f
/
\ EMPA
/
\
NRA
m\
/
/W)
2 f
/rj I I 15
I
I I 10-7’
I
I
s 5 I% -fi .-e cl
-___, IF
I I KY’*
I O-
I,
I 10-1’
E I
[Ref. p. 30
0 I liquid) Olfost)
mech.sect.
/ /
ranges accessible to various methods
I
I I I I K-lo m2/s 10
Fig. 25. Illustration of the ranges of diffusion coeflicients which arc accessible to various experimental methods. The following abbreviations have been used: Tracer = radiotracer method, SIMS = secondary ion mass spectrometry, AES = Auger electron spectroscopy, EMPA = electron microprobe analysis, RBS = Rutherford backscattering, NRA = nuclear reaction analysis, AE = mechanical or magnetic after-effect, IF = internal friction, Gorski = Gorski effect, NMR = nuclear magnetic relaxation, MBS = Mijssbauer spectroscopy, QENS = quasielastic neutron scattering. On the upper scale some values of diffusion coeficients have been indicated: D (liquid) = typical value in a liquid metal, D (fast) = typical value for very fast diffusors in solids, D(T,) = typical value for self-diffusion in metals near the melting temperature, D(2/3 T,) = typical value for self-diffusion at 2/3 T,, D(7;) = typical value for diffusion in amorphous alloys near their crystallisation temperature.
1.6.3 Comparison of diffusivity ranges accessible to various methods Approximate rangesof diffusion coefficients which can be determined by various direct and indirect methods discussed in subsections 1.6.1 and 1.6.2 are illustrated in Fig. 25. Nowadays, the radiotracer method can cover an enormous range of diffusivities provided that microsectioning techniques (e.g.sputtering) and mechanical sectioning techniques (lathe-, microtome- grinder sectioning) are combined. Up to now it is the standard method for studies of self- and foreign atom diffusion provided that appropriate radioisotopes are available. SIMS and AES techniques both utilize depth profiling by sputtering and are therefore appropriate for small diffusion coefficients. The use of AES dictates that the diffusion of foreign atoms other than the major constituents be studied since AES discriminates between different elements only. In SIMS and in SNMS experiments the composition analysis is performed in mass spectrometers which can discriminate between different isotopes of the same element as well. Nevertheless, these techniques are mainly appropriate for foreign atom diffusors. Self-diffusion studies can be performed with enriched natural isotopes. However, they suffer from a background problem due to the natural abundance of these isotopes. RBS and NRA methods are restricted to small diffusion coefficients becauseof the limited penetration ranges of the analyzing ion beams and becauseof the effectsof beam straggling which becomemore serious for larger penetrations. RBS is particular appropriate for heavy solutes in a light solvent whereas NRA is appropriate for somelight solutes including hydrogen. A prerequisite for NRA studies of diffusion profiles is a nuclear reaction with a narrow resonance. EMPA is restricted to relatively large chemical diffusion coefficients since the depth resolution is limited by the size of the volume excited by the electron beam. The number of atomic jumps performed by the diffusing speciesduring anelastic or magnetic after-effect (e.g. Snoek effect) studies of diffusional processes is typically in the order of one. Internal friction studies are particular sensitive to diffusion processesin the sample when the jump rate of atoms is comparable to the vibration frequency of the internal friction device. When applicable the after-effect and the internal friction methods can monitor very small to small diffusion coefficients mainly for interstitial diffusors. The Gorski ejj-,ct is an anelastic after-effect in metal-hydrogen systems.Its cause is hydrogen redistribution by diffusion over distances which are comparable to the sample dimension. This can be monitored for sufliciently large diffusion coeflicients. Amongst the nuclear methods NRA covers the widest range of diffusivities. The range indicated in Fig. 25 can be observed in materials with large gyromagnetic ratios and small non-diffusive contributions to the relaxation rates (in metals e.g. the electronic contributions). MBS and QENS, when applicable, are limited to fast diffusion processes. Landolt-BBmstein New Series III/26
Ref. p. 301
1.7 Diffusion along dislocations, grain boundaries and on surfaces; 1.8 Temperature dependence of diffusion
25
1.7 Diffusion along dislocations, grain boundaries and on surfaces Any real crystalline sample usually contains dislocations, often grain boundaries and always free surfaces. In the context of diffusion these one- or two-dimensional defectsare denoted as diffusion short-circuits or aspaths of high difisivity. They have in common that the jump frequency of an atom in these regions is usually much higher than that of the same atom in the lattice [63S, 66A, 85P, 88K1, 89Sl]. The higher diffusivity in these regions is of interest for two reasons: In experiments made by any of the methods discussed in section 1.6 to determine the diffusivity in the volume, the question arises how much high-diffusivity paths contribute to the measured diffusion coefficient. However, in properly designed experiments these contributions can be reduced to a negligible extent. Effects of surface diffusion can be eliminated by removing the near surface region after the diffusion anneal and before a determination of what is intended to be a volume diffusion coefficient is performed. Obviously single crystals or at least coarse grain polycrystals are to be preferred in accurate measurementsof volume diffusion. Dislocation diffusion can never be completely avoided in metals. However, it can be made negligible by working with well-annealed samples and at relatively high temperatures. This is due to the fact that short circuiting diffusion rates increase less rapidly with increasing temperature than volume diffusion rates. It has been realized that the transport of matter along high-diffusivity paths plays a key role in several important technologies. This is particular obvious for diffusion along free surfaces and for grain boundary diffusion in fine-grain materials. Nowadays it is possible in properly designedexperiments to determine diffusion coefficients in these regions. The few data available for dislocation difision are collected in chapter 11. The data for grain-boundary difjitsion and those for surface diffusion are collected in chapters 12 and 13, respectively. In chapters 11 to 13 introductions to the various phenomena and to the pertaining experimental methods will be given as well.
1.8 Temperature dependence of diffusion Measurements of the diffusion coefficients are usually performed at a series of temperatures. In solids often an Arrhenius equation D=D” exp(-Q/kT) (1.50) describeswell the temperature dependencewithin the studied range. Do is denoted as preexponential factor and Q as activation enthalpy. T denotes the absolute temperature and k Boltzmann’s constant. Typically, for metals and alloys, the pre-exponential factors are in the range low6 m*s-’ & Do 5 10e3 rnzsml and the activation enthalpies in the range 50 kJmol-1 $ Q & 600 kJmol-’ depending essentially on the melting point of the material and on the diffusion mechanism (e.g.direct interstitial or vacancy mechanism) which is operating. In this volume the experimental data will primarily be reported in terms of Do and Q whenever this is possible. In addition the data will be often also represented either as data points or as an Arrhenius line in an Arrhenius diagram - a plot of the logarithm of the diffusion coefficient as a function of reciprocal temperature. When several measurementsexist for the same system an attempt has been made to select what appear to be the most recommended ones. Usually the recommended data will be included in the Arrhenius diagram. Experimentally the Arrhenius diagram is sometimescurved: In such casesthe data may be better represented by a sum of two Arrhenius terms according to D=D?exp(--Q,jkT)+Diexp(-Q&T)
(1.51)
where 0: and 0: have the meaning of pre-exponential factors and Q1 and Qz denote activation enthalpies. In the casesof so-called anomalous metals like B-Ti and B-Zr a representation of curved Arrhenius diagrams by D = D’ exp(- Q’jkT) exp(A/kT’) (1.52) is physically even more meaningful [77S, 88K2]. D’ and Q’ represent “normal” activation parameters and A a curvature parameter. Land&Bhnstein New Series III/26
Mehrer
26
1.8 Temperature dependence of diffusion
[Ref. p. 30
If tits of (1.51) or of (1.52) to the data have been performed by the authors either values of @, @, Q, and Q2 or values of D’, Q’ will also be reported. However, also Arrhenius diagrams are indispensible, whenever the data deviate substantially from a simple Arrhenius equation. Only in some relatively simple casescan the Arrhenius parameters of equation (1.50) be interpreted in a straightfonvard manner in terms of properties of atomistic defects.We mention three such cases: For the &&ion OJ interstitial solirtes which migrate by the direct interstitial mechanism (see Fig. 8 a) in a cubic crystal the diffusion coefficient can be written as D=ga’vOexpz
exp -g . (1.53) ( > Here v” is an attempt frequency of the order of magnitude of the Debye frequency, a the cubic lattice parameter. HM is the activation enthalpy that is necessaryto overcome the barrier between two adjacent interstitial sites and SMthe pertaining entropy. g is a geometric factor which depends on the lattice structure and on the type of interstitial sites involved. E.g. for octahedral interstitial sites we have g = 1 in the fee structure and g = l/6 in the bee structure. in a pure cubic metal - provided that diffusion occurs only by the monovacancy For tracer selfdiffirsion mechanism (seeFig. 9) - the diffusion coefficient of the tracer atoms is given by D = a2jvo exp[(SF + S”)/k] exp[ - (HF + H")/k
T].
(1.54)
In (1.54) HF and HM denote the enthalpies of formation (superscript F) and migration (superscript M) of a vacancy. SF and SMare the corresponding entropies. f is the correlation factor which for the monovacancy mechanism in cubic lattices is a temperature independent constant (fee: 0.781,bee: 0.727,diamond: 0.5).In these casesthe meaning of the pre-exponential factor and of the activation enthalpy are by comparison of equations (1.50) and (1.54) Q=HF+HM (1.54a) and Do = a2fvo exp [(SF+ S”)/k]. (1.54b) For impurity
di$lrsion
in cubic metals
D = a2j2v(:
via the monovacancy
mechanism
exp[(SF + Sy - SB)/k]*exp[-
D
can be written as
(HF - HB + Hy)/kT].
(1.55)
Here Hy is the enthalpy barrier for an exchange of sites between impurity and vacancy and v: the pertaining attempt frequency. Sy is the pertaining entropy. HB and SDdenote the binding enthalpy and entropy between vacancy and impurity. In contrast to self-diffusion the correlation factor f2 for impurity diffusion depends on temperature (see,e.g., [66A, SSP]).Strictly speaking, according to (1.55) D has no longer the Arrhenius form. It is however common practice to recast the temperature variation of D into the form of an Arrhenius law by defining an “effective” activation enthalpy as Q=-kg.
(1.56)
If equation (1.56) is applied to (1.55) one obtains (1.57)
Q=HF-H'+Hy-C
and Do = u2f2v:
exp[(SF + Sy - SB)/k] . exp( - C/k T).
(1.58)
The quantity C is defined as (1.59) and accounts for the temperature dependenceof the correlation factor. If C depends on 7; Q and Do will also depend on r Often the temperature dependence of f2 can be approximated by an Arrhenius equation S2(77 =fpOl
expW)F
T),
(1.59a)
where T denotes the average temperature of the temperature range investigated. Then Q and Do are indeed constant and may be written as Q= HF-H'+HyDo = a"f~v~
C(T)
exp[(SF + S,M- SB)/k]. Mehrer
(1.58a) (1.58b) Landolt-BBmstein New Series III/26
Ref. p. 301
1.9 Mass- and pressure dependence of diffusion
21
For slow diffusion C(T) is usually small, whereas for rapid diffusion by substitutional migration C(F) can be several tens of kJmol-‘; however, its dependence on F is often negligible. As already mentioned experimentally observed Arrhenius plots even for self-diffusion are sometimescurved. The departure from a straight line can be more or less pronounced. In some cases only curvature at high temperatures is observed. In the caseof the so-called “anomalous” bee metals a continuous curvature over the whole temperature range investigated can be present. Sometimes two straight lines with different slopes have been reported. In general, the activation enthalpy increases with increasing temperature. However, in some materials (like e.g. a-Fe) which undergo a magnetic order-disorder transition the activation enthalpy may also increase with decreasing temperature. Several explanations for deviations fom straight Arrhenius diagrams have been put forward: (i) The activation parameters depend on temperature: This has originally been proposed for normal metals [7562]. The idea of temperature dependent activation parameters and their relation with bulk properties has been extensively discussed in [86V]. It is very likely the reason for the strong curvatures observed for some anomalous metals [87H, 88K2] and for different reasons in systemswith order-disorder transitions like a-iron [77H2, 89H2]. The strong curvatures in anomalous metals have been attributed to anomalies in the phonon dispersion curves [87H, 88K2, 89H3]. (ii) Diffusion occurs by more than one lattice diffusion mechanism. This is the case when several defects contribute to the total diffusion coefficient. The slight curvatures of the Arrhenius diagrams of self-diffusion in fee metals which are observed above about 2/3 of the melting temperature have been attributed to the simultaneous contribution of mono- and divacancies to the diffusivity [7OS,78P, 78M]. The tracer self-diffusion coefficient is then given by (1.60) D=D,v+D,v, where D,, and D,, denote the mono- and divacancy contributions, respectively. Since the monovacancy mechanism has a lower activation enthalpy than the divacancy mechanism it will always dominate at lower temperatures. With increasing temperature the relative contribution of divacancies increasesand may cause a slight upward curvature of the Arrhenius diagram. If the mono-/divacancy interpretation is adopted, the activation parameters from a two-exponential fit according to (1.51) can be attributed to the two vacancy type defects. (iii) Diffusion occurs by one mechanism but by several types of atomic jumps. For example, interstitially incorporated foreign atoms may diffuse by jumps between neighbouring octahedral sites as well as by jumps between octahedral and tetrahedral sites. Double jumps of atoms have been proposed to contribute to self-diffusion in the close neighbourhood of the melting temperature [845].
1.9 Mass- and pressure dependence of diffusion Measurements of the diffusion coefficients of self- and foreign atom diffusion are sometimesperformed with tracer atoms of different isotopic mass. The mass dependence of diffusion is of special interest becauseit can provide information about atomic mechanisms of diffusion (seesection 1.5).Isotope effect data are collected in chapter 10, which also contains a brief introduction into the necessaryconcepts. Diffusion coefficients in solids depend on the hydrostatic pressure p. Often the equation D(P) = D(O) ev(-
pAl//kT)
(1.61)
describesthe pressure dependencesufficiently well. The quantity AI/’ is denoted as activation volume. Activation volumes for solid state diffusion are typically in the range between a few tenths of the atomic volume and 1.5 atomic volumes. Activation volumes of diffusion are of practical importance and of scientific interest. The pertaining data are collected in chapter 10 as well.
Land&-Biirnstein New Series III/26
Mehrer
28
1.10 Diffusion in amorphous alloys; 1.11 Further readings
[Ref. p. 30
1.10 Diffusion in amorphous alloys Amorphous metallic alloys are also denoted as metallic glasses or as glassy metals. Diffusion data for amorphous metallic alloys are collected in chapter 7. The study of diffusion in amorphous alloys is a difficult topic from an experimental point of view. Progress was only achieved in the last decade.The difficulties stem entirely from the facts that amorphous alloys are non-equilibrium structures and that the diffusion temperatures and times are limited by the need to avoid crystallization. This entails diffusional penetrations of the order of 0.1 urn and never exceeding 1 pm. Only those methods of section 1.6 for shallow profiles and some indirect methods can be used in diffusion studies of amorphous materials. Diffusion in amorphous alloys is of considerable technological and of scientific interest as we!!. It is of vital concern for the thermal stability of these materials which is determined by the processesof relaxation and crystallization. Di!fusion in non-equilibrium structures without long range order and its atomistic mechanisms are still not as well understood as for crystalline materials.
1.11 Further readings 1.11.1 Textbooks on diffusion Seith. W., Heumann, Th.: DilJlrsion in Metal/err (2nd Edition). Berlin: Springer, 1955. Shcwmon, P.: DilJlrsion in Solids. New York, San Francisco, Toronto, London: McGraw-Hi!!, 1963. Adda, Y, Philibert, J.: La DiJ’irsion dons les Solides. Paris: PressesUniversitaires de France, 1966. Manning, J.R.: Dilfirsion Kinetics of Atoms in Crystals. Princeton: van Nostrand, 1968. Jest, W: Difirsion in Solids, Liquids atin Gases(2nd Edition). New York: Academic Press, 1969. Flynn, C.P.: Poinf Dejects nnd Dilfirsion. Oxford: Clarendon Press, 1972. Shaw, D., (ed.): Atomic Diji~sion in Semiconductors. London, New York: Plenum Press, 1973. Tuck, B.: Introduction to Diffirsion in Semiconductors. IEE Monograph Series 16, Inst. Electr. Eng., 1974. Crank, J.: The Mofhemntics oj DiJiaion (2nd Edition). Oxford: Clarendon Press, 1975. Nowick. A.S., Burton, J.J.,(eds): Diffirsion in Solids - Recent Developments. New York: Academic Press, 1975. Wever, H.: Elektro- und Thermotransport in Metallen. Leipzig: Johann Ambrosius Barth, 1975. Stark, J.P.:Solid Stare Dilfirsion. New York: Wiley, 1976. Larikov, L.N., Geichenko, V.V., Fal’chenko, V.M.: Diffusion Processes in Ordered Alloys. Kiev, 1975. Eng!. Transl. published by Amerind Publ. Comp. New Dehli: 1981. Murch, G.E., Nowick, A.S.: D~j’irsion in Crystalline Solids. New York: Academic Press, 1984. Philibert, J.: Diffirsion et Transport de MariPre dons les Solides. Les editions de physique, France, 1985. Borovskii, LB., Gurov, K.P., Marchikova, I.D., Ugaste, Yu, E.: Interdiffusion in Alloys, 1973, Gurov, K.P., (ed.). Transl. from Russian by the National Bureau of Standards. New Delhi: Amerind. Pub!. Comp., 1986. Kirkaldy, J.S.,Young, D.J.: Dilfirsion in the Condensed Stare. Brookfield, USA: The Insitute of Metals, 1987. Borg. R.J.,Dienes, G.J.: An Introduction to Solid Stare Dijjiision. Boston: Academic Press, 1988. Kaur, I., Gust, W.: Fundnmenrals oj Grain and Interphase Boundary Dij’iision. Stuttgart: Ziegler Press, 1988. Shewmon, P.: Diffirsion in Solids (2nd Edition) Warrendale, Pennsylvania: The Minerals, Metals and Materials Society, 1989.
1.11.2 Collections of diffusion data and data of related phenomena Diffusion data and data of diffusion-related phenomena have also been gathered in: DlQj’irsionData. Wiihlbier, EH., (ed.),Vol. 1-7. Cleveland (USA) and Solothurn (Switzerland): Diffusion Informa-
tion Center. Di@rsion ond Defect Daro (DDD). From 1967, Vol. Sff, Wiihlbier, EH., Fisher, J.D., (eds.).Switzerland: Trans.
Tech. Publicatons; a review appears about three times a year. Adda, Y, Philibert, J.: Lo Diffirsion dons les Solides. Paris: PressesUniversitaires de France, 1966. Neumann, G., Neumann, G.M.: Surface SeljlDiffusion of Metals. Diffusion and Defect Monograph Series,No. 1; Wiihlbier, E, (ed.) 1972. Pratt, J.N., Sellers, P.G.R.: Hecrrorransporr in Metals and Alloys. Diffusion and Defect Monograph SeriesNo. 2. Adda, Y, Le Claire, A.D., Slilkin, L.M., Wiihlbier, EH., (eds.) 1973. Landolt-Btmstein New Series III/26
1.l 1 Further readings
29
Frischat, G.H.: Ionic Dgfusion in Oxide Glasses. Diffusion and Defect Monograph Series No. 314.Adda, Y, Le Claire, A.D., Slifkin, L.M., Wiihlbier, EH., (eds.) 1975. Wever, H.: Elektro- and Thermotransport in Metallen. Leipzig: Johann Ambrosius Barth, 1975. Burton, B.: Dffusion Creep of Polycrystalline Materials. Diffusion and Defect Monograph SeriesNo. 5. Adda, Y, Le Claire, A.D., Slifkin, L.M., Wbhlbier, EH., (eds.) 1977. Dariel, M.P.: Diffusion in rare earth metals, in: Handbook on the Physics and Chemistry of Rare Earths. Gschneidner jr., K.A., Eyring, L. (eds.)Amsterdam: North Holland, 1978, p. 847. Smithells Metals Reference Book (6th Edition). Brandes, E.A., (ed.), Washington: Butterworths, 1983, Chapter 13-1. Butrymowicz, D.B.: Diffusion rate data and mass transport phenomena in copper systems. Vol. 8, INCRA Series, New York, 1983. Kaur, I., Gust, W., Kozma, L.: Handbook of Grain and Interphase Boundary Diffusion Data. Vol. 1 and 2. Stuttgart: Ziegler Press, 1989.
1.11.3 Proceedings Some results concerning diffusion and related subjects are contained in proceedings of international conferences or symposia. The more recent ones are listed below: Cubic Metals. Proc. Int. Conf. held in Gatlinburg, USA, 1964; Wheeler, jr. J.A., Winslow, F.R., (eds.).Metals Park, Ohio: American Society for Metals, 1965. Vacancies and Znterstitials in Metals, Proc. Int. Conf. held in Jiilich, Germany, 1968; Seeger,A., Schumacher, D., Schilling, W!, Diehl, J., (eds.).Amsterdam: North Holland, 1970. Dzffusion in metallischen Werkstoffen, 7. Metalltagung in Dresden, DDR, 1970. Leipzig: VEB Deutscher Verlag fur Grundstoftindustrie, 1970. Atomic Transport in Solids and Liquids, Proc. Int. Conf. held in Marstrand, Sweden, 1970; Lodding, A., Lagerwall, T, (eds.).Z. Naturforsch. 26a, 1971. Diffusion Processes, Proc. Int. Conf. held in Glasgow; Sherwood, J.N., Chadwick, A.V, Muir, WM., Swinton, FL., (eds.).2 Volumes, London: Gordon and Breach, 1971. La Diffusion dans les Milieux Condenses: Thkorie et Application, 19’ Colloque Metallurgie. Saclay: INSTN, 1976. Low Temperature Dgfusion and Applications to Thin Films; Gangulee, A., Ho, P.S.,Tu, K.N., (eds.).Thin solid films 25 (1975) No. 1-2. Properties of Atomic Defects in Metals, Proc. Int. Conf. held in Argonne, USA, 1976; Peterson,N.L., Siegel,R.W, (eds.).J. Nucl. Mater. 69-70 (1978). Point Defects and Defect Interactions in Metals, Proc. Int. Conf. held in Kyoto, Japan, 1981; Takamura, J.I., Doyama, M., Kiritani, M., (eds.).University of Tokyo Press, 1982. Mass Transport in Solids; Benibre, E, Catlow, C.R.A., (eds.),Nato series,Series B, Vol. 97. London, New York: Plenum Press, 1983. DZMETA 82 - Dzffusion in Metals and Alloys, Proc. Int. Conf. held in Tihany, Hungary, 1982; Kedves, EJ.,Beke, D.L., (eds.).Diffusion and Defect Monographs Series No. 7 (1983). Nontraditional Methods in Diffusion, Proc. Symp. held in Philadelphia, USA, 1983; Murch, G.E., Birnbaum, H.K., Cost, JR., (eds.).The Metallurgical Society of AIME (1984). DiJfusion in Solids: Recent Developments. Proc. Symp. held in Detroit, USA 1984; Dayananda, M.A., Murch, G.E., (eds.).The Metallurgical Society (1985). Solute-Defect Interactions - Theory and Experiment. Proc. Int. Seminar held in Kingston, Canada, 1985; Saimoto, S., Purdy, G.R., Kidson, G.V, (eds.).Oxford, New York: Pergamon Press, 1986. Vacancies and Znterstitials in Metals and Alloys, Proc. Int. Conf. held in West-Berlin, 1986; Abromeit, C., Wollenberger, H., (eds.).Materials Science Forum 15-18 (1987). Diffusion in High-Technology Materials, Proc. ASM Symposium held in Cincinnati, USA, 1987; Gupta, D., Romig, A.D., Dayananda, M.A., (eds.),Trans. Tech. Publications, 1988. DIMETA-Diffusion in Metals and Alloys, Proc. Int. Conf. held in Balatonfiired, Hungary, 1988; Kedves, EJ., Beke, D.L., (eds.).Defect and Diffusion Forum 66-69 (1989). Diffusion in Body-Centered
Land&-BCmstein New Series III/26
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30
1.12 References for 1
1.12 References for 1 1894B 33M 11s 48D 49D 52s 53B 55s 55H 59c 59R 62s 63M 63s 645 66A 66C 68F 68M 7OLl lOL2 70s 71F 72N 72V 74s 7sc 75Gl 7562 77Hl 77H2 77s 18M 78P 80G 82K 83B 84Bl 84B2 84F 84H 84J 84L 84Ml 84M2 84M3 84P 84R
Boltzmann, L.: Ann. Physik 53 (1894) 960. Matano, C.: Jpn. Phys. 8 (1933) 109. Smigelkas, A.D., Kirkendall, E.O.: Trans. Metall. Sot. AIME 171 (1947) 130. Darken, L.S.: Trans. Metall. Sot. AIME 175 (1948) 184. Darken, L.S.: Trans. Metall. Sot. AIME 180 (1949) 430. Seith, W., Kottmann, A.: Z. Angew. Chem. 64 (1952) 379. Ballufli, R.W.: J. Metals 5 (1953) 726. Seith, W, Heumann, Th.: Diffusion in Metallen. Berlin: Springer, 1955. Hauffe, K.: Reaktionen in und an festen Stoffen. Berlin: Springer, 1955. Carslaw, H.S., Jaeger,J.C.: Conduction of Heat in Solids. Oxford: Clarendon Press, 1959. Ruth, V.: Z. Phys. Chem. Neue Folge 20 (1959) 313. Sauer, E, Freise, V: Z. Elektrochemie 66 (1962) 353. Malkovitch, R.Sh.:Fiz. Met. Metalloved. 15 (1963)880; Phys. Met. Metallogr. USSR (English Transl.). Shewmon, P.: Diffusion in Solids. New York, San Francisco, Toronto, London: McGraw-Hill, 1%3. Jost, W.: Diffusion in Solids, Liquids and Gases.New York: Academic Press,(2”d Edition) 1964. Adda, Y, Philibert, J.: La Diffusion dans les Solides. Paris: PressesUniversitaires de France, 1966. Ceresara, S., Frederighi, T, Pieragostini, E: Phys. Status. Solidi 16 (1966) 439. Fogelson, R.L.: Fiz. Met. Metalloved. 35 (1968) 492. Manning, J.R.: Diffusion Kinetics for Atoms in Crystals. Princeton: von Norstrand, 1968. LeClaire, A.D.: Correlation Effects in Diffusion in Solids, in: Physical Chemistry - an Advanced Treatise, Vol. X, Chapt. 5. New York, London: Academic Press, 1970. van Loo, EJ.J.:Acta Metall. 18 (1970) 1107. Seeger,A., Mehrer, H., in: Vacanciesand Interstitials in Metals. Seeger,A., Schumacher, D., Schilling, W, Diehl, J., (eds.).Amsterdam: North-Holland 1970, p. 1. Fogelson, R.L.: Fiz. Tverd. Tela 13 (1971) 1028. Nowick, AS., Berry, B.S.:Anelastic Relaxation in Crystalline Solids. New York: Academic press,1972. Volkl, J.: Ber. Bunsenges.76 (1972) 797. Schmalzried, H.: Solid State Reactions. New York: Academic press, 1974. Crank, 1: The Mathematics of Diffusion, Oxford: Clarendon Press,(2”d Edition) 1975. Gupta, D.: Thin Solid Films 25 (1975) 231. Gilder, M., Lazarus, D.: Phys. Rev. 145 (1975) 507. Heumann, Th.: Z. Naturforsch. 32a (1977) 54. Hettich, G., Mehrer, H., Maier, K.: Ser. Metall. 11 (1977) 795. Sanchez,J.M., De Fontaine, D.: J. Phys. (Paris) C7-38 (1977) 444. Mehrer, H.: J. Nucl. Mater. 69 + 70 (1978) 38. Peterson, N.L.: J. Nucl. Mater. 69 + 70 (1978) 3. Goltz, G., Heidemann, A., Mehrer, H., Seeger,A., Wolf, D.: Philos. Mag. A 41 (1980) 723. Kanert, 0.: Phys. Rep. 91 (1982) 183. Bocquet, J.L., Brebic, G., Limonge, Y: Diffusion in Metals and Alloys, in: Physical Metallurgy 1983. Cahn, R.W., Haasen, P., (eds.).Amsterdam: North-Holland Physics Publishers (yd edition), 1983, p. 385. Bakker, H., in: Diffusion in Crystalline Solids. Murch, G.E., Nowick, A.S.,(eds.).New York: Academic Press, 1984, p. 189. Berry, B.S., Pritchet, W.C.: in [84Ml]. Frank, W, Gosele, U., Mehrer, H., Seeger,A.: Diffusion in Silicon and Germanium, in: Diffusion in Crystalline Solids. Murch, G.E., Nowick, A.S., (eds.).New York: Academic Press, 1984, p. 62. Horvath, J., Dyment, E, Mehrer, H.: J. Nucl. Mater. 126 (1984) 206. Jacucci, G.: in [84Ml]. Lanford, W.A., Beneson, R., Burman, C., Wielunski, L.: in [84Ml]. Murch, G.E., Birnbaum, H.K., Cost, J.R. (eds.):Nontraditional Methods in Diffusion, Proc. Symp. held in Philadelphia, USA, 1983. The Metallurgical Society of AIME (1984). Mullen, J.G.: in [84Ml]. Myers, S.M.: in [84Ml]. Petuskey, W.T.: in [84Ml]. Rothman, S.J.:The Measurement of Tracer Diffusion Coefficients in Solids, in: Diffusion in Crystalline Solids. Murch, G.E., Nowick, A.S. (eds.).New York: Academic Press, 1984, p. 1. Mehrer
Landolt-BBmstein New Series III/26
1.12 References for 3 84s 842 85M 85P 85V 86B 86H 86V 87G 87H 88G 88Kl 88K2 89Gl 8962 89Hl 89H2 89H3 89K 89Sl 8982
Stokes, H.T.: in [84Ml]. Zabel, H.: in [84Ml]. Mehrer, H., in: Solute-Defect Interactions - Theory and Experiment. Saimoto, S., Purdy, G.R., Kidson, G.V, (eds.).Oxford, New York: Pergamon Press, 1985, p. 162. Philibert, J.: Diffusion et Transport de Mat&e dans les Solides. Les editions de physique, France, 1985. Vogl, G., Petry, W: Diffusion in Metals Studied by Mijssbauer Spectroscopy and Quasielastic Neutron Scattering; Festkiirperprobleme XXV (Advances in Solid State Physics), Grosse, P., (ed.).Braunschweig: Friedrich Vieweg und Sohn, 1985, p. 655. Borovskii, LB., Gurov, K.P., Marchukova, I.D., Ugaste, Yu.E.: Interdiffusion in Alloys, 1973, Gurov, K.P., (ed.). Transl. from Russian by the National Bureau of Standards. New Delhi: Amerind. Publ. Company, 1986. Hagenschulte, H.: Diplomarbeit Universitat Miinster, 1986. Varotsos, P.A., Alexopoulos, K.D.: Thermodynamics of Point Defects and their Relation with Bulk Properties. Amsterdam: North Holland, 1986. Geise, J., Mehrer, H., Herzig, Chr., Weyer, G.: Mater. Sci. Forum 15-18 (1987) 443. Herzig, Chr., Kiihler, U.: Mater. Sci. Forum 15-18 (1987) 301. Gunther, B.: Untersuchungen atomarer Bewegungen in Festkorpern mit Methoden der kernmagnetischen Relaxation. Habilitationsschrift, Universitat Dortmund, 1988. Kaur, I., Gust, W.: Fundamentals of Grain and Interphase Boundary Diffusion. Stuttgart: Ziegler Press, 1988. Kiihler, U., Herzig, Chr.: Philos. Mag. A 58 (1988) 769. Gail, I.: in [89K]. Greenwood, G.W.: in [89K]. Hagenschulte, H., Heumann, Th.: J. Phys. Condensed Matter, 1 (1989) 3601. Hirano, K.-I., Iijima, Y.: in [89K]. Herzig, Chr.: Ber. Bunsenges.Phys. Chem. 93 (1989) 1247. Kedves, F.J.,Beke, D.L. (eds.):DIMETA 88 - Diffusion in Metals and Alloys, Proc. Int. Conf. held in Balatonftired, Hungary, 1988. Defect and Diffusion Forum 66-69 (1989). Shewmon, P.: Diffusion in Solids, 2nd edition. Warrendale, Pennsylvania: The Minerals, Metals and Materials Society, 1989. Slitkin, L.: Metallurgical Transactions 20A (1989) 2577.
Land&-Biimstein New Series III/26
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32
2.1 Introduction
[Ref. p. 81
2 Self-diffusion in solid metallic elements 2.1 Introduction Self-diffusion is the most basic diffusion processin solids. In this chapter self-diffusion data are presented for solid metallic elements.Only data are given for “pure” metals. Data for tracer self-diffusion of binary alloys are tabulated in chapter 4 and the relatively few tracer self-diffusion data available for ternary alloys are included in chapter 6. Data on diffusion in the semiconducting elements Si and Ge have not been tabulated, but can be found in [89L]. For a description of experimental methods used in self-diffusion studies the reader is referred to section 1.6 of the “General introduction”.
2.1.1 Order of elements In this chapter data are compiled in the tables and figures according to the position of the substancesin the periodic table in the following order: alkali metals group, alkaline earth metals group, scandium group metals, rare earth metals, titanium group metals, vanadium group metals, chromium group metals, manganesegroup metals, iron group metals, cobalt group metals, nickel group metals, noble metals, zinc group metals, aluminum group metals, group IVB metals, group VB semimetals, group VIB semimetals, actinide group metals.
2.1.2 Use of tables and figures In the tables all measurementsare reported whenever possible in terms of the preexponerztialfictor Do and the octiwtion elltknlpy Q introduced in equation (1.50) of the “General introduction”. In some casesDo and Q values are not given in the original work. Do and Q values which were calculated from the original data points by the present authors are indicated as “recalculated”. The tempctwtwe range given in the tables is the range over which measurements were made and used to calculate Do and Q. Long extrapolations beyond this range may in some casesnot give reliable values for the diffusion coefficient as will be evident from the graphical representation. For zrnimiol crystals Do and Q values are given for diffusion perpendicular and parallel to the crystal axis, whenever experiments on oriented single crystals have been performed. The crystal orientation is indicated by the remarks “I c axis” and “ 11c axis” in the Do column of the table. For mctols wifh dotropic rran.y’htarions Do and Q values for the various crystal structures are reported. The pertaining crystal structure is indicated by a corresponding remark - e.g.“a-Fe” or “y-Fe” -in the Do column of the table as well. The column “Methon/Rernnrks” usually contains the information (i) to (v): (i)
The esperinmtol method is briefly characterized. - In by far the. most self-diffusion studies the thin layer method has been applied in combination with radiotracers (seesubsection 1.6.1.2.1of the “General introduction”). In thesecasesthe radioisotope used -for example 19’Au - will be stated. In some.casesmore than one isotope of the sameelement -e.g. “Na and 24Na - were used and will then be stated as well. In very few cases stable isotopes and mass spectrometry were used and will be mentioned explicitly. Mehrer, Stolica, Stolwijk
Land&-B6mstcin New Series 111~‘26
Ref. p. 811
2.1 Introduction
33
- If a serial sectioning technique in combination with counting of the section activity was used for the
(ii) (iii) (iv) (v)
measurement of the concentration depth profile, which is often the case,this will be indicated by one of the following keywords: “mechanical sectioning”, “sputter sectioning”, “chemical sectioning”, “electrochemical sectioning” or “anodic oxidation”. The keyword “mechanical sectioning” implies either sectioning by a lathe, by a precision grinder, or by microtome cutting or by combinations of these tools. If a serial sectioning technique was applied and not the section activity but the residual activity of the sample was measured this feature will be stated as well. - In some studies indirect methods (see subsection 1.6.2 of the “General introduction”) like nuclear magnetic relaxation (NMR), quasielastic neutron scattering (QENS) or transmission electron microscope observations (TEM) were used.In such casesthe above mentioned abbreviations plus someadditional keywords will be stated. The nominal purity of the samples will be stated whenever this information is available. For a more detailed specification of the purity, which only in some casesis available in the original work, the reference should be consulted. The use of single - or polycrystals will be stated. The grain size of polycrystals will be indicated, whenever this information is available. For uniaxial crystals it is indicated whether both crystallographic directions have been investigated or not. If both diffusion coefficients, D,, and D,, have been measured, a statement which of the two is larger is included. For metals which undergo (an) allotropic transformation(s) a statement is included which crystal structure(s) has (have) been investigated in this particular reference.
The column “Method/Remarks” may also contain some optional information which concerns the following items: [vi) Sometimesin the original work the temperature dependence of the diffusion coefficient is analyzed not only in terms of the simple Arrhenius relationship given by equation (1.50) of the “General introduction” but also in terms of more sophisticated expressions. The most common example is a sum of two exponentials as given by equation (1.51) of the “General introduction”. If this is the case the pertaining preexponential factors 0: and Di and the activation enthalpies Q, and Q, will be stated. If the authors adopt a certain interpretation like for example monoand divacancy contributions to the diffusion coefficient (seeequation (1.60)of the “General introduction”), this will be also mentioned. rvii) If in the same paper additional experiments like e.g. isotope effect experiments, or high-pressure diffusion experiments, or diffusion experiments with other isotopes and/or other matrices were performed this will be indicated as well. Central to the present chapter are the tables. From the tables referencesare made to the figures. For all metals where sufficiently reliable data were available an Arrhenius diagram - a semilogarithmic plot of the diffusion coefficient as a function of the reciprocal absolute temperature-has been included in the figure section. For a given metal those data which are strongly recommended have been included in the pertaining figure. Often data from several different references,which sometimes but not always cover different temperature ranges, are Included in the Arrhenius diagram. This procedure enables the user of chapter 2 to get an impression about the quality of the recommended self-diffusion data. Generally in a figure pertaining to a given metal its melting temperature T, is indicated. Values of T, are :aken from [83Sl]. Several metals undergo an allotropic transformation which transforms one crystal structure nto another when the temperature is raised or lowered. Some metals like for example iron even undergo more :han one allotropic transformation. Usually an allotropic transformation manifests itself by a stepwise change If the diffusion coefficient in the Arrhenius diagram. For metals with (an) allotropic transformation(s) the :ransformation temperature(s) is(are) indicated in the figure. The values of the transformation temperatures are :aken from [73H]. Figures 46 to 48 are the only ones to which no reference is made from the tables. Each of these figures :ontains a whole series of Arrhenius lines pertaining to metals with the same crystal structure. A homologous .eciprocal temperature scaleis used in thesecases.The normalization is performed with the melting temperature If each individual metal. The reader may find these figures useful to get a quick overview over the self-diffusion ,ehaviour of some important metals.
Landolt-Miirnstem
New Series III/26
Mehrer, Stolica, Stolwijk
2.2.1 Self-diffusion in alkali metals
34
[Ref. p. 81
2.2 The self-diffusion tables DO
Q
10-4mZs-1
kJmo!-’
Temperature range K
Method/Remarks
Fig.
Ref.
2.2.1 Self-diffusion in alkali metals Li, Na, K, Rb, Cs, Fr Lithium
(Li)
I.24
55.3
300..*453
NMR: spin lattice relaxation times Tr and T2; ‘Li signal in natural Li; 99.95%; dispersion of 12 urn particles in an oil; liquid Li also studied, Na and Rb also studied
-
55H
3.39
56.9
343 . . *443
6Li in natural Li as stable tracer; polycrystals; 99.8%; mechanical sectioning, mass spectrometry
-
59N
-
50.1
190...240
NMR: spin lattice relaxation time in rotating frame T,,; ‘Li signal in natural Li; dispersion of 15 urn Li-particles in mineral oil
-
65Al
3.123 16Li in ‘Li) D.120 [‘Li in 6Li) -
53.1
308 . ..451
1
7OL
54.0
308 .+.451
6Li in nearly pure ‘Li and ‘Li in nearly pure 6Li as stable tracer; mechanical sectioning, mass spectrometry
54
x 312...450
NMR: spin lattice relaxation time T,; 99.98%; dispersion of 10 urn particles in paraffin oil; T, also studied for dilute Li alloys containing 2, 4, 8 at% Mg; 1.5, 3 at% Cd and 2.75 at% Ag
-
72T
-
47.2
223 ... 373
NMR: spin lattice relaxation in rotating frame TIP; ‘Li signal in natural Li; 99.8%; dispersion of 15 urn particles in mineral oil
-
73w
0.133 (from T, data)
52.75
s 300...455
NMR: spin lattice relaxation times Tl and T,,;
-
75M
(continued)
Mehrer, Stolica, Stolwijk
LandolbB6mstein New Series III,/26
Ref. p. 811
2.2.1 Self-diffusion in alkali metals
DO
Q
10-4m2s-1
kJmol-’
35
Temperature range K
Method/Remarks
Fig.
Ref.
Lithium (Li), continued 0.038 (from TIP data)
50.2
x 192...350
various dispersions of small Li-spheres; purity not specified; Arrhenius diagram slightly curved, two-exponential fit: 07 = 0.038 . 10M4mz s-l Q, = 50.2 kJmol-‘, D,O= 9.5. 10m4m2s-r Qz = 67 kJmol-‘, mono-fdivacancy interpretation
-
75M
-
-
195.**450
NMR: spin lattice relaxation times 7” and T,,; ‘Li in ‘Li; deviation from Arrhenius behaviour, two-exponential fit: 0: = 0.06. 10m4m2s-r Q1 = 50.2 kJmol-‘, 0: = 28.8 . 10m4m2 s-l Qz = 69.5 kJmol-‘, mono-Jdivacancy interpretation
-
76M3
0.33
55.0
220...454
P-NMR: spin-lattice relaxation of polarized radioactive sLi nuclei using asymmetric P-decay; deviation from Arrhenius behaviour, two-exponential fit: 0: = 0.19. 10m4rn’s-’ Q, = 53 kJmol-‘, Di = 95. 10e4 m2s-1 Q, = 76.2 kJmol-‘, mono-/divacancy interpretation
1
85Hl
Sodium (Na) 0.20
41.9
E 223 ... 370
NMR: spin lattice relaxation times TI and T,; 23Na signal in natural Na; 99.95%; dispersion of 12 pm particles in oil; liquid Na also studied, Li and Rb also studied
-
55H
0.242
43.7
273...368
“Na; coarse grain polycrystals; purity not specified; diffusion couple of 22Na doped and undoped Na; mechanical sectioning; effects of hydrostatic pressure also studied
-
52N
(continued)
Landolt-B6irnstein New Series III/26
Mehrer, Stolica, Stolwijk
36
2.2.1 Self-diffusion in alkali metals
Q kJmol-’
[Ref. p. 81
Temperature range K
Method/Remarks
Fig.
Ref.
Sodium (Na), continued 0.145
42.2
273 ... 370
ZZNa, 24Na; polycrystals; 99.95%; mechanical sectioning; Arrhenius diagram slightly curved presumably due to K impurity; isotope effect also studied
2
66M
-
-
194.5... 370
22Na; 99.9995% ; mechanical sectioning; Do and Q values not given, Arrhenius diagram curved, two-exponential tit: 0: = 0.0057m2se1 Q1 = 35.7 kJmol-‘, Dy= 0.72.10m4m2s-’ Q2 = 48.1 kJmo!-‘, mono-/divacancy interpretation; effect of pressure also studied, isotope effect also studied
2
71Ml
0.12
41.5
349..-370
QENS: mono- and polycrystals; purity not specified; dependenceof quasielastic line width on momentum transfer also studied
-
79A
-
-
323...371
QENS; single crystal; 99.999% ; dependenceof quasi-elastic line width on momentum transfer studied for various crystallographic directions; data discussed together with radiotracer data; mono-/divacancy interpretation
-
80G
-
-
zl60...260
NMR: spin lattice relaxation times TI and T,p; 23Na signals in natural Na; 99.95%; dispersion of small particles in paraffin; two-exponential tit: Dy= 0.004~10-4m2sT1 Q, = 35.9 kJmo!-‘, Dz=2.6.10m4 m2sm1 Qz = 46.4 kJmo!-‘, mono-/divacancy interpretation
-
80B
Mehrer, Stolica, Stolwijk
Land&-B6mstein New Series III/26
Ref. p. 811
2.2.2 Self-diffusion in alkaline earth metals
DO
Q
10V4m2s-’
kJmol-’
Temperature range K
Method/Remarks
37
Fig.
Ref.
3
67M
3
71M2
-
55H
4
66D
Potassium (K) 0.31
40.8
42K.
273...333
polyirystals; 99.95% ; mechanical sectioning 0.16
39.2
42K.
22l.s.335
99.9; %;
mechanical sectioning; Arrhenius diagram slightly curved, two-exponential fit: 0: = 0.05 . 10m4m2 s-l Q, = 37.2 kJmol-‘, Di = 1 1IO-4m2s-1 Q, = 47 kJmol-’
Rubidium (Rb) 0.23
39.3
E 280 ... 312
NMR: spin lattice relaxation times TI and T,; *‘Rb and *‘Rb signals in natural Rb; purity not specified; dispersion of 50 urn particles in oil; liquid Rb also studied, Li and Na also studied
Cesium (Cs) No data available.
Francium (Fr) No data available.
2.2.2 Self-diffusion in glkaline earth metals Be, Mg, Ca, Sr, Bs, Ra
Beryllium (Be) 0.52
157.4
836...1342
165
841...1321
160.8
923.s.1473
(I c axis) D.62
[II c axis)
3.36
Land&Bhstein New Series III/26
I and 11hexagonal c axis investigated: ‘Be; single crystals; purity not specified; mechanical sectioning and measurement of residual activity; DII ’ D, ‘Be; polycrystals; 99.9%; mechanical sectioning and residual activity measurement .
Mehrer, Stolica, Stolwijk
68P2
[Ref. p. 81
2.2.3 Self-diffusion in scandium group and rare earth metals
38
DO
Q
10-4m2s-’
kJmo!-’
Temperature range K
Method/Remarks
Fig.
Ref.
Magnesium (Mg) 1.5 :l c axis) tfc axis)
136.1
74l.e.908
134.8
741 as.908
1.75 [I c axis) 1.78 [II c axis)
138.2
775...906
139
775 ..a906
56s
1 and 11hexagonal c axis investigated: 28Mg; single crystals; 99.9%; mechanical sectioning I and II hexagonal c axis investigated: 2*Mg; single crystals; 99.99%; mechanical sectioning and section activity as well as residual activity measurement; anisotropy carefully investigated and found to be weak DJD,, x 1.1 3.. 1.2
Calcium (Ca) 161.2
8.3
68Pl
45Ca; polycrystals; 99.95% ; mechanical sectioning and residual activity measurement; 14C 5gFe, 235U and 63Ni diffusion in &I also studied
773 ..* 1073
Strontium (Sr)
No data available.
Barium @a)
No data available.
Radium (Ra)
No data available.
2.2.3 Self-diffusion in scandium group and rare earth metals 2.2.3.1 Scandium group metals SC,Y, La
Scandium (SC)
No data available
Yttrium (Y) 280.9 tl” c axis a-Y) 0.82 (II c axis a-Y)
252.5
1173..*1573 1173...1573
a-Y, 1 and (1hexagonal c axis investi-
7
70Gl
8
69D2
gated: ‘lY; single crystals; mechanical sectioning and measurement of residual activity; D,, ’ DA
Lanthanum (La) 1.5 (B-W
188.8
923.s.1123
fee B-La investigated: r4’La; polycrystals (0.1 to 0.2 mm grain size); 99.95%; mechanical sectioning
(continued) Mehrer, Stolicaj Stolwijk
LandobB6mstein New Series III/26
Ref. p. 811
2.2.3 Self-diffusion in scandium group and rare earth metals
39
Temperature range K
Method/Remarks
Fig.
Ref.
102.6
1140...1169
bee r-La investigated: 14’La; strongly twinned samples; 99.95%; mechanical sectioning
8
73D
125.2
1151... 1183
bee y-La investigated: 140La; polycrystals; 99.85%, (detailed specification of purity); mechanical sectioning
8
74L3
fee y- and bee 6-Ce investigated: 141C!e; coarse grain polycrystals; 99.9%; mechanical sectioning
9
71D
1018...1064
bee 6-Ce investigated: 141C!e; polycrystals; 99.9%; mechanical sectioning with measurement of section and residual activity; data from [71D] also listed
9
73L2
1003,1028
bee 6-Ce investigated: 141Ce; polycrystals; 99.9%; mechanical sectioning; pressure dependence at two temperatures studied
-
74L2
fee y-Ce investigated: 141Ce; polycrystals; 99.9%; mechanical sectioning; pressure dependence studied
-
76M2
10
69Dl
DO
Q
10-4m2s-1
kJmol-’
Lanthanum (La), continued 1.3. 10-Z
(G-4 0.11 W4
2.2.3.2 Rare earth metals Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu
Cei-ium (Ce) 153.2
801..+ 965
0.012 (&Ce)
90
992... 1044
0.007 (&Ce)
84.7
0.55 We)
-
-
-
-
930
Praseodymium (Pr) 0.087 (P-W
123.1
1075~~~1150 bee p-Pr investigated: 14’Pr; polycrystals; 99.96%; mechanical sectioning; p-Pr classified among “anomalous” bee metals; ‘141n, 14’La, ‘(j6Ho also studied in j3-Pr
Neodymium (Nd) No data available.
Land&-BBmstein New Series III/26
Mehrer, Stolica, Stolwijk
40
2.2.3 Self-diffusion in scandium group and rare earth metals
DQ
Q
10-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
[Ref. p. 81 Fig.
Ref.
11
77F
12
77F
13
72s
hcp a- and bee y-Yb investigated: 16gYb; polycrystals; 99.9%; mechanical sectioning
14
74F
bee y-Yb investigated: r6’Yb; polycrystals; 99.9%; mechanical sectioning; pressure dependencestudied at these temperatures
-
Prometheum (Pm) No data available.
Samarium (Sm) No data available.
Europium (Eu) 1.0
144.0
771 *.* 1074
bee Eu investigated: ls2Eu; polycrystals; 99.7%; mechanical sectioning
Gadolinium (Gd) 0.01 (B-G4
136.9
1549...1581
bee g-Gd investigated: “‘Gd; polycrystals; 99.5%; mechanical sectioning; non-Gaussian penetration curves in the temperature range 1538*..1548 K
Terbium (Tb) No data available.
Dysprosium (Dy) No data available.
Holmium (Ho) No data available.
Erbium (Er) 4.51 (1 c axis) 3.71 (II c axis)
302.6
1475 .+.1685
301.6
1475...1685
1 and 11hexagonal c axis investigated: 169Er. single cr&tals; 99.9%; mechanical sectioning; DJD,, = 1.11... 1.16
Thulium (Tm) No data available.
Ytterbium (Yb) 0.034 (a-Yb) 0.12 (y-W
146.8
813...990
121.0
995 .** 1086
-
-
1003,1033, 1073
14
75F
Lutetium (Lu) No data available.
Mehrer, Stolica, Stolwijk
Landoh-kimstein New Series Ill/26
Ref. p. 811
2.2.4 Self-diffusion in titanium group metals
DO
Q
10-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
41 Fig.
Ref.
-
63L
2.2.4 Self-diffusion in titanium group metals Ti, Zr, Hf
Titanium (Ti) 6.4. lo-* (a-Ti)
122.7
-
-
963...1123
44Ti.
poly&ystals; 99.9%; mechanical sectioning and residual activity measurement 1172... 1813
(P-V
44Ti; polycrystals; 99.9%; mechanical sectioning; curved Arrhenius plot, two-exponential fit: 0: = 3.58. 10m8rn’s-l Q1 = 130.6kJmol-‘, 0: = 1.09. 10e4 m2sm1 Q, = 251.2 kJmol-‘; 48V in Ti also studied
15
64M2 .
1.9. 10-3 (P-W
152.8
1173:.. 1856
44Ti; polycrystals; 99.9%; mechanical sectioning and residual activity measurement
-
68Wl
4.54.10-4 (P-V
131.0
1228... 1784
44Ti; co-diffusion with g4Nb or g5Nb; polycrystals; 99.97% ; mechanical sectioning; TiNb alloys also studied
-
79P
6.6. 10-s (a-Ti)
169..l
1013...1149
15
80D
[P-Ti)
-
1176...1893
44Ti; polycrystals; 99.97%; mechanical sectioning and residual activity measurement; great-depth tails observed 44Ti. poly:rystals; 99.98%; mechanical sectioning; curved Arrhenius plot: interpreted as phonon softening effect on monovacancy migration, data including [64M2] described as D = 3.5 . 10T4 exp( - 328.0 kJ/RT) . exp(4.1 T,/T”) rn’s-l, T in K
15
87Kl
Land&-Biirnstein New Series III/26
Mehrer, Stolica, Stolwijk
42
2.2.4 Self-diffusion in titanium group metals
DO
Q
10-4m2s-1
kJmo!-’
Temperature range K
Method/Remarks
[Ref. p. 81 Fig.
Ref.
Zirconium (Zr) 2.4. 10-4 P-W
126.0
1441... 1776
g5Zr; polycrystals; metallic impurity content specified; mechanical sectioning; influence of a-g transition also studied
16
61K
-
1174...2020
g5Zr; polycrystals; 99.94%; mechanical sectioning; curved Arrhenius plot described by D = 3. 10-10(T/1136)15~6 _ [82.06+0.1294(7’-1136)]kJ
16
63F
&Zr)
RT g5Nb in Zr also studied 2.1 . lo-’
113.0
1013~~~1130 g5Zr; polycrystals; 99.99% ; mechanical sectioning and residual activity measurement; “Nb in Zr also studied
-
68Dl
-
1215...2088
8gZr; co-diffusion with “Zr. polycrystals (5 .. .7 mm grain size); detailed specifications of purity; mechanical sectioning; Do and Q not given; influence of preannealing examined; isotope effect also studied
16
70G2
-
1124
g7Zr; single crystals; purity not specified; mechanical sectioning; D = 5.6.10-18 m*s-1 D”=42.10-18~*~-1: 26A< 44Ti, 51Cr, 54Mn, 5gke, 6oCo and l**Sb in Zr also studied
16
74Hl
1189...2000
g5Zr and 88Zr; polycrystals; 99.985%; mechanical sectioning; curved Arrhenius plot: data including [61K, 63F, 70G2] described by D = 0.3 * 10m4exp( - 301.0 kJ/RT) * exp(3.39 Tz/T') m*s-‘, T in K; isotope effect also studied
16
79H
[or-Zr)
WW
[a-Zr)
ww
(continued)
Mehrer, Stolica, Stolwijk
LandoIl-BBmslein New Series III/26
Ref. p. 811
2.2.4 Self-diffusion in titanium group metals
DO
e
10-4m2s-1
kJmol-’
43
Temperature range K
Method/Remarks
Fig.
Ref.
Zirconium (Zr), continued 6.8 . 10-4 (P-W
145.0
1218... 1518
g5Zr; polycrystals; nuclear grade; mechanical sectioning; “Fe and ‘lC!r in Zr also studied
-
81P
3.1 . 10-s (P-W
105.3
1167... 1476
“Zr. poly&ystals; nuclear grade; mechanical sectioning; 48V in Zr also studied
16
82P
(c+Zr)
-
779... 1128
“Zr. , single crystals of the same random orientation; 99.99% ; sputter sectioning; downward curved Arrhenius plot
16
84H
Hafnium (Hf) 1.2. 10-3 W-W
162.0
2068 . . .2268
l8lHf; polycrystals; 97.9% (Zr 2.1%); mechanical sectioning
17
65W2
7.3. 10-6 @-HO
174.2
1197... 1756
17’Hf and ‘*lHf; polycrystals; 97.3% (Zr 2.7%); mechanical sectioning and residual activity measurement
-
68Dl
4.8. 1O-3 (P-W
183.4
2058...2431
175Hf and ‘*lHf; polycrystals; 97.3% (Zr 2.7%); mechanical sectioning and residual activity measurement
-
68Wl
0.86 (II c axis of cl-Hf) 0.28 (1 c axis of a-Ho
370.1
1470... 1883
17
72D
348.3
1538... 1883
a-Hf 1 and 11hexagonal c axis investigated: “lHf; single crystals; 97.9% (Zr 2.1%); mechanical sectioning; DL ’ DII
1.1 . 10-3 (P-W
159.2
2012...2351
‘8lHf; polycrystals; 97.1% (Zr 2.9%); mechanical sectioning; isotope effect also studied
17
82H
-La”*olt-tlornsfe*” ..-.. New Series III/26
Mehrer, Stolica, Stolwijk
44
2.2.5 Self-diffusion in vanadium group metals
DO
Q
10-4mZs-’
kJmo!-’
Temperature range K
Method/Remarks
[Ref. p. 81 Fig.
Ref.
-
65Ll
I8
65P2
18
74P
18
79MI
-
81T
2.2.5 Self-diffusion in vanadium group metals V, Nb, Ta
Vanadium (V) 0.011
255.4
1275... 1673
49.
singie crystals; 99.7%; mechanical sectioning; separate Arrhenius term for 1873...2161 K: Do = 58. 10e4 m’s-‘, Q = 383.1 kJmo!-’ 0.36
308.4
1153...1629
49.
singie crystals (99.99%), polycrystals (99.9%); mechanical and chemical sectioning; separate Arrhenius term for 1629...2106 K: Do = 214. 10e4 m’s-‘, Q = 394.1 kJmol-‘; grain boundary diffusion observed; “Fe in V also studied 0.288
309.6
997... 1915
48V.
singie crystals; 99.9%; mechanical sectioning and anodic oxidation; great-depth tails observed; separate Arrhenius term for 1915...2115 K: Do = 173. 10m4m’s-‘, Q = 409.3 kJmo!-’ 0.0208
272.1
1446... 1649
48~.
singie crystals; 99.7%; mechanical sectioning; separate Arrhenius term for 1649...2166 K: Do = 79.9. 10m4m*s-’ Q = 385 kJmo!-‘; two-kxponential analysis also given -
308.8
1200~~~1600 NMR: motional narrowing and relaxation time T,; slV signals in natural V; polycrystals; 99.9%; Do not given; monovacancy interpretation; oxygen migration also studied, effects of oxygen-vacancy pairs discussed
(continued) Mehrer, Stolica, Stolwijk
Land&-Bhstein New Series III/26
Ref. p. 811
2.2.5 Self-diffusion in vanadium group metals
DO
e
10-4m2s-1
kJmol-’
45
Temperature range K
Method/Remarks
Fig.
Ref.
1323... 1823
48v.
18
83A
18
83Gl
Vanadium (V), continued 1.79
331.9
single crystals and polycrystals; 99.97% (s.c.); mechanical sectioning, residual and section activity measurement; separate Arrhenius term for 1823...2147K: Do = 26.81 . 10m4rn’s-l, Q = 372.4 kJmol-‘; enhancement factors due to alloying with Fe and Ta also determined 0.10
298.1
1333 ... 1840
NMR: relaxation time T,,; ‘IV signal in natural V; polycrystals; 99.95% and 99.8%; mono-vacancy interpretation: Do includes correlation factor J;,, = 0.727; oxygen migration also studied
Niobium (Nb) 12.4
439.6
1858;..2393
g5Nb; polycrystals; 99%; mechanical sectioning
-
60R.I
1.3
397.7
1970...2430
g5Nb; polycrystals (5 mm grains); purity not specified; autoradiographic method and mechanical sectioning; 6oCo and 55Fe in Nb also studied
-
62P
1.1
401.9
1224...2668
g5Nb; polycrystals (99.75%) and single crystals; mechanical sectioning and anodic oxidation; greath-depth-tails observed; no appreciable effect of oxygen found; 18’Ta in Nb also studied
19
65L2
0.61
397.3
1421...2509
g5Nb; single crystals (99.9%) and polycrystals; mechanical sectioning and anodic oxidation; residual and section activity measurement; 5gFe,6oCo and 63Ni in Nb also studied
19
77Al
Land&-Biirnstein New Series III/26
Mehrer, Stolica, Stolwijk
(continued)
46
2.2.5 Self-diffusion in vanadium group metals
DO
Q
10-4m2s-’
kJmol-’
Temperature range K
Method/Remarks
[Ref. p. 81 Fig.
Ref.
Niobium (Nb), continued 0.524
395.6
1354...2690
g5Nb; single crystals; 99.98%; mechanical sectioning and anodic oxidation; Do and Q recalculated from given data, two-exponential fit: 07 = 0.008. 10m4m2sm1 Q, = 349.3kJmol-‘, D, = 3.7. 10e4 m2s-’ Q, = 438.0 kJmol-‘, mono-/divacancy interpretation; no influence of oxygen content found
-
-
1929...2673
g5Nb, g2Nb; single crystals; purity not specified; mechanical sectioning; two-exponential tit: 0: = 0.015. 10e4 m2s-’ Q, = 354.1 kJmol-‘, 0: = 4.6. low4 m2s-’ Q2 = 442.9 kJmol-‘, mono-/divacancy interpretation; isotope effect also studied
-
-
2300’..2510
g5Nb; crystal type not specitied; purity not specified; electromigration study; mechanical sectioning; “Fe, 6oCo, ‘*‘Ta and ‘lCr in Nb also investigated Tantalum
0.124
78El
8332
(Ta)
413.2
1523.s.2576
‘s2Ta; mono- and polycrystals; 99.67%; mechanical sectioning and anodic oxidation; g5Nb in Ta also studied; Do and Q calculated from DNb/DT"= 1.85
65Pl
423.6
1261...2993
“‘Ta; single crystals; 99.98%; mechanical and sputter sectioning; monovacancy interpretation
83Wl
Mehrer, Stolica, Stolwijk
Land&-Bhstein New Series III/26
Ref. p. 811
2.2.6 Self-diffusion in chromium group metals
DO
e
10-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
47 Fig.
Ref.
2.2.6 Self-diffusion in chromium group metals Cr, MO, W
Chromium (Cr) 0.28
306.5
1473... 1873
“Cr; large grain polycrystals; 99.99% ; mechanical sectioning and residual activity measurement
-
62Hl
1.6
339.1
1273...2023
51Cr. mono- and polycrystals (2 ... 3 mm); 99.98%; mechanical sectioning; great-depth-tails observed; ‘ICr and 63Ni diffusion in NiCo alloys also studied
-
7lA
970
435.4
1369...2093
51Cr; single crystals; 99.995%; mechanical sectioning; isotope effect also studied
21
76M4
1280
441.9
1073... 1446
51Cr. singIL crystals; 99.99% ; sputter sectioning; analysis includes data of [76M4]
21
81M
Molybdenum (MO) 4
481.5
2073 . . .2448
ggMo; polycrystals; 99.3% (0.7% w); sectioning method not specified, residual activity measurement; la5W in MO also studied
22
59B
2.77
464.7
1973...2193
“MO* polycjstals (1 *. .2 mm grain size); 99.97% ; mechanical and electrochemical sectioning; only three data measured
22
60B2
0.38
422.0
2173...2353
“MO; polycrystalline wires; purity not specified; electrochemical sectioning in radial direction; effects of grain boundary diffusion and recrystallization also observed
-
61D
(continued) Land&Biimstein New Series III/26
Mehrer, Stolica, Stolwijk
48
2.2.6 Self-diffusion in chromium group metals
DO
Q
10-4m2s-1
kJmo!-’
[Ref. p. 81
Temperature range K
Method/Remarks
Fig.
Ref.
Molybdenum (MO), continued 0.1
386.0
2123.3.2618
ggMo; single crystals; purity not specified; mechanical sectioning; also measurementson polycrystals yielding higher diffusion coefficients
-
63A
8
488.2
1360...2113
ggMo; single crystals; 99.99%; mechanical and sputter sectioning; two-exponential fit: 0: = 0.126. 10m4rn’s-’ Q, = 437.1 kJmo!-‘, 0: = 139. 10e4 m2s-’ Q2 = 549.0kJmo!-‘, mono-/divacancy interpretation
22
79M2
-
65A2
23
69P
23
llA2
23
78M
Tungsten (W) 42.8
641.0
2939 ... 3501
18SW.
single’crystals; 99.99%; mechanical sectioning; le3Re and lB4Re in W also studied 1.88
587.4
2073 ..- 2676
188~.
single’crystals; purity not specified; anodic oxidation; greath-depth tails observed; g5Nb and ‘**Ta in W also studied 15.3
626.3
2042...2819
187W.
single’crystals; purity indicated by residual resistivity ratio 10’; mechanical sectioning and anodic oxidation; seealso [84A] -
-
1705...3409
‘s7W and lssW; single crystals; 99.999% ; mechanical sectioning and anodic oxidation; greath-depth tails observed; two-exponential fit: 0: = 0.04. 10V4 m*s-’ Q, = 525.8kJmo!-‘, 0: = 46. 10T4 m*s-’ Q2 = 665.7 kJmo!-‘, mono-/divacancy interpretation
Mehrer, Stolica, Stolwijk
Landok-B6mstein New Series III/26
2.2.7, 8 Self-diffusion in manganese, iron group metals
Ref. p. 811
DO
Q
10-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
49 Fig.
Ref.
-
69A
-
64N
2.2.7 Self-diffusion in manganese group metals Mn, Tc, Re
Manganese (Mn) -
-
1390... 1508
54Mn; polycrystals; 99.95% and 99.3%; mechanical sectioning; great-depth tails observed; preliminary data for bee and fee phase; Do and Q not given
Technetium (Tc) No data available.
Rhenium (Re) -
511.4
1520... 1560
field ion microscopy, time dependence of needle shape; purity not specified; Do not determined
2.2.8 Self-diffusion in iron group metals Fe, Ru, OS
Iron (Fe) 118 (paramagnetic cl-Fe)
281.5
970... 1167
a-Fe investigated: 55Fe; coarse grain polycrystals; high purity material (not specified); influence of magnetic order-disorder transition on D observed; Do and Q values only from D values at least 50 K above Curie temperature
24
60Bl
239.5
1082...1178
-
61B
270
1337... 1666
w und y-Fe investigated: 55Fe; single and polycrystals; 99.97%; sectioning and residual activity measurements as well as surface decrease method employed; influence of magnetic order-disorder transition on D observed; Do and Q values for a-Fe only from D values at least 20 K above Curie temperature
238.6
1686... 1781
&Fe investigated: 59Fe; polycrystals; high purity material (not specified); mechanical sectioning; Co diffusion in &Fe also studied
-
63B
I
Land&-Bijmstein New Series III/26
Mehrer, Stolica, Stolwijk
(continued)
50
2.2.8 Self-diffusion in iron group metals
DO
Q
10-4m2s-1
[Ref. p. 81
Method/Remarks
Fig.
Ref.
kJmol-’
Temperature range K
240.7
1701... 1765
24a
665
240.7
999...1157
CL-and &Fe investigated: 55Fe, “Fe; coarse grain polycrystals; 99.97%; only data for &Fe included in Fig. 24 a; 6oCo diffusion in u- and &Fe also studied
311.1
1223... 1473
y-Fe investigated: 55Fe; coarse grain polycrystals (0.1 .*.0.3 mm); surface decreasemethod
24a
6612
284. 1
1444... 1634
y-Fe investigated: 5gFe, 55Fe; coarse grain polycrystals (2.. .5 mm); 99.98%; mechanical sectioning; data taken from Fig. 3 of [68H]; isotope effect also studied
24a
68H
-
1168,1169
24a
68W2
-
1641
-
1683... 1733
a-, y- and &Fe investigated: 52Fe, 5gFe; polycrystals; 99.97%; mechanical sectioning; Do and Q values not given; mainly isotope effect in a-, y- and &Fe studied CL-,y- and &Fe investigated: 55Fe, 5gFe. coarse grain polycrystals (3. **4 mm); 99.999% ; mechanical sectioning; Do and Q values not given; mainly isotope effect in u-, y-, &Fe studied
24a
69G
Iron (Fe), continued 2.01
:&Fe) 2.01 baramagnetic u-Fe)
0.49
(Y-Fe)
(a-Fe) (Y-Fe) (b-Fe)
(a-Fe) We) :6-Fe)
993,1043, 1142
-
1394,161l 1725
Iferromagnetic a-Fe)
-
784...1017
ferromagnetic a-Fe investigated: 5gFe; single crystals; samples with different purity studied; sputter sectioning; influence of magnetic order-disorder transition on D investigated; strong deviation from Arrhenius behaviour observed
24a 24b
77H
121 [paramagnetic a-Fe)
281.6
1067...1168
paramagnetic a-Fe investigated: 5gFe; polycrystals with 300 urn average grain size; 99.97%; mechanical sectioning; 48V diffusion in u-Fe also studied
24a
87G
(continued)
Mehrer, Stolica, Stolwijk
LandoltTl6mstein New Series III/26
51
2.2.9 Self-diffusion in cobalt group metals
Ref. p. 811
DO
Q
10-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
766... 1148
“Fe, “Fe; coarse grain polycrystals; 99.97%; sputter sectioning; influence of magnetic order-disorder transition on D investigated; strong deviation from Arrhenius behaviour observed; isotope effect also studied
24b
881
754...1163
paramagnetic and ferromagnetic a-Fe investigated: “Fe, 55Fe; single crystals; 99.98%; mechanical and sputter sectioning; influence of magnetic order-disorder transition on D investigated; strong deviation from Arrhenius behaviour observed; dislocation diffusion also studied
24a 24b
89M, 9OL
6Oco. coarse grain polycrystals; 99:4% ; mechanical sectioning and measurement of residual activity; 6oCo and 63Ni diffusion in Co-Ni ,alloys and in Ni also studied
25
62H2
Iron (Fe), continued iara- and ferromagnetic a-Fe)
-
(para- and ferromagnetic a-Fe)
-
Ruthenium (Ru)
No data available.
Osmium (OS)
No data available.
2.2.9 Self-diffusion in cobalt group metals Co, Rh, Ir
Cobalt (Co) 274
1045 ... 1321
260.5
1465... 1570
1.66
287.5
1320... 1584
6OCo; polycrystals with 500 urn average grain size; 99.5%; mechanical sectioning and measurement of residual activity; ‘j°Co and 63Ni diffusion in Co -Ni alloys also studied
-
65Hl
0.55 (ferro- and paramagnetic Co)
288.5
896... 1745
To, -co, 6Oco; coarse grain polycrystals; 99.99% ; mechanical and sputter sectioning; no significant influence of the ferromagnetic order transition observed; isotope effect also studied for five temperatures
25
79B
iejrromagnetic Co) 0.17
[paramagnetic Co)
Land&-Biirnstein New Series III/26
Mehrer, Stolica, Stolwijk
(continued)
[Ref. p. 81
2.2.10 Self-diffusion in nickel group metals
52
DO
Q
10-4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
944...1743
S’Co; single crystals; 99.999% ; lathe und sputter sectioning; Doand Q values from a forced Arrhenius fit, small deviations attributed to divacancy contributions and magnetic ordering
25
88L
-
70s
26
86A
Cobalt (Co), continued 2.54 (ferro- and paramagnetic Co)
304
Rhodium (Rh) -
391
903 ... 2043
high temperature creep; polycrystals; 99.98%; requires a model of high temperature creep caused by diffusion; Do not obtained
Iridium (Ir) 0.36
438.8
2092 ... 2664
l g21r; single crystals; 99.9%; mechanical sectioning; correction for evaporation applied
2.2.10 Self-diffusion in nickel group metals Ni, Pd, Pt
Nickel (Ni) 1.27
279.7
1384...1521
63Ni; polycrystals; mechanical sectioning and residual activity measurement
56H
3.36
292.2
1423...1673
63Ni.
59M
polycrystals; mechanical sectioning and residual activity measurement; evidence of grain boundary diffusion below 1423 K 1.9
284.7
1315...1677
63Ni; coarse grain polycrystals; 99.95%; mechanical sectioning
64Ml
1.9
279.7
748...923
‘j3Ni; single crystals; 99.97% ; surface decreasemethod; polycrystals also studied for grain boundary diffusion
65Wl
(continued)
Mehrer, Stolica, Stolwijk
LandolbB6mstein New Series III!26
Ref. p. 811
2.2.10 Self-diffusion in nickel group metals
DO
Q
10-4m2s-1
kJmol-’
Temperature range , K
53
Method/Remarks
Fig.
Ref.
1173...1473
63Ni; mono- and polycrystals; 99.99%; surface decreasemethod
-
6611
Nickel (Ni), continued 2.59 (from single crystal data) 2.22 (from polycrystal data)
293.5
1.77
285.1
1253... 1670
63Ni; single crystals; 99.999%; mechanical sectioning and residual activity measurement; slight curvature of Arrhenius diagram observed, three-exponential fit: 0: = 0.38 . 10e4 m2s-l Q1 = 271.3 kJmol-‘, 0: = 3.07 . 10m4m2sm1 Qz = 309.9kJmol-‘, 0: = 0.017 rnzs-l Q3 = 377.5kJmol-‘, mono-, di-, trivacancy interpretation
27
68Bl
2.2
292.6
1323... 1477
63Ni; polycrystals; 99.7%; 63Ni in Ni,Al also studied
-
75B
2.6
279.1
1103... 1273
63Ni.
-
76F
290
single crystals; surface decreasemethod; D-values below 1073 K influenced by diffusion short circuits 1.33
280.8
815...1193
63Ni; single crystals; 99.997%; sputter sectioning; two-exponential fit to own data and those of [68Bl] 07 = 0.92. low4 rn’s-’ Q1 = 278 kJmol-‘, 0: = 0.037 m2 s-l Qz = 357 kJmol-‘, mono-/divacancy interpretation
27
76Ml
1.82
285.2
1323 ... 1673
63Ni; single crystals; 99.98% to 99.999%; mechanical sectioning
-
83V
0.205
266.3
1323... 1773
28
64P
Palladium (Pd) lo3Pd, ’ “Pd; single crystals; 99.999%; mechanical sectioning; isotope effect also studied
Mehrer, Stolica, Stolwijk
54
2.2.11 Self-diffusion in noble metals
DO
Q
10-4mZs-1
kJmol-’
Temperature range K
Method/Remarks
[Ref. p. 81 Fig.
Ref.
Platinum (Pt) 0.33
285.6
1598...1873
mixture of 193Pt, 195mPtand 19’Pt obtained by neutron activation of pure Pt; polycrystals; 99.99% ; mechanical sectioning
29
57K
0.22
278.8
1523... 1998
r=pt; coarse grain polycrystals; 99.999%; surface decreasemethod
29
62C
0.05
257.6
850... 1265
19’Pt; single crystals; 99.99%; sputter sectioning; two-exponential fit to own data and those of [57K]: 0: = 0.06. low4 mz s- ’ Q, = 259.7 kJmol-‘, D”=06t06~10-4mZs-1 Q: = 365 to 388 kJmol-‘, mono-/divacancy interpretation
29
78R
-
68B2
2.2.11 Self-diffusion in noble metals Cu, Ag, Au
0.19
196.4
Copper (Cu) 973 ... 1263 64Cll; single crystals; purity not specified; mechanical sectioning; pressure dependencealso studied for Cu, Au, Al
0.31
200.7
663...833
TEM observation of the annealing of quenched-in voids; 99.999% ; requires a model for void annealing caused by diffusion
-
69B
II.78
211.3
972...1334
30
69Rl
D.11 [from Wu data)
190.1
64cu, 67cu; single crystals; 99.999% ; mechanical sectioning; isotope effect also studied I 63Cu stable isotope
-
69E
D.15
193
[from ‘j5Cu data)
1003...1123
65Cu stable isotope; NMR: relaxation times 7, and 7”; Cu particles < 8 urn; 99.999% ; liquid Cu also studied (continued)
Mehrer, Stolica, Stolwijk
landok-BCmstein New Series III/26
Ref. p. 811
2.2.11 Self-diffusion in noble metals
DO
Q
10-4m2s-’
kJmol-’
55
Temperature range K
Method/Remarks
Fig.
Ref.
Copper (Cu), continued -
614...654
Tu; single crystals; 99.999%; sectioning by anodizing and stripping, only three temperatures studied; D-values agree with those of [77M], Do and Q values not given
-
74Ll
1.05
210.3
845.+.1111
NMR: 63Cu relaxation time in the rotating frame; Cu powder 3...3Onm; 99.99%
-
74w
0.35
203.6
574...905
64cu. 30 single crystals with low dislocation density; 99.999% ; sputter sectioning; Do and Q values from fit of one Arrhenius term to own data and those of [69Rl], two-exponential fit: 0: = 0.1 . 10e4 rn’8-l Qr = 196.8kJmol-‘, @’ = 2. 10e4m2sv1 Qz = 233.5 kJmol-l, mono-fdivacancy interpretation
77M
-
-
lOlO... 1352
64Cu; single crystals; 99.997%; mechanical sectioning; Do and Q values not given, two-exponential fit to own data and those of [69Rl, 77M]: 0: = 0.13. 10e4 m2se1 Q1 = 198.5kJmol-‘, D~=4.6.10-4m2s-1 Qz = 238.6 kJmol-r, mono-/divacancy interpretation
78Bl
0.68
209.4
1078... 1348
64Cu; coarse grain polycrystals; 99.999% ; mechanical sectioning; two-exponential fit to own data and those of [77M]: 07 = 0.15. 10e4 m2sm1 Q, = 198.8kJmol-‘, Dt = 4.8 . 10e4 m2 s-l Q2 = 243.1 kJmol-I, mono-fdivacancy interpretation
79K
0.877
211.3
992... 1355
Tu; coarse grain polycrystals; 99.998% ; mechanical sectioning
82F
_Landolt-Bornstem ..-.. New Series III/26
Mehrer, Stolica, Stolwijk
30
30
2.2.11 Self-diffusion in noble metals
56
DO
Q
10-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
[Ref. p. 81 Fig.
Ref.
Silver (Ag) -
-
1183
llomk single crystals; 99.99%; measurementsat 1183 K only; pressure dependencealso studied at 1183 K for “OrnAg, ‘141n and 124Sb in Ag
-
65B
3.278
181.7
1038...1218
“OrnAg. polycrystals; mechanical sectioning and residual activity measurement
-
68K
0.67
190.1
913...1228
105~~,
31
70R
31
72R
llomAg;
single crystals; 99.999% ; mechanical sectioning; isotope effect also studied losAg, “ornAg; single crystals; 99.999%; mechanical sectioning; Do and Q values not given; isotope effect also studied; mono-/divacancy interpretation of diffusion and isotope effect data
-
-
946.e.1227
0.041
169.8
547...777
‘lo mAg. single ciystals; 99.999%; sectioning by anodizing; Do and Q are “best values” for monovacancies taken from two-exponential fit to own data and those of [70R]: 0: = 0.041 . 10e4 m*s-’ Q, = 169.8kJmol-‘, D~=4.8.10-4m2s-1 Q2 = 211 to 221 kJmol-‘, mono-/divacancy interpretation
31
73Ll
0.235
179.5
630..+ 854
11omAg; single crystals; 99.99% ; chemical sectioning; Do and Q values from tit of Arrhenius equation to own data and those of [70R, 73Ll], two-exponential tit of own data together with various sets of other data [70R, 73Ll] performed, mono-/divacancy interpretation
31
74B
(continued)
1
Mehrer, Stolica, Stolwijk
Landolt-BBmsIein New Series III/26
Ref. p. 811
2.2.11 Self-diffusion in noble metals
DO
Q
1()-4m2S-1
kJmol-’
Temperature range K
57
Method/Remarks
Fig.
Ref.
105Ag,
31
78B2
31
82R
-
57M
32
63D
-
65D
-
65Gl
-
6562
-
68B2
Silver (Ag), continued 0.043
-
0.091
169.8
580...834
ttomAg;
single crystals; 99.9995%; sputter sectioning; comparison with other microsectioning studies performed 1tomA . g, single crystals; 99.999% ; sputter sectioning; two-exponential fit to own data and data from [70R, 73L1,74B]: 0: = 0.046 . low4 m2 s-l Q1 = 169.8kJmol-‘, D,O= 3.3 . 10m4m2 s-l Qz = 218.1 kJmol-‘, mono-/divacancy interpretation; pressure dependence also studied
-
594...994
174.6
Gold (Au) 198AU, 1077 ... 1321 polyc&tals; 99.95%; mechanical sectioning
0.117
176.3
975...1172
-
-
1133...1233
0.107
176.6
623...733
0.107
176.9
1123...1323
0.043
167.5
973 ... 1263
Land&-Biimstein New Series III/26
198AU.
coarse’grain polycrystals; 99.93%; mechanical sectioning and residual activity measurement; diffusion of 59Fe,6oCo and ‘j3Ni in Au also studied 198AU. single ‘crystals; 99.99%; mainly pressure dependenceat three temperatures studied 195A~; polycrystals; purity not specified; L-X ray absorption method i95Au; single crystals; 99.97%; mechanical sectioning 198AU, single ‘crystals; purity not specified; mechanical sectioning; pressure dependence of self-diffusion also studied for Au, Cu and Al
Mehrer, Stolica, Stolwijk
(continued)
2.2.12 Self-diffusion in zinc group metals
58
Q kJmol-’
[Ref. p. 81
Temperature range K
Method/Remarks
Fig.
Ref.
559...685
198AU,
32
69R2
rg’Au, rg8Au; single crystals; 99.999%; mechanical sectioning; mono-/divacancy interpretation; Co diffusion in Au, isotope effect of self-diffusion and Co diffusion also studied
32
78Hl
“‘Au; single crystals; 99.999% ; sputter sectioning; pressure dependencealso studied
32
83W2
I and (1hexagonal c axis investigated: 65Zn; single crystals; 99.999% ; mechanical sectioning; D,, ’ D.l 1 and 11hexagonal c axis investigated: 65Zn, 6gZn; single crystals; 99.999%; mechanical sectioning; q > D,; mainly isotope effect studied for Zn and Cd diffusion
33
53s
33
67B
I and 11hexagonal c axis investigated: 65Zn, 6gZn; single crystals; 99.999% ; mechanical sectioning; D,, > D,; isotope effect also studied
33
67P
Gold (Au), continued 0.026
166.9
single ‘crystals; 99.99% ; sectioning by anodic oxidation and residual activity measurement 0.084
0.027
165
603...866
2.2.12 Self-diffusion in zinc group metals Zn, Cd, Hg Zinc (Zn) 0.58 (1 c axis) 0.13 (II c axis)
101.7
513.e.683
91.3
513...683
-
-
0.18 (1 c axis) 0.13 (II c axis)
655 ... 685
96.3
513...691
91.7
513...691
(continued)
Mehrer, Stolica, Stolwijk
LandolbB6mstein New Series III/26
59
2.2.12 Self-diffusion in zinc group metals
Ref. p. 811
DO
Q
10m4m2s-l
kJmol-’
Zinc (Zn), continued -
Temperature range K
Method/Remarks
Fig.
Ref.
573...673
I and 11hexagonal c axis investigated: 65Zn; single crystals; 99.999% ; mechanical sectioning; Do and Q values not given; mainly pressure effects investigated
-
72C
1 and 11hexagonal c axis investigated: “‘Cd; single crystals; 99.5%; mechanical sectioning; D,, > D,; polycrystals also investigated
34
55w
Cadmium (Cd) 0.10 (1 c axis) 0.05 (II c axis)
80
383...588
76.2
383...588
0.05
73.7
350...420
polycrystals investigated; NMR: spin relaxation times 7” and T,: l13Cd signal in natural Cd; 15 urn foil
-
58M
0.68 (II c axis)
86.2
453...573
II hexagonal c axis investigated: “‘Cd; single crystals; 99.99% ; surface decreasemethod; polycrystals also investigated, 65Zn and ‘lo “Ag in Cd also studied
34
67H
0.08
78.7
473...553
polycrystals investigated: l15Cd; fine grain polycrystals; 99.99% ; mechanical sectioning
-
67A
0.18 (1 c axis) 0.12 (II c axis)
82
420... 587
34
72M
77.9
420...587
-L and II hexagonal c axis investigated: rogCd; single crystals; 99.999% ; mechanical sectioning; D,, > D,; Zn-, Ag-, In-, Hg- and Au-diffusion also studied
-
523...593
I and II hexagonal c axis investigated: “‘Cd; single crystals; 99.999%; mechanical sectioning; Do and Q values not given; only pressure effects studied
-
73B
-
Mercury (Hg) No data available. Land&-B6rnstein New Series III/26
Mehrer, Stolica, Stolwijk
60
2.2.13 Self-diffusion in aluminum group metals
DO
e
10-4mZs-1
kJmol-’
Temperature range K
Method/Remarks
[Ref. p. 81 Fig.
Ref.
2.2.13 Self-diffusion in aluminum group metals AI, Ga, In, Tl
Aluminum (Al) 1.71
142.4
729...916
26AI (radiotracer with low specific activity); single crystals and coarse grain polycrystals; 99.99% ; mechanical sectioning; 54Mn in AI also studied
35
62L
-
144.4
673*..883
26A1(radiotracer with low specific activity); single crystals; purity not specified; mechanical sectioning; pressure dependence also studied, selfdiffusion and its pressure dependence also studied for Cu and Au
-
68B2
0.176
126.4
358 . ..482
TEM observation of the annealing of quenched-in voids; 99.9999%; requires model of void shrinkage caused by self-diffusion
35
68V
120.4
512...820
NMR: spin lattice relaxation time in the rotating frame T, p of 100% abundant stable isotope 27Al
-
71F
123.5
515...770
NMR: spin lattice relaxation time in rotating frame T,@of 100% abundant stable isotope 27Al; 27 . . .30 urn foils; 99.999%; data reanalyzed in [87D]
35
74M
-
722
26AI; semi-infinite diffusion couple; D = 1.05. lo-l4 m2s-‘; agreeswith previous radiotracer data [62L, 68B2J
-
8582
-
68C
-
Gallium (Ga) D in 10-17
5.3 5.3 7.8 9.3 42
m2s-l
283 293.2 298.2 300.7 303
72Ga; single crystals and coarse grain polycrystals; 99.9999% ; results are becauseof experimental difficulties only of qualitative interest, no clear evidence of anisotropy was observed
Mehrer, Stolica, Stolwijk
Landolt-BBmstein New Series III/26
61
2.2.14 Self-diffusion in group IV B metals
Ref. p. 811
DO
Q
10-4m2s-’
kJmol-l
Temperature range K
Method/Remarks
Fig.
Ref.
36
59D
-
710
37
55s
37
85C
38
60M
38
64C
Indium (In) 78.5
312...417
;‘1’ c axis) 2.7 (II c axis)
78.5
312...417
-
-
392, 406, 422
I and 11tetragonal axis investigated: “41~. single ciystals; 99.97%; mechanical sectioning; DA > D,, I and 11tetragonal axis investigated: 1141111~. single crystals; 99.999% ; mainly pressure effects studied at 3 temperatures
Thallium (Tl) 94.6
420...500
hcp ct- and bee P-T1investigated: 204Tl.
;: c axis of hcp a-Tl) 95.9
420...500
83.7
515...550
80.2
513...573
Il;“c axis of hcp LXT1)
single ciystals; 99.9% ; mechanical sectioning; in c+Tl: D, > D,,
Kc P-Tl) 0.42 (bee P-Tl)
bee P-T1investigated: ‘04T1; coarse grain polycrystals; 99.999% ; mechanical sectioning; interpretation of slightly curved Arrhenius diagram in terms of mono- and divacancies
2.2.14 Self-diffusion in group IVB metals Sn, Pb Self-diffusion data for semiconducting elements Si, Ge can be found in [89L]
Tin (Sn) 97.6
451...495
107.2
451*..495
105.1
433...501
107.2
433...501
t;” c axis) ,“,i2caxis)
10.7 (I c axis) ii’c axis)
I and 11tetragonal c axis investigated: lt3Sn; single crystals; 99.998%; mechanical sectioning; D, ’ DII I and 11tetragonal c axis investigated: lt3Sn; single crystals; 99.999%; mechanical sectioning; D, > D,,; pressure dependence also studied
(continued) Land&-B6mstein New Series III/26
Mehrer, Stolica, Stolwijk
[Ref. p. 81
2.2.15 Self-diffusion in group V B semimetals
62
DO
Q
10-4m2s-1
Method/Remarks
Fig.
Ref.
kJmol-’
Temperature range K
108.4
455 ... 500
I and 11tetragonal c axis investigated:
38
74H2
Tin (Sn), continued 21.0 (1 c axis) 12.8 (II c axis)
l13Sn.
108.9
455~..500
single crystals; 99.999% ; mechanical sectioning; D1 ’ D!69‘& 124Sb-,
65~~~
diffusion in Sn
also studied’
Lead (Pb) 0.281
0.887
101.4
447 . . * 595
2’oPb; single crystals; 99.999%; mechanical (microtome) sectioning
39
55N
109.1
480...596
“‘Pb; coarse grain polycrystals; 99.99%; mechanical sectioning; diffusion of Tl and Bi in Pb-Tl tem also studied
39
61R
39
69M
1 and II rhombohedral (trigonal) c axis investigated: lz4Sb; single crystals; 99.998%; mechanical sectioning; D, > D,,; results influenced by surface defects and microcracks
-
64H
I and II rhombohedral (trigonal) c axis investigated: lz4Sb; single crystals; 99.9999% ; serial sectioning by chemical polishing; D.L’ D,,
40
66C
106.8
470..* 573
sys-
“‘Pb; single crystals; 99.999%; mechanical (microtome) sectioning; ’ lsmCd diffusion in Pb also studied
2.2.15 Self-diffusion in group VB semimetals P, As, Sb, Bi Self-diffusion data for P, As are not included.
Antimony (Sb) 185.9
770... 870
197.2
830... 890
149.9
773..*903
201
773 . ..903
;: c axis) ,ii’c axis)
0.10 (1 c axis)
c axis)
Mehrer, Stolica, Stolwijk
(continued)
Land&-Bhstein New Series III/26
63
2.2.16 Self-diffusion in group VI B semimetals
Ref. p. 811
!.I0
Q
10-4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
746... 856
lz4Sb; polycrystals; 99.9% ; mechanical sectioning and counting of residual activity; D at T, is 2.9 . IO-l4 m2s-‘; penetration profiles with tails presumably due to grain boundaries
-
65H2
Antimony (Sb), continued 1.05
165.4
Bismuth (Bi) Vo reliable data available.
2.2.16 Self-diffusion in group VIB semimetals S, Se, Te, PO self-diffusion data for S are not included. Selenium (Se) LOO I c axis) 1.2 11c axis)
135.1
1.0082 11c axis)
115.8
425 . ..488
115.8
350...480
I and 11trigonal c axis investigated: 75Se; 41 single crystals grown from vapour phase; purity specified by conductivity between 2. 10m5and 10m6R-’ cm-‘; mechanical sectioning and measurement of residual activity; great-depth tails observed; D, > D,,; 41 11trigonal axis investigated: NMR: spin lattice relaxation times q and Tie of stable isotope 77Sein natural Se; single crystals; 99.999%; three-exponential fit performed; Do and Q refer to dominating term (dashed line in Fig. 41), data also published in [8362] Tellurium
3.91 * 104 (I c axis) 130 (II c axis)
195.9
579...663
168.8
600...673
166
496...640
147.6
Land&Biirnstein New Series III/26
85G
(Te)
I and II trigonal c axis investigated: 127mTe; single crystals; 99.9%; mechanical sectioning; D, > D,, ; influence of I- and Al-doping also studied
42
67G
I and II trigonal c axis investigated:
42
83W3
127rnTe.
(“Y c axis) ii”c axis)
70B
single cryktals; 99.999%; sputter sectioning; D /DA = 1 . ..2.5. lZ14Sbdiffusion also studied
Mehrer, Stolica, Stolwijk
(continued)
64
2.2.17 Self-diffusion in actinide group metals
DO
Q
10-4m2s-’
kJmo!-’
[Ref. p. 81
Temperature range K
Method/Remarks
Fig.
Ref.
485...650
11trigona! c axis investigated: NMR: spin lattice relaxation times TI and T,@of stable isotope 125Tein natural Te; single crystals; 99.999%; good agreement with D,, from [83W2], similar data in [81G]
-
85G
43
67s
Tellurium (T’e),continued 0.12
139.9
(II c axis)
Polonium (PO) No data available.
2.2.17 Self-diffusion in actinide group metals AC, Th, Pa, U, Np, Pu etc. Data are available only for Th, U and Pu.
Thorium (Th) 395 (a-Th)
299.8
998..-1140
fee u-Th investigated: 228Th; polycrystals; 99.85% (detailed specification of purity given); u-spectroscopy method; 231Paand 233U diffusion in u-Th also studied
Uranium (U) 0.0018 (Y-U)
115.1
1073...1323
bee y-U investigated; diffusion couple of natural U and U enriched with 235U; polycrystals; purity not specified; mechanical sectioning and measurement of residual u-activity; y-U diffusion is anomalous
44
59Al
0.0135 WJ)
175.8
973 ... 1028
B-U investigated; diffusion couple of natural U and U enriched with 235U; polycrystals; purity not specified; mechanical sectioning and measurement of residual u-activity
44
59A2
(continued)
Mehrer, Stolica, Stolwijk
Ref. p. 811
2.2.17 Self-diffusion in actinide group metals
DO
Q
10-4m2s-1
kJmol-’
65
Temperature range K
Method/Remarks
Fig.
Ref.
Uranium (U), continued 0.00233 (Y-u)
119.3
1075... 1342
bee y-U investigated; 235U (93 % enriched); polycrystals; 99.998%; mechanical sectioning; Do and Q values anomalous
44
60R2
0.002 WJ)
167.5
853...923
orthorhombic a-U investigated; diffusion couples of natural U and U enriched with 235U; polycrystals; purity not specified; mechanical sectioning and measurement of residual a-activity; small anisotropy of diffusion in agrains
44
62A
0.0028 WJ)
185.1
973 ... 1023
P-U investigated: 235U; polycrystals; mechanical sectioning and measurement of residual activity; grain boundary diffusion also studied
-
68F
Plutonium
(Pu)
4.5. 10-3 (6-Pu)
99.6
623...713
fee 6-Pu investigated: diffusion couples of two cylinders, one enriched with 238Pu; polycrystals; purity not specified; lathe sectioning; from autoradiographic experiments concluded that grain boundary diffusion is unlikely
45
64T
0.02 (E-PU)
77.5
773...885
bee E-PUinvestigated; diffusion couples consisting of Pu with either 1% or 8% 240Pu; polycrystals; purity not specified; grinder sectioning and measurement of residual activity
45
68D2
0.003 (E-PU)
65.7
788...849
bee E-PUinvestigated; polycrystals; 99.9% (detailed specification of purity and isotopic composition is given); mechanical sectioning and measurement of residual activity; diffusion in E-PUis anomalous; pressure effects also studied
45
71C2
(continued)
Land&-Bknstein New Series III/26
Mehrer, Stolica, Stolwijk
[Ref. p. 81
2 Self-diffusion in solid metallic elements (Figures)
66
DO
Q
IOw4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
66.9
765 ... 886
45
78W
-
730...750
126.4
594...715
118.4
484...546
108
409...454
bee E-Pu, bet-6’-Pu, fee &Pu, face-centered orthorhombic y-Pu, body-centered monoclinic p-Pu investigated: 239Pu; polycrystals; z 99.9% (detailed specification of purity and isotopic composition given); grinder sectioning; short circuiting effects observed for yand p-Pu; Do and Q values for 6’-Pu given in [78w] are highly questionable
Plutonium (Pu), continued 3.5. 10-3 I&-PU) :6’-Pu) 5.17.10-2 I&-Pu) 3.8. 1O-2 :Y-pu) 1.69. 1O-2 :B-pu)
Figures for 2 -T KP
300
400 K
200
250
ml/s 10-l’
c
0 10-1s
6.5 X+K-’ 55 4.0 l/l Fig. 2. Na. Semilogarithmic plot of the self-diffusion coeflicient vs. reciprocal temperature from ‘*Na and 24Na tracer measurements[66M] (triangles) and [71Ml] (circles). 2.5
Fig. 1. Li. Semilogarithmic plot of the self-diffusion coefl?cient vs. reciprocal temperature from measurementswith 6Li and ‘Li as stable tracers (full circles) [7OL] and from P-NMR measurements(open circles) [UHI].
Mehrer, Stolica, Stolwijk
3.0
3.5
Landolt-BBmstein New Series Ill/26
Ref. p. 811
2 Self-diffusion in solid metallic elements (Figures)
!OO I
lo-"0 m*/s
lO“[ m2/s
67
Be 2-.
lo-"
10-l” ,o-l:
I 4
I Q , o-1:
10-1'3
IO-"4
10-1'4
10-f i
3.0
3.5
4.0
4.5
1o-l5 0
5.0.10-3K-' 5.5
1.0
1/T -
I.1
.,0-33K-l
l/T -
Fig. 3. K. Semilogarithmic plot of the self-diffusion coefficient vs. reciprocal temperature from 42K tracer measurements [67M] (full circles) and [71M2] (open circles).
Fig. 4. Be. Semilogarithmic plot of the self-diffusion coefticients vs. reciprocal temperature from 7Be tracer measurements parallel (full circles) and perpendicular (open circles) to the hexagonal axis [66D].
-7
IO“ m2/
1100 K 1000 ,=1116K f 7"
900 I
-
800
Ca
-T
900 K
4.10‘12, m2/s
I
1"
I
850 '
800
750
lo-
E
2
1o-1
I
8
10-1'2 8
I Q 8
6
10-l
I Q4 0
2
I l
IO-"3
10-l
:
4
o 01
e
&
l
1.00
1.05
1.10
1.15
1.20
:
1.25 .10-3K' 1.35
1o-1" 0.8
l/lFig. 5. Mg. Semilogarithmic plot of the self-diffusion coefficients vs. reciprocal absolute temperature from ‘sMg tracer measurements parallel (full circles) and perpendicular (open circles) to the hexagonal axis [71Cl]. Land&-Biimstein New Series III/26
J 0.9
1.0
1.1 l/T -
1.2
I.3 .lcr331c' 1
Fig. 6. Ca. Semilogarithmic plot of the self-diffusion coefficient vs. reciprocal temperature from 45Ca tracer measurements [68Pl].
Mehrer, Stolica, Stolwijk
2 Self-diffusion in solid metallic elements (Figures)
68 -1
-1
1600
lom’/
[Ref. p. 81
00 I
1100 K I
10-l'Or
Y
Ip+,=llX
ml/ s
l[
K
,=lE03K
lo-’I1 _
7
lo-13 _
0 1o-’12 _
.
a1 10’14 _
0
I a
.
10”13 _
0
lo-15 _ lo- 1L _
-
lo-16 I0.55
c
0.80 -10 -’ 0.90
10’I5
0.81 I
0 ,
I
0.95
.l 0-3K-l 1.10
1.00
l/T Fig. 7. Y Semilogarithmic plot of the self-diffusion cocfftcients vs. reciprocal tcmpcrature from “Y tracer mcasurcments parallel (full circles) and pcrpcndicular (open circles) to the hesagonal axis of a-Y [70Gl].
Fig. 8. La. Semilogarithmic plot of the self-diffusion coefticicnts vs. reciprocal temperature from r4’La tracer measurements in fee p-La [69D2] (open triangles) and bee y-La [73D] (open circles) and [74L3] (full triangles).
-1 -T
10 m’/
950
1050 K
I ,
071K
5.10-" m’/sl
850 I
1200 K
Pr I t
1
1150
4
1100
L
4
'y.b=999K
I,,=1205 K
Ce
J
r~g=106BK
3
lo-
lo-’ t a
0 8
10-l
8 0.875 0.900 -10. c-1 0.950 l/l Fig. 10. Pr. Semilogarithmic plot of the self-diffusion coefftcicnt vs. reciprocal temperature from ‘42Pr tracer measuremcnts in bee S-Pr [69Dl]. 0.800 0.825
0 cl
10-l
0.850
c
10-l
0.90 0.95 1.00
1.05 1.10 l/l-
4 Fig. 9. Ce. Semilogarithmic plot of the self-diffusion coefficients vs. reciprocal temperature from 14’Ce tracer measure1.15 alO-‘K-’ 1.25 ments in feey-Ce 171D] (open circles) and beeS-Ce[71D] (full circles) and [73L2] (triangles).
- .
1
Mehrer, Stolica, Stolwijk
Land&BBmstein New Series 111'26
2 Self-diffusion in solid metallic elements (Figures)
Ref. p. 811 -T
1000 K
lo-'[ m2/s
9cIO
.&i m2/s
I
r
Eu
-T 1580Kl570
800
69
1560
1550
1540
3.3
8
IO-"
3.2 e 3.1 0
~I lo"2
I 3.0 Q
8
2.9 0
2.8
lo-l3
3
2.7 10-14 0.8
0.9
1
1.0
2.6 0.625
1 .W3 K-'1.4
0.630
0.635
0.640 l/T-
l/TFig. 11. Eu. Semilogarithmic plot of the self-diffusion coeflicient vs. reciprocal temperature from rs2Eu tracer measurements [77F].
3.10-13 m2/s
t'
I. = 1795 K
1600 I
Er
0.655
Fig. 12. Gd. Semilogarithmic plot of the self-diffusion coefficient vs. reciprocal temperature from “‘Gd tracer measurements in bee /3-Gd [77F].
-7 1700 K 1
0.645 -1O-3K-'
1o-1'
1500
m2/s
I'
I 10-l"
,o-l:
I Q , o-l: 0 0
0
10-l'
0
IO-lb s 6.10-15 0.54
0
,o-l:
0.56
0.58
0.60 l/T-
0.62
0.64 .10-3K'
0.68
Fig. 13. Er. Semilogarithmic plot of the self-diffusion coeficient vs. reciprocal temperature parallel (full circles) and ,erpendicular (open circles) to the hexagonal axis from r6’Er .racer measurement [72S].
Land&-Biimstein New Series III/26
0.90
0
0.95
1.00
1.10 1.05 l/T -
1.15 .10- C“ 1.25
Fig. 14. Yb. Semilogarithmic plot of the self-diffusion coefficients vs. reciprocal temperature from rC9Yb tracer measurements in polycrystals of hcp a-Yb and bee y-Yb [74F].
Mehrer, Stolica, Stolwijk
2 Self-diffusion in solid metallic elements(Figures)
70
[Ref. p. 81
2000K 1500
10-l t-n’/
1000
800
10-l lo-li
10-n
10-
10-’ 10-l
I a
I
10“
10-16 10-1s
a
I
I
I
I
10-l’ 10-n
10’ lo“r 10“s 10’
1,o-l!o-l9
10’17
0.4
10-Z’ 10-20
0.5
0.6
0.7
0.8
0.9 .10-3K-’ 1.1
10a
l/l Fig. 15. Ti. Semilogarithmic plot of the self-diffusion coefticients vs. reciprocal temperature from 44Ti tracer measurements in hcp a-Ti polycrystals [80D] (full circles) and bee S-Ti [64M2] (open circles) and [87Kl] (triangles).
10-2;
10-2: [
a
0.6
0.8
1.0
1.2.10-3K-’1.4
1I200
3.10-l rn2/f
-I
-11361
10-l
I a ,o-li
Fig. 16. Zr. Semilogarithmic plot of the self-diffusion coef- b kients vs. reciprocal temperature from tracer measurements tn (a) hcp a-Zr single crystals parallel (‘I) and perpendicular 10-13 [v) to the hexagonal axis [74Hl], hcp a-Zr single crystals of the same random orientation (+) [84H] and bee S-Zr ac:ording to [61K] (x), [63F] (o), [70G2] (o), [79H] (+) and 4.10-nL [82P] (A). (b) same as Fig. a) for bee p-Zr on an enlarged 0.4 scale. b
Mehrer, Stolica, Stolwijk
b
I
0.5
0.6
0.7
0.8
W’K-
l/l-
Land&-B6mstein New series III!26
Ref. p. 811
1Cl-'" mvs Hf
2 Self-diffusion in solid metallic elements (Figures) -1 2000
2500 K
1700
71
4 Fig. 17. Hf. Semilogarithmic plot of the self-diffusion coefticients vs. reciprocal temperature from tracer measurements in hcp o-Hf parallel (full triangles) and perpendicular (open triangles) to the hexagonal axis [72D] and bee 8-Hf [65W2] (open circles) and [82H] (full circles).
1500
IO-" 10-l' 10.1:
m2/s I
-T 1500 I
2000 K I &2175K
+a,
1000
1200 1
,,
I”
I
I
I
I
I
I
I
I
I
IP
I b
10-'4
10-'5
10-16 10-171
I
"I
10-17
lo-'* 0.'
0.40
0.45
0.50 0.55 l/T-
0.60 .W3 K-' 0.70
* IO-20 lo-"II 0.4
-1
..
0.5
0.6
0.7 l/F-
0.8
0.9 W3 K'
1.1
Fig. 18. 8. Se&logarithmic plot of the self-diffusion coefficient vs. reciprocal temperature from @V tracer measurements [65P2] (open circles), [74P] (full triangles), [79Ml] (full circles), [83A] (crosses) and from NMR measurements [83Gl] (open triangles).
4 Fig. 19. Nb. Semilogarithmic plot of the self-diffusion coefficient vs. reciprocal temperature from gsNb tracer measurements [65L2] (open circles), [77Al] (full circles), [78El] (full triangles) and [81B] (open triangles). 0.3
Landolt-Bijmstein New Series III/26
0.4
0.5
0.6 l/T-
0.7
0.8X+ Kd0.9
Mehrer, Stolica, Stolwijk
[Ref. p. 81
2 Self-diffusion in solid metallic elements(Figures)
72
C-T 1500
-7 10-l' lO-'1
3000 K
2000 2000
1500 1300 1500 1300
3.
ml/s
lo-" ml/s
10-11
10-l"
10-13
1o-l3
10“‘
10-l‘
10'15
lo-'5
lo-16
I a
K
1200 1100
10-16 10-l'
~I 10-l'
2000
I
I
I
I - 0
I
‘I 10-18.
10-18
lo-l9
10‘19
. 10-m
10-m
. 10-I'
10-n
10-222 lo-" 0.2 0.2
.
10-4 OA 0.3
0.L
0.5
0.6
0.7
-10.'K-'
0.9
l/l Fig. 20. Ta. Semilogarithmic plot of the self-diffusion coefficient vs. reciprocal temperature from ‘a2Ta tracer measurements [65Pl] (full circles) and [83Wl] (open circles). -I 2500 K 2000
10"
0.5
0.6
0.7 l/T-
0.8
t0.9~10-3K-' 1.0
Fig. 21. Cr. Semilogarithmic plot of the self-diffusion coefticient vs. reciprocal temperature [76M4] (open circles) and [81M] (full circles).
1700 1500
m'/s lO“j
10-2' 4 Fig. 22. MO. Semilogarithmic plot of the self-diffusion coef10‘" 0.2
ficient vs. reciprocal temperature from ggMo tracer measure0.3
0.1
0.5 l/l-
0.6
0.740~k'O.8
ments[59B](open circles).
Mehrer, Stolica, Stolwijk
circles),(60B2](triangles)and
[79M2](full
Landoh-BBmstein New Series III,/26
2 Self-diffusion in solid metallic elements (Figures)
Ref. p. 811 -1 5000 K 3000 1IF*, I I ' I . m*/s 10-1’3
1. =3673K$
2500 I
2000 I
0.4
0.5
1700 I,
w
. 8
10-22 0.2
0.3
_ . 0.6 WK-' 0.7
l/l-
Fig. 23. W Semilogarithmic plot of the self-diffusion coefficient vs. reciprocal temperature from tracer measurements [69P] (open circles), [77A2] (triangles) and [78M] (full circles).
a
1o-23 0.50
0.65
0.80
0.95 l/T-
-T
Fig. 24. Fe. Semilogarithmic plot of the self-diffusion coefficients vs. reciprocal temperature from tracer measurements in (a) bee o-Fe [60Bl] (x), [68W2] (a), [69G] (m), [77H] (+), [87G] (A), 18811(0) and [89M] (0); fee y-Fe [6612](v), [68H] (A), [68W2] (0) and [69G] (m) and bee S-Fe [66J] (v), [68W2] (0) and [69G] (m); (b) same as (a) for bee a-Fe according to [77H] (+), [881] (0) and [89M, 9OL] (0).
Land&Biirnstein New Series III/26
b
Mehrer, Stolica, Stolwijk
l/T-
1.10
.I,,-3K-1
1.40
2 Self-diffusion in solid metallic elements(Figures)
[Ref. p. 81
-J
2a,o.,32800K 2600 2500 2600 2300 2200 2100 d!V”i’:‘l
)
I
I I I0.425 0.450 W’K“ 0.500 l/fFig. 26. Ir. Semilogarithmic plot of the self-diffusion coefticient vs. reciprocal temperature from “‘Ir tracer measuremcnts [86A]. 0.350
l/JFig. 25. Co. Semilogarithmic plot of the self-diffusion cocfRcient vs. reciprocal temperature from tracer measurements :62H2] (open circles), [79B] (full circles) and [88L] (triangles).
I
I 0x00
0.375
-1
,o-,22000 K d/s
1700 I ,
A!
1.=lrmK
I
I FJ
I
I
0.6
0.7
0.8
0.9
1.0
1.1 XI5 K-l
1.3
l/J -
Fig. 27. Ni. Semilogarithmic plot of the self-diffusion coefficient vs. reciprocal temperature from 63Ni tracer measurements [68BI] (open circles) and [76Ml] (full circles).
0.50
I
I
) Pd 1 8
,,o-l3lJ_J
Q5
i500 I ’
I
I
1400 I ’
I
1300 ’
I
I
I I
I
I
0.80 0.65 0.70 W3K-' l/JFig. 28. Pd. Semilogarithmic plot of the self-diffusion coefficient vs. reciprocal temperature from ro3Pdand ‘12Pd tracer measurements[64P].
Mehrer, Stolica, Stolwijk
0.55
0.60
Land&-B6mstein New Series Ill!26
Ref. p. 811
2 Self-diffusion in solid metallic elements (Figures)
Fig. 30. Cu. Semilogarithmic plot of self-diffusion coeffi- b cient vs. reciprocal temperature from ‘%u and 67Cu tracer measurements [69Rl] (open circles), [77M] (full triangles), [78Bl] (full circles) and [82F] (open triangles). ,o-,,2500
-T 1800 K 1400 1200
IU -
-T 1200 K 1000 900
800
700
600
m2/s 1o-l3
1000 900
800
m% 10-1'2
. 10‘2' 0.4
1o-231 0.6 0.6
0.8
1.0
0.8
1.0
1.2.10-3K' 1.4
1.2 l/T-
IX
1.4 l/T-
1.6
1.6Xr3 K-'1
l/T-
Fig. 29. Pt. Semilogarithmicplot of the self-diffusion coefticient vs. reciprocal temperature from tracer measurements [57K] (open circles), [62C] (triangles) and [78R] (full circles).
Fig. 31. Ag. Semilogarithmic plot of the self-diffusion coefficient vs. reciprocal temperature from losAg and lromAg tracer measurements [7OR] (open circles), [72R] (squares), [73Ll] (full circles), [74B] (open triangles), [78B2] (full triangles) and [82R] (crosses). 0.8
Land&-B6rnst.h New Series III/26
Mehrer, Stolica, Stolwijk
1.0
1.2
1.8.10~W22.0
[Ref. p. 81
2 Self-diffusion in solid metallic elements (Figures)
76 -7 lZO0 1200K 1000
18” mr/s
700
800
600 I
lCT2
4 Fig. 32. Au. Semilogarithmic plot of the self-diffusion coefficient vs. reciprocal temperature from 19’Au and ‘98Au tracer measurements [63D] (crosses), (65DJ (open circles), [69R2] (open triangles), [78Hl] (full circles) and [83W2] (full triangles).
Au
-1
10-n
600 I
‘00 K 650 &lo-' I I ’ I.- 693K m*/!
10-l’
10-l
;‘” L-
I
I
520 1
550 I
I
I
.
0 A
~I 10-l I
I
AI 0
I
I
I
I
I A
I
I
!
.
I
lo-’ lo-”
147~K-’1.8 a A
2.10”
1.7 1.8 .,0-j K-’ 2.0 l/l Fig. 33. Zn. Semilogarithmic plot of the self-diffusion coefficients parallel (full symbols) and perpendicular (open symbols) to the hexagonal axis vs. reciprocal temperature from 6SZn and 69Zn tracer measurements [53S] (triangles), [67B] (squares) and [67R] (circles). 1.5
&lo-” m2/s
600 K 550
500
450
I
I
I A
1.8
2.0 l/l
10-u
,
1.6
2.2 -
1.6
4 Fig. 34. Cd. Semilogarithmic plot of the self-diffusion coefficients parallel (full symbols) and perpendicular (open symD bols) to the hexagonal axis vs. reciprocal temperature from 26 .10-k’ 2.6 lo9Cd and rr5Cd tracer measurements [55w] (squares), [67H] (circles) and [72M] (triangles). I IA 0
Mehrer, Stolica, Stolwijk
Landok-Bk-nstein New
Series III/26
Ref. p. 811
2 Self-diffusion in solid metallic elements (Figures) --I
1000K 800 700 600
500
400
350
10-1'3 m2/s
420 K 1 I
-1 380 1
3 40
360
320
In 0 lo-l4 00 . .
0
~I lo-l5 0 .
0 .
1o-l6
1O-l7 2.3
n A A A A A
-T
10-22
10-l
0 K
540
!O T-
m2/r fzi10-23 lo-24 1.0
3.1 .lO"K- 3.3
2.9
Fig. 36. In. Semilogarithmic plot of the self-diffusion coefficients parallel (full circles) and perpendicular (open circles) to the tetragonal axis vs. reciprocal temperature from rr41n tracer measurements [59D].
IO-JO 10-2'
2.7 l/T -
2.5
-
4EIO I,
460 ,
440 I
42 I
=507 F
n
TI 1.4
1.8
2.2
2.6 @K-'
:
10-l
l/T-
Fig. 35. Al. Semilogarithmic plot of the self-diffusion coefficient vs. reciprocal temperature from 26A1tracer measurements [62L] (open circles), from the TEM observation ofvoid shrinkage [68v] (triangles), and from NMR measurements [74M] (full circles).
“pf ,o-l:
I ~ IO"
-
’ 8
10.1"
lo-"
Fig. 37. Tl. Semilogarithmicplot of the self-diffusion coefti- b cients vs. reciprocal temperature from ‘04T1 tracer measurements in bet a-T1 parallel (full circles) and perpendicular (open circles) to the tetragonal axis [55S], bee S-T1[55S] (full triangles) and [85C] (open triangles). Landolt-Biknstein New Series III/26
10-l';
Mehrer, Stolica, Stolwijk
!.2 l/T-
.,O-3K-’ :
2 Self-diffusion in solid metallic elements(Figures)
78
10-1'3
ow,4 I 540 I K ,I520 II500
060
10-16
480 I,
460 I ,
440 I ,
I
[Ref. p. 81
600 K 560 550 520 500 480 &60
lTl’/S
DL
I 6.10-” 1.8
1.9
2.0
23 2.2 2.3W’K’2.1 l/T Fig. 38. Sn. Semilogarithmic plot of the self-diffusion coefticients parallel (full symbols) and perpendicular (open symbols) to the tetragonal axis vs. reciprocal temperature from “%n tracer measurements [60M] (squares), [64C] (circles) and [7482] (triangles).
1.6
1.7
1.8
1.9 2.0 l/l-
2.1 .lO-‘K-’ 2.3
Fig. 39. Pb. Semilogarithmic plot of the self-diffusion coefkicnt vs. reciprocal temperature from ‘rOPb tracer measurements [55N] (full circles), [61R] (triangles) and [69M] (open circles). 350 I
J++l 1: 1
I
‘tt
l-19 11
0
I
0
I
10-2s
‘o-‘52 1
I
I
‘++,
4
0
I
1.05
1.15
1.20 l/1 -
b i
4
10-Z’I I
I
A
I
l
t
4,
IdI DL
I
1.10
-
‘(+
10-22
.IO -16
tt
1.25
-10-s K-’ 1.35
Fig. 40. Sb. Semilogarithmic plot of the self-diffusion coefficients vs. reciprocal temperature parallel (full circles) and perpendicular (open circles) to the trigonal c axis from 124Sb tracer measurements[66C].
t
o
1o-23 2.00
2.15
2.30
2.45 l/7-
2.60
7 ++t ~. . -lO-‘K-’ 2.90
Fig. 41. Se. Semilogarithmic plot of the self-diffusion coefficients vs. reciprocal temperature parallel (full triangles) and perpendicular (open triangles) to the trigonal taxis from 75Setracer measurements [70B] and values parallel to the trigonal axis (circles) from NMR measurements[SSG].
Mehrer, Stolica, Stolwijk
Land&-BBmstein New series III/26
Ref. p. 811
2 Self-diffusion in solid metallic elements (Figures) C-T
-T 600 I 'I
,o-,4 700 K 650 AI 1'
550
500 I
I
1O-15 m2/s
I
1150 K
1100
1000
1050
10-1'6 I a
lo-17ai
I Q . 0. .
10‘19 l
n
Dll
0
0
0,
4.10~'81 0.85 0 . 0
10-m
10-2' 1.4
1.00 .10-3K' 1.05
0.95 l/T-
Fig. 43. Th. Semilogarithmic plot of the self-diffusion coefficient in fee u-Th vs. reciprocal temperature from “*Th tracer measurements [67S]. -T 2.1
10-g
Fig. 42. Te. Semilogarithmicplot ofthe self-diffusion coefficients vs. reciprocal temperature parallel (full symbols) and perpendicular (open symbols) to the trigonal c axis according to 127mTetracer measurements [67G] (squares) and [83W3] (circles).
m2/s lo-"0
1.5
1.6
1.7 1.8 1/r -
1.9
.@K'
C-T 10-l'
0.90
,”
1400 K
1200 1100
1000
900 800K 700
600
400
500
10-l' lo-l2
900
m2/s
I 1o-l3
10-12
~ lo-l4 lo-l5 lo-l6 lo-'7 lo-'8
lo-l6 1o-l7 0.6
0
IO“9
0 0 0
0.7
0.8
0.9 l/T-
1.0
.,o-3K'
1.2
Fig. 44. U. Semilogarithmic plot of the self-diffusion coeffr:ients vs. reciprocal temperature from 234U and 235U tracer neasurementsin orthorhombic CL-Upolycrystals [62A] (open :ircles); tetragonal S-U polycrystals [59A2] (full triangles); act y-U [59Al] (open triangles) and [60R2] (full circles).
Land&-Biirnstein New Series III/26
10-20 0.8
1.1
1.4
1.7
2.0
.,O-3,(-l
l/TFig. 45. Pu. Semilogarithmic plot of the self-diffusion coefficients vs. reciprocal temperature from Pu tracer measurements in monoclinic S-Pu polycrystals [78w] (open circles); orthorhomic face centered y-Pu polycrystals [78w] (open circles); fee 6-Pu [78w] (open circles), and [64T] (open triangles); bet 6’-Pu [78w] (open circles); bee E-PU [68D2] (full triangles), [71C2] (full circles) and [78w] (open circles).
Mehrer, Stolica, Stolwijk
[Ref. p. 81
2 Self-diffusion in solid metallic elements(Figures)
80
lo-“‘0 m2/s
lo-” 10-u 1o-l3 lo-‘&
1P
~I 10-15
10-‘6 I ~ lo-”
10-16
lo-“8
10-l’
lo-“9
10-18
10-m
10-19
10-Z’
10-20 1.0
I
I
I
I
I
lo-l::
I\
1 I\
\
I c>r*g I
I I
1 ‘Pb 1
I I
t
I
1
250 1, /l Fig. 46. Semilogarithmic plot of the self-diffusion cocfficients vs. reciprocal temperature normalized to the melting tempcraturcs T, for several fee metals.
1.2
1.4 1,/r -
1.6
1.8
2.0
Fig. 47. Semilogarithmic plot of the self-diffusion coeflicicnts vs. reciprocal temperature normalized to the melting tempcraturcs T, for several bee metals or metals with bee high-temperature phases [87K2].
Fig. 48. Semilogarithmic plot of the self-diffusion coefticicnts vs. reciprocal temperature normalized to the melting temperatures T, for some bee high-temperature phases including lanthanides and actinides [87K2].
Mehrer, Stolica, Stolwijk
Landok-BBmstei Ne\v Series 11112
2.3 References for 2
81
2.3 References for 2 52N 53s 55H 55N 55s 55w 56H 56s 57K 57M 58M 59Al 59A2 59B 59D 59M 59N 60Bl 60B2 60M 60Rl 60R2 61B 61D 61K 61R 62A 62C 62Hl 62H2 62L 62P 63A 63B 63D 63F 63L 64C 64H 64Ml 64M2 64N 64P 64T 65Al 65A2 65B 65D 65Gl 6562 65Hl 65H2 65Ll 65L2
Nachtrieb, N.H., Catalano, E., Weil, J.A.: J. Chem. Phys. 20 (1952) l;85. Shirn, G.A., Wajda, E.S., Huntington, H.B.: Acta Metall. 1 (1953) 513. Holcomb, D.E, Norberg, R.E.: Phys. Rev. 98 (1955) 1074. Nachtrieb, N.H., Handler, G.S.: J. Chem. Phys. 23 (1955) 1569. Shirn, G.A.: Acta Metall. 3 (1955) 87. Wajda, E.S., Shirn, G.A., Huntington, H.B.: Acta Metall. 3 (1955) 39. Hoffmann, R.E., Pikus, IX, Ward, R.A.: Trans. Metall. Sot. AIME 206 (1956) 483. Shewmon, P.G.: Trans. Metall. Sot. AIME 206 (1956) 918. Kidson, G.E, Ross, R.: Proc. UNESCO Int. Conf. Radioisotopes in Sci. Res., Ist, Paris 1957, p. 185. Makin, S.M., Rowe, A.D., Le Claire, A.D.: Proc. Phys. Sot. (London) B70 (1957) 545. Masuda, Y;: J. Phys. Sot. Jpn. 13 (1958) 597. Adda, Y, Kirianenko, A.: J. Nucl. Mater. 1 (1959) 120. Adda, Y, Kirianenko, A., Mairy, C.: J. Nucl. Mater. 3 (1959) 300. Borisov, YR, Gruzin, P.L., Pavlinov, L.V, Fedorov, G.B.: Metall. Metalloved. 1 (1959) 213. Dickey, J.E.: Acta Metall. 7 (1959) 350. MacEvan, JR., MacEvan, J.U., Yaffe, L.: Can. J. Chem. 37 (1959) 1623. Naumov, A.N., Ryskin, G.y Sov. Phys.-Tech. Phys. 4 (1959) 162. Borg, R.J., Birchenall, C.E.: Trans. Metall. Sot. AIME 218 (1960) 980. Bronfin, M.B., Bokshtein, S.Z., Zhukhovitsky, A.A.: Zavod. Lab. 26 (1960) 828; Ind. Lab. (English Transl.) 26 (1960) 886. Meakin, J.D., Klokholm, E.: Trans. Metall. Sot. AIME 218 (1960) 463. Resnick, R., Castleman, L.S.: Trans. Metall. Sot. AIME 218 (1960) 307. Rothman, S.J.,Lloyd, L.T., Harkness, A.L.: Trans. Metall. Sot. AIME 218 (1960) 605. Buflington, ES., Hirano, K.I., Cohen, M.: Acta Metall. 9 (1961) 434. Von Danneberg, W, Krautz, E.: Z. Naturforsch. 16a (1961) 854. Kidson, G.V, McGurn, .I: Can. J. Phys. 39 (1961) 1146. Resing, H.A., Nachtrieb, N.H.: J. Phys. Chem. Solids 21 (1961) 40. Adda, Y, Kirianenko, A.: J. Nucl. Mater. 6 (1962) 130. Cattaneo, F., Germagnoli, E.: Philos. Mag. 7 (1962) 1373. Hagel, WC.: Trans. Metall. Sot. AIME 224 (1962) 430. Hirano, K.I., Agarwala, R.P., Averback, B.L., Cohen, M.: J. Appl. Phys. 33 (1962) 3049. Lundy, TX, Murdock, J.E: J. Appl. Phys. 33 (1962) 1671. Peart, RI?, Graham, D., Tomlin, D.H.: Acta Metall. 10 (1962) 519. Askill, J., Tomlin, D.H.: Philos. Mag. 8 (1963) 997. Borg, R.J., Lai, D.Y.E, Krikorian, 0.: Acta Metall. 11 (1963) 867. Duhl, D., Hirano, K.-I., Cohen, M.: Acta Metall. 11 (1963) 1. Federer, J.I., Lundy, IS.: Trans. Metall. Sot. AIME 227 (1963) 592. Libatini, C.M., Dyment, I?: Acta Metall. 11 (1963) 1263. Coston, C., Nachtrieb, N.H.: J. Phys. Chem. 68 (1964) 2219. Huntington, H.B., Ghate, P.B., Rosolowski, J.H.: J. Appl. Phys. 35 (1964) 3027. Monma, K., Suto, H., Oikawa, H.: J. Jpn. Inst. Met. 28 (1964) 188. Murdock, J.E, Lundy, T.S., Stansbury, E.E.: Acta Metall. 12 (1964) 1033. Noimann, Kh., Kloze, G., Sokol’skaya, I.L.: Sov. Phys. Solid State (Engl. Transl.) 6 (1964) 1369. Peterson, N.L.: Phys. Rev. A 136 (1964) 568. Tate, R.E., Cramer, E.M.: Trans. Metall. Sot. AIME 230 (1964) 639. Alion, D.C., Slichter, C.P.: Phys. Rev. 137 (1965) 235. Andelin, R.L., Knight, J.D., Kahn, M.: Trans. Metall. Sot. AIME 233 (1965) 19. Bonanno, ER., Tomizuka, CT.: Phys. Rev. 137 (1965) 1264. Dickerson, R.H., Lowell, R.C., Tomizuka, C.T.: Phys. Rev. 137 (1965) 613. Gainotti, A., Zecchina, L.: Nuovo Cimento 40B (1965) 295. Gilder, H.M., Lazarus, D.: J. Phys. Chem. Solids 26 (1965) 2081. Hassner, A., Lange, W: Phys. Status Solidi 8 (1965) 77. Hassner, A., Hassner, R.: Phys. Status Solidi 11 (1965) 575. Lundy, TS., McHargue, C.J.:Trans. Metall. Sot. AIME 233 (1965) 243. Lundy, TS., Winslow, ER., Pawel, R.E., McHargue, C.J.:Trans. Metall. Sot. AIME 233 (1965) 1533.
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82
2.3 References for 2 1
65Pl 65P2 65Wl 65W2 66C 66D 6611 6612 665 66M 67A 67B 67G 67H 67M 67P 67s 68Bl 68B2 68C 68Dl 68D2 68F 68H 68K 68Pl 68P2 68V 68Wl 68W2 69A 69B 69Dl 69D2 69E 69G 69M 69P 69Rl 69R2 70B 70Gl 70G2 7OL 70R 70s 71A 7lCl 71C2 71D 71F 71Ml
7lM2 710 72C
Pawel, R.E., Lundy, T.S.:J. Phys. Chem. Solids 26 (1965) 937. Peat-t, RI? J. Phys. Chem. Solids 26 (1965) 1853. Wazzan, A.R.: J. Appl. Phys. 36 (1965) 3596. Winslow, ER., Lundy, ‘IS.: Trans. Metal!. Sot. AIME 233 (1965) 1790. Cordes, H., Kim, K.: J. Appl. Phys. 37 (1966) 2181. Dupouy, J.M., Mathie, J., Adda, Y: Mem. Sci. Rev. Metall. 63 (1966) 481. Ivantsov, I.G.: Fiz. Metal. Metalloved. 22 (1966) 725, Phys. Met. Metallogr. USSR (English Transl.) 5 (1966) 77. Ivantsov, I.G., Blinkin, A.M.: Fiz. Met. Metalloved. 22 (1966) 876. James,D.W, Leak, G.M.: Philos. Mag. 14 (1966) 701. Mundy, J.N., Barr, L.W, Smith, EA.: Philos. Mag. 14 (1966) 785. Apel, K., Hantzsch, S., Preshu, K.E.: Z. Metallkd. 58 (1967) 401. Batra, A.P.: Phys. Rev. 159 (1967) 487. Ghoshtagore, R.N.: Phys. Rev. 155 (1967) 598. Hirschwald, W., Schroedter, W: Z. Phys. Chem. NE 53 (1967) 392. Mundy, J.N., Barr, L.W., Smith, EA.: Philos. Mag. 15 (1967) 411. Peterson, N.L., Rothman, S.J.:Phys. Rev. 163 (1967) 645. Schmitz, E, Fock, M.: J. Nucl. Mater. 21 (1967) 317. Bakker, H.: Phys. Status Solidi 28 (1968) 569. Beyeler, M., Adda, Y: J. Phys. (Paris) 29 [4] (1968) 345. Carter, AC., Wilson, C.G.: Brit. J. Appl. Phys. 1 (1968) 515. Dyment, E, Libatini, C.M.: J. Mater. Sci. 3 (1968) 349. Dupouy, M., Calais, D.: Trans. Metall. Sot. AIME 242 (1968) 1679. Fedorov, G.B., Smirnov, E.A., Moiseenko, S.S.:Metall. Metalloved. Chist. Met. 7 (1968) 124. Heumann, Th., Imm, R.: J. Phys. Chem. Solids 29 (1968) 1613. Kaygorodov, XN., Klotsman, S.M., Timofeev, A.N., Trakhtenberg, I.Sh.: Fiz. Met. Metalloved. 25 (1968) 910. Pavlinov, L.V, Gladyshev, A.M., Bykov, XN.: Fiz. Met. Metalloved. 26 (1968) 823. Pavlinov, L.V, Grigorev, G.X, Sevastianov, VG.: Fiz. Met. Metalloved. 25 (1968) 565. Volin, TE., Balluffi, R.W: Phys. Status Solidi 25 (1968) 163. Walsiie de Reca, N.E., Libatini, C.M.: Acta Metall. 16 (1968) 1297. Walter, C.M., Peterson, N.L.: Phys. Rev. 178 (1968) 922. Askill, J.: Phys. Status Sohdi 33 (1969) K 105. Bowden, H.G., Balluffi, R.W.: Philos. Mag. 19 (1969) 1001. Dariel, M.P., Erez, G., Schmidt, G.M.J.: Philos. Mag. 19 (1969) 1045. Dariel, M.P., Erez, G., Schmidt, G.M.J.: Philos. Mag. 19 (1969) 1053. El-Hanany, U., Zamir, D.: Phys. Rev. 183 (1969) 809. Graham, D.: J. Appl. Phys. 40 (1969) 2386. Miller, J.W: Phys. Rev. 181 (1969) 1095. Pawel, R.E., Lundy, TS.: Acta Metall. 17 (1969) 979. Rothman, S.J.,Peterson, N.L.: Phys. Status Solidi 35 (1969) 305. Rupp, W!, Ermert, U., Sizmann, R.: Phys. Status Solidi 33 [2] (1969) 504. Briitter, P., Gobrecht, H.: Phys. Status Solidi 37 (1970) 869. Gorny, D.S., Altovskii, R.M.: Fiz. Met. Metalloved. 30 (1970) 85. Graham, D., Hanes, E.R.: NASA Technical Note D 5905,NASA, Washington D.C. 1970,unpublished. Lodding, A., Mundy, J.N., Ott, A.: Phys. Status Solidi 38 (1970) 559. Rothmann, S.J.,Peterson, N.L., Robinson, J.T.:Phys. Status Solidi 39 (1970) 635. Shalayev, VI., Tkachenko, LB., Pavlov, VA., Timofeyev, N.I., Gushchina, A.V: Fiz. Metal. Metalloved. 39 (1970) 1061. Askill, J.: Phys. Status Solidi (a) 8 (1971) 587. Combronde, J., Brebec, G.: Acta Metall. 19 (1971) 1393. Cornet, J.A.: J. Phys. Chem. Solids 32 (1971) 1489. Dariel, M.P., Dayan, D., Languille, A.: Phys. Rev. B4 (1971) 4348. Fradin, EY: PhD Thesis, University of Illinois;1971. Mundy, J.N.: Phys. Rev. B3 (1971) 2431. Mundy, J.N., Miller, T.E., Porte, R.J.: Phys. Rev. B3 (1971) 2445. Ott, A., Norden-Ott, A.: J. Appl. Phys. 42 (1971) 3745. Chhabildas, L.C., Gilder, H.M.: Phys. Rev. B5 (1972) 2135. Mehrer, Stolica, Stolwijk
Landolt-BBmsteil New Series III/26
2.3 References for 2 72D 72M 72R 72s 72T 73B 73D 73H 73Ll 73L2 73w 74B 74F 74Hl 74H2 74Ll 74L2 74M 74P 74w 75B 75F 74L3 75M 76F 76Ml 76M2 76M3 76M4 77Al 77A2 77F 77H 77M 78Bl 78B2 78El 78Hl 78M 78R 78W 79A 79B 79H 79K 79Ml 79M2 79P 80B 80D 80G 81B
83
Davis, R.E., McMullen, WD.: Acta Metall. 20 (1972) 593. Mao, C.: Phys. Rev. B5 (1972) 4693. Reimers, P., Bartdorff, D.: Phys. Status Solidi (b) 50 [I] (1972) 305. Spedding, EH., Shiba, K.: J. Chem. Phys. 57 (1972) 612. Titman, J.M., Moores, B.M.: J. Phys. F 2 (1972) 592. Buescher, B.J.,Gilder, H.M., Shea, N.: Phys. Rev. B7 (1973) 2261. Dariel, M.P.: Philos. Mag. 28 (1973) 915. Hultgren, R., Desai, ED., Hawkins, D.T, Gleiser, M., Kelley, K.K., Wagman, D.D.: Selected Values of the Thermodynamic Properties of the Elements. Metals Park, Ohio: American Society for Metals, 1973. Lam, N.Q., Rothman, S.J.,Mehrer, H., Nowicki, L.J.: Phys. Status Solidi (b) 57 (1973) 225. Languille, A., Dariel, M.P., Calais, D., Coqblin, B.: Mem. Sci. Rev. Metall. 70 (1973) 241. Weithase, M., Noack, E: Phys. Status Solidi (b) 57 (1973) Klll. Backus, J.G.E.M., Bakker, H., Mehrer, H.: Phys. Status Solidi (b) 64 (1974) 151. Fromont, M., Languille, A., Calais, D.: J. Phys. Chem. Solids 35 (1974) 1367. Hood, G.M., Schultz, R.J.:Acta Metall. 22 (1974) 459. Huang, EH., Huntington, H.B.: Phys. Rev. B9 (1974) 1479. Lam, N.Q., Rothman, S.J.,Nowicki, L.J.: Phys. Status Solidi (a) 23 (1974) K35. Languille, A., Calais, D., Fromont, M.: J. Phys. Chem. Solids 35 (1974) 1373. Messer, R., Dais, S., Wolf, D., in: Proc. 18th Ampere Congress, Allen, P.S.,Andrew, E.R., Bates, C.A. (eds.).Nottingham, England, 1974. Pelleg, J.: Philos. Mag. 29 (1974) 383. Weithase, M., Noack, E: Z. Phys. 270 (1974) 319. Bronfin, M.B., Bulatov, G.S., Drugova, I.A.: Fiz. Met. Metalloved. 40 [2] (1975) 363. Fromont, M.: J. Phys. Chem. Solids 36 (1975) 1397. Languille, A., Calais, D.: J. Phys. Chem. Solids 35 (1974) 1461. Messer, R., Noack, E: Appl. Phys. 6 (1975) 79. Feller-Kniepmeier, M., Griindler, M., Helfmeier, H.: Z. Metallkd. 67 [8] (1976) 533. Maier, K., Mehrer, H., Lessmann, E., Schiile, W: Phys. Status Solidi (b) 78 (1976) 689. Marbach, G., Fromont, M., Calais, D.: J. Phys. Chem. Solids. 37 (1976) 689. Messer, R.: Magnetic Resonanceand Related Phenomena, Proc. 19th Congress Ampere, Heidelberg, Brunner, H. (ed.) (Heidelberg, Groupement Ampere) 1976, p. 269. Mundy, J.N., Tse, C.W, McFall, WD.: Phys. Rev. B13 (1976) 2349. Ablitzer, D.: Philos. Mag. 35 (1977) 1239. Arkhipova, N.K., Klotsman, SM., Rabovskiy, A., Timofeev, A.N.: Fiz. Met. Metalloved. 43 (1977) 779; Phys. Met. Metallogr. USSR (English Transl.) 43 (4) (1977) 88. Fromont, M., Marbach, G.: J. Phys. Chem. Solids 38 (1977) 27. Hettich, G., Mehrer, H., Maier, K.: Ser. Metall. 11 (1977) 795. Maier, K.: Phys. Status Solidi (b) 44 (1977) 567. Bartdorff, D., Neumann, G., Reimers, P.: Philos Mag. 38 (1978) 157. Bihr, J., Mehrer, H., Maier, K.: Phys. Status Solidi (a) 50 (1978) 17. Einziger, R.E., Mundy, J.N., Hoff, H.A.: Phys. Rev. B 17 (1978) 440. Herzig, Ch., Eckseler, H., Bussmann, W, Cardis, D.: J. Nucl. Mater. 69/70 (1978) 61. Mundy, J.N., Rothman, S.J.,Lam, N.Q., Hoff, H.A., Nowicki, L.J.: Phys. Rev. B18 (1978) 6566. Rein, G., Mehrer, H., Maier, K.: Phys. Status Solidi (a) 45 (1978) 253. Wade, WZ., Short, D.W, Walden, J.C., Magana, J.W: Metall. Trans. 9A (1978) 965. Ait-Salam, M., Springer, T, Heidemann, A., Alefeld, B.: Philos. Mag. A39 (1979) 797. Bussmann, W, Herzig, Ch., Rempp, W, Maier, K., Mehrer, H.: Phys. Status Solidi (a) 56 (1979) 87. Herzig, Ch., Eckseler, H.: Z. Metallkd. 70 (1979) 215. Krautheim, G., Neidhardt, A., Reinhold, U., Zehe, A.: Krist. Tech. 14 (1979) 1491. Macht, M.P., Frohberg, G., Wever, H.: Z. Metallkd. 70 (1979) 209. Maier, K., Mehrer, H., Rein, G.: Z. Metallkd. 70 (1979) 271. Pontau, A.E., Lazarus, D.: Phys. Rev. B19 (1979) 4027. Briinger, G., Kanert, O., Wolf, D.: Phys. Rev. B22 (1980) 4247. Dyment, E, in: Titanium 80, Kimura, H., Izumi, O., (eds.)Proc. 46th Int. Conf. on Titanium, Kyoto, Japan, 1980, p. 519. Giiltz, G., Heidemann, A., Mehrer, H., Seeger,A., Wolf, D.: Philos. Mag. A41 (1980) 723. Bussmann, W, Herzig, Ch., Hoff, H.A., Mundy, J.N.: Phys. Rev. B 23 (1981) 6216.
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84 31G 31M 91P 81T 52F 82H B2P B2R B3A B3Gl B3G2 B3Sl
83S2 63V 83Wl 83W2 83W3 84A 84H 8% 85G 85Hl 85H2 86A 87D 87G 87Kl 87K2 881 88L 89L 89M 9OL
2.3 References for 2
Gunther, B., Kanert, O., Mehring, M., Wolf, D.: Phys. Rev. B24 (1981) 6747. Mundy, J.N., Hoff, H.A., Pelleg, J., Rothman, S.J.,Nowicki, L.J., Schmidt, EA.: Phys. Rev. B24 (1981) 658. Patil, R.X, Tiwari, G.P., Sharma, B.D.: Philos. Mag. A 44 (1981) 717. Tiers, J.E, Chabre, Y: J. Phys. E 11 (1981) 1943. Fujikawa, S., Hirano, K.I., in: Proc. of Yamada Vth Conf. on Point Defects and Defect Interactions in Metals, Takamura, J.I., Doyama, M., Kiritani, M., (eds.).Univ. of Tokyo Press 1982, p. 554. Herzig, Ch., Manke, L., Bussman, W, in: Proc. of Yamada Vth Conf. on Point Defects and Defect Interactions in Metals, Takamura, J.I., Doyama, M., Kiritani, M., (eds.).Univ. of Tokyo Press, 1982, p. 578. Pruthi, D.D., Agarwala, R.P.: Philos. Mag. A 46 (1982) 841. Rein, G., Mehrer, H.: Philos. Mag. A45 [3] (1982) 467. Ablitzer, D., Haeussler, J.P.,Sathyaraj, K.X: Philos. Mag. A47 (1983) 515. Gunther, B., Kanert, 0.: Acta Metal!. 31 (1983) 909. Gfinther, B., Kanert, O., Wolf, D.: Solid State Commun. 47 (1983) 409. Smithells, L.J.: Smithells Metals Reference Book (6th Edition), Brandes, E.A.J., (ed.). Washington: Butterworths, 1983. Serruys, Y, Brebec, G., in: DIMETA 82, Proc. Int. Conf. on Diffusion in Metals and Alloys, Tihany, 1982, Kedves, EJ., Beke, D.L., (eds.).Trans. Tech. Publication, Switzerland, 1983, p. 351. Vladimirov, A.B., Kaigorodov, VN., Klotsman, SM., Tracktenberg, I.S., in: DIMETA 82, Proc. Int. Conf. on Diffusion in Metals and Alloys, Tihany, 1982, Kedves, EJ., Beke, D.L., (eds.).Trans. Tech. Publication, Switzerland, 1983, p. 338. Weiler, D., Maier, K., Mehrer, H. in: DIMETA 82, Proc. Int. Conf. on Diffusion in Metals and Alloys, Tihany, 1982, Kedves, EJ., Beke, D.L., (eds.).Trans. Tech. Publication, Switzerland, 1983, p. 342. Werner, M., Mehrer, H.: in DIMETA 82, Proc. Int. Conf. on Diffusion in Metals and Alloys, Tihany, 1982, Kedves, EJ., Beke, D.L., (eds.).Trans. Tech. Publication, Switzerland, 1983, p. 393. Werner, M., Mehrer, H., Siethoff, H.: J. Phys. C: Solid State Phys. 16 (1983) 6185. Arkhipova, N.K., Klotsman, S.M., Polikarpova, I.P., Tatrinova, G.N., Timofeev, A.N., Veretennikov, L.M.: Phys. Rev. B30 (1984) 1788. Horvath, J., Dyment, E, Mehrer, H.: J. Nucl. Mater. 126 (1984) 206. Chiron, R., Faivre, G.: Philos. Mag. A51 (1985) 865. Gunther, B., Kanert, 0.: Phys. Rev. B31 (1985) 20. Heitjans, P., Kiirblein, A., Ackermann, H., Dubbers, D., Fujiwara, E, Stockmann, H.J.: J. Phys. F 15 (1985) 41. Hood, G., in: “Solute-Defect Interaction - Theory and Experiment”, Saimoto, S., Purdy, G.R., Kidson, G.V, (eds.),Oxford, New York: Pergamon Press, 1985, p. 83. Arkhipova, N.K., Klotsman, S.M., Polikarpova, I.P, Timofeev, A.N., Shepatkovskii, P.: Fiz. Met. Metalloved. 62 (1986) 1882 (in Russian). Dais, S., Messer, R., Seeger,A.: Mat. Sci. Forum 15-18 (1987) 419. Geise, J., Herzig, C.: Z. Metallkd. 78 (1987) 291. Kohler, U., Herzig, Ch.: Phys. Status Solidi (b) 144 (1987) 243. Kiihler, U.: PhD Thesis, University of Miinster, 1987. Iijima, Y, Kimura, K., Hirano, K.: Acta Metall. 36 (1988) 2811. Lee, Ch.G., Iijiama, Y, Hirano, K.: The Ninth Japan Symposium Thermophysical Properties, i988, p. 1. Landolt-Bornstein, NS, Vol. III/22 b: Semiconductors. Heidelberg, Berlin, New York: Springer, 1989. Mehrer, H., Ltibbehusen, M.: Defect and Diffusion Forum 66-69 (1989) 591. Liibbehusen, M., Mehrer, H.: Acta Metall., in press.
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85
3 Diffusion of impurities in solid metallic elements 3.1 Introduction By “impurity diffusion” is meant the diffusion of a solute element present in such low concentrations in a solvent (matrix) that the solute atoms may be regarded as diffusing quite independently of one another, i.e. with Ino mutual interaction. It represents the very simplest type of binary diffusion and so is of particular interest as being the most likely to be amenable to theoretical understanding. For this reason very considerable ,experimental effort has been devoted over the last thirty or forty years to systematic measurementsof impurity ,diffusion in metals of all types. Impurity diffusion in metals usually occurs by a vacancy mechanism (see 1.5.3). The same is true for self-diffusion of the matrix metal. Depending on the interaction between solute atom and vacancy the impurity ,diffusion coefficient will be either larger or smaller than the self-diffusion coefficient (seechapter 2). However, in a temperature range between 2/3 T, and T, (T, = melting temperature of the matrix metal) the difference ;between impurity and self-diffusion coefficient will usually not exceed one to two orders of magnitude as long as solute and self-atoms migrate via the same diffusion vehicle. Some solute atoms show “anomalous” fast diffusion. For fast diffusors the impurity diffusion coefficient texceedsthe self-diffusion coefficient by several orders of magnitude. Fast diffusing solutes usually have a low solubility in the matrix crystal as well. The phenomenon of fast diffusion has been observed mainly for 1polyvalent matrix metals like Pb, Sn, In, Tl, titanium and vanadium group metals and to some extent for alkali 1metals. Many solutes in Si and Ge are also fast diffusors. However, in this chapter diffusion data are compiled iFormetallic matrices only. It is commonly agreed that a low ratio between the atomic radii of solute and matrix atoms is favourable jibr fast diffusion and that this phenomenon is basically due to rapid transport of solute atoms via interstitial :rites of the matrix crystal. However, the question whether this rapid transport occurs via a pure interstitial Ivzechanism (see 1.5.1) or a interstitial-substitutional exchange mechanism (see 1.5.6) has been resolved only for 7very few solute-matrix combinations.
3.1.1 Methods of measurement The advent of readily available radioactive isotopes just after the war made it possible for the first time to aork with solute concentrations low enough to satisfy completely the conditions for true impurity diffusion, ;‘or extremely small concentrations of radioactive isotopes are accurately measurable. For this reason too the i deal method of measurementwith radioactive isotopes is the thin layer method (see1.6.1.2.1),for the condition 1;hat the thickness h 6 (D t)1/2 is very readily satisfied; extremely thin layers frequently suffice, often only a few I:ens of atoms thick. The thin layer method with serial sectioning and measurement of the activity of each section is quite the (:ommonest method employed, the diffusion coefficient D being calculated from equation (1.I 1). Alternative I procedures are to use the “residual activity” (Gruzin-Seibel) method or the surface decreasemethod. For reasons outlined in 1.6.1.2.1, these two methods are generally regarded as less reliable, although the residual activity method is capable of comparable accuracy when the emitted radiation is of low energy so that the integrated activity from below the surface becomes negligible. The surface decreasemethod is rarely used nowadays. Methods of sectioning and analysis for the thin layer methods are reviewed in 1.6.1.2.1. Either mechanical serial sectioning techniques (lathe sectioning, grinder sectioning, microtome sectioning) or microsectioning techniques (sputter sectioning, anodic stripping, . . .) may be used. Occasionally, penetration profiles follow, and are then analysed in terms of, equation (1.14) rather than equation (1.11); this is when the diffusant solubility is so small that the surface concentration remains at its maximum (solubility) value for the whole of the diffusion anneal. This solubility can then also be determined from the measurements. When the surface concentration maintains its maximum saturation value for only part of the anneal time, measurementsmay be analysed by a solution due to Malkovitch (Fiz. Met. Metalloved. 15 (1963) 880).
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86
Sometimesnon-radioactive diffusants are employed, either with the thin-layer method or, occasionally, with diffusion couple or in- or out-diffusion methods. Sufficiently sensitive methods of chemical analysis are then needed becauseof the necessarily very low concentrations; electron microprobe analysis (EMPA), secondary ion mass spectroscopy (SIMS), scanning laser mass spectroscopy (SLMS), spark source mass spectroscopy (SSMS), Rutherford back scattering (RBS) and nuclear reaction analysis (NRA) are among methods that can be employed. Electrical resistivity measurementsand X-ray diffraction methods (see1.6.1.2.3) provide another means of monitoring concentration changes and occasionally have been used to determine impurity diffusion coefficients. Apart from one or two measurementsby the Mijssbauer effect, “indirect methods”, (see1.6.2) have found little or no application to substitutional solute impurity diffusion, with which this chapter is principally concerned. This is in marked contrast with the diffusion of the interstitial solutes C, N, 0 and H dealt with in chapters 8 and 9.
3.1.2 Use of tables and figures In this chapter impurity diffusion data are compiled in tables and figures according to the positions of the nrorrix metals in the periodic table in the following order: alkali group metals, alkaline earth group metals, scandium group metals, rare earth metals, titanium group metals, vanadium group metals, chromium group metals, manganesegroup metals, iron group metals, cobalt group metals, nickel group metals, noble metals, zinc group metals, aluminum group metals, group IV B metals, group VB (semi) metals, actinide group metals This order of matrix elements is the same as in chapter 2 on self-diffusion. Within the table that refers to a given matrix metal the data for solute elements are compiled according to the same order of elements. The matrix metal can be found on top of the pertaining table. The solute element can be found in the column ‘Sohrte” of the table. Diffusion data are reported whenever possible in terms of thepre-exponenfiulfaclor Do (secondcolumn) and the nclhafion enfhnby Q (third column) introduced in equation (1SO) of the “General introduction”. Occasionally, diffusion coefficients have been listed in these two columns. This procedure was chosen whenever the original data did not justify an analysis in terms of equation (1.50). Possible reasons could be either too few data points or physically significant deviations from equation (1.50) already discussed in section 1.8. An example is diffusion in u-iron: When diffusion is studied over a wide enough temperature range the magnetic transition causes significant deviations from a simple Arrhenius behaviour. Occasionally curved Arrhenius diagrams were analyzed in terms of a sum of two Arrhenius terms. In these casesblanks occur in the Do and Q columns and the result of the two-exponential tit is listed in the “Method/Remarks” column (seebelow). The temperature range quoted is the range over which measurementswere made and used by the author(s) to calculate the quoted values of Do and Q. Extrapolation too far outside this range may not in somecasesgive reliable diffusion coefficients. For imitlxinl matrix metals Do and Q values are given for diffusion parallel (II) and perpendicular (I) to the crystal axis whenever experiments on single crystals of different orientation were performed. The orientation will be indicated in the Do column of the table. For matrh met& with allotropic transformations Do and Q values are listed for the various crystal structures. Either diffusion data are collected separately (like e.g. in the case of cr-Ti and I%Ti) or the modification is indicated by a corresponding remark (e.g. “y-Fe” or “S-Fe”) in the “Temperature range” column.
Le Claire
3.1 Introduction
87
The column “Method/Remarks” usually contains the following information: (i)
(ii) (iii) (iv) (v) (vi)
The experimental method is briefly characterized: - Thin layer methods If a thin layer method together with a radioactive diffusant was used the diffusant is stated together with its mass number. If concentration-depth curves were determined by serial sectioning and counting the sectioning technique is stated. If the residual activity method or the surface decreasemethod was employed together with radioactive diffusants this is stated by the remark “residual activity” or “surface decrease”. If a thin layer method is used together with non-radioactive diffusants the diffusing element is stated without mass number. The technique for the concentration-depth curve measurement (e.g., “electron microprobe analysis”, SIMS, . . .) is stated. - Diffusion couple methods or in- and out-diffusion methods or indirect methods are specified in tables. The statement “polycrystal” or “single crystal” is employed to indicate the microstructure of the material. The nominal purity of the material will be stated. Appropriate additional information on the method, additional information contained in the paper and remarks about the reliability of the quoted results may be added in the “Method/Remarks” column. When a curved Arrhenius plot has been analyzed by the sum of two exponentials according to equation (l.Sl), the pre-exponential factors 0: and 0; and the activation enthalpies Q, and Q, are tabulated in the “Method/Remarks” column. Very occasionally the various forms in which results are reported in a paper (tabulated, graphical, in text etc.) may be found to be incompatible with one another. Careful assessmentof the data has usually made possible identification of what is most likely the most correct result. It is stated explicitly where this has been necessary.
Central to the present chapter are the tables. From the tables references are made to the figures. Selected data have been plotted in the figures as indicated in the column “Figure” (Fig.). In the figures of sections 3.2.1 to 3.2.9 and 3.2.16 (sections treated by A.D. Le Claire) the temperature ranges of the D values shown in the figures agreewith those of the temperature range given in the tables. In most figures of sections 3.2.10 to 3.2.15 (sections treated by G. Neumann) Arrhenius lines are shown over a temperature range of typically 213 T, to T,. This temperature range is not identical with the temperature range over which the measurements were performed. The temperature range of measurements can be found in the tables. In most figures self-diffusion according to chapter 2 is shown for comparison. In most figures melting temperatures of the matrix metals and, if necessary,allotropic transformation temperatures have been indicated.
Land&-BBmstein New Series III/26
Le Claire
88
3.2.1 Impurity diffusion in alkali metals
[Ref. p. 203
3.2 The impurity diffusion tables Solute
Do
e
10-4m2s-1
kJmol-r
Temperature range K
Method/Remarks
Fig.
Ref.
3.2.1 Impurity diffusion in alkali metals Li, Na, K, Rb, Cs, Fr Matrix:
lithium (Li)
Li
-
-
-
seechapter 2 on self-diffusion
132
Na
0.41
52.80
325...449
1
67Ml
0.44
52.02*
317..,435
22Na* polyciystals; 99.8 %; microtome sectioning 22Na; polycrystals; purity not specified; microtome sectioning; diffusion in 7Li and 6Li studied; * Do and Q for 7Li estimated from graphical data by present authors 22Na, 24Na; polycrystals; 99.98%; microtome sectioning; isotope effect also determined
2
71Ll
-
73Ml
-
6901
1
73M2
-
6801
1
73Ml
1
6802
,cu
Ag
Au
D = l.16~10-11 m2sV1
423
0.047 *
38.60*
323...394
0.3
41.87
362...420
0.37
53.72
340...434
0.54
53.72
323 . ..423
0.21
46.01
319...426
64Cu; polycrystals; 99.98%; microtome sectioning; * values reassessedby present authors 64Cu; polycrystals; 99.98%; penetration plots curved Malkovitch solution 1’om&; polycrystals; 99.98%; microtome sectioning losAgt ‘lomAgi polycrystals; 99.98%; microtome sectioning; isotope effect also determined 195Au; polycrystals; 99.95%; microtome sectioning
(continued)
Le Claire
Land&-BCmslein New Series III/26
Ref. p. 2031 Solute
3.2.1 Impurity diffusion in alkali metals
Do
Q
10-4m2s-’
kJmol-’
89
Temperature range K
Method/Remarks
Fig.
Ref.
‘95AU. polyc&tals
2
7103
Matrix: lithium (Li), continued 0.10
43.47
300...441
0.141
44.93
300**.441
Zn
0.57
54.34
330...446
65Zn. polycrystals; 99.98%; microtome sectioning
69Ml
Cd
0.62
62.80
355...449
115mC4 polycrystals; 99.98% ; microtome sectioning
7001
Hg
1.04
59.37
331...447
‘03Hg; polycrystals; 99.98%; microtome sectioning
7001
Ga
0.21
54.05
389...447
72Ga; polycrystals; 99.98%; microtome sectioning
7001
In
0.39
66.44
348s.. 443
114mIn;
6803
Au
of 95 % 6Li;
microtome sectioning lg5Au: 2, 3 polycrystals of 92.5 % ‘Li; microtome sectioning; separate Arrhenius terms for 300...359 K: Do = 8.5. 10m6m2 s-l; Q = 42.83 kJmol-‘; 371...441 K: Do = 0.24. 10m4m2 s-l; Q = 46.52 kJmol-’ (seeFig. 3)
polycrystals; 99.95%; microtome sectioning Sn
0.62
66.32*
380...447
Sn (radioisotope not specified); polycrystals; 99.95%; microtome sectioning; * values reassessedby present authors
6902
Pb
1.6. IO4
105.5*
401 .*. 443
Pb (radioisotope not specified); polycrystals; 99.95% ; microtome sectioning; * values reassessedby present authors
6902
Land&-Bknstein New Series III/26
Le Claire
90 Solute
3.2.1 Impurity diffusion in alkali metals Do
Q
10-4m2s-1
kJmol-’
[Ref. p. 20
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: lithium (Li), continued Sb
1.6. 1012
173.8*
413 . ..449
Sb (radioisotope not specified); polycrystals; 99.95%; microtome sectioning * values reassessedby present authors
1
6902
Bi
5.3 . 10’4
198.0*
413...450
Bi (radioisotope not specified); polycrystals; 99.95% ; microtome sectioning; * values reassessedby present authors
1
6902
Matrix: sodium (Na) Na
-
-
seechapter 2 on self-diffusion
4
Li
1.8
49.1
291...358
4
64Nl
-
-
297...353
6Li, ‘Li; polycrystals; purity not specified; diffusion couple method; microtome sectioning and mass spectroscopy 6Li; polycrystals; 99.95%; microtome sectioning
-
83Bl
0.08
35.29
273...365
42~.
4
67Bl
K
poly&ystals; 99.95%; microtome sectioning Rb
0.15
35.55
272..-359
s6Rb; polycrystals; 99.95% microtome sectioning
4
67Bl
Ag
0.02
21.39
298..-351
1’omAg. polycrystals; 99.95% ; microtome sectioning
4
83Bl
Au
3.34. 10-4
9.25
274...350
‘=Au; polycrystals; 99.95%; microtome sectioning; solubility determined from the erfc-profile : c, = 540 exp (- 47.0 kJ/RT)
4
69Bl
Le Claire
Ref. p. 2031 Solute
Matrix:
3.2.2 Impurity diffusion in alkaline earth metals
Do
Q
10-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
273...363
“%Zd; polycrystals;
91 Fig.
Ref.
sodium (Na), continued
Cd
0.37
40.86
83Bl
99.95 % ;
microtome sectioning In
1.79
48.73
293...363
l141n; polycrystals;
83Bl
99.95 %;
microtome sectioning Tl
0.52
42.62
297...356
204Tl.
83Bl
poly&stals; 99.95 % ;
microtome sectioning Sn
0.54
43.92
316 ... 363
l13Sn; polycrystals;
83Bl
99.95 %;
microtome sectioning Matrix:
potassium (IL)
K
-
-
-
seechapter 2 on self-diffusion
Na
0.058
31.19
273...335
22Na* polyciystals;
67Bl
99.95 % ;
microtome sectioning Rb
0.09
36.76
273...333
‘(jRb; polycrystals;
69Sl
99.95 % ;
microtome sectioning Au
1.29. lO-3
13.52
279...326
lg8Au; polycrystals;
7OSl
99.95 %;
microtome sectioning; (erfc and Malkovitch solutions) Matrix:
rubidium (Rb) - No impurity diffusion data available (for self-diffusion data seechapter 2)
Matrix:
caesium (Cs) - No data available
3.2.2 Impurity diffusion in alkaline earth metals Be, Mg, Ca, Sr, Ba, Ra Matrix:
beryllium (Be)
Be
-
-
-
Ce
3.1 . 102
303.5
1223 ... 1513
seechapter 2 on self-diffusion
6
141C!e;
6
76Al
6
76Al
polycrystals; 99.7%;
residual activity (erfc solution) V
29
243.0
1173...1423
4av.
pol&rystals; 99.7%;
residual activity (erfc solution) Land&-BGmstein New Series III/26
[Ref. p. 203
3.2.2 Impurity diffusion in alkaline earth metals Temperature range K
Method/Remarks
Fig.
Ref.
Matrix beryllium (Be), continued 359.6 Nb 2. lo4
1318...1513
g5Nb; polycrystals; residual activity (erfc solution)
6
76Al
Fe
Fe; polycrystals; diffusion couple method and electron microprobe analysis; solubility limit also determined “Fe. polydrystals;
-
62Dl
6
66Nl
6
79Gl
6
70Al
combined data of [65Dl] and [74Ml] on single crystals: 64Cu; serial sectioning (for T > 950K); diffusion following ion implantation studied by Rutherford backscattering (for T < 950K)
6
65D1, 74Ml
1’om&; polycrystals;
-
66Nl
Solute
Do
Q
10-4m2s-1
kJmol-’
1.0
221.9
1073...1373
0.53
216.9*
973...1349
99.75 % ;
residual activity; * values reassessedby present authors co
27
287.2
1253... 1493
5’co; polycrystals; 99.8%;
residual activity Ni
0.2
243.0
1073 . . 1523
63Ni; polycrystals; 99.7 % ;
residual activity cu
Ag
11c 0.38
198.6
733 ... 1273
I c 0.42
193.3
693 ... 1273
6.2
193.0*
923...1183
99.75 % ;
11c 0.43 Ic 1.76
164.5* 180.9*
929...1170 929...1170
residual activity; * values reassessedby present authors “om&; single crystals;
6
99.75 % ;
D,, = 3.1 . lo-l3 m2se1 D
I = 13. . 10-13m2s-1
1053 1053
residual activity; * values reassessedby present authors single crystals;
75Ml
99.95 %;
in-diffusion studied by Rutherford backscattering analysis
Ik Claire
Landolt-BBmstein New Series lIlj26
3.2.2 Impurity diffusion in alkaline earth metals
Ref. p. 2031
93
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: beryllium (Be), continued D = 1.5 * lo-“3 m2s-1 Au D”=28.10-‘6~2~-1 I . D,, =4.4.10-15 m2sm1 D I =65.10-‘5m2s-l .
938 938 1053 1053
single crystals; 99.95% ; in-diffusion studied by Rutherford backscattering analysis; 99.95%; D in polycrystals of 10 urn grainsize about 10 times larger than in single crystals
6
75M3
Al
1068 *.+1356
26A1. polyirystals; 99.91%; residual activity (erfc solution)
6
76Gl
Matrix: magnesium (Mg) Mg
-
seechapter 2 on self-diffusion
7, 8
Be
8.06
157.0
773...873
Be; diffusion couple method with couple of Mg and Mg 0.2 % Be alloy; layerwise spectral analysis (erfc solution)
7
66Yl
La
2.2. 10-2
102.2
813...868
dissolution of precipitates in diffusion couple
-
66Ll
Ce
450
175.8
823...871
dissolution of precipitates in diffusion couple
-
66Ll
Fe
4.10-6
88.8
673.e.873
“Fe; polycrystals; 99.95% ; residual activity
7
68Pl
Ni
1.2. 10-5
95.9
673...873
63Ni; polycrystals; 99.95% ; surface decreasemethod
7
68Pl
Ag
0.34
119.3
749...894
7
67Ll
11c 3.62 J-c 17.9
133.1 148.2
752...913 752...913
‘lomAgi polycrystals; 99.875% ; serial sectioning ‘lomAgi single crystals; 99.99%; lathe and grinder sectioning
8
72Cl
Zn
0.41
119.7
740...893
65Zn; polycrystals; 99.875%; serial sectioning
7
67Ll
Cd
11c 1.29 I c 0.46
140.7 132.7
733...898 733...898
“‘Cd; single crystals; 99.99%; lathe and grinder sectioning
8
72Cl
Solute
andolt-BBmstein \Tew Series III/26
Do
e
10-4m2s-1
kJmol-’
1.0
168.3
Le Claire
Golute
[Ref. p. 203
3.2.2 Impurity diffusion in alkaline earth metals
94 Da
e
10-4m2s-’
kJmol-’
Ref.
Temperature range K
Method/Remarks
l141n; polycrystals; 99.875%; serial sectioning 114mIn; single crystals; 99.99%; lathe and grinder sectioning
67Ll
l13Sn.
72Cl
Fig.
Matrix: magnesium(Mg), continued [n
Sn
5.2. 10-2
118.9
745...883
(Ic 1.75 Ic 1.88
143.4 142.4
747..-906 747.~~906
11c 4.27
149.9
748 ..-903
72Cl
single’crystals; 99.99% ; lathe and grinder sectioning; D,/D,, = 1 at 902.3 K; D,/D,, = 1.13 at 858.2 K Sb
11 c 2.57 I c 3.27
137.3 138.2
781...896 781...896
124Sb; single crystals; 99.99% ; lathe and grinder sectioning (erfc solution)
72Cl
u
1.6. lo-’
114.7
773...893
235~.
68Pl
polyc’rystals; 99.95% ; residual activity Matrix: calcium (Ca) Ca
-
-
-
seechapter 2 on self-diffusion
Fe
3.2. lo-’
124.8
823. . - 1073
“Fe; polycrystals; 99.95% ; residual activity
68Pl
Ni
l.lo.10-5
121.0
823. . .1073
63Ni; polycrystals; 99.95%; surface decrease
68Pl
U
1.1 . 10-s
145.7
773*..973
23su; polycrystals; 99.95%; residual activity
68Pl
Matrix: strontium (Sr) - No data available Matrix: barium (Ba)
- No data available
Matrix: radium (Ra) - No data available
Le Claire
Land&-B6msIei New Series Ill/26
solute
95
3.2.3 Impurity diffusion in SC group and rare earth metals
Ref. p. 2031 Do
Q
10-4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
3.2.3 Impurity diffusion in scandium group and rare earth metals 3.2.3.1 Scandium group metals SC,Y, La Matrix: scandium (SC) SC
-
-
-
no data available
-
Fe
1.5. 10-3
54.0
1241s.. 1528 (Cl-SC) 1643 1702 1755 1790 (P-W
Fe; diffusion couple method using scanning laser mass spectroscopy; polycrystals; 99.96%; electro-mobility and effective valence also determined
10
seechapter 2 on self-diffusion
11
D=4.1.10-gm2s-’ 2.6 . IO-’ m2 s-l 3.4. IO-’ m2 s-l 4.4. IO-’ m2 s-l
Matrix: yttrium (Y) Y
-
86Al
Fe
1.8. lO-2
85.0
1173...1603 (a-Y>
“Fe; diffusion couple method; 99%; lathe sectioning; electro-mobility and effective valence also determined; similar data in [8201]
11
75M2
co
1.4. 10-2
83.3
1290... 1620 (a-Y)
11 co; diffusion couple method with couple of pure Y and Y 0.05% Co alloy; polycrystals; 99.6%; laser-ionization mass spectroscopy; electro-mobility and effective valence also determined
8201
Ni
5.8. 1O-2
96.5
1290...1580 (a-Y)
Ni; 11 diffusion couple method with couple of pure Y and Y 0.05% Ni alloy; polycrystals; 99.6%; laser-ionization mass spectroscopy; electro-mobility and effective valence also determined
8201
Ag
5.4. 10-3
77.0
1178... 1453 (f=Y>
llom&; diffusion couple method; 99%; lathe sectioning; electro-mobility and effective valence also determined
11
75M2
Land&-Biimstein New Series III/26
Le Claire
3.2.3 Impurity diffusion in SC group and rare earth metals
96 Solute
[Ref. p. 203
Method/Remarks
Fig.
kJmo!-’
Temperature range K
-
-
seechapter 2 on self-diffusion
12
1139~~~1170
141Ce.
12
76Fl
(-f-W
polycrystals; serial sectioning 12
69Dl
Do
Q
10-4m2s-’
Ref.
Mah-ix: lanthanum (La) La Ce
Au
1.8. IO-’
2.2 * 10-2
104.7
75.8
873 ... 1073 (P-W
rgOAu; polycrystals; 99.97%; lathe sectioning; self-diffusion also studied
3.2.3.2 Rare earth metals Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu Matrix: cerium (Ce) Ce
-
-
seechapter 2 on self-diffusion
13
La
3.8. lo-*
102.6
998 ..- 1048 (&Ce)
i4’La; polycrystals; 99.95% ; lathe sectioning
13
73Dl
Gd
1.2. 10-2
100.5
1003... 1048 (&Ce)
Gd (radioisotope not specified); polycrystals; purity not specified; serial sectioning
13
76Ml
Mn
7.2. IO-’
37.0*
888...973
54Mn; polycrystals; 99.9%; lathe sectioning; * evaluated from 3 graphical data points by present authors
13
75Dl
Fe
D=2.78.10-10m2s-’
10!Fe) (&Ce)
3.3. 10-4
19.3
173.e.923 We)
1.7. 10-2
49.8
2.0. 10-3
32.2
875.e.990 (v-C4 1005... 1046 (6-Ce)
5gFe; polycrystals; 99.8 % ; diffusion couple method and nondestructive/destructive y-counting; electro-mobility and effective valence also determined 5gFe; polycrystals; 99.9 % ; lathe sectioning
Le Claire
73Cl
13
75Dl
Landolt-BBmslei! New Series III!26
3.2.3 Impurity diffusion in SC group and rare earth metals
Ref. p. 2031 Solute
Do
Q
10-4m2s-1
kJmol-’
Temperature range K
97
Method/Remarks
Fig.
Ref.
6OCo.
13
73Cl
13
76Ml
13
72Dl
13
73Cl
72Dl
Matrix: cerium (Ce), continued
co
Ag
Au
46.1
1.0. 10-2
1.6. 1O-3
35.6
1.2. 10-3
33.5
2.5. 10-2
88.3
1.2 * 10-l
92.9
1.4
117.2
4.4. 10-3
62.4
9.5. 10-2
85.8
823...923 (r-W
~920~~*1000 (r-C@ 1003.*. 1048 (h-Ce)
polycjstals; 99.8%; diffusion couple method and nondestructive/destructive y-counting; electro-mobility and effective valence also determined 6Oco. polyc;ystals; serial sectioning (erfc solution)
852...969 We> 996... 1049 (&Ce) 873...973 (r-C4
‘lomAgi polycrystals; 99.9 %; lathe sectioning llomAg; polycrystals; 99.8 %; diffusion couple method and nondestructive/destructive y-counting; electro-mobility and effective valence also determined
823...973 We> 999... 1048 (6-Ce)
l98Atl; polycrystals; 99.9 ?$; lathe sectioning
13
-
seechapter 2 on self-diffusion
14
Matrix: praseodymium (Pr) Pr
-
La
D = 1.1 .
HO
IO-l3 m2 s-1 *
1.8. 1O-2
107.6
D = 3.35 . IO-“
m2 s-1 *
9.5. 10-3
Land&-BBmstein New Series III/26
-
110.1
1039 14’La; (a-Pr) polycrystals; 1080~~~1190 99.96% ; lathe sectioning; (P-W * value estimated from published graph by present authors 1004 (cl-Pr) 1085...1180 (P-W
166~~.
polycjstals 99.96% ; lathe sectioning; * value estimated from published graph by present authors
Le Claire
14
69D2
14
69D2
3.2.3 Impurity diffusion in SC group and rare earth metals
98 Solute
Do
Q
10P4m2s-’
kJmol-’
[Ref. p. 203
Temperature range K
Method/Remarks
Fig.
Ref.
930 ... 1000 (u-Pr) 1111~~*1166 (P-W
54Mn. po1yc;ysta1s; 99.9 % ; lathe sectioning; * evaluated from graphical data by present authors
14
75Dl
885... 1060 (mPr) 1075.+.1180 (B-W 885...1036 (cc-Pr) 1092 1151 (P-W 926...1059 (u-Pr) 1086.+.1187 @-w 886... 1040 (cc-Pr) 1085...1195 (WV 870...1015 (a-Pr) 1075...1185 1o$-W
59Fe; polycrystals; 99.9 % ; lathe sectioning
14
75Dl
6Oco; polycrystals; 99.93%; lathe sectioning
14
69D3
b4cu; polycrystals; 99.9 % ; lathe sectioning
14
71Dl
11omAg. polycryitals; 99.93% ; lathe sectioning
14
69D3
19’Au; polycrystals; 99.93% ; lathe sectioning 19’Au; single crystals; 99.94% lathe sectioning (erfc solution)
14
69D3
14
81Dl
65Zn; polycrystals; 99.97% ; lathe sectioning
14
70Dl
‘141n;
14
69D2
Matrix: praseodymium (Pr), continued
Fe
co
1.06.10-j
63.2 *
2.6. lo-’
25.1*
2.1 * 10-3
39.4
4.10-3
43.5
4.7. 10-Z
68.7
D=4.6-10-9m2s-1 D=5.0~10-9m2s-1 cu
Ag
Au
Zn
8.4. lo-*
75.8
5.7. 10-2
74.5
0.14
106.3
3.2. lo-*
90.0
4.3. 10-2
82.5
3.3. 10-2
84.2
D =4.4.jO-10m2s-1 D”=37.10-‘0m*s-’ D1 = 4.6 +lO-‘o m2sm1 D”=4.0.10-10m2s-1 1 0.18 103.8 0.63
113.0
In 9.6. lo-*
121.0
(cl-Pr) 1053 (u-Pr) 876...1040 (a-Pr) 1095...1194 (VW 1039 (u-Pr) 1075...1200 (P-W
polycrystals; 99.96% ; lathe sectioning; * values estimated from published graph by present authors
3.2.3 Impurity diffusion in SCgroup and rare earth metals
Ref. p. 2031 Solute
Matrix:
Do
Q
10-4mZs-1
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
no self-diffusion data available
-
54Mn; polycrystals;
15
75Dl
15
75Dl
neodymium (Nd)
-
Nd
-
Mn
D = 4.17 . IO-” m2 s-1 * 6.02 . 10-l’ mz s-l
1.12~10-‘0m2s-1* 1.61 . lo-” m2 s-l Fe
4.6. 1O-3
51.1
1028 1075
(a-Nd) 1148
99.9 %;
lathe sectioning; * values estimated from published graph by present authors
1182 (P-W 955...1136*
(a-Nd) 0.01
56.9
1162... 1231* (P-W
“Fe; polycrystals; 99.9%;
lathe sectioning; * values estimated from published graph by present authors
Matrix:
prometheum (Pm) - No data available
Matrix:
samarium (Sm)
- No data available
Matrix:
europium (Eu)
- No impurity diffusion data available; for self-diffusion seechapter 2
Matrix:
gadolinium (Gd)
- No impurity diffusion data available; for self-diffusion seechapter 2
Matrix:
terbium (Tb)
- No data available
Matrix:
dysprosium (Dy)
- No data available
Matrix:
hobnium (Ho)
- No data available
Matrix:
erbium (Er)
Er
-
Au
-
11c 4.73.10-3 * 64
lc1.95.10-2*
-
seechapter 2 on self-diffusion
1270..+ 1485
lg8Au; 16 single crystals; 99.91%; lathe sectioning (erfc solution); three temperatures only; * values estimated from published graph by present authors
99
- No data available
Matrix:
thulium (Tm)
Matrix:
ytterbium (Yb) - No impurity diffusion data available;
for self-diffusion seechapter 2 Matrix:
99
lutetium (Lu)
andolt-Bhnstein lew Series III/26
- No data available
Le Claire
16 79Dl
Solute
[Ref. p. 203
3.2.4 Impurity diffusion in titanium group metals
100
Do
Q
10-4mZs-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
17 -
79Sl
3.2.4 Impurity diffusion in titanium group metals Ti, Zr, Hf Matrix:
titanium (Ti)
r-titanium Ti
-
-
seechapter 2 on self-diffusion
259.0
933.e.1133
‘Be; polycrystals; 99.5%; residual activity
1124 1072
s4Mn. polyc;ystals; 99.998%; lathe sectioning; solvent and solute diffusion in bee Ti-Co and Ti-Mn alloys also studied 54Mn* 18 single’crystals; 99.94% ; lathe sectioning; D,,/D, = 3.84.e.1.68; effect of oxygen on Mn diffusion also studied
75Sl
59Fe; single crystals; 99.96% ; lathe sectioning; D,,/D ,, = 5.15 . ..2.01 s9Fe; polycrystals; purity not specified; residual activity
18
83Nl
-
73Kl
6OCo; polycrystals; 99.998%; lathe sectioning; solvent and solute diffusion in bee Ti - Co and Ti - Mn alloys also studied 6OCo; single crystals; 99.96% ; lathe sectioning; similar data in [83N2]; isotope effect also studied
-
75Sl
18
85N1, 85N2
Be
14.103
Mn
D = 1.42. lo-l3 rn’s-l 5.21 . lo-l4 m2s-l
Fe
co
1 c 0.6 ii c 4.9 . lo-’
189.2 160.5
878...1135 878...1135
lc 6.4. lo-’ iic 4.7. 1O-3
144.2 112.3
877...1136 877...1136
1.2. 10-4
110.5
973...1123
D=6.65~10-‘2m2s-’ 3.64. lo-l2 m2 s-l
1129 1072
lc 3.2. lO-2 Iic 1.9. 10-Z
875...1135 875...1135
126.1 114.1
Le Claire
88N2
Landok-BBmstei New Series Ill/21
Ref. p. 2031 Solute
3.2.4 Impurity diffusion in titanium group metals
Do
e
10-4mZs-1
kJmol-’
101
Temperature range K
Method/Remarks
Fig.
Ref.
912 971 1059 1117 1141
63Ni; polycrystals; “high purity”; lathe sectioning; * value reassessedby present authors 63Ni; single crystals; 99.96%; lathe sectioning
-
72HI
18
85N2
I7
76Pl
17
85R 1
Matrix: titanium (a-Ti), continued Ni
D = 6.7. 10-14m2s-i I.8 . IO-l3 m2 s-l 76.10-‘3m2s-l*
2.3 . IO-r2 m2 s-l 2.1 . IO-l2 m2 s-l I c 5.4 .10-2 11c 5.6. IO-’
141.8 137.2
877... 1100 877... 1100
9.7. 10-s
115.1
973...1123
7.4. 10-7
156.4
873...1123
Si
4.4. 10-7
105.2
923 ... 1073
Si (ion-implanted); polycrystals; 99.9 % ; nuclear reaction analysis; solubility of Si also determined
17
86Rl
P
l.c 0.155 11 c 4.7
138.2 172.3
973...1123 973...1123
32~.
4.1 . 10-7
114.5
p-titanium Ti Be
Al
Al; polycrystals; X-ray diffraction method Al (ion implanted); polycrystals; 99.9 % ; nulcear reaction analysis
I7
86NI
1020+.. 1124
single crystals; 99.96% ; lathe sectioning; for T < 973 K D values are smaller than calculated from Do and Q; P diffusion in Ti 2.35 at% 0 also studied -
18
78Fl
-
-
seechapter 2 on self-diffusion
17,18
0.8
168.3
1188...1573
7Be; polycrystals; 99.62%; residual activity
17
69Pl
SC
4.0. 10-3
135.7
1213... 1843
46sc. polycrystals; 99.95% ; lathe sectioning; similar data in [65Al]
18
7IAl
Zr
4.7. 10-3
148.2
1193...1773
“Zr; polycrystals; 98.94% ; residual activity
18
67PI
U
Land&-Biimstein New Series III/26
102 Solute
3.2.4 Impurity diffusion in titanium group metals Do
Q
10-4mZs-*
kJmo!-’
Mafrix: titanium @Ti), continued v
[Ref. p. 203
Temperature range K
Method/Remarks
Fig.
Ref.
1175...1816
49.
18
64Ml
pol$rysta!s; 99.9 % ; lathe sectioning; two-exponential tit to the [64Ml] data: 0: = 7.9. lO-1o m*s-l, Q, = 101.1 kJmo!-‘, 0: = 0.21 . 10v4 m* s-l, Q2 = 209.0 kJ mol-’ ; seealso [65Al] Nb
-
-
1273... 1923
2.91 .10-4
129.9
1228... 1784
-
-
Ta
Cr
-
90Nl
“Nb; polycrystals; 99.7%; lathe sectioning and autoradiowphy; two-exponential fit: 07 = 5 . IO-’ m* s-l, Q, = 164.5 kJmo!-‘, 0: = 20. low4 m*s-*, Q2 = 305.6 kJmol-I; seealso [65Gl] g’Nb; polycrystals; 99.97% ; lathe sectioning; only three temperatures; diffusion of Ti and Nb in Ti -Nb alloys also studied
18
63Gl
-
79Pl
1187...1869
“*Ta; polycrystals; “iodide Ti”; lathe sectioning; two-exponential fit: 0: = 3. 10-8m2s-1, Q, = 140.3 kJmol-‘, 0: = 13 * lob4 m*s-‘, Q2 = 309.8 kJmo!-’
18
66A1
1243... 1923
51Cr; polycrystals; 99.7.**99.9%; lathe sectioning and autoradiowphy ; two-exponential fit: D~=5~10-7m2s-1, Q, = 147.8 kJmo!-‘, 0: = 4.9. 10e4 m* s-l, Q2 = 255.4 kJmo!-‘; seealso [65Gl]
18
63Gl
L42Claire
Land&-BBmsteir New Series III/26
Ref. p. 2031 Solute
3.2.4 Impurity diffusion in titanium group metals
Do
Q
10-4m2s-1
kJmol-’
Matrix: titanium (fl-Ti), continued MO
W
103
Temperature range K
Method/Remarks
Fig.
Ref.
1173...1923
“MO; polycrystals; 99.7*..99.9%; lathe sectioning; two-exponential tit: 0: = 8 . 10d7 m2 s-l, Q, = 180 kJmol-r, 0: = 20. 10m4m2 s-l, Q, = 305.6 kJmol-‘; seealso [65Gl] ggMo; polycrystals; 98.94%; residual activity; * Q and Do values from single exponential tit to given temperature ranges
18
63Gl
-
67Pl
185w.
18
67Pl
0.24 2.82. 1O-4
214.8 * 139.0*
1373... 1833 1173*..1373
3.6. 1O-3
183.8
1173...1523
polyciystals; 98.94%; surface decreasemethod Mn
?e
Land&-Bihstein New Series III/26
-
-
1203..- 1923
54Mn ’ polyciystals; 99.7 % ; lathe sectioning; two-exponential fit: 0: = 6.1 . 10e7 m2 s-l, Q, = 141.1 kJmol-‘, 0: = 4.3 . 10e4 m2 s-l, Q, = 242.8 kJmol-‘; seealso [65Gl]
18
63Gl
-
1193...1923
55Fe; polycrystals; 99.7 % ; lathe sectioning and autoradiographs ; two-exponential fit: 0: = 7.8. lo-’ m2 s-l, Q, = 132.3 kJmol-‘, 0: = 2.7. 10m4m2 s-l, Q, = 230.3 kJmol-l; seealso [65Gl] 5gFe; polycrystals; “iodide Ti”; lathe sectioning; pressure effects also studied “Fe; polycrystals; purity not specified; residual activity
18
63Gl
-
67132
-
73Kl
D = 9.9. 10-‘3m2sml
1175
5.6. 1O-3
1273... 1473
131.0
Le Claire
104 Solute
3.2.4 Impurity diffusion in titanium group metals Do
Q
10-4m2s-1
kJmol-’
[Ref. p. 203
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: titanium (&Ti), continued
co
-
1183.a.1923
6oco. polyc~ystals; 99.7 % ; lathe sectioning; two-exponential tit: 0: = 1.2 * 10T6 m2s-‘, Q, = 128.1 kJmo!-‘, 0: = 2. 10-4m2s-1, Q, = 219.8 kJmo!-‘; seealso [65Gl]
18
63Gl
Ni
-
1203.+. 1923
63Ni.
18
63Gl
polyfrystals; 99.7%; lathe sectioning and autoradiographs ; two-exponential tit: 0: = 9.2. lo-’ m2 s-l, Q, = 123.9 kJmo!-‘, 0: = 2. 10m4m2s-', Q2 = 219.8 kJ mol-‘; seealso [65Gl] -
1233... 1733
Cu; polycrystals; “iodide Ti”; electron microprobe analysis; two-exponential fit: 0: = 2.1 . 10e7 m2 s-l, Q, = 122.3 kJmo!-‘, Dg= 11.3.10-4m2s-‘, Q, = 252 kJmo!-’
17
69Cl
3.0. 10-3
180.0
1213...1863
llom&* polycry~tals; 99.95%; lathe sectioning
17
71Al
-
-
1226...1868
l13Sn; polycrystals; 99.7%; lathe sectioning; two-exponential tit: 0: = 3.8 . lo-* m2 s-l, Q, = 132.3 kJmo!-‘, 0: = 9.5. 10m4m2 s-l, Q2 = 289.7 kJ mol-‘; seealso [65Gl]
17
65A1
113c&.
-
7751
cu
Sn
D~8.8.1()-~~m~s-* 4.9.10-13m2s-1 8.9. lo-l3 m2s-’ 1.8. lo-l2 m2s-’ 1.2.10-l1 m2s-’
1245 1388 1481 1581 1798
polyciystals; 99.97%; lathe sectioning; isotope effect also studied; D values agree with [65Al]
Le Claire
Landolt-B6mstci New Series W/2(
Ref. p. 2031 Solute
3.2.4 Impurity diffusion in titanium group metals
Do
e
10-4m2s-1
kJmol-l
Matrix: titanium (fi-Ti), continued P
105
Temperature range K
Method/Remarks
Fig.
Ref.
1218...1873
32p.
17
65A 1
pol&ystals; 99.9%; lathe sectioning; two-exponential tit : 07 = 3.62. IO-’ m2 s-l, Q, = 100.9 kJmol-‘, 0: = 5. 10m4 m2 s-l, Q, = 236.6 kJmol-‘; seealso [65Gl] U
2.10-3
138.1
1188 .-. 1298
U (natural); polycrystals; 99.34%; fission fragment radiography
-
67Dl
5.1 . 10-4
122.7
1173... 1473
23qJ.
-
7OP2
18
78Fl
7lL2
polycjstals; 99.62% ; residual activity -. two-exponential tit: 0: = 1.6. 10m9 m2 s-l, Q, = 89.2 kJmol-‘, 0: = 2. 10m6m2 s-l, Q, = 192.6 kJmol-’
-
-
1173**.1773
1.4. 10-6
64.1*
1173~~~1400 Pu; polycrystals; diffusion couple method; electron microprobe analysis and a-radiography; * values reassessedby present authors
18
r-zirconium Zr -
-
-
seechapter 2 on self-diffusion
19,20
Rb
1.17. 102
255.4
iO33...1136
Rb; polycrystals; out-diffusion method; possible grain-boundary influence
19
68Sl
Be
0.33
133.6
993...1120
‘Be; polycrystals; 99.99% ; grinder sectioning and residual activity
19
76Tl
Ce
3.54.10-7
106.2
923..*1123
141Ce; polycrystals; “high purity”; residual activity
20
68P2
PU
Matrix: zirconium (Zr)
Land&-Blimstein New Series III/26
3.2.4 Impurity diffusion in titanium group metals
106 Solute
Do
Q
10-4m2s-1
kJmol-’
[Ref. p. 203
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: zirconium (a-Zr), continued Ti
D = 9.4. j()-”
m2s-’
1116
44Ti; single crystal of unspecified orientation; 99.93% ; lathe sectioning
20
74Hl
V
1.12.10-8
95.9
873...1123
48V.
20
68Al
g5Nb; polycrystals; 99.99%; residual activity; self-diffusion in hcp Ti, Zr, Hf also studied
20
68Dl
182Ta.
20
58Bl
-
72Tl
20
83B2
ggMo; polycrystals; “high purity”; residual activity
20
68P2
893 ... 1083
54Mn; polycrystals; 99.5 and 99.999% ; residual activity and serial sectioning
20
73Tl
973 1071
5gFe; polycrystals; 99.93% ; lathe sectioning 5gFe; single crystal of unspecified orientation; 99.93%; lathe sectioning
-
72Hl
-
74Hl
pol&rystals; 99.84%; residual activity Nb
6.6. 10-6
131.9
Ta
1 * 102
293.1
973 ... 1073
polyc;ystals; 99.6%; residual activity 4.9. 10-j
126.0
896...1105
I c 0.2 11 c 0.2
162.7 153.3
1023...1121 1023...1121
MO
6.22. 1O-8
103.7
Mn
2.4. 1O-3
126.4
Fe
D=3.7.10-‘2m2s-1 3.5.10-l’ m2s-’
Cr
1113
5’Cr. polycrystals; 99.5 and 99.999%; grinder sectioning and residual activity 51Cr; single crystals; 99.99% ; serial sectioning; considerably lower D values reported in [65A2]
Le Claire
Land&-BBmsteil New Series 111’2h
Ref. p. 2031 Solute
107
3.2.4 Impurity diffusion in titanium group metals Temperature range K
Method/Remarks
Fig.
Ref.
D II = 2.22. 10-‘3m2s-1
765 834 871 934 980.5 983 1032 1093 1131 1133 871 980.5 1032 1131
5gFe. single crystals; 99.98%; lathe sectioning
20
88N2
1.75 . IO-l2 m2 s-l 4.70 . IO-l2 m2 s-l 3.70 IO-” m2 s-l 5.5...7.1.10-11m2s-1 6.1 . 10-l’ m2 s-l 1.68 . IO-lo m2 s-l 2.25 . 10-l’ m2 s-l 2.2~~~3.6~10-‘0m2s-’ 2.85 . 1O-1o m2 s-l D I =1f~.1O-‘~m~s-~ . 1.2. lo-” m’s11 3.4. IO-” rn2sm1 9.9 .10-l’ m2 s-l I c 1.2 .103 Ic 37 11 c 4.104
< 873 > 923 860...990
5sco, 6OCo;
20
81Kl
63Ni; single crystals of unspecified orientation; 99.93%; lathe sectioning 63Ni; single crystals; “crystal bar Zr”; lathe sectioning; Ni diffusion in Zr alloys also studied
20
72Hl
20
87H2
64CU; single crystals; 99.95%; lathe sectioning
19
75Hl
-
74Tl
-
89Tl
19
89Vl
19
71Hl
Do
Q
10-4m2s-1
kJmol-’
Matrix: zirconium (a-Z+, continued Fe
co
183.4 145.8 191.2
single crystals; 99.7 and 99.9%; microtome sectioning
D = 1.2 - 10-11 m2 s-1 4.10-11 m2s-1 9.10-l’ m2s-1 8. lo-11 m2s-’
971 1023 1074 1103
D = 1.6 . 1O-‘o m2 s-1 D’= 6. 1()-‘0m2s-’ II
1123 1123
cu
I c 0.25 11 c 0.40
154.5 148.7
888...1132 888...1132
Ag
5.1 . 10-3
187.1
1037... 1120
I c 5.9 . 10-4 11 c 6.7 1O-2
173.7 212.3
2.2 6.8. 10-2
245.0 210.0
D = 1.3 . lo-l5
m2 s-l
Ni
Au
Land&-Biimstein New Series III/26
“oAg~ polycrystals; 99.99%; serial sectioning 1063...1118 11am-k 1063...1118 single crystals; 99.996%; grinder sectioning 938...1117 (SC) “OrnAg; 895 . . .I1 17 (PC) single crystals (99.93%); polycrystals (99.993% and 99.96%); microtome and grinder sectioning 1113
rg8Au; single crystal of unspecified orientation; 99.93%; lathe sectioning Le Claire
3.2.4 Impurity diffusion in titanium group metals
108 Solute
Do
Q
10-4m2s-’
kJmo!-’
[Ref. p. 203
Temperature range K
Method/Remarks
Fig.
Ref.
1099
65Zn; single crystal of unspecified orientation;
19
7lHl
-
74Hl
19
85R2
19
59Gl
19
74Hl
19
67Vl
Matrix: zirconium (a-Zr), continued Zn
D=2.8~10-‘5m2s-’
99.93%; lathe sectioning Al
D=3.4~10-17m2s-’
1108
26Al; single crystal of unspecified orientation;
99.93%; 17
280.0
873...1073
lathe sectioning Al (ion-implanted); polycrystals;
99.8%; nuclear reaction analysis Sn
1.0. 10-e
92.1
113c&.
“u-phase”
polyc;ystals;
99...99.9%; residual activity Sb
D= l.4~~~2.6~t0-‘7m2s-1
1120
r**Sb; single crystal of unspecified orientation;
99.93%; lathe sectioning s
8.9
185.1
870...1080
J5S; polycrystals;
99.94%; serial sectioning g-zirconium Zr
-
-
seechapter 2 on self-diffusion
19
-
Rb
8.8. 10-4
153.7
1153...1303
Rb; polycrystals; out-diffusion method
19
68Sl
Be
8.33.10-2
130.2
1188...1573
‘Be; polycrystals; 99.7 and 99.99%; residual activity
19
69P1, 76Tl
Ce
-
-
1153...1873
14’Ce; polycrystals; “high purity”; residual activity; two-exponential tit: 07 = 3.16. 10m6m*s-‘, Q, = 173.3 kJmo!-‘, 0: = 42.2* 10e4 m*s-r, Q, = 310.2 kJ mol-’
20
68P2
h Claire
Land&-B6mstein New Series III/26
3.2.4 Impurity diffusion in titanium group metals
Ref. p. 2031 Solute
Do
Q
10-4m2s-1
kJmol-’
Matrix: zirconium (fi-Zr), continued Hf
Temperature range K 1190... 1943
109
Method/Remarks
Fig.
Ref.
‘81Hf.
20
87H3
polyc&stals; 99.9 and 99.99%; microtome sectioning; two-exponential fit to the [87H3] data: 0: = 2.8 . 10mgm2 s-l Q, = 107.6 kJmol-’ 0: = 0.30. 10e4 m2sm1 Q, = 251.3 kJmol-1 V
Nb
7.59. 1o-3 0.32
191.8 239.5
1143...1473 1473... 1673
8.9. 1O-5
116.5
1166... 1480
-
-
1155...2031
7.8. 1O-4
153.2
1503 ... 1908
1.23. 1O-4
131.9
1167... 1433
Ta
5.0. 10-5
113.0
1173...1473
Cr
4.17.10-3
134.0
1173...1473
48~.
90Nl
20
68Al
-
82Pl
g5Nb; polycrystals; 99.94% ; lathe sectioning; two-exponential tit to the [63Fl] data: 0: = 2.7 . IO-’ m2 s-l Q, = 116.9 kJmol-’ 0: = 0.26. 10m4m2se1 Q, = 238.4 kJmol-‘; self-diffusion in j3-Zr also studied g5Nb; polycrystals; residual activity g5Nb; polycrystals; 99.77%; serial sectioning
20
63Fl
policrystals; 99.84%; residual activity 48V; polycrystals; 99.8%; lathe sectioning; V and Zr diffusion in Zr - V alloys also studied
9ONl
-
69Fl
-
73T2
“‘Ta; polycrystals; 99.6 %; residual activity
20
58Bl
51Cr; polycrystals; 99.7 %; residual activity
-
67Pl
(continued)
Land&-BBmstein New Series III126
Le Claire
310 Solute
3.2.4 Impurity diffusion in titanium group metals Do
Q
10-4mZs-’
kJmol-’
[Ref. p. 203
Temperature range K
Method/Remarks
Fig.
Ref.
51Cr. polydrystals; 99.92’..99.999%; serial sectioning s’Cr. polydrystals; “high purity”; lathe sectioning; electro-mobility and effective valence also determined
20
79Nl
-
8921
ggMo; polycrystals; 99.7%; residual activity ggMo; polycrystals; “high purity”; residual activity; two-exponential fit: 07 = 1.99. lo-’ m’s-‘, Q, = 147.4 kJ mol-‘, 0: = 2.63 . 10e4 mz s-l, Q2 = 285.9 kJ mol-’
-
67Pl
20
68P2
20
67Pl
20
73Tl
-
79P2
Matrix: zirconium (BZr), continued Cr
MO
w
7.10-3
142.3
1187.+.1513
3.1
219.0
1630...1910
3.63.10-* 1.29
185.9 243.7
1173...1473 1628...1833
-
-
1173...1873
0.41
233.6
1173...1523
1SSw.
polyc;ystals; 99.7 % ; surface decrease Mn
Fe
5.6. 1O-3
138.2
1225... 1420
5.38. IO-’
140.6
1173...1473
9.1 . 10-3
113.0
1173..+1673
7.4. 10-J
108.0
1176...1886
54Mn; polycrystals; 99.5 and 99.999%; residual activity 54Mn; polycrystals; 99.99%; serial sectioning; Zr and Mn diffusion in Zr-Mn alloys also studied
“Fe; polycrystals; 99.7%; residual activity 5gFe. 20 polycrystals; “high purity”; lathe sectioning; Co and Fe diffusion in Zr-Nb alloys and isotope effect for Co in j3-Zr also studied
67Pl
87Hl
(continued)
Le Claire
Landolt-BCmstein New Series 111’26
Ref. p. 2031 Solute
3.2.4 Impurity diffusion in titanium group metals
Do
Q
10-4m2s-1
kJmol-’
Matrix: zirconium @-Zr), continued Fe 6.2. 10-3110.9
co
Ag
Sn
111
Temperature range K
Method/Remarks
Fig.
Ref.
1557... 1950
5gFe; polycrystals; “high purity”; lathe sectioning; electro-mobility and effective valence also determined
-
89Zl
6Oco; polycrystals; 99.99% ; lathe sectioning 57co. polyciystals; “high purity”; lathe sectioning 6OCo; polycrystals; “high purity”; lathe sectioning; electro-mobility and effective valence also determined
20
69Kl
-
87HI
-
89Zl
“‘Ag; polycrystals; 99.99%; serial sectioning and residual activity llomAg* polycryitals; “high-purity”; lathe sectioning; two-exponential Iit: 0: = 4.2. 10m8m2 s-l, Q, = 132.3 kJmol-‘, 0: = 190.5 . lop4 m2 s-l, Q, = 324.4 kJ mol- 1; isotope effect also studied
-
74TI
I9
82Ml
I9
59GI
19
7OVl
19
67VI
3.26. 1O-3
91.4
1193 ... 1878
3.3. 10-3
92.0
1193.*. 1741
4.7. 10-3
96.5
1600... 1950
5.7. 10-4
136.9
1224... 1463
-
-
1199... 1988
5.0. 10-3
163.3
“P-phase”
113&.
polycjstals; 99...99.9%; residual activity 0.33
139.4
1223++.1473
32~.
pol;crystals; 99.94% ; residual activity 27.6
162.4
1428 ... 1523
35s.
policrystals; 99.94%; serial sectioning
Land&-Biirnstein New Series III/26
Le Claire
Solute
[Ref. p. 203
3.2.5 Impurity diffusion in vanadium group metals
112 Do
Q
10-4mZs-’
kJmo!-’
Matrix: zirconium (&Zr), continued 111.4 8.15.10-s U
Temperature range K 1223...1573
1223... 1773
-
Method/Remarks
Fig.
Ref.
23su.
-
7OPl
20
71Fl
polyc’rystals; 99.61%; residual activity 23qJ.
polycjstals; serial sectioning; two-exponential fit: D”=30.1()-10mZs-1 Q: = 82.5 kJmol-I, ’ 0: = 3.6 * 10v5 mz s-l, Q2 = 242.8 kJ mol-’ Matrix: hafnium (Hf) Hf
-
-
-
seechapter 2 on self-diffusion
21
Cr
0.14
213.9
1183+..2173 (CL-and g-Hf)
5’Cr., polycrystals; 99.99% ; residual activity
21
76Dl
co
5.3. 10-3
95.5
1106...1798 W-W
6Oco; polycrystals; 99.99%; residual activity
21
76Dl
AI
170
357.0
1023...1173
AI (ion implanted); polycrystals; 97% Hf + 3% Zr; nuclear reaction analysis
21
85R2
3.2.5 Impurity diffusion in vanadium group metals V, Nb, Ta Matrix: vanadium (V) v
-
-
-
seechapter 2 on self-diffusion
22
Ti
0.1 34.1
285.0 363.9
1373...1623 1623...2076
4gTi ; polycrystals; 99.98% ; lathe sectioning; V and Ti diffusion in V-Ti alloys also studied
22
68M1, 78Pl
Zr
81
369.2
1578...1883
g5Zr. polycrystals; 99.95% ; lathe sectioning; V and Zr diffusion in V-Zr alloys also studied
22
84Pl
Le Claire
Landolt-BCmsIein New Series III126
Ref. p. 2031 Solute
3.2.5 Impurity diffusion in vanadium group metals
Do
Q
10-4m2s-’
kJmol-’
113
Temperature range K
Method/Remarks
Fig.
Ref.
1371..*2079
‘82Ta.
22
77Pl
Matrix: vanadium (V), continued Ta
0.244
301.4
polycljstals; 99.9%; grinder sectioning Cr
9.54.10-3
270.5
1173..*1473
51Cr; polycrystals; 99.8%; residual activity
22
64Wl
Fe
0.6
295.2
1115...1444
22
65P3
0.373 274
297.3 385.9
1233... 1618 1688...2090
“Fe; single and polycrystals; 99.9 and 99.99% ; lathe and chemical sectioning; self-diffusion also studied 55Fe, “Fe; single crystals; “zone refined”; lathe and chemical sectioning; two-exponential fit to the [68Cl] data: 0: = 2.6. 10m6m’s1 Q, = 269.9 kJmol-’ 0: = 0.11 m2se1 Q2 = 411.0 kJmol-i; isotope effect also studied “Fe, Fe; single and polycrystals; detailed specification of purity in [81Al]; sectioning and electron microprobe analysis
-
68Cl
2.48 31.7
318.7 356.6
1473... 1823 1823. ..2088
co
1.12
295.0
1298... 2126
Ni
0.18
266.2
Al
8.4. lo-’
2.45. lo-’
90Nl
22
81Al
6oco* single’ crystals; 99.9 % ; grinder sectioning
22
75Pl
1175... 1948
63Ni; single and polycrystals; 99.9 % ; residual activity
22
86Pl
268.2
1273..a 1773
Al; polycrystals; X-ray diffraction method
22
85Ml
208.5
1473 .‘. 1723
32~.
22
7OVl
22
69Vl
po&rystals; 99.8 %; residual activity 3.1 . 10-Z
142.4
1320... 1520
35s.
po&rystals; 99.8%; residual activity
Land&-Biirnstein New Series III/26
Le Claire
Solute
[Ref. p. 203
3.2.5 Impurity diffusion in vanadium group metals
114 Do
Q
10-4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
235~.
22
71F2
Matrix: vanadium (V), continued LJ
1.10-4
257.1
1373.e.1773
polycjstals. residual ac&ity Matrix: niobium (Nb) Nb
-
-
seechapter 2 on self-diffusion
23
873
Li (implanted); nuclear reaction analysis (?)
-
74Bl
-
76Bl
23
71Gl
23
7OP3
23
70Rl
Zr; polycrystals; 99.9 % ; electron microprobe analysis g5Zr; single crystals; 99.97%; grinder sectioning
23
70Rl
23
78El
48v.
23
68Al
23
70Rl
23
65Ll
Li
D = 1.7. lo-l6 m2s-’
Sr
11.7
479.8
x 2040 ..* 2500 out-diffusion of snallation-uroduced *‘Sr from polycrystalline foil
Y
1.5. 10-3
232.8
1473...1873
Ti
Zr
V
Ta
9.9. 10-2
364.0
1267es.1765
0.4
370.5
1898.s.2348
0.47
364.0
1855...2357
0.85
379.4
1923...2523
2.21
355.9
1273..-1673
0.47
377.0
1898...2348
1.0
415.7
1376...2346
91y.
singie crystals; 99.8 and 99.9%; residual activity 44Ti. sing;e crystals; 99.98% ; anodizing and stripping Ti; polycrystals; 99.9 % ; electron microprobe analysis
singie crystals; 99.98%; residual activity 48V, v. polycjstals; 99.9%; surface decreaseand electron microprobe analysis 182Ta.
single’crystals; 99.76% ; lathe, grinder and anodizingstripping sectioning; self-diffusion also studied
Le Claire
Land&-BBmstein New Series III!26
Ref. p. 2031 Solute
3.2.5 Impurity diffusion in vanadium group metals
Do
Q
10-4m2s-1
kJmol-l
115
Temperature range K
Method/Remarks
Fig.
Ref.
51Cr. singlk crystals; > 99.98%; anodizing-stripping sectioning “Cr; polycrystals; 99.96%; anodizing-stripping sectioning
23
69P2
-
69P3
MO; polycrystals; 99.9%; electron microprobe analysis “MO. polycl;stals . residual actibity
23
70Rl
23
73Fl
Matrix: niobium (Nb), continued Cr
MO
W
0.3
349.6
1226... 1708
0.13
337.5
1220... 1766
92
511.0
1988. ..2455
1.3. 10-z
350.4
1973..+2298
5.10-4
383.9
2073 . ‘. 2473
185~.
23
69F2
polyciystals; 99.8 %; residual activity W; polycrystals; 99.9%; electron microprobe analysis
23
70Rl
23
62Pl
23
77Al
7.104
653.1
2175...2443
1.5
325.3
1663.‘.2373
0.14
294.3
1663...2168
Ru
29.3
460.1*
2026 . . .2342
lo3Ru; polycrystals; 99.9 % ; grinder sectioning and residual activity; * Do and Q values calculated by present authors from tabulated D values
-
79S2
co
0.74
295.2
1834...2325
23
62Pl
4.18 . IO-*
257.2
1347...2173
6OCo; polycrystals; 99.74%; residual activity analyzed by autoradiography 6OCo; single crystals; 99.98%; grinder sectioning
23
76P2
Fe
“Fe. polydrystals; 99.74%; residual activity analyzed by autoradiography “Fe, Fe; polycrystals; 99.9 % ; lathe and grinder sectioning and electron microprobe analysis
(continued) Land&Biimstein New Series III/26
L43Claire
Solute
Matrix:
co
[Ref. p. 203
3.2.5 Impurity diffusion in vanadium group metals
116
Do
Q
10-4m2s-1
kJmo!-’
Temperature range K
Method/Remarks
Fig.
Ref.
1580... 1920
co 6oco-
23
77Al
63Ni ; polycrystals; 99.82%; residual activity 63Ni, Ni; polycrystals; 99.9 % ; grinder sectioning and electron microprobe analysis
23
72Al
23
77Al
niobium (Nh), continued
0.11
274.7
single cryLa!s; 99.9%; grinder sectioning and electron microprobe analysis 9.3
336.6
1261 . ..I519
7.7.10-2
264.2
1433...2168
Pd
2.38
399.5 *
1965... 2341
Pd; polycrystals; 99.9%; electron microprobe analysis; * Do and Q values calculated by present authors from tabulated D values
-
7982
cu
D=3.71~10-14m2s-1
1829 1909
cu; polycrystals; 99.9%; electron microprobe analysis
23
77Al
Ni
1.02. IO-l3 m2s-’
Zn
5.89
411.3
x 2000 .** 2600 out-diffusion of spallation-produced 65Zn from polycrystalline foil
-
76Bl
Al
450
430.1
1700...2000
out-diffusion method
-
78Nl
Sn
0.14
330.3
2123...2663
l13Sn; polycrystals; 99.85%; lathe sectioning
23
65A3
5.1 * 10-2
215.6
1573...2073
32~.
23
68Vl
23
68V2
23
65Pl
-
7lF2
single crystals; 99.9%; residual activity 2.6. IO’
306.0
1370...1770
35s.
single and polycrystals; 99.6%; serial sectioning 8.9. lO-2
321.5
1773... 2273
235~.
polyc’rystals; 99.55% ; residual activity 5.10-6
321.1
1993..+2373
235~;
polycrystals; details of method not specified
L.e Claire
Ref. p. 2031 Solute
3.2.5 Impurity diffusion in vanadium group metals
Do
Q
10-4m2s-1 Matrix: tantalum (Ta) Ta Rb
2.9. 10-S
117
Method/Remarks
Fig.
kJmol-’
Temperature range K
-
-
seechapter 2 on self-diffusion
24
235.0
x 1700. . .3100 out-diffusion of spallation-produced Rb from polycrystalline foil
-
77Bl
i-
Ref.
cs
8.3. 1O-5
237.0
e 1700. . .3100 out-diffusion of spallation-produced Cs from polycrystalline foil
-
77Bl
Ba
0.21
334.0
z 1700. . .3100 out-diffusion of spallation-produced Ba from polycrystalline foil
-
77Bl
Sr
4.3. 10-2
338.0
E 1700 . . .3100 out-diffusion of spallation-produced Sr from polycrystalline foil
-
77Bl
Y
0.12
302.3
1473 ‘.. 1773
24
71Gl
-
77Bl
91y.
singie crystals; 99.8 to 99.9%; residual activity
I
Hf
1.6. 1O-2
352.0
z 1700. . .3100 out-diffusion of spallation-produced Hf from polycrystalline foil
Nb
0.23
413.2
1194..*2757
g5Nb; 24 single and polycrystals; 99.7 % ; lathe, grinder and anodic stripping sectioning; two-exponential fit to the [65P2] data: 0: = 2.6 . 10m6m2 s-l Q, = 382.7 kJmol-’ D!j!= 14 . 10e4 m2 s-l Q, = 511.4 kJmol-‘; self-diffusion also studied
65P2
90Nl
MO
1.8. 1O-3
339.1
2023 ... 2493
ggMo; polycrystals; residual activity
24
68Bl
Fe
0.505
298.9
$203... 1513
24
55Vl
5.9. 10-2
329.9
2053 ... 2330
method and purity not specified; polycrystals “Fe. polydrystals; lathe sectioning
24
76A2
6OCo. 24 polycjrstals; lathe sectioning; * values estimated from graphical representation of results
76A2
co
D = 1.4 +IO-l3 m2 se1 8.0. lo-l3 m2 s-l
Land&-Biimstein New Series III/26
2128* 2330*
Le Claire
Solute
[Ref. p. 203
3.2.6 Impurity diffusion in chromium group metals
118 Do
Q
10-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: tantalum (Ta), continued Ni
D = 1.1 . lo-l3 m2se1 1.14. lo-l2 m2s-’
Al
1.5
306.2
As
0.12
346.0
0.01
293.1
24 63Ni; polycrystals; residual activity; * values estimated from graphical representation of results 1750~~~2050 out-diffusion method w 1700... 3100 out-diffusion of spallation-produced As from polycrystalline foil
2053* 2330*
1970...2110
35s.
76A2
78Nl 77Bl
24
69Vl
24
71F2
24
77Sl
pol;crystals; 99.0%; residual activity 7.6 . lo-’
353.4
1873.s.2423
1.03.10-6
117.2
2186...2530
235U; polycrystals; residual activity U (nat.); polycrystals; 99.9997%; diffusion profiles deduced from fission fragment radiography
3.2.6 Impurity diffusion in chromium group metals Cr, MO, W Matrix: chromirml (Cr) Cr v
3s1*
419.0*
-
seechapter 2 on self-diffustion
25
1595...2041
48v.
25
76M2
singie crystals; 99.998% ; grinder sectioning; * Do and Q values calculated from tabulated D values; isotope effect of Cr self-diffusion also studied MO
2.7. 1O-3
242.8
1373...1693
25 ggMo; polycrystals; residual activity; possible grain boundary influence
6362
Fe
0.47 1.1 . lo+*
332.0 169.1*
1518...1686 1256...1518
“Fe; polycrystals; residual activity; * possible grain boundary influence
25
64Wl
Le Claire
Ref. p. 2031 Solute
3.2.6 Impurity diffusion in chromium group metals
Do
Q
10-4mZs-1
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix : molybdenum (MO) MO
-
-
-
seechapter 2 on self-diffusion
26
Li
0.65
141.0
1193...1243
-
75Wl
0.01
470.6
1570...1970
permeation through polycrystalline membrane; possible grain boundary influence Li (nat.); single crystals; out-diffusion
26
77Ll
Rb
27.5
555.2
2200 . ..2870
out-diffusion of spallation produced 84Rb from polycrystalline foil
-
76B3
Sr
75.8
587.2
2200 . . .2870
out-diffusion of spallation-produced %r from polycrystalline foil
-
76B3
y
1.8. lO-4
214.8
1473.+. 1873
9ly.
26
71Gl
-
76B3
singie crystals; 99.8...99.9%; residual activity out-diffusion of spallation-produced “Y from polycrystalline foil
9.33
432.5
2200 . . .2870
Zr
56.2
503.2
2200 ... 2870
out-diffusion of spallation-produced 88Zr from polycrystalline foil
-
76B3
V
2.9
473.1
1803 ... 1998
V; polycrystals; diffusion couple method and electron microprobe analysis
26
72Rl
Nb
14
452.6
2123 . ‘. 2623
26
65A4
2.9
569.4
1998. ..2453
26
72Rl
1.7. 10-Z
379.3
1973...2373,
g5Nb; polycrystals; 99.98%; lathe sectioning Nb; polycrystals; diffusion couple method and electron microprobe analysis “Nb; polycrystals; residual activity
26
73Fl
3.5. 10-4
347.5
1993..-2423
26
68Bl
1.9
473.1
2098 ... 2449
‘*‘Ta; polycrystals; residual activity Ta; polycrystals; diffusion couple method and electron microprobe analysis ls2Ta; polycrystals; grinder sectioning
26
72Rl
Ta
D = 1.09 . lo-l4 m2 s-l
Land&Biimstein New Series III/26
2373
Le Claire
79Ml
Solute
[Ref. p. 203
3.2.6 Impurity diffusion in chromium group metals
120
Do
Q
30-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
51Cr. polydrystals. residual acti;ity “Cr. singlk crystals; 99.8%; details of method not specified
26
68Bl
26
71Ml
1ssw.
-
67Al
-
68Bl
-
72Rl
26
74El
Matrix: molybdenum (MO), continued Cr
W
2.5. 10-4
226.1
1273... 1773
1.88
342.5
1273...1423
1.7
460.5 *
1973... 2533
poly&stals; serial sectioning; * Do and Q values from data of [67Al] and [64Bl] 4.5. 10-4
324.5
1973... 2423
165W.
poly&stals. residual activity W; polycrystals; diffusion couple method and electron microprobe analysis; four data points w; single crystals; electron microprobe analysis
140
569.4
2093 ..+2453
3.6
515.8
2173...2541
Re
9.7 * 10-2
396.5
1973’..2373
ls6Re; polycrystals; serial sectioning
26
64B2
Fe
0.15
346.2
1273e.a1623
73Nl
3.7 * 10-3
291.8
1200..- 1478
3.0
418.7
2213...2603
18
446.7
2123...2632
6
324.5
1273+.. 1773
26 “Fe; polycrystals; 99.96%; residual activity 5gFe. poly&ystals; 99.96 and 99.99% ; residual activity; possible grain boundary influence 6OCo; polycrystals; autoradiographic analysis 6OCo; 26 single and polycrystals; 99.98%; serial sectioning and autoradiographic analysis; rcilso [65A3] 26 polyc’rystals. residual act&ity 63Ni; single crystals; residual activity
7lM2
co
Ni
D = 2.4~~~3.2~10-16m2s-1 1623
26
74Ll
62Pl 65A4
68Bl
Landok-B6mstein New Series Ill/26
Ref. p. 2031 Solute
3.2.6 Impurity diffusion in chromium group metals
Do
e
10-4m2s-1
kJmol-’
121
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: molybdenum (MO), continued Zn
0.55
387.7
2200 ... 2870
out-diffusion of spallation-produced Zn from polycrystalline foil
-
76B3
P
0.19
337.0
2273 ... 2493
32~.
26
68Vl
26
68V3
-
74Ll
single crystals; 99.97% ; residual activity S
32*
422.9 *
2493 ... 2743
35s.
single crystals; 99.97% ; layerwise radiometric analysis (erfc solution); * values reassessedby present authors 3.4. 10-2
297.3
1238... 1443
35s.
pol&ystals . residual ac&ity ; possible grain-boundary influence Se
2.19. lo3
639.0
2200 ... 2870
out-diffusion of spallation-produced 15Sefrom polycrystalline foil
-
76B3
U
7.6. 1O-3
319.9
1773.e.2273
235U; polycrystals; 99.98%; residual activity
26
65Pl
1.3.10-6
316.5
2073 ... 2373
235~.
26
71F2
polycjrstals; details of method not specified Matrix: tungsten (IV) w
-
-
-
Ba
10.7
619.0
w 2400.9*3100 out-diffusion of spallation-produced Ba from polycrystalline foil
Y
6.7. 1O-3
285.1
1473... 1873
seechapter 2 on self-diffusion
91y.
singie crystals; 99.8 ... 99.9%; residual activity out-diffusion of spallation-produced Y from polycrystalline foil
27 -
76B2
27
71Gl
-
76B2
1.8. 1O-3
342.0
2400... 3100
Ce
2.88. 1O-2
426.0
2400...3100
out-diffusion of spallation-produced Ce from polycrystalline foil
-
76B2
Pm
6.2. 1O-2
440.0
2400...3100
out-diffusion of spallation-produced Pm from polycrystalline foil
-
76B2
Landolt-BBmstein New Series III/26
Le Claire
122 Solute
3.2.6 Impurity diffusion in chromium group metals Do
e
10-4m2s-*
kJmo!-’
[Ref. p. 203
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: tungsten (W), continued Eu
7.6. 1O-3
390.0
2400...3100
out-diffusion of spallation-produced Eu from polycrystalline foil
-
76B2
Gd
0.19
466.0
2400...3100
out-diffusion of spallation-produced Gd from polycrystalline foil
-
76B2
Tm
1.5.10-2
406.0
2400...3100
out-diffusion of spallation-produced Tm from polycrystalline foil
-
76B2
Yb
5.1 . 10-2
435.0
2400...3100
out-diffusion of spallation-produced Yb from polycrystalline foil
-
76B2
Lu
7.8. 1O-3
390.0
2400...3100
out-diffusion of spallation-produced Lu from polycrystalline foil
-
76B2
Hf
1.5. 10-Z
440.0
2400...3100
out-diffusion of spallation-produced Hf from polycrystalline foil
-
76B2
Nb
3.01
576.1
1578...2640
69P4
Ta
3.05
585.7
1578...2648
6.2
601.6
2102...2906
g5Nb; 27 single and polycrystals; sectioning by anodic stripping; self-diffusion also studied 182Ta. 27 single’and polycrystals; sectioning by anodic stripping; self-diffusion also studied ‘**Ta; 27 single crystals; residual resistivity ratio 2 ... 5 . I04; grinder and anodic sectioning
Cr
0.85
545.9
1909.*. 2658
89Kl
MO
0.05
506.6
2273 ... 2673
0.3
423.0
1973.s.2373
0.15
529.7
2281 es.2528
1.4
567.3
1909...2658
Cr; 27 single crystals; residual resistivity ratio 2 .. .5. 104; SIMS analysis; preliminary data in [87Kl]; isotope effect also studied ggMo; polycrystals; details of method not specified “MO; polycrystals; residual activity MO; single crystals; electron microprobe analysis; three data points only MO; single crystals; 27 residual resistivity ratio 2 ... 5 . 104; SIMS analysis; isotope effect also studied
Le Claire
69P4
84Al
67L2 68Bl 74El 89KI
Landolt-B6mstein New Series III!26
Ref. p. 2031 Solute
123
3.2.6 Impurity diffusion in chromium group metals
Do
Q
10-4m2s-1
kJmol-i
Fig.
Ref.
Temperature range K
Method/Remarks
27 ls3Re,‘84Re. > single crystals; 99.99% ; grinder sectioning 186Re; 27 polycrystals; details of method not specified ‘*‘jRe; 27 single crystals; residual resistivity ratio 2.. .5 . 104; grinder and anodic sectioning; similar data in [82Al]
65A5
Matrix: tungsten (W), continued 275
681.6
2939...3501
19.5
590.3
2373 . ..2673
4.0
597.0
2110...2900
Fe
1.4 ’ 10-z
276.3
1213...1513
“Fe; polycrystals; details of method not specified
27
55Vl
OS
0.64
538.4
2105...2928
191@.
27
84Al
Re
67L2 84Al
single ‘crystals. residual resistivity ratio 2 .. .5 . 104; grinder and anodic sectioning co
4.3 1.3. 10-6
418.0 210.0
1365... 1533 1673... 2324
S7Co’ single’ crystals; 99.98%; grinder sectioning
27
89Ll
Ir
0.32
506.2
2007 . . .2960
ig21r; 27 single crystals; residual resistivity ratio 2 . . .5 . 104; grinder and anodic sectioning
84Al
Ni
D = fj. lo-l5 mzsel
1913
electron microprobe analysis of W-Ni layer grown during liquid phase sintering of W-Ni
27
79M2
P
26.8
2153...2453
32p.
27
7811
27
7211
27
68Sl
-
71F2
-
77Sl
510.0
single crystals; 99.99%; in-diffusion S
2.17. 1O-5
292.2
2153...2453
35s.
single crystals; residual activity U
1.8. lo-’
389.4
2245 . . .3000
out-diffusion method; polycrystals; 99.99%
2.10-3
433.3
1973...2473
235u.
3.34.10-4
Land&-Bihstein New Series III/26
259.2
2407 . . .2608
polyc’rystals; details of method not specified U (nat.); polycrystals; 99.9998%; fission fragment autoradiographic analysis
Le Claire
[Ref. p. 203
3.2.7, 8 Impurity diffusion in Mn, Fe group metals
124 Solute
Do
Q
10-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
3.2.7 Impurity diffusion in manganese group metals Mn, Tc, Re There are no reported measurements of impurity diffusion in the manganesegroup metals.
3.2.8 Impurity diffusion in iron group metals Fe, Ru, OS Matrix: iron (Fe) The various allotropic modifications of Fe are denoted in the following way (Tc: Curie temperature, T,: melting temperature): r-f-Fe r-p-Fe y-Fe &Fe
ferromagnetic bee iron paramagnetic bee iron fee iron bee iron
T, = 1043 K) (T < T,; (T, v > T > T,; T. ” = 1183 K) (T,, > T > 6,;; T,:; = 1663 Kj Vi, > T> Ty.s; T,= 1809K) .
“.I
Fe
-
-
-
Be
5.34
218.1
6862
0.1
241.2
28 1073... 1773 ‘Be; (u and &Fe) polycrystals; 99.9%; residual activity; u-phase stabilized by x 1 wt% Be 28 1373...1623 ‘Be; polycrystals; We) 99.9%; residual activity
9.104
473.1
1438... 1593 (y-Fe)
29
65Sl
3.6. 10’
407.4
1371... 1626 We)
rssHf; polycrystals; 99.95%; residual activity 18lHf. polycjstals; 99.98%; residual activity
29
70Bl
0.75 *
264.2
1393...1653 We)
“V; polycrystals; 99.98% ; residual activity; * value reassessedby present authors
-
70Bl
124
274.0
1058...1172 (u-p-Fe) 1210+..1607 (NW 1433-e. 1563 We)
4av.
29
87Gl
-
65Sl
Hf
v
Nb
0.62
273.5
530
344.6
seechapter 2 on self-diffusion
30
68Gl
pol&ystals; 99.98%; microtome sectioning 9%; polycrystals; 99.95%; residual activity
Le Claire
Land&-BBmstcin New Series III/26
Ref. p. 2031 Solute Do
125
3.2.8 Impurity diffusion in iron group metals
Q 10-4m2s-’
Temperature range kJmol-’
Method/Remarks
1221... 1474 We)
g5Nb; polycrystals; 99.99% ; serial sectioning g5Nb; polycrystals; 99.97%; microtome sectioning
Fig.
Ref.
-
83Kl
-
85Gl
K
Matrix: iron (Fe), continued Nb
0.75
264.0
50.2
252.0
993 1025 (u-f-Fe) 1059..+ 1162
0.83
266.5
I2!)-‘-:$4 ...
D = 1.0. lo-l6 m2sm1 5.4. lo-l6 m2 s-l
(y-Fe) 1070... 1150 (a-p-Fe) 1233.a- 1669 We) 1043... 1150 (a-p-Fe)
8.52
250.8
10.8
291.8
90
271.0
37.3
885... 1174 267.4 . (1 + 0.133s2)* (a-Fe)
MO
0.3
205.1
1023... 1123 (a-Fe)
Mn
1.49
233.6
0.35
219.8
0.16
261.7
0.11*
251.6
973 ... 1033 (a-f-Fe) 1073...1173 (u-p-Fe) 1193... 1553 6-W 1082... 1174 (a-p-Fe)
0.76
224.6
Cr
(a-p-Fe and &Fe)
Land&-BBmstein New Series III/26
Le Claire
29 29
51Cr. polydrystals; 99.98%; residual activity 51Cr. poly&ystals; serial sectioning 51Cr* poly&ystal (6 mm grain size); serial sectioning; *s: ratio of spontaneous magnetization at T[K] to that at OK. “MO; polycrystals; “pure Fe”; residual activity and surface decrease; possible grain boundary influence 54Mn; polycrystals; 99.97%; residual activity
-
70Bl
29
89Hl
-
9OLl
-
66Bl
29
70Nl
29
54Mn; 29 single crystals; 99.99.**99.999%; microtome sectioning; * D" refers to purest Fe investigated (Do increases with impurity content) combined data of [73K2] (diffu- 29 sion couple; polycrystals; 1719.a. 1767 K; electron microprobe analysis; D independent of concentration for 0.. .4 % Mn) and [70Nl]
7212
73K2
Solute
[Ref. p. 203
3.2.8 Impurity diffusion in iron group metals
126
Do
Q
10-4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
30
63BI
29
63B2
-
64SI
30
6651
Matrix: iron (Fe), continued co
118
285.9
5.5
256.2
9.5
260.8
7.19
260.4
6.38
257.1
6.38
257.1
1.0
301.9
2.9. 10-2
247.4
2120. IO-** m* s- l D=358~10-23m2s-’ 2.35 . IO-** m* s-l 1.31 . IO-*’ m* s-l 3.28 . lo-** m* s-l 1.91 f IO-*O m*s-’ 5.54.1O-*O m* s-’ 7.46. IO-*’ m* se1 1.85. IO-l9 m2sP1 2.90. IO-l9 m* s-l 3.82. lo-” m* s-l 6.40.10-” m* s-’ 9.04. lo-l9 m*s-l 1.84. 10-‘8m2s-1 1.83. lo-” rn*s-l 9.30. IO-‘* m* s-l 1.33 . IO-” m* s-l 1.80 . IO-” m* s-’
6Oco; polycrystals; 99.999% ; residual activity; influence of magnetic transition on Co diffusion also studied 6OCo; 1669...1775 polycrystals; (&Fe) lathe sectioning and residual activity 1103~~~1161 6OCo; polycrystals; (a-p-Fe) 99.97%; serial sectioning 6OCo; 956...1000 single crystals; (a-f-Fe) 99.95%; 1081...1157 residual activity (a-p-Fe) 6OCo; 1702...1794 polycrystals; (&Fe) 99.95% ; lathe sectioning 1409... 1633 thin film and diffusion couple method; We) polycrystals; 99.999% ; electron microprobe analysis 1233... 1493 6Oco; polycrystals; We) 99.9 % ; residual activity single To, crystals; 6OCo. 785.5 823 1044...1177 (u-p-Fe)
824 857.5 873.5 907 926 934 945 960 963 976 976 991 993 1021 1034 1036 (u-f-Fe)
29
29
69B2, 61SI
29
75H2
29, 30 82M2
99.997% ; sputter sectioning; graphical data in [82M2]; numerical D-values tabulated in [84Kl]; deviations from Arrhenius behaviour due to influence of magnetic transition studied in detail (see Fig. 30)
(continued)
Le Claire
Land&BBmstein New Series III,/26
3.2.8 Impurity diffusion in iron group metals
Ref. p. 2031 Solute
Do
Q
10-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
127 Fig.
Ref.
Matrix: iron (Fe), continued
co
D = 5.30. lo-l7 m’s-’ 8.48 . lo-‘? m2 s-l 1.01 . IO-l6 m2 s-l 3.68 . lo-l6 m2 s-l 5.60. lo-l6 m2se1 1.68. 10-15m2s-1 -
-
29, 30
1058.5 1072 1081 1105.5 1122 1163.5 (u-p-Fe)
6Oco;
30
89Hl
29
6lHl
polycrystals; -(a-f-Fe and a-p-Fe) sputter sectioning; graphical data only; deviations from Arrhenius behaviour due to influence of magnetic transition studied in detail Ni
1.4
245.8
873 . ..953 (a-f-Fe)
1.3
234.5
1083 ... 1173 (a-p-Fe)
0.77
280.5
1203... 1323 We)
D = 3.75 . lo-” 9.96. IO-‘* 2.32. lo-l7 4.70. IO-l7
m2 s-l m2 s-l m2 s-l m2 s-l
9.9
259.2
3.0
314.0
972.6 996.7 1013.2 1032.4 (a-f-Fe) 1054... 1173 (a-p-Fe) 1409 ... 1633 (y-Fe)
1.09
296.8
1426... 1560 We)
63Ni.
single crystals; 99.97% ; residual activity and surface decrease 63Ni; single and polycrystals; 99.97%; residual activity 63Ni; polycrystals; 99.97%; residual activity (j3Ni; polycrystals; 99.999% ; residual activity
29
29
29
63Bl
29 Ni; thin film and diffusion couple method; polycrystals; 99.999% ; electron microprobe analysis; Do and 0 from combined data of [69;2] and [59Ml] 63Ni. 9 polycrystals; residual activity
29
69B2
29
78Hl (continued)
Land&-Bijmstein New Series III/26
Le Claire
Solute
[Ref. p. 203
3.2.8 Impurity diffusion in iron group metals
128
Do
Q
10-4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
788 788 833.2 833.2 877.8 877.8 922.5 968.5 1013.5 (u-f-Fe) 1048 1088 1123.3 1160 (a-p-Fe)
‘j3Ni; polycrystals (3.5 mm grain size); 99.999%; sputter sectioning; deviations from Arrhenius behaviour due to influence of magnetic transition
29
89Cl
63Ni. polydrystals (3.5 mm grain size); 99.999% ; sputter and microtome sectioning
29
lo3Pd; 29 polycrystals; 99.97% ; residual activity (and grinder sectioning); self-diffusion in Pd -Fe alloys also studied
Matrix: iron (Fe), continued Ni
D=1.85-10-21 mzswl 1.09. 10m2’ m2se1 1.84. 10mzom2sb1 8.69 . lo-*’ m2 s-l 1.20. lo-l9 m2se1 9.59 . 10V20m2 s-l 7.09. lo-l9 m2 s-l 3.86.10-‘* m2 s-’ 3.19 .10-l’ m2 s-l
D= 1.55*10-16m2s-1 5.69 * lo-l6 m2s-’ 1.96. lo-l5 m2s-’ 4.82 . lo-” m2 s-l Pd
0.41
280.9
1373..*1573 We)
Pt
2.7
296.0
1233.e.1533 (y-Fe)
Cu
1.8
295.0
1183...1293 (~-Fe)
D = 1.8 . 1O-15 m2 s-l 2.2. lo-” m2 s-’ 5.1 . lo-l5 m2 s-’
1127.5 1140 1174.6 (u-p-Fe) 1558...1641 We)
2.86
306.7
D = 4.81 11O-18 m2s01 9.55.10-‘* 1.78.10-” 4.10.10-” 8.26.10-l’
m2sw1 m2sw1 m2 s-l m2 s-l
300
283.9
0.19
272.6
4.16
305.0
963 978 993 1008 1024 (a-f-Fe) 1045...1173 (a-p-Fe) 1198...1323 (y-Fe) 1378... 1483 (y-Fe)
193mpt;
77Fl
29
73M3
28
66S1
28
68Rl
polycrystals; residual activity Cu; polycrystals; electron microprobe analysis 64cu. single or bicrystals; 99.91%; grinder sectioning 64Cu; single crystals; 99.91% ; grinder sectioning Cu; single crystals; 99.999% electron microprobe analysis; solubility of Cu also determined
28
28
7782
28 Cu; polycrystals; 99.999% ; electron microprobe analysis 64Cu; polycrystals; 99.96%; residual activity
Le Claire
28 28
78Ml
Landok-B6mstein New Series III/26
Ref. p. 2031 Solute
129
3.2.8 Impurity diffusion in iron group metals
Do
Q
10-4mZs-1
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
I
Matrix: iron (Fe), continued 1.95 * 103
288.9
1021... 1161 (a-p-Fe)
230
278.0
973 ... 1033 (cl-f-Fe)
38
259.2
1053... 1173 (ct-p-Fe)
D = 9.58 . IO-‘* 2.69.10-l’ 5.49.10-l’ 1.58 . lo-l6
m2 s-l
m2 s-l m2 s-l m2 s-l
“‘Au; polycrystals; 99.999% ; residual activity
31.0
261.2
972.1 997.8 1012.8 1034.4 (a-f-Fe) 1055...1174 (cl-p-Fe)
Zn
60
262.6
1072+*.1169 (u-p-Fe)
Zn; single crystals; residual resistivity ratio > 3000; electron microprobe analysis; chemical diffusion below Tc also measured
28
81R1
Al
1.8
228.2
1003... 1673
Al; polycrystals; 99.9 % ; X-ray diffraction method; no influence of a-y transition observed (?)
-
83Al
Si
1.7
229.1
28
89Bl
0.07
243.0
x 1100... 1173 Si; (a-p-Fe) polycrystals; 1273... 1463 electron microprobe analysis on Fe/Fe 1 . . .3.3 % diffusion We) couples; D values from extrapolation of chemical diffusion
5.4
232.4
28
72T2
&
Au
Sn
973 ... 1033 (a-f-Fe) 1073.+.1183 (a-p-Fe) 1300... 1510 We)
2.4
221.9
9.10-4
175.8
6.1 . lo4
316.4
896... 1023 (a-f-Fe)
0.845
261.7
1197...1653 (y-Fe)
Land&-Biimstein New Series III/26
“‘Ag; polycrystals; serial sectioning 11om& polycryitals; 99.97 %; residual activity
28
71Bl
28
73El
28 28
63Bl
28
l13Sn.
polycljstals . residual actibity 28 ‘13Sn; polycrystals; 99.8%; residual activity l13Sn; single crystals; 99.98% residual activity l13Sn; polycrystals; > 99.97% ; serial sectioning
Le Claire
28
75M3
28
84Hl
28
86Kl
3.2.8 Impurity diffusion in iron group metals
130 ;olute
Do
Q
10-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
3zp.
[Ref. p. 203 Fig.
Ref.
Matrix: iron (Fe), continued 3
4s
Sb
s
U
6.3. lo-*
193.4
1223...1573 We)
8.10’
314.0
1.38 . 10’
332.0
2.87. lo*
271.O
783...923 (cc-f-Fe) 932...1017 (a-f-Fe) 1078...1153 (u-p-Fe)
4.3
219.8
0.58
246.6
4.4. lo*
270.0
1040...1173 (a-p-Fe)
80
269.9
773..-873 (u-f-Fe)
2.7
205.0
0.5
209.3
1.7
221.9
34.6
231.5
2.10’
347.6
x 1050.. . 1150 sulfurization and desulfurization measured by electrical resistance (u-p-Fe) 1208... 1298 on polycrystalline foils (y-Fe) 35s. 1223...1523 polycrystals. (94 residual actibity 35s. 973...1173 polycrystals; (a-Fe) 99.996% ; residual activity surface segregation rate studied 770... 1000 with Auger electron spectros(u-f-Fe) copy on single crystals
7.10-s
133.2
28 po&rystals; 99.99% ; residual activity surface segregation rate studied 28 by Auger electron spectroscopy 32~. 28 pol;crystals* residual ac&ity
1223.s.1653 diffusion couple method; (u-stabilized) 0.5 ... 5% As; u-stabilized; electron microprobe analysis 1323..+1573 diffusion couple method; 0...1.2% As; (94 electron microprobe analysis
1223...1348 We)
124Sb; single and polycrystals; residual activity Sb (ion implanted); nuclear reaction analysis
thin layer method and fission fragment radiography; polycrystals
-
64M2
81Ll 83Ml
76B4
28
28
75Bl
28
78M2
-
7OWl
28
71H2
28
72Gl
28
86A2
-
67Dl
Matrix: ruthenium (Ru) - No data available Matrix: osmium (OS)
- No data available
Le Claire
Land&-LGmstein New Series III!26
Solute
131
3.2.9 Impurity diffusion in cobalt group metals
Ref. p. 2031 Do
Q
10-4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
3.2.9 Impurity diffusion in cobalt group metals Co, Rh, Ir Matrix: cobalt (Co) Diffusion data are available for ferromagnetic fee Co (f-Co) and for paramagnetic fee Co (p-co). The Curie temperature is Tc = 1393 K. -
-
co
-
v
D=3.41.10-16m2s-’ 6.56 . lo-l6 m2 s-l 2.46. lo-l5 m2s-’
1273 1328 1388 (f-Co)
D = 9.34. lo-l5 1.65 . lo-l4 2.39. IO-l4 3.92 . lo-l4
m2 s-l m2 s-l m2 s-l m2 s-l
3.15.10-2
232.4
1.1 .1o-2
217.7
0.04
239.4
1433 1473 1523 1563 (P-CO) 1133...1378 (f-Co) 1424... 1519 (P-CO) 1139*** 1510 (f and p-Co)
0.11
253.3
1409... 1629 (P-CO)
0.34
259.6
0.16
248.7
1.25
301.9
lOgI... T, (f-Co) TC... 1573 @-Co) 1425...1673 (P-CO)
0.34
269.2
Mn
Fe
Ni
seechapter 2 on self-diffusion
31
48v.
31
86K2
policrystals; 99.9985%; residual activity ; each D value is the mean of two results
1045.+. 1321 (f-Co)
31
7711
54Mn* polycjstals; 99.95%; residual activity
31
5gFe; single crystals; 99.97% ; residual activity diffusion couple method; polycrystals; 99.999% ; electron microprobe analysis; Do and Q values from combined data of [69B2] and [55Ml] 5gFe. sing16crystals; residual activity
31
65A7
31
69B2
31
74B2
63Ni; polycrystals; 99.5%; surface decrease
-
59Ml
63Ni.
31
62Hl
-
-
polycrystals; 99.2%; residual activity; 63Ni and 6oCo diffusion in Co - Ni alloys also studied (continued)
Landolt-B6mstem New Series III/26
Le Claire
Solute
[Ref. p. 203
3.2.10 Impurity diffusion in nickel group metals
132 Do
Q
10-4mZs-1
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: cobalt (Co), continued Ni
1465... 1570 (P-CO) 1500...1690 @-Co>
0.10
252.0
3.35
297.3
0.40
282.2
1409... 1643 @-Co)
Pt
0.65
219.3
CU
z 1.0
Zn
S
31 31
65Hl
31
69B2
1354...1481 1g3mpt; (f- and p-Co) polycrystals; 99.99% ; residual activity
31
73M3
x 275
1158, 1273 (f-Co)
Cu; polycrystals; 99.5%; 0..*5% cu; in-diffusion method; electron microprobe analysis; two temperatures only
31
84A2
0.12
266.7
1081... Tc (f-Co)
65Zn, single crystals; residual activity
31
74B2
0.08
254.5
1.3
226.1
T, ... 1573 @-Co> 1423... 1523
35s.
31
64Pl
63Ni; polycrystals; 99.5%; residual activity; 63Ni and 6oCo diffusion in Co-Ni alloys also studied Ni; diffusion couple method; polycrystals; 99.999% ; electron microprobe analysis
polycrystals; 99.99%; residual activity
@-Co)
Matrix: rhodium (Rh) - No impurity diffusion data available; for self-diffusion seechapter 2 Matrix: iridium (Ir)
- No impurity diffusion data available; for self-diffusion seechapter 2
3.2.10 Impurity diffusion in nickel group metals Ni, Pd, Pt Matrix: nickel (Ni) Ni Ce
0.66
-
-
seechapter 2 on self-diffusion
254.6
973...1370
14’Ce; polycrystals; 99.99%; grinder sectioning; non-Gaussian diffusion profiles
Le Claire/Neumann
32, 33 71Pl
Land&BBmstein New Series Ill:26
Ref. p. 2031 Solute
3.2.10 Impurity diffusion in nickel group metals
Do
Q
10-4m2s-1
kJmol-l
133
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: nickel (Ni), continued Nd
0.44
250.5
973 ... 1373
147Nd; polycrystals; 99.99% ; grinder sectioning; non-Gaussian diffusion profiles
-
71Pl
Hf
1.8*
251.0*
1023.‘. 1423
Hf; polycrystals; 99.99% ; electron microprobe analysis (Ni/ Ni 0.5; 3.8% Hf sandwich samples); * estimated values
-
72Bl
V
0.87
278.4
1073... 1573
497.
-
68M2
‘ICr; polycrystals; 99.95%; lathe sectioning; distinct data scattering
-
64M3
185~.
-
64M5
32
78V3
pol&rystals; 99.99% ; residual activity; grinder sectioning Cr
1.1
272.6
W
2.0
299.4
1373...1541
polyc;ystals; 99.95%; lathe sectioning 2.87
308.1
1346... 1668
181~.
single’crystals; 99.98% ; lathe sectioning
, Fe
1.0
269.4
1478... 1669
“Fe; single crystals; 99.999% ; grinder sectioning
32
71B2
co
2.77
285.1
1335.., 1696
To; single crystals; 99.98%; lathe sectioning
32
78V3
Pt
2.5
286.8
1354... 1481
193Pt; polycrystals; 99.99% ; residual activity
-
73M3
64cI.I. polyc;ystals; 99.95% ; lathe sectioning
-
64M4
‘.
cu
0.57
258.3
1327..: 1632:
(continued)
Land&-Biirnstein New Series III/26
Neumann
iolute
[Ref. p. 203
3.2.10 Impurity diffusion in nickel group metals
134 Do
Q
10-*mzs-’
kJmo!-’
Temperature range K
Method/Remarks
Fig.
Ref.
64Cu; polycrystals; 99.95% ; residual activity Cu; polycrystals; 99.95%; sectioning; atomic absorption analysis
-
65A8
32
84Tl
-
76T2
32
78Vl
-
55Kl
33
81G2
32
78V2
-
81Gl
33
88N3
32
83M2
Matrix: nickel (Ni), continued 0.724
255.4
1123...1323
0.61
255.0
1080...1613
8.25
282.2
1123...1323
8.94
279.4
1297.s. 1693
9U
2.0
272.1
1173..*1373
Al
1.0
260
914...1212
In
6.78
270.5
1274+..1659
3U
4g
1.1
Ge
2.1
250
264
777..*1513
939 ... 1675
“OAg; single crystals; 99.99% ; residual activity 11oAgt 105Ag* single crystals’; 99.98% ; lathe sectioning ‘98A,,, polycjstals; 99.98%; autoradiography Al; single crystals; 99.99% ; sputter sectioning; SIMS analysis (27Al+ signal) l141n.
single’crystals; 99.98% ; lathe sectioning In; single crystals; 99.99% ; sputter sectioning; SIMS analysis (‘l’In+, 131n+ signals); two-exponential tit of the [78V2] and [81Gl] data: 0: = 1.26 * 10v4 m2s-‘, Q, = 251 kJmo!-‘, 0: = 1.9m2s-‘, Q2 = 397.8 kJ mol-’ 68Ge (implanted); single crystals; 99.99% ; grinder and sputter sectioning
Neumann
Landolt-B6mstein New Series III/26
solute
135
3.2.10 Impurity diffusion in nickel group metals
Ref. p. 2031 Do
e
10-4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: nickel (Ni), continued 3n
4.56
267.2
1242.e. 1642
l13Sn; single crystals; 99.98%; lathe sectioning
32
79Vl
!LS
1.39
251.8
1239.~. 1634
73As; single crystals; 99.98% ; lathe sectioning
32
79V2
Sb
3.85
264.0
1203... 1674
“‘Sb; single crystals; 99.98%; lathe sectioning
32
76Vl
s
1.4
219.0
1078.e. 1495
35s.
32
75Vl
‘23Te; single crystals; 99.99% ; microtome sectioning
32
89Nl
235~.
-
7121
68B2
single crystals; 99.98%; lathe sectioning Te
2.6
254.0
1135... 1553
u
1.0
236.1
1248... 1348
polyc’rystals; 99.998% ; autoradiography; solubility also measured: c,= 6.2exp(-83.7kJmol-‘/RT) Pu
0.17
213.5
1298.a. 1398
239Pu; polycrystals; 99.9%; autoradiography; solubility also measured: c, increases from 30 ppm at 1300 K to 80 ppm at 1400 K
Matrix: palladium (Pd) Pd
-
-
-
seechapter 2 on self-diffusion
34
Fe
0.18
260.0
1373... 1523
5gFe; polycrystals; 99.95% ; grinder sectioning
34
77Fl
-
seechapter 2 on self-diffusion
1273..a 1673
Fe; polycrystals; 99.99% ; electron microprobe analysis (Pt/Pt 2.06 % Fe sandwich samples)
34 -
78Bl
Matrix: platinum (Pt) Pt
-
Fe
0.025
243.4
(continued) Landolt-BBmstein New Series III/26
Neumann
[Ref. p. 203
3.2.11 Impurity diffusion in noble metals
136
Temperature range K
Method/Remarks
Fig.
Ref.
Uatrix: platinum (Pt), continued :0 19.6 310.7
1023... 1323
To; polycrystals; 99.9%; surface decreasemethod; distinctly curved Arrhenius plot
-
68Kl
4g
0.13
258.1
1473...1873
Ag; polycrystals; 99.99% ; electron microprobe analysis (Pt/ Pt 2.4% Ag sandwich samples)
78Bl
4u
0.13
252.0
850...1265
199Au; single crystals; 99.99% ; sputter sectioning
78Rl
41
1.3.10-3
193.6
1373..+ 1873
Al; polycrystals; 99.99%; electron microprobe analysis (Pt/ Pt 1.23% Al sandwich samples)
iolute
Do
Q
10-4m2s-1
kJmol-’
34
78Bl
3.2.11 Impurity diffusion in noble metals Cu, Ag, Au Matrix: copper (Cu) cu -
-
-
seechapter 2 on self-diffusion
35...38
Be
0.66
195.9
973 ..* 1348
Be; polycrystals; purity not specified; X-ray diffraction analysis
36
73F3
Ii
0.693
196
983 .** 1283
Ti; polycrystals; 99.998% ; electron microprobe analysis (Cu/Cu 2 ... 3 % Ti sandwich samples)
-
7712
V
2.48
215
995...1342
4av.
-
77Hl
-
7OS2
pol&rystals; 99.998%; residual activity; grinder sectioning; anomalous diffusion profiles Nb
2.04
251.5
1080...1179
95Nb; polycrystals; 99.999% ; residual activity; grinder sectioning; penetration profiles only 15 pm
Neumann
Land&-BBmsfein New Series III./26
Ref. p. 2031 Solute
3.2.11 Impurity diffusion in noble metals
Do
Q
10-4m2s-1
kJmol-’
137
Temperature range K
Method/Remarks
Fig.
Ref.
51Cr. polylrystals; 99.995%; residual activity 51Cr; polycrystals; 99.99% ; residual activity; grinder sectioning; near-surface effect for x < 15 urn 51Cr. polycrystals; 99.998%; residual activity; grinder sectioning; anomalous diffusion profiles ‘Wr; single crystals; 99.999% ; microtome sectioning; long Gaussian profiles; D(1200 K) = 1.4. lo-l3 m2s-’
-
71B3
-
71Sl
-
77Hl
-
83Rl
Mn; polycrystals; purity not specified; X-ray diffraction analysis 54Mn’ polyciystals; 99.998%; residual activity; grinder sectioning; anomalous diffusion profiles 54Mn; single crystals; 99.998% ; electrochemical sectioning
36
73F2
-
77Hl
-
79M3
59Fe; single crystals; 99.998%; lathe sectioning s9Fe* singlk crystals; 99.998% ; lathe sectioning 59Fe; single and polycrystals; 99.995%; residual activity
35
58Ml
-
61Ml
-
71B3
Matrix: copper (Cu), continued Cr
Mn
Fe
1.02
224.0
1073... 1343
1.6
240.7
IlOO...
0.337
195
999 ... 1358
-
-
1195... 1202
0.74
195.5
973...1348
1.02
200
873 ... 1323
1.42
204.3
773...976
1.4
216.9
992... 1347
1.01
213.3
990... 1329
1.36
217.7
923 ... 1343
(continued)
Land&-Biimstein New Series III/26
Neumann
Solute
[Ref. p. 203
3.2.11 Impurity diffusion in noble metals
138 Do
Q
10W4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
“Fe; single crystals; 99.999% ; electrolytical sectioning Fe; polycrystals; specpure; resistometric method
-
73Bl
-
78Sl
Matrix: copper (Cu), continued 1.3
215.6
1005... 1297
1.13
214.1
1063*.* 1274
Ru
8.5
257.5
1221... 1335
lo3Ru; single crystals; 99.999% ; electrolytical sectioning; solubility determined from the erfc-profile: c, = 0.018 * exp(- 100.5 kJ mol-‘/RT)
35
73Bl
co
1.93
226.5
975 ... 1351
35
58Ml
1.69
225.7
1163...1306
-
72B2
0.43
214.3
640 . . a848
6OCo; single crystals; 99.998% ; lathe sectioning 6OCo; polycrystals; specpure; lathe sectioning 6OCo; single crystals; 99.999% ; sputter sectioning and SIMS analysis (sgCo+ signal) two-exponential tit of the [58Ml] and [84Dl] data: Dy= 0.74*10m4m’s1r, Q, = 217.2 kJmol-‘, 0: = 736 . 10m4m2 s-l, Q, = 312.8 kJmol-’
-
84Dl
38
88N3
Fe
Rh
3.3
242.8
1023... 1348
Rh; polycrystals; purity not specified; X-ray diffraction analysis
35
72F2
Ir
10.6
276.4
1185...1303
1921r.
35
78Kl
35
58Ml
singld crystals; 99.99% ; lathe sectioning Ni
2.7
236.6
1016+..1349
63Ni ; single crystals; 99.998% ; lathe sectioning
(continued)
Neumann
LandolbB6mstein New Series III/26
Ref. p. 2031 Solute
3.2.11 Impurity diffusion in noble metals
Do
Q
10-4m2s-1
kJmol-’
Matrix: copper (Cu), continued Ni 3.8 237.8
139
Temperature range K
Method/Remarks
Fig.
Ref.
968 ... 1334
63Ni.
-
5911
-
64M4
-
71F3
-
72A2
-
83M3
38
88N3
1.7
231.5
1172-s. 1340
2.3
235.3
973.e. 1323
1.94
232.8
1128...1328
0.76
225.0
613...950
single crystals; 99.99% ; lathe sectioning 63Ni s polydrystals; 99.99% ; lathe sectioning Ni; polycrystals; purity not specified; X-ray diffraction analysis 66Ni; polycrystals; 99.99% + 99.999%; lathe sectioning Ni; single crystals; 99.999% ; sputter sectioning; SIMS analysis; two-exponential tit to the [58Ml, 64M4, 72A2, 8311131 data: 0: = 0.7.10e4 m2se1, Q, = 225 kJmol-‘, 0: = 0.025 m2s-‘, Q, = 299.3 kJ mol-’
Pd
1.71
227.6
1080... 1320
lo3Pd; single crystals; 99.999%; lathe sectioning
35
63Pl
Pt
0.67
233
1023 ... 1348
-
72Fl
0.56
233
1149... 1352
Pt; polycrystals; purity not specified; X-ray diffraction analysis isrpt, igspt; single crystals; 99.999% ; microtome sectioning
35
82Nl
0.63
194.7
37
60Nl
0.61
194.7
-
70B2
0.574
195.0
(1053 ... 1353) ““Ag* single ‘crystals; specpure; lathe sectioning (823 ... 1273) “OAg; single and polycrystals; 99.99% ; residual activity 1049... 1352 “o& single and polycrystals; 99.99% ; lathe sectioning and residual activity
-
7262
Ag
Land&-Biimstein New Series III/26
Neumann
Solute
[Ref. p. 203
3.2.11 Impurity diffusion in noble metals
140 Do
Q
10-4mZs-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: copper (Cu), continued Au
Zn
Cd
(1053 ... 1353) lg*Au; single crystals; specpure; lathe sectioning 195Au. 1085... 1342 single crystals; 99.99% ; lathe sectioning ig6Au; 993 ..* 1350 single crystals; 99.999%; microtome sectioning “‘Au; 633 . ..982 single crystals; 99.999% ; sputter sectioning
0.69
210.6
0.897
212.5
0.537
205.6
0.0803
191.2
0.34
190.9
878...1322
0.41
192.8
1168,122O
0.73
198.9
1165...1348
0.24
188.8
1073..*1313
0.28
189.3
993...1193
0.935
191.3
998...1223
0.73
188.8
(1053.s.1353)
I.27
194.6
1032... 1346
1.2
194
983...1309
35, 38 60NI
-
77Gl
-
87FI
38
65Zn; single crystals; specpure; lathe sectioning 65Zn; single crystals; 99.999% ; lathe sectioning; two data points only 65Zn* polyciystals; 99.99% ; lathe sectioning 65Zn; polycrystals; 99.99% ; lathe sectioning Zn; polycrystals; specpure; resistometric method
37
57Hl
-
67P3
-
69K2
-
72A2
-
79D2
“‘Cd; single crystals; 99.98%; lathe sectioning “%d; single crystals; specpure; lathe sectioning logCd; single crystals; 99.99% ; lathe sectioning “‘Cd; polycrystals; 99.998% ; grinder sectioning
36
58Hl
-
60Nl
-
7262
-
82Hl
Neumann
Landolt-B6mstein New Series 1111’26
Ref. p. 2031 Solute
141
3.2.11 Impurity diffusion in noble metals
Do
Q
10-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: copper (Cu), continued Hg
0.35
184.2
(1053 ... 1353) ‘03Hg; single crystals; specpure; lathe sectioning
36
60Nl
Al
0.08
181.3
973 ..- 1348
37
73F4
Ga
0.78
196.4
-
60Nl
0.523
192.7
-
71Kl
0.58
193.8
37
77F2
1.30
193.6
37
7262
1.87
196.4
-
78K2
0.219
178
(1053 ... 1353) 72Ga; single crystals; specpure; lathe sectioning 1153 ... 1352 67~~. polycjstals; 99.99% ; lathe sectioning 973...1323 Ga; polycrystals; purity not specified; X-ray diffraction analysis 1051... 1351 1141~. single’ and polycrystals ; 99.99% ; lathe sectioning “41~. 1071... 1354 polycjrstals; 99.999% ; microtome sectioning 602... 1351 In; single crystals; 99.9998% ; sputter sectioning; SIMS analysis (lisIn+ signal) two-exponential tit to the [7262, 78K2, and 83Gl] data: 07 = 0.29. 10m4m2 s-l, Q, = 179.6 kJmol-‘, 0: = 0.311 rn’s-l, Q, = 295.4 kJ mol-’
-
83Gl
38
88N3
In
Al; polycrystals; purity not specified; X-ray diffraction analysis
Tl
0.71
181.3
1058... 1269
‘04T1; single crystals; 99.999% ; lathe sectioning
37
63Kl
Si
0.07
171.7
973 ... 1323
Si; polycrystals; purity not specified; X-ray diffraction analysis
37
73F3
Ge
0.397
187.4
975 ..’ 1289
6*Ge. single crystals; 99.998%; lathe sectioning
36
70R2
Landolt-Biimstein New Series III/26
Neumann
(continued)
Solute
[Ref. p. 203
3.2.11 Impurity diffusion in noble metals
142 Do
Q
10-4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
68Ge; polycrystals; 99.99%; lathe sectioning
-
71Kl
36
73Gl
-
74Fl
-
79Kl
210Pb; single crystals; 99.99% ; lathe sectioning
36
77Gl
32~.
37
76Sl
37
6ONl
-
70Kl
124Sb; single crystals; 99.99% ; lathe sectioning ’ 24Sb; single crystals; 99.99%; lathe sectioning 124Sb; polycrystals; 99.999% ; microtome sectioning
36
6011
-
73Gl
-
79Kl
2o’Bi; single crystals; 99.99% ; lathe sectioning
37
77Gl
Matrix: copper (Cu), continued Ge
0.315
185.5
1111. ..I326
Sn
0.842
188.2
1011..a 1321
0.82
187.6
973.e. 1348
0.67
184.4
1018...1355
Pb
0.862
182.4
1006...1225
P
3.05.10-3
136.1
847... 1319
1lQ.
single’crystals; 99.99% ; lathe sectioning Sn; polycrystals; purity not specified; X-ray diffraction analysis “%n; polycrystals; 99.999% ; microtome sectioning
single crystals; 99.999% ; microtome sectioning As
Sb
Bi
0.12
175.8
0.202
176.4
(1053 ... 1353) 76As; single crystals; specpure; lathe sectioning 1086...1348 73As* polycrystals; 99.99% ; lathe sectioning and residual activity
0.34
175.8
873 ... 1275
0.616
182.7
1011.a. 1321
0.48
179.6
1049...1349
0.766
178.1
1074...1348
Neumann
Ref. p. 2031 Solute
143
3.2.11 Impurity diffusion in noble metals
Do
Q
10-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
1073... 1273
35s.
36
691112
Matrix: copper (Cu), continued S
23
206.6
single crystals; 99.999%; electrolytical sectioning Se
1.0
180.5
878...1150
‘?Se (implanted); single crystals; 99.999% ; microtome sectioning
37
89Rl
Te
0.97
180.5
822... 1214
“rTe (implanted); single crystals; 99.999% ; microtome sectioning
37
89R.I
Matrix: silver (Ag) Ag
-
-
seechapter 2 on self-diffusion
Ti
198
1051..* 1220
Ti; polycrystals; 99.999%; electron microprobe analysis (Ag/Ag 0.23; 0.45 % Ti sandwich samples)
39,40 79M4
1.33
V
2.72
209
1012..* 1218
49.
/
-
19M4
-
79M4
39
81Nl
-
79M4
po&rystals; 99.999%; residual activity; grinder sectioning; non-Gaussian diffusion profiles 3.29
210
1023... 1215
1.1
192.6
976 ... 1231
4.29
196
883 ... 1212
Cr
Mn
Land&-BBmstein New Series III/26
‘Cr. polyirystals; 99.999% ; residual activity; grinder sectioning; non-Gaussian diffusion profiles 51Cr* singlb crystals; 99.9999%; microtome sectioning; solubility determined from the erfc-profile: c, = 1620 * exp(- 170.0 kJmol-‘/RT) s4Mn; polycrystals; 99.999% ; residual activity; grinder sectioning; non-Gaussian diffusion profiles
Neumann
3.2.11 Impurity diffusion in noble metals
144 Solute
Do
Q
10-4m2s-1
kJmol-’
Temperature range K
[Ref. p. 203 Fig.
Ref.
sgFe; single crystals; 99.99% ; lathe sectioning (1073 .*. 1205) 5gFe; single crystals; 99.999% ; electrolytical sectioning 1062... 1213 “Fe; single crystals; 99.999%; lathe sectioning; near-surface effect 1066...1219 103R” 106~~. single ‘crystals: 99.99% ; lathe sectioning; pronounced near-surface effect
39
6lMl
-
73Bl
-
77B2
-
59Pl
Method/Remarks
Matrix: silver (Ag), continued Fe
242
205.3
992... 1201
2.6
205.2
1.9
206.7
Ru
180
275.5
co
1.9
204.1
(973 ... 1214)
6oCo; single crystals; 99.999% ; electrolytical sectioning
39
73Bl
Ni
21.9
229.3
1022... 1223
-
6lH2
15
217.3
904...1199
63Ni; single crystals; 99.99% ; lathe sectioning; pronounced near-surface effect
-
76Ll
-
78Sl
63Ni.
single crystals; 99.999%; electrolytical sectioning; solubility determined from the erfc-profile: c, = 0.7 .exp(-33.7kJmol-‘/IV) Ni; polycrystals; specpure; resistometric method
2.8
230.4
1023..+ 1193
Pd
9.57
237.6
1009~~~1212
lo3Pd; single crystals; 99.999% ; lathe sectioning
39
63Pl
Pt
6.0
238.2
923 +.. 1223
-
75Fl
1.9
235.7
1094... 1232
Pt; polycrystals; purity not specified; X-ray diffraction analysis lg*Pt, r=pt; single crystals; 99.9999% ; microtome sectioning
39
82Nl
Neumann
Land&-BBmslein New Series HI/26
Ref. p. 2031 Solute
3.2.11 Impurity diffusion in noble metals
Do
Q
10-4mZs-1
kJmol-’
Temperature range K
145
Method/Remarks
Fig.
Ref.
64cu;
40
57Sl
-
80Dl
-
56Jl
-
57Ml
-
63Ml
Matrix: silver (Ag), continued
cu
Au
Zn
Cd
Land&-Bijmstein New Series III/%
1.23
193.0
990... 1218
0.029
164.1
699...897
0.262
190.5
923 ... 1223
0.41
194.3
929...1178
0.85
202.1
991...1198
0.62
199.0
0.54
174.6
916... 1197
0.532
174.6
970... 1225
0.85
176.3
953...1165
0.44’
174.6
866... 1210
0.504
176.8
1042... 1226
0.079
159.5
926... 1221
single crystals; 99.99% ; lathe sectioning CU; single crystals; 99.99%; sputter sectioning; SIMS analysis (63Cu signal) 198Au. single crystals; 99.99% ; lathe sectioning “‘Au; polycrystals; 99.99% ; microtome sectioning 198Au. single crystals; 99.99% ; lathe sectioning best tit to data from [56Jl, 57M1, 63MlJ 65Zn. single crystals; 99.99% ; lathe sectioning 65Zn; single crystals; 99.999% ; lathe sectioning Zn; polycrystals; specpure; resistometric method
39 55Sl
40
67Rl
-
79D2
“%d; single crystals; 99.99% ; lathe sectioning “‘Cd; polycrystals; 99.999% ; chemical sectioning and residual activity
40
54Tl
-
69K4
‘03Hg. singe &ystals; 99.99% ; lathe sectioning
39
57Sl
Neumann
solute
[Ref. p. 203
3.2.11 Impurity diffusion in noble metals
146 Do
Q
10-4mZs-1
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: silver (As), continued 91
0.13
159.5
873...1223
Al; polycrystals; purity not specified; X-ray diffraction analysis
39
75F2
3a
0.42
162.9
873...1213
Ga; polycrystals; purity no specified; X-ray diffraction analysis
40
77F2
h-i
0.41
170.1
886.a. 1209
l141n.
40
54Tl
-
67Kl
40
84Ml
single’crystals; 99.99% ; lathe sectioning 0.55
175.0
1044...1215
1 141n.
polycjstals; 99.999%; chemical sectioning and residual activity i141n: single crystals; 99.999%; sputter sectioning
0.36
169.0
553.e.838
Tl
0.15
158.7
(918 ..a 1073)
‘04T1; polycrystals; purity not specified; lathe sectioning and residual activity
40
58H2
Ge
0.084
152.8
(948...1123)
‘lGe; polycrystals; purity not specified; lathe sectioning and residual activity
39
58H2
Sn
0.25
165.0
865.+.1210
40
54Tl
0.472
171.0
1026...1227
113Sn; single crystals; 99.99% ; lathe sectioning “jSn, l19Sn; polycrystals; 99.999%; chemical sectioning and residual activity
-
69K3
Pb
0.22
159.5
(973 . . .1073)
210Pb; polycrystals; purity not specified; lathe sectioning; three data points only
-
55Hl
As
0.042
149.6
915...1213
As; polycrystals; 99.999% ; electron microprobe analysis (vapour deposited film of inactive As)
-
75H3
Neumann
Landoh-BBmstein New Series III/26
3.2.11 Impurity diffusion in noble metals
Ref. p. 2031 Solute
Do
Q
10-4m2s-’
kJmol-’
147
Temperature range K
Method/Remarks
Fig.
Ref.
iz4Sb; single crystals; 99.99% ; lathe sectioning 124Sb; polycrystals; 99.999% ; chemical sectioning and residual activity
39
54Sl
-
67K2
35s.
-
67B2
Matrix: silver (Ag), continued Sb
S
0.169
160.4
742... 1215
0.234
163.6
1053... 1225
1.65
167.5
873+..1173
policrystals; 99.999% ; grinder sectioning Se
0.285
157.4
759...1109
75Se(implanted); single crystals; 99.999% ; microtome sectioning
40
89Rl
Te
0.47
162.9
1043... 1213
-
69K3
0.21
154.7
65O.a.1169
“‘Te; polycrystals; 99.999% ; chemical sectioning “‘Te (implanted); single crystals; 99.999% ; microtome sectioning
40
8763
Matrix: gold (Au) Au
-
-
-
seechapter 2 on self-diffusion
41
Fe
0.19
172.5
973 ... 1323
Fe; polycrystals; purity not specified; X-ray diffraction analysis
41
77F3
co
0.22
183.4
973 ... 1323
-
77F3
0.25
185.2
1030.**1335
co; polycrystals; purity not specified; X-ray diffraction analysis 57co; single crystals; 99.999% ; microtome sectioning
41
78H2
0.30
192.6
1153 ... 1210
63Ni.
-
57Rl
973 ... 1323
poly&ystals; 99.96%; lathe sectioning Ni; polycrystals; purity not specified; X-ray diffraction analysis
41
76F2
Ni
0.25
Land&-B&n&n New Series III/26
188.4
Neumann
148 Solute
3.2.11 Impurity diffusion in noble metals Do
Q
10-4mZs-’
kJmol-’
[Ref. p. 203
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: gold (Au), continued Pd
0.076
195.1
973...1273
Pd; polycrystals; purity not specified; X-ray diffraction analysis
41
78F2
Pt
0.095
201.4
973...1273
Pt; polycrystals; purity not specified; X-ray diffraction analysis
41
78F2
cu
0.105
170.2
973...1179
Cu (vapour deposited 1 u layer); polycrystals; 99.99% ; electron microprobe analysis
41
66Vl
Ag
0.072
168.3
943 ... 1281
-
63Ml
0.08
169.1
1046.~31312
-
65Kl
0.086
169.3
1004.~. 1323
“‘Age single crystals; 99.99% ; lathe sectioning “‘Ag; polycrystals; 99.99% ; electrochemical sectioning and residual activity “‘Ag, losAg; single crystals;
41
74H2
99.999 % ;
microtome sectioning Zn
0.082
158.1
969.a.1287
65Zn; single and polycrystals; 99.999%; microtome sectioning
41
77Cl
Hg
0.116
156.5
877...1300
203Hg; single crystals; 99.994% ; lathe sectioning
41
65Ml
AI
0.052
143.6
773... 1223
Al; polycrystals; purity not specified; X-ray diffraction analysis
41
78F3
In
0.075
153.7
(973 ... 1273)
l141n.
41
71D2
41
77Cl
polycjstals; 99.999% ; lathe sectioning and electron microprobe analysis (Au/Au 0.3% In sandwich samples) Ge
0.073
144.5
lOlO...
68Ge.
single and polycrystals; 99.999%; microtome sectioning
Neumann
Iandolt-Bhstein New Series Ill,/26
Solute
149
3.2.12 Impurity diffusion in zinc group metals
Ref. p. 2031 Do
Q
10-4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
Sn; polycrystals; 99.999% ; electron microprobe analysis (Au/Au 0.3 % Sn sandwich samples)
-
72H2
“3Sn.
41
Matrix: gold (Au), continued Sn
0.0412
143.3
970... 1268
0.0399
143.1
962... 1272
polyciystals; 99.999% ; lathe sectioning Sb
0.0114
129.4
1003 ..+ 1278
Sb; polycrystals; 99.999% ; electron microprobe analysis (Au/Au 0.15 . ..0.4% Sb sandwich samples)
-
72H3
Te
0.063
140.9
908...1145
“‘Te (implanted); single crystals; 99.999% ; microtome sectioning
41
89Rl
3.2.12 Impurity diffusion in zinc group metals Zn, Cd, Hg Matrix: zinc (Zn) Zn
-
-
seechapter 2 on self-diffusion
42,43
63Ni.
42
67M2
11 c 8.1 I c 0.43
136.6 121.5
564...664
11c 2.22 I c 2.00
123.6 125.3
611 .*a688
64cLl; single crystals; 99.999% ; lathe sectioning
42
66B2
11c 0.32 I c 0.45
108.9 115.6
544...686
“OAg; single crystals; 99.999% ; lathe sectioning
42
61Rl
AU
11 c 0.97 I c 0.29
124.5 124.4
588...688 620...688
198Au; single crystals; 99.999%; lathe sectioning
42
63G3
Cd
11c 0.114 Ic 0.117
86.0 85.5
498...689
l15Cd; single crystals; 99.999% ; lathe sectioning
43
63G3
Ni
cu
Land&-Bhstein New Series III/26
single crystals; 99.999%; autoradiography
Neumann
3.2.12 Impurity diffusion in zinc group metals
150 Solute
Do
Q
10-4m2s-1
kJmol-’
[Ref. p. 203
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: zinc (Zn), continued
Hg
11c 0.056 1 c 0.073
82.5 84.5
533.~~686
203Hg; single crystals; 99.999% ; lathe sectioning
43
67B3
Ga
11 c 0.016 lc 0.018
77.0 76.0
513...676
72Ga; single crystals; 99.999%; lathe sectioning
43
66B2
In
11 c 0.062 lc 0.14
80.0 82.1
444 9. ~689
l141n; single crystals; 99.999%; lathe sectioning
43
61Rl
Sn
IIC 0.15 lc 0.13
81.2 77.0
571 . ..673
1’3Sn; single crystals; 99.999%; lathe sectioning
43
7OW2
-
-
seechapter 2 on self-diffusion
11c 2.21
106.3
(453 .** 573)
67Hl
(Ic 1.40 1 c 0.68
103.2 105.0
(478 . . .583)
“OAg; single crystals; 99.99% ; surface decreasemethod “‘Ag; single crystals; 99.999% ; lathe sectioning
44 -
44
72Ml
Au
11 c 1.40 lc 3.16
106.6 110.7
(453 . . - 578)
‘g5Au; single crystals; 99.999%; lathe sectioning
44
72Ml
Zn
11c 0.13 1 c 0.084
75.5 75.4
(428 . . .588)
65Zn; single crystals; 99.999; lathe sectioning
44
72Ml
Hg
11c 0.21 1 c 0.21
78.6 78.6
(423 . . .573)
2o3Hg* single crystals; 99.999% ; lathe sectioning
44
72Ml
In
11c 0.10 1 c 0.090
73.1 70.9
(433 ... 573)
r141n; single crystals; 99.999%; lathe sectioning
44
72Ml
Pb
11 c 0.060 1 c 0.071
68.9 65.8
514*..571
210Pb; single crystals; 99.999%; lathe sectioning
44
81Yl
Matrix: cadmium (Cd) Cd A!2
Matrix: mercury (I-&) - No data available
Neumann
Landolt-Kmstein New Series III/26
3.2.13 Impurity diffusion in aluminum group metals
Ref. p. 2031 Solute
Do
Q
10V4m2s-’
kJmol-’
Temperature range K
Method/Remarks
151 Fig.
Ref.
3.2.13 Impurity diffusion in aluminum group metals Al, Ga, In, Tl Matrix: aluminum (Al) Al
-
-
seechapter 2 on self-diffusion
45,46
126
803.e.923
Li; polycrystals; 99.993% ; resistometric method
46
87Ml
24Na. po1ycrysta1s; purity not specified; surface decreasemethod
-
7783
137&.
-
73T3
Li
0.35
Na
6.7. 1O-4
719...863
cs
0.0104
453...573
polyciystals; 99.997%; residual activity; grinder sectioning; pronounced near-surface effect ; determination of D from deeper penetrations 667...928
28Mg; single crystals; 99.999% ; microtome sectioning
46
74Rl
242.0
804..+913
g5Zr. polyirystals; 99.999%; residual activity; grinder sectioning; distinct data scattering
-
73M4
253.0*
859.s.923
51Cr single crystals; 99.999%; microtome sectioning; * recalculated by present authors
45
7OP4
MO
250.0
898...928
MO; polycrystals; 99.99% ; electron microprobe analysis (Al/ Al 0.2 ... 0.3 % MO sandwich samples)
-
83Cl
Mn
211.4
s6Mn, “Mn (implanted); single and polycrystals; 99.999% ; electrochemical sectioning
45
71H3
W
1.24
Zr
728
Cr
1.85. IO3*
(continued)
Land&-BBmstein New Series III/26
Neumann
3.2.13 Impurity diffusion in aluminum group metals
152 Solute
Do
Q
10-4m2s-1
kJmo!-’
[Ref. p. 203
Temperature range K
Method/Remarks
Fig.
Ref.
Mn; polycrystals; 99.99% ; electron microprobe analysis (Al/ A! 0.5 ... I % Mn sandwich samples) s4Mn ; polycrystals; 99.99% ; microtome sectioning
-
73B3
-
87F2
“Fe; single crystals; 99.999% ; lathe sectioning sgFe (implanted); single and polycrystals; 99.99 to 99.999%; lathe and microtome sectioning ‘gFe; polycrystals; 99.995% ; microtome sectioning (profile evaluation by taking into account the formation of an intermetallic compound in the near-surface range) 5gFe (implanted); single crystals; 99.9995% ; microtome sectioning; mainly pressure dependence studied; two data points close to the results of [70HI]
-
70A3
-
70HI
-
87BI
-
89B2
6OCo; single crystals; 99.999% ; microtome sectioning 6OCo; polycrystals; 99.995%; lathe sectioning and residual activity co; polycrystals; 99.995% ; resistometric method 6oCo (implanted); single crystals; 99.999% ; lathe sectioning
45
7OP4
-
72A3
Matrix: aluminum (Al), continued Mn
Fe
co
I215
229.0
773 . ..923
317
217
843 . ..927
135
192.6
823...906
9.1 . 105
258.7
792...931
53
183.4
793 . ..922
-
(220)
855, 896
464
174.8
695...921
250
174.6
673...913
141
169.0
742.e.912
506
175.7
724...930
Neumann
78E2
-
83Hl
Land&-BCmstein New Series III/26
Ref. p. 2031 Solute
153
3.2.13 Impurity diffusion in aluminum group metals
Do
Q
10-4m2s-1
kJmol-l
Temperature range K
Method/Remarks
Fig.
Ref.
45
78E2
Matrix: aluminum (Al), continued Ni
4.4
145.8
742...924
Ni; polycrystals; 99.995%; resistometric method
cu
0.647
135.1
706...925
0.654
136.1
594...928
0.13
117.2
615...883
0.16
118.9
665...868
0.118
116.5
644...928
0.077
113.0
696... 882
0.27
121.0
723...873
0.131
116.4
642.a.928
0.259
120.8
630...926
0.30
121.4
(700 . . .920)
7OP4 64cu. 45 single crystals; 99.999% ; microtome sectioning 89Fl 67Cu; polycrystals; 99.999%; microtome sectioning (743 .a.928 K); grinder sectioning and residual activity measurement (594 . . .743 K) slight near-surface effect below 743 K 70A3 “‘Ag; single crystals; 99.999% ; lathe sectioning 70B3 “o&* single ‘crystals; 99.995% ; grinder sectioning and electron microprobe analysis (vapour deposited film of inactive Ag) 7OP4 ‘l”Ag; 46 single crystals; 99.999%; microtome sectioning 70A3 lg8Au; single crystals; 99.999% ; lathe sectioning 70B3 “‘AU; single crystals; 99.995% ; grinder sectioning 7OP4 “‘AU; 46 single crystals; 99.999%; microtome sectioning 7OP4 65Zn; single crystals; 99.999% ; microtome sectioning 65Zn; 7263 polycrystals; 99.99% ; residual activity; grinder sectioning (continued)
&
Au
Zn
LandolGB6mstein New Series III/26
Neumann
3.2.13 Impurity diffusion in aluminum group metals Solute
Matrix:
Do
Q
10-4mZs-1
kJmol-’
[Ref. p. 203
Temperature range K
Method/Remarks
Fig.
Ref.
Zn; polycrystals; 99.99% ; electron microprobe analysis (AI/Al 1% Zn sandwich samples) 65Zn; polycrystals; 99.999% ; residual activity; grinder sectioning 65Zn. polycrystals; 99.99% ; grinder sectioning Zn; polycrystals; 99.995%; resistometric method 65Zn. singld crystals; 99.999% ; microtome sectioning; evaluation together with the results of [7OP4] 65Zn; polycrystals; 99.99% ; microtome sectioning; *two sets of measurements; evaluation together with the results of [72G3, 77B33
-
73B3
-
76F3
-
77B3
-
78E2
-
78P2
aluminum (Al), continued
0.2
120.6
613...913
0.177
118.1
438...918
0.27
117.8
614..-890
0.20
120.7
650...903
0.325
117.9
688 ..*928
0.16 0.26
117.0 119.1
714 ... 893* 674 ‘.. 837*
0.245
119.6
(614 ... 920)
Cd
1.04
124.3
714..-907
“‘Cd; single crystals; 99.999% ; lathe sectioning
Hg
15.3
141.8
718...862
2o3Hg* polycjstals; 99.999%; residual activity; near-surface effect (oxide hold-up); determination of D from deeper penetrations
7882
Ga
0.49
123.1
680.~~926
72Ga; single crystals; 99.999%; microtome sectioning
46
7OP4
In
0.123
115.6
(673 .*. 873)
‘141n; polycrystals; purity not specified; residual activity
-
70A2
Zn
Neumann
83B3
46 46
70A3
Land&-B6mstein New Series 111126
Ref. p. 2031 Solute
3.2.13 Impurity diffusion in aluminum group metals
Do
Q
10-4m2s-1
kJmol-’
155
Temperature range K
Method/Remarks
Fig.
Ref.
46
71H4
Matrix: aluminum (Al), continued In
1.16
122.7
715...929
l141n (implanted); single crystals; 99.999% ; microtome sectioning
Tl
116
152.7
737...862
204T1; polycrystals; 99.999%; residual activity; near-surface effect (oxide hold-up); determination of D from deeper penetrations
78S2
Si
0.35
123.9
618 . ..904
-
73B2
2.02
136.0
753 ... 893
Si; polycrystals; 99.99% ; electron microprobe analysis (Al/Al 0.5 % Si sandwich samples) Si; polycrystals; 99.999% ; electron microprobe analysis (Al/ Al 0.58 .+. 1.15% Si sandwich samples)
-
78F4
Ge
0.481
121.3
674...926
71Ge. single crystals; 99.999%; microtome sectioning
46
7OP4
Sn
0.245
119.3
(673 *. ~873)
113&.
-
70A2
46
90El
polycjstals; purity not specified; residual activity 113Sn (implanted); single crystals; 99.9998% ; microtome sectioning; pressure effects also studied
0.84
118.6
649...905
Pb
50
145.6
777 ... 876
210Pb; polycrystals; 99.999%; residual activity; near-surface effect (oxide hold-up); determination of D from deeper penetrations
7882
Sb
0.09
121.7
721...893
124Sb; polycrystals; specpure Al; residual activity; grinder sectioning
68B3
Land&BBmstein New Series III/26
Neumann
-
Solute
[Ref. p. 203
3.2.13 Impurity diffusion in aluminum group metals
156 Do
Q
10-4mZs-1
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
798.e.898
235U. polycjstals; purity not specified; autoradiography
-
68B4
47 -
74Al
Matrix: aluminum (Al), (continued) u
0.1
117.2
Matrix: gallium (Ga) - No data available Matrix: indium (In) [n
-
-
-
seechapter 2 on self-diffusion
cl0
1.2.10-S
25.1*
383...423
6OCo; single crystals; 99.997% ; microtome sectioning; distinct data scattering; * diffusion in (111) direction
4g
IIC 0.11 1 c 0.52
48.1 53.6
(298 ... 423)
“‘Ag* single crystals; 99.99%; microtome sectioning
47
66A2
AU
9.10-3
28.1
(198...423)
lgOAu; single crystals with random orientation; 99.99%; microtome sectioning
47
66A2
l-i
0.049
64.9
323... 429
204T1; polycrystals; 99.9 % ; microtome sectioning
47
52El
Matrix: thallium (Tl) ri
-
-
-
seechapter 2 on self-diffusion
48
4g
11 c 0.027 1 c 0.038
46.9 49.4
(360, 480) (a-Tl)
48
68A2
0.042
49.8
(510 ... 570) (P-TO
“‘Ag; single crystals; 99.9999% ; microtome sectioning; two data points only bee polycrystals; same procedure as for single crystals
IIC 2-10-s 1 c 5.3 * 10-Q
11.7 21.8
(390, 490) (or-Tl)
48
68A2
5.2. 1O-4
25.1
(510 ..* 570) (B-V
lgOAu; single crystals; 99.9999% ; microtome sectioning; two data points only bee polycrystals; same procedure as for single crystals
Au
Neumann
Landolt-B6mstein New Series 111126
Ref. p. 2031 Solute
3.2.14 Impurity diffusion in group IV B metals
Do
Q
10-4m2s-1
kJmol-’
Temperature range K
Method/Remarks
157 Fig.
Ref.
3.2.14 Impurity diffusion in group IVB metals Sn, Pb Diffusion data for semiconducting elements Si, Ge are not included. They can be found in [89L2]. Matrix: tin (Sn) Sn
-
-
seechapter 2 on self-diffusion
49, 50 78S3
Fe
4.8. lO-4
51.2
387...462
co; polycrystals; 99.9995% ; MijDbauer spectroscopy (57Fe signal)
Ni
11 c 1.99 . IO-’ Ic 1.87. lo-’
18.1 54.2
298...373 393 . ..473
63Ni; single crystals; 99.999% ; lathe sectioning
50
84Yl
cu
Ic 2.4. lO-3
33.1
(413 .** 503)
64Cu; single crystals; purity not specified; microtome sectioning
50
67D2
&
11c 7.1 . 10-3 ..Lc 0.18
51.5 77.0
(403 . . .503)
“OAg; single crystals; purity not specified; microtome sectioning
50
66D2
Au
11 c 5.8 . lO-3 Ic 0.16
46.1 74.1
(403 . . * 503)
lg8Au; single crystals; purity not specified; microtome sectioning
50
66D2
Zn
11 c 1.1 . 10-Z I c 8.4
50.2 89.2
(410... 500)
65Zn; single crystals; 99.999%; lathe sectioning
50
74H3
Cd
11c 220 Ic 130
118.1 115.6
(460 . . .500)
logCd; single crystals; 99.999% ; lathe sectioning
49
74H3
Hg
11 c 7.5 Ic 30
105.9 112.2
448 . ..499
‘03Hg; single crystals; 99.9999%; microtome sectioning
49
72Wl
In
11 c 12.2 Ic 34.1
107.2 108.0
454... 494
’ 141n; single crystals; 99.998%; lathe sectioning
49
58Sl
Land&-Bhstein New Series III/26
Neumann
Solute
[Ref. p. 203
3.2.14 Impurity diffusion in group IV B metals
158 Do
e
10-4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: tin (Sn), continued TI
1.3 * 10-J
61.5
410..+489
‘04T1; polycrystals; 99.999% ; lathe sectioning and autoradiomphy ; grain-boundary contributions
-
69B3
Sb
IIC 71.0 I c 73.0
121.8 123.1
466.s.499
124Sb; single crystals; 99.999%; lathe sectioning
49
71H5, 7483
Matrix: lead (Pb) Pb
-
-
seechapter 2 on self-diffusion
Na
6.3
118.5
522...586
22Na; single crystals; 99.9999%; microtome sectioning; distinct data scattering
51 -
7201
co
9. lo-’
46.4
383 ... 573
sgCo (implanted; ny6’Co, activation analysis); polycrystals; 99.9999%; microtome sectioning; pronounced near-surface effect
-
78K3
Ni
1.0. 10-z
44.5
(481 . . .593)
63Ni.
51
73C2
singlk crystals; 99.9999% ; microtome sectioning 63Ni; polycrystals; 99.999% ; lathe sectioning
-
8282
51
75D2
1.1 . 10-z
45.4
423.a. 523
Pd
3.4. 10-3
35.4
(470 . *. 590)
rogPd; single crystals; 99.9999% ; microtome sectioning
Pt
1.1 . 10-2
42.3
490..*593
cu
7.9. 10-3
33.6
(498 . . .598)
8OVl Pt; 51 single crystals; 99.9999%; microtome sectioning (Pt concentration determined by observing the variation in the melting curve for each slice); solubility determined from the erfc-profile: c, = 21.9 *exp(- 51.0 kJmol-‘/RT) 64Cu; 66Dl single and polycrystals; purity not specified; microtome sectioning (continued)
Solute
Do
Q
10-4m2s-1
kJmol-’
Matrix: lead (Pb), continued (23.4) * (8.6 * 10-y cu
Au
Temperature range K
Method/Remarks
Fig.
Ref.
491... 803
64cu;
-
72C2
51
75D3
-
65Cl
-
66Dl
-
74A2
-
75D2
51
82H2
lQ8Au; polycrystals; 99.99% ; microtome sectioning
-
56Al
195~~.
-
61Al
198~~.
-
66A3
single Lystals; 99.999%; microtome sectioning lQ8Au; single crystals; 99.999% ; lathe sectioning
-
66Kl
single crystals; 99.9999%; microtome sectioning; D(p) measured between 0 and 5.6 GPa; * partly erroneous zero-pressure results reanalysis of the results of [72C2], using an improved pressure calibration ** Do and Q represent the zeropressure parameters
8.6. 10-3
34.2 **
-
-*
(470 . . .750)
4.6. lo-’
60.5
(398 ... 598)
4.42. 1O-2
60.8
437.e.572
4.8. 1O-2
60.8 **
4.6. 1O-2
60.8
423...573
2.8. 1O-3
37.3
463 ... 569
4.1 * 10-3
39.1
367...598
&
159
3.2.14 Impurity diffusion in group IV B metals
Ref. p. 2031
“OAg; single crystals; 99.999%; microtome sectioning; D(p) measured between 0 and 3.9 GPa; * zero-pressure values for Do and Q not evaluated “‘Ag. single ‘crystals; purity not specified; microtome sectioning “OAg; single crystals; 99.998%; microtome sectioning reanalysis of the results of [65Cl] using an improved pressure calibration; ** Do and Q represent the zeropressure fitting parameters “OAg; polycrystals; 99.999% ; lathe sectioning
single Lystals; 99.999%; microtome sectioning 2.5. 1O-3
8.7. 1O-3
Land&-BBmstein New Series III/26
36.6
41.9
(353 ... 523)
(463 . . .593)
Neumann
(continued)
Solute
[Ref. p. 203
3.2.14 Impurity diffusion in group IV B metals
160
Do
Q
10-4m2s-1
kJmol-’
Fig.
Temperature range K
Method/Remarks
(444 . . .693)
ig8Au; single crystals; 99.9999% ; microtome sectioning; D(p) measured between 2.1 and 3.9 GPa; * Do and Q represent the zeropressure parameters reanalysis of the results of [71Wl], using an improved pressure calibration; * Do and Q represent the zeropressure parameters ig5Au; single crystals; 99.9999%; microtome sectioning ‘9’Au. 51 single crystals; 99.9999%; microtome sectioning 65Zn. single crystals; 99.9999%; microtome sectioning 65Zn. 51 singld crystals; 99.9999% ; microtome sectioning; D(p) measured between 0 and 4.7 GPa; * Do and Q represent the zeropressure parameters “‘Cd; single crystals; 99.9999%; microtome sectioning 51 “‘Cd; single crystals; 99.9999%; microtome sectioning; D(p) measured between 0 and 4 GPa; * Do and Q represent the zeropressure parameters zo3Hg. single crystals; 99.9999% ; microtome sectioning
Ref.
Matrix: lead (Pb), continued Au
Zn
Cd
Hg
5.6. 1O-3
39.7 *
5.8 . lo- 3
40.3 *
3.62. 1O-3
37.4
411*.*511
5.2. lo-’
38.6
(334 ... 563)
1.6. lo-*
47.3
455... 572
1.65.10-*
47.8 *
(453 ... 773)
0.409
88.9
(423 ... 593)
0.92
92.8 *
(523 ... 823)
1.05
95.0
466...573
71Wl
75D2
75W2
79D3
74R2
77Dl
69M3
77Vl
73Wl
(continued)
Neumann
Land&BSmstein New Series W/26
Solute
161
3.2.15 Impurity diffusion in group V B semimetals
Ref. p. 2031
Do
Q
10-4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: lead (Pb), continued
H&?
1.5
96.7 *
(523 ... 823)
‘03Hg* single crystals; 99.9999% ; microtome sectioning; D(p) measured between 0 and 3.8 GPa; * Do and Q represent the zeropressure parameters
51
77Vl
In
33
112.2
437.e.493
In; single crystals; 99.999%; electron microprobe analysis (5 urn film of inactive In deposited on the crystal)
-
69K5
Tl
0.511
101.9
480..+596
‘04T1; polycrystals; 99.99% ; microtome sectioning
51
61R2
Sn
0.41
94.4 *
(523 . . .723)
“3Sn.
51
77D2
single’crystals; 99.9999% ; microtome sectioning; D(p) measured between 0 and 3 GPa; * Do and Q represent the zeropressure parameters Sb
0.29
92.9
461...588
lz4Sb; single crystals; 99.9999%; microtome sectioning; distinct data scattering
-
72Nl
Bi
6.8
112.2
564, 596
‘loBi; polycrystals; 99.99% ; microtome sectioning; only two data points
-
61R2
3.2.15 Impurity diffusion in group VB semimetals P, As, Sb, Bi Matrix: phosphorus (P) - No data available Matrix: arsenic (As)
- No data available
Matrix: antimony (Sb) Sb
-
-
-
seechapter 2 on self-diffusion
-
Ag
67
119.7
603...879
li”Ag; polycrystals; 99.9 % ; serial sectioning
-
Matrix: bismuth (Bi) - No data available Land&-BGmstein New Series III/26
Neumann
73K3
iolute
[Ref. p. 203
3.2.16 Impurity diffusion in actinide group metals
162 Do
Q
10-4mZs-1
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
3.2.16 Impurity diffusion in actinide group metals AC, Th, Pa, U, Np, Pu, etc. vlatrix: actinium (AC) - No data available vlatrix: thorium (Th) [-thorium
rh
-
-
-
seechapter 2 on self-diffusion
‘e
5.10-3
80.8
1238...1558
52 Fe; polycrystals; 99.95% ; diffusion couple method and spark source mass spectroscopy; electro-mobility and effective charge also determined
79w ‘1
5. 1o-4
55.3
1238... 1558
52 co; polycrystals; 99.95%; diffusion couple method and spark source mass spectroscopy; electro-mobility and effective charge also determined
79Wl
Ni
4.10-3
77.9
1238...1558
52 Ni; polycrystals; 99.95%; diffusion couple method and spark source mass spectroscopy; electro-mobility and effective charge also determined
79Wl
Pa
1.26. lo2
312.8
231Pa; polycrystals; 99.84%; profile determination via u-emission spectra
52
67Sl
LJ
2.21 . lo4
332.0
233~.
52
67Sl
963...1150
52
polycjstals; 99.84% ; profile determination via a-emission spectra g-thorium Th Zr
1.73 . lo4
-
-
no self-diffusion data for g-Th available
384.0
1773... 1873
52 Zr; polycrystals; 99.977%; diffusion couple method and scanning laser mass spectroscopy; electro-mobility and effective charge also determined
84Sl
Landolr-B5mslein New series III/26
Ref. p. 2031 jolute
3.2.16 Impurity diffusion in actinide group metals
Do
e
10m4m2sK1
kJmol-’
163
Temperature range K
Method/Remarks
Fig.
Ref.
1693 1963
‘8iHf.
52
65Rl
Matrix: thorium @Th), continued Hf
D=1.09.10-12m2s-1 2.09 . IO-” m2 s-l
polycjstals; lathe sectioning
V
0.019
129.8
1653.'.1939
52 v; polycrystals; 99.95%; diffusion couple method and spark source mass spectroscopy; electro-mobility and effective charge also determined
7834
Nb
0.5
201.8
1643... 1933
52 Nb; polycrystals; 99.95% ; diffusion couple method and spark source mass spectroscopy; electro-mobility and effective charge also determined
7884
Ta
0.57
210.6
1648...1933
52 Ta; polycrystals; 99.95%; diffusion couple method and spark source mass spectroscopy; electro-mobility and effective charge also determined
78S4
MO
15.1
216.0
1698... 1873
52 MO; polycrystals; 99.977% ; diffusion couple method and scanning laser mass spectroscopy; electro-mobility and effective charge also determined
84Sl
W
0.103
160.0
1683...1818
52 W; polycrystals; 99.977% ; diffusion couple method and scanning laser mass spectroscopy; electro-mobility and effective charge also determined
84Sl
Re
4.04.10-3
84.0
1663 ... 1943
52 Re; polycrystals; 99.977% ; diffusion couple method and scanning laser mass spectroscopy; electro-mobility and effective charge also determined
84Sl
Fe
4.10-3
71.6
1633... 1898
52 Fe; polycrystals; 99.95%; diffusion couple method and spark source mass spectroscopy
79Wl
Land&-Biimstein New Series III/26
Le Claire
Solute
[Ref. p. 203
3.2.16 Impurity diffusion in actinide group metals
164 Do
Q
10V4mzs-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
co;
52
79Wl
52 Ni; polycrystals; 99.95%; diffusion couple method and spark source mass spectroscopy
79Wl
Matrix: thorium (Th), continued co
4.10-j
65.3
1633... 1898
polycrystals; 99.95%; diffusion couple method and spark source mass spectroscopy Ni
4 * 10-4
38.1
1633.s.1898
Matrix: protactinium (Pa) - No data available Matrix: uranium (U) u-uranium u -
-
seechapter 2 on self-diffusion
-
918
polycrystals; D determined from precipitate dissolution
53
-
seechapter 2 on self-diffusion
53
D = 1.77. lo-l3 m2s-l
1021.2
53
62R 1
D=3.60~10-14mZs-1 6.45. lo-” rn’s-l 3.41 . lo-l4 m2 s-l * 5.36. lo-l4 m2 s-l 1.61 . lo-l4 m2s-’ 1.51 . lo-l3 m2sT1* 1.07. lo-l3 m2sT1
943 953 968.8 985.7 993 1002.5 1013
51Cr; polycrystals; 99.993% ; lathe sectioning 51Cr; polycrystals; 99.98% ; lathe sectioning; * mean of two values
53
70D2
Fe
D = 8.71 . lo-i3 m2s-‘* 2.6.10-12m2s-1*
974 1033
5gFe; polycrystals; 99.993% ; lathe sectioning; * mean of two values
53
62Rl
co
1.54.10-2
114.9
964.e. 1036
6OCo. polycjstals; 99.98% ; lathe sectioning
53
70D2
-
-
seechapter 2 on self-diffusion
53
Fe
Dz3.10-14m2s-1
p-uranium u Cr
-
y-uranium u -
-
72Sl
Nb
4.87. 1O-2
166.0
1063...1376
g5Nb; polycrystals; 99.99%; lathe sectioning
53
64P2
Cr
5.47.10-3
102.4
1070~~~1311 51Cr; polycrystals; 99.99% ; lathe sectioning
53
64P2
Le Claire
Landolt-BBmsfein New Series III/26
Ref. p. 2031 Solute
165
3.2.16 Impurity diffusion in actinide group metals
Do
Q
10-4m2s-’
kJmol-’
Temperature range K
Method/Remarks
Fig.
Ref.
Matrix: uranium (y-u), continued Mn
1.81. 1O-4
58.1
1060..+ 1212
54Mn. polyciystals; 99.99% ; lathe sectioning
53
64P2
Fe
2.69. 1O-4
50.3
1059... 1263
5gFe* polydrystals; 99.99% ; lathe sectioning
53
64P2
co
3.51 . 10-4
52.6
1056... 1263
6Oco. polyckystals; 99.99% ; lathe sectioning
53
64P2
Ni
5.36. 1O-4
65.6
1059... 1313
63Ni; polycrystals; 99.99% ; lathe sectioning
53
64P2
cu
1.96. 1O-3
100.7
1059... 1312
53
64P2
Au
4.86. 1O-3
127.3
1057.~. 1280
64Cu; polycrystals; 99.99% ; lathe sectioning ‘95Au. polycjstals; 99.99% ; lathe sectioning
53
61R3
Matrix: neptunium (Np) - No data available Matrix: plutonium (pu) S-plutonium Pu -
-
-
seechapter 2 on self-diffusion
54
co
1.2. 10-2
53.2
617...699
6OCo; polycrystals; grinder sectioning
54
75Cl
Ag
D = 1.08 . lo-l4 m2 s-i
695
“OAg; polycrystals; grinder sectioning
54
76Cl
Au
D=2.37.10-i4m2s-’
713
lg8Au; polycrystals; grinder sectioning
54
76Cl
s-plutonium Pu -
-
-
seechapter 2 on self-diffusion
54
co
1.4. 10-3
41.4
757...894
6OCo. polyc’rystals; grinder sectioning
54
75C2
cu
1.0. 10-3
51.5
773...853
cu; polycrystals; diffusion couple method
54
76C1, 7OLl
Land&-BBmstein New Series III/26
Le Claire
3 Diffusion of impurities in solid metallic elements (Figures) Solute
Do
Q
10-4mZs-1
kJmol-’
Temperature range K
[Ref. p. 203
Method/Remarks
Fig.
Ref.
l*om&;
54
76Cl
lg8Au; polycrystals; grinder sectioning
54
76Cl
1
Matrix: plutonium (E-Pu), continued
Ag
4.9. 10-s
40.2
772...884
polycrystals; grinder sectioning Au
5.7 * 10-s
43.1
788...844
Figures for 3 c-T 1u
i
10-Q
I ,
T,=QXK
m2/s
-T
350
400 K
.,-10
I
Matrices -6Li . I‘Lie
‘I
m7fs 1o-'o
‘i-13 6
2.1,
2.6
2.8
3.040-k’ :
4.10-‘” I
2.1
I/T-
‘ig. 1. Li. Semilogarithmic plot of impurity diffusion coeficicnts in lithium vs. reciprocal temperature. Na: [67Ml], 31: [73M2]. Ag: [73Ml], Au: [6802], Zn: [69Ml], Cd: 70011, Hg: [7001], Ga: [7001], In: (68031,Sn: [6902], ‘b: (69021. Sb: [6902], Bi: [6902]. Self-dimusion according
\ 2.3
2.5
2.1 l/T-
2.9
I 40°K.’
3.3
Fig. 2. 6Li and ‘Li. Semilogarithmic plot of diffusion coeficicnts vs. reciprocaltemperaturein near pure 6Li and ‘Li matrices.Na: [71Ll], Au: [7101]. The lines for 6Li in 6Li and for ‘Li in ‘Li areestimatedfrom ‘Li and7Li mutualdiffusion data 171Ll].
o chapter 2 is shown for comparison.
Ik Claire
3 Diffusion of impurities in solid metallic elements (Figures)
Ref. p. 2031
-T 2*lP
I
m*/s T,,=454 K
-1
350
400 K I
300 I
I
I
IO-'0 *
I
4mg m*/s
I
300
350 K
275
10-g
Matrices : “Li,7Li
I
167
h
I
IV"
1o-10
a
I a 10-l'
IOP
10-11 IO-'3 1 2.2
2.4
2.6
2.8 l/T-
3.0
.,0-j K-1
Fig. 3. 6Li and ‘Li. Semilogarithmic plot of Au diffusion coefficients in 6Li (full circles) and 7Li (open circles). The solid line indicates the analysis of 7Li data in terms of two separate Arrhenius terms [7101]. -T 4.1o‘g m*/s
10-13 i
2.8
3.0
3.2 l/T-
3.4
.,o-3K-'
Fig. 4. Na. Semilogarithmic plot of impurity diffusion coefficients in sodium vs. reciprocal temperature. Li: [64Nl], K: [67Bl], Rb: [67Bl], Ag: [83Bl], Au: [69Bl], Cd: [83Bl], In: [83Bl], Tl: [83Bl], Sn: [83Bl]. Self-diffusion according to chapter 2 is shown for comparison.
10-g
10-1'0 I a IO“'
+i;--I,
-T lo-"O m*/s
1400 K 1200
800
1000
IO-" ,o-l;
,0-l>
lo-l3 10-K
2.6
2.8
3.0
3.2 l/T-
3.4
.10-j K-1
3.8
Fig. 5. K. Semilogarithmic plot of impurity diffusion coefticients in potassium vs. reciprocal temperature. Na: [67Bl], Rb: [69Sl], Au: [7OSl]. Self-diffusion according to chapter 2 is shown for comparison.
I a
IO.14 ,0-l:
10-'E 10-l
Fig. 6. Be. Semilogarithmic plot of impurity diffusion coefficients in beryllium vs. reciprocal temperature. Ce: [76Al], V: [76Al], Nb: [76Al], Fe: [66Nl], Co: [79Gl], Ni: [70Al], Cu: [65Dl, 74Ml], Ag: [66Nl], Au: [75Ml], Al: [76Gl]. Self-diffusion according to chapter 2 is shown for comparison. Land&-Bihstein New Series III/26
10-l 10-l 0.60
Le Claire
0.75
0.90
1.05 l/T-
1.20
.lO“K-'
1.50
[Ref. p. 203
3 Diffusion of impurities in solid metallic elements (Figures)
168
10-l’ ml/s
900K
1100K ,, ,
lO”O,
-1 1000 I
I
900 ’ I
I’
800
1
Matrix : Co
10-‘2 10.‘3 lo-‘j I lo-” a I 10-14 Q
10-H
10-n 10-16 10-n 1°lil 0
1.125
1.200
1.275 l/T -
1.350 .lO-sK-’ 1.5f
:ig. 7. Mg. Semilogarithmic plot ofimpurity diffusion coeficients in magnesium vs. reciprocal temperature. Be: (66Yl], ig: [67Ll], Zn: [67Ll], In: [67Ll], Fe: [68Pl], Ni: [68Pl], J: [68Pl]. Self-diffusion according to chapter 2 is shown for :omparison
10-l’
10-19 0.850
0.925
1.000
1.075
1.150 .lO-sK-’ 1.300
Fig. 9. Ca. Semilogarithmic plot of impurity diffusion coefficients in calcium vs. reciprocal temperature. Fe, Ni, U [68Pl]. Self-diffusion according to chapter 2 is shown for comparison.
10-l’ ml/s;
900 K
I
I
750 I
Matrix : Mg 1
,o-l’; 1
I Q
10-l”3-
1
lo-” 1.0:i
1.10
1.15
1.20
1.25
1.30
1.3540% 1.40
Fig. 8. Mg. Semilogarithmic plot of impurity diffusion coeffkients in magnesium single crystals vs. reciprocal temperature. Ag, Cd, In, Sn, Sb [72Cl]. Selfdiffusion according to chapter 2 is shown for comparison.
Le Claire
Land&BBmstein New Series 111.l26
Ref. p. 2031
3 Diffusion of impurities in solid metallic elements (Figures)
169
-T KY7 2000 10-7 2000 K
1750
1500
1500
1750 K 10-e lT m2/s
1250
m2/s
1250
10-g lo-8 lo-"O
I Q 10-g
10-I'
QI 10-12
lo-lo 0.50
0.55
0.60
0.65 0.70 l/T-
0.75 .@K-' 10-13
Fig. 10. SC. Semilogarithmic plot of Fe impurity diffusion coeffkients in scandium vs. reciprocal temperature [86Al]. 10-14
-T IC m
1100 K 1 I T, =
1000
900 I
lo-l5
Matrix : Ce
1ln71K
lo-;
IO
0.60
IO1-9
-10
11LOl/OMII 1
1:
I:
A) [72011\. Ag oh 1
I
I ',
CeA
I t
La\! IO-11
1
0.70 0.75 1/T-
0.80 .10-3K-' 0.90
coT?3c11/-
1200 K
10-g m2/s
X-t-M+t-Au 1) 1
1000
1100
900
h+Ag[7iCl1 1
Id, I
I
0.65
Fig. 11. Y. Semilogarithmic plot of impurity diffusion coefficients in hcp a-yttrium vs. reciprocal temperature. Ag and Fe : [75M2], Ni and Co : [8201]. Self-diffusion according to chapter 2 is shown for comparison.
.
IO I Q
;I
800
m,Ag[72011
1
1.
lo-"[
’
10-l'
-1 ‘I
IO-12
yibcc))
I
I
0.95 4 IT
1.00
PCfcc)
I ,0-l:
Matrix : La
Q ’ Stbccl
I\
, o-1:
IO-13
10-l IO-14 0.90
\
0.95
1.00 1.05
1.10 l/T-
1.15
1.20 .10-3K-' 1.: 10-l'
Fig. 13. Ce. Semilogarithmic plot of impurity diffusion coefticients in fee y- and bee 6-cerium vs. reciprocal temperature. La: [73Dl], Gd: [76Ml], Mn: [75Dl], Fe: [73Cl, 75Dl], Co: [73Cl, 76Ml], Ag: [72Dl, 73Cl], Au: [72Dl]. Self-diffusion according to chapter 2 is shown for comparison. Land&-Biirnstein New Series III/26
U
I
0.85
0.90
1.05 .lOJK-'
1
Fig. 12. La. Semilogarithmic plot of impurity diffusion coeffkients in fee- and bee y-lanthanum vs. reciprocal temperature. Au: [69Dl], Ce: [76Fl]. Self-diffusion according to chapter 2 is shown for comparison.
Le Claire
[Ref. p. 203
3 Diffusion of impurities in solid metallic elements (Figures)
170
-T 2 ,o.q
Ed
rn?/s
in-8
K
1
1100 1
1, =1205K
I I
1
1000 la,p =1068K
‘I
I
1200 1100 10-s m2/s n=1289 t,blll,,
900 I
I Matrix : Pr
Matrix
-5 .I
10-q
F
10-s I-
I cl 1o-l0
: Nd
Pfbcc) lo-‘[
]cc(hcp)
oi
0
1 I
o Mn
I 10-l’
10-l’ 0.80 Pfbcc] 1
0.85
0.90
0.95 l/T-
1.00
: -1104K-’ 110
Fig. 15. Nd. Semilogarithmic plot of impurity diffusion coefficients in a- and S-neodymium vs. reciprocal temperature. Mn: (75Dl], Fe: [75Dl].
orfhcp)
10-n 0 In 0 Lo
10-l’
.Ho -T
10-n
0.80 0.85
0.90
0.95 1.00 l/T-
. . 1.05 .lO-‘K-’ ;5
10-g
1700K
1500
1250
m2k
Fig. 14. Pr. Semilogarithmic plot of impurity diffusion coefficicnts in hcp u- and bee L%praseodymiumvs. reciprocal temperature. La: [69D2], Ho: [69D2]. Mn: [75Dl], Fe: [75Dl], Co: [69D3], Cu: [7lDl], Ag: [69D3], Au: [69D3], Au in single crystals: [SlDl], Zn: [70Dl], In: [69D2]. Selfdiffusion according to chapter 2 is shown for comparison.
1o-q
lo-lo A
1
10“’
10-n 0. 5
0.70 0.75 40-3K-’ I l/TFig. 16. Er. Semilogarithmic plot of Au impurity diffusion coeftkicnts for hexagonal erbium single crystals vs. reciprocal temperature [79Dl]. Self-diffusion according to chapter 2 is shown for comparison.
I.82Claire
0.60
0.65
Land&-BGmstein New Seriec 111126
Ref. p. 2031
3 Diffusion of impurities in solid metallic elements (Figures) -7
,o-8 2000 K
1500 I ' m2/s T,=1940K
1250
1000 I I /'&=1155K
1o-7 m2/s
-I 1500 2000 K I 11 I T,=2125K
I
1000
II
I
I
I
Tu.p=1136K I
I,
IF9 s'
173
P(bcc) 1 dhcp) I I II
IO-"O
11 Mairix : Zr
lo-" ,o-l;
1O-l3 ~I lo-l4 10-15 Si
1
10-1'6 IO.17
k
Y Agtsc)
lo-"B IO-'91 0.4
10-19 10-2[ 0.5
0.6
0.7
0.8 l/T-
0.9
1.0
.lO-'K-'
Fig. 17. Ti. Semilogarithmic plot of diffusion coefficients for non-transition element impurities in titanium vs. reciprocal temperature. Be: [69Pl], Cu: [69Cl], Ag: [71Al], Al: [76Pl, 85Rl], Sn: [65Al], Si: [86Rl], Pin a-Ti: [86Nl], Pin S-Ti: [65Al]. Self-diffusion according to chapter 2 is shown for comparison.
, ‘I 0.5
0.7
0.8 l/T-
0.9
1.0 40JK'
1.2
Fig. 19. Zr. Semilogarithmic plot of diffusion coefficients for non-transition element impurities in zirconium vs. reciprocal temperature. Matrix u-Zr: Rb: [68Sl], Be: [76Tl], Cu: [75Hl], Ag single crystals (SC)and polycrystals: [89Vl], Au: [71Hl], Zn: [71Hl], Al: [85R2], Sn: [59Gl], Sb: [74Hl], S: [67Vl]. Matrix S-Zr: Rb: [68Sl], Be: [69Pl] and [76Tl], Ag: [82Ml], Sn: [59Gl], P: [7OVl], S: [67Vl]. Self-diffusion according to chapter 2 is shown for comparison.
For Fig. 18 seenext page.
Land&-Biirnstein New Series III/26
0.6
Le Claire
172
3 Diffusion of impurities in solid metallic elements(Figures)
[Ref. p. 203
-1 ,o.q
Too0
1500 I
K
d/s
1250
1000
I
10-q
1P
10-l'
10-'2
~I lo-l3
\
lo-‘&
\
lo-l5
10-1’6
10‘"
10-nL cL5
0.6
0.7
0.8
0.9
1.0
1.1.lO-‘K-’ 1.2
l/TFig. 18. Ti. Semilogarithmic plot ofdiffusion coefftcients for transition element impurities in titanium vs. reciprocal temperature. Matrix a-Ti: Mn: [88N2], Fe: [83Nl], Co: [85Nl, 85N2], Ni: [85N2], U: [78Fl]. Matrix P-Ti: SC:[71Al], Zr: [67Pl], V: [64Ml], Nb: [63Gl], Ta: [66Al], Cr: [63Gl], MO: [63Gl], W: [67Pl], Mn: [63Gl], Fe: [63Gl], Co: [63Gl], Ni: [63Gl], U: [78Fl], Pu: [71L2]. Self-diffusion according to chapter 2 is shown for comparison.
Le Claire
Land&-B6mstein New series III!26
Ref. p. 2031
3 Diffusion of impurities in solid metallic elements(Figures)
1500 I
ZOOOK I r, = 2125K
lo-* d/s
I T
1000 I
‘ti,P’
I
! I w&J
800 1
Matrix : Zr I
1136K
1U9
I
173
I
ICP
IO-" ,o-l;
1 Q
IL?
lo-"C
IO‘"
I I
lo-'C
/3(bccl I
I iI T3Y”1
10-1'1
lo-'1 1o-l!
t# 0.4
I
I
I
0.5
0.6
0.7
m 0.8 l/T-
0.9
1.0
1.1
^
-10" K-'
1.3
Fig. 20. Zr. Semilogarithmic plot of diffusion coefficients for transition element impurities in zirconium vs. reciprocal temperature. Matrix cL-Zr: Ce: [68P2], Ti: [74Hl], V: [68Al], Nb: [68Dl], Ta: [58Bl], Cr: [83B2], MO: [68P2], Mn: [73Tl], Fe: [88N2], Co: [81Kl], Ni: [72Hl, 87H2]. Self-diffusion in cL-Zr according to chapter 2 is shown for comparison. Matrix p-Zr: Ce: [68P2], Hf: [87H3], V: [68Al], Nb: [63Fl], Ta: [58Bl], Cr: [79Nl], MO: [68P2], W: [67Pl], Mn: [73Tl], Fe: [87Hl], Co: [69Kl], U: [71Fl].
Land&-Bknstein New Series III/26
Le Claire
3 Diffusion of impurities in solid metallic elements (Figures)
174
0.L
05
0.6
0.7 l/T-
-lo5 K-’
0.8
[Ref. p. 203
1.0
Fig. 21. Hf. Semilogarithmic plot of impurity diffusion coefficicnts in hafnium vs. reciprocal tcmpcraturc. Cr: [76Dl], Co: [76Dl], Al: [85R2]. Self-diffusion according tochapter 2 is shown for comparison. -T 10-10
2000K 1
1750 I ’ I
1500 I’ I
I I
I I
I I
I I
I I
I
0.50
0.55
0.60
0.65
0.70
0.75
m%
I
1250 I
I
I
I
I
10-l’ ,o-l;
, 0 -1:
10-n t
Q
,0-l!
10.” 10-l’ 10-u ,o -1:
0 i
I
I
\I
0.80 .W3K-’ 0.90
Fig. 22. V. Semilogarithmic plot of impurity diffusion coeftkients in vanadium vs. reciprocal lempcrature. Ti: [68Ml, 78Pl], Zr: [84Pl], Ta: [77Pl], Cr: [64Wl], Fe: [65P3, 81Al], Co: [7SPl], Ni: [86Pl], Al: [85Ml], P: [7OVl], S: [69Vl], U: [71F2]. Self-diffusion according to chapter 2 is shown for comparison Le Claire
Land&-BCmrlein New Series III!26
Ref. p. 2031
175
3 Diffusion of impurities in solid metallic elements (Figures) -T 2500 K 2250 IF9 I I m2/s r,=27LOK I I
2000
1500 I
1750 I
I
I
Matrix : Nb
\
h
hNi-l72All
\i
1
10-l'
1O-'6
10-19 \
A,\
1o-2o 1o-n 0.35
0.10
0.45
0.50
0.55 l/T-
0.60
0.65
0.70
.10‘3 K-'
0.80
Fig. 23. Nb. Semilogarithmic plot of impurity diffusion coefficients in niobium
vs. reciprocal temperature.Y: [71Gl], Ti: [70Rl, 7OP3], Zr: [70Rl, 78El], V: [70Rl, 68Al], Ta: [65Ll], Cr: [69P2], MO: [70Rl, 73Fl], W: [69F2, 70Rl], Fe: [62Pl, 77Al], Co: [76P2, 77A1, 62Pl], Ni: [72Al, 77Al], Cu: [77Al], Sn: [65A3], P: [68Vl], S: [68V2], U: [65Pl]. Self-diffusion according to chapter 2 is shown for comparison.
Land&Bihstein New Series III/26
Le Claire
176
[Ref. p. 203
3 Diffusion of impurities in solid metallic elements(Figures) -1 lo-” nn'/s
I-
I,=
2500 K 2250 2000
^^L.. jLWK
II
I
1750
II
1500 II I
I
1
I
1250 I
I
I
Matrix : la 1U lo-” 1o“5 10‘”
Y’\‘\ \
I
~I 10-l’
\
I \
lo-‘8
I I I IW
lo-‘9
I I
IIlo-‘O
1o-23 0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75 .lO-‘K-’ 0
l/TFig. 24. Ta. Semilogarithmic plot of impurity diffusion coefficients in tantalum vs. reciprocal temperature. Y: [71Gl], Nb: [65P2], MO: [68Bl], Fe: [55Vl, 76A2], Co: [76A2], Ni: [76A2], S: [69Vl], U: [71F2, 77Sl]. Self-diffusion according to chapter 2 is shown for comparison. -T
Fig. 25. Cr. Semilogarithmic plot of impurity diffusion coefftcicnts in chromium vs. reciprocal temperature.V: [76M2], MO: [6362], Fe: [64Wl]. Self-diffusion according to chapter 2 is shown for comparison.
Le Claire
0.45
0.50
0.55
0.60 l/T-
0.65
0.70 .lO”K-’ 0.80
Iandolt-B6mstein Nen Series III/26
Ref. p. 2031
3 Diffusion of impurities in solid metallic elements (Figures)
I".10
177
2500 K 289’3 :s I
\[\\
I
l.\I\
\I
I Irl71Mll \ I
lo-'" 10-1'9 10-20 0.35
0.40
045
0.50
0.55
0.60 l/T-
0.65
0.70
0.75
.10-K-’
0.85
Fig. 26. MO. Semilogarithmic plot of impurity diffusion coefficients in molybdenum vs. reciprocal temperature. Li: [77Ll], Y: [71Gi], V: [72Rl], Nb: [65A4, 72R1, 73Fl], Ta: [68Bl, 72Rl], Cr: [68Bl, 71Mi], W: [74El], Re: [64B2], Fe: [73Nl], Co: [65A4, 68Bl], Ni: [71M2], P: [68Vl], S: [68V3], U: [65Pl, 71F2]. Self-diffusion according to chapter 2 is shown for comparison.
Land&-BGmstein New Series III/26
Le Claire
178
3 Diffusion of impurities in solid metallic elements (Figures)
10-23 0.25
0.30
0.35
0.40
0.45
0.50 l/T-
0.55 0.60
[Ref. p. 203
0.65 010-~K-’0.75
Fig. 27. W. Semilogarithmic plot of impurity diffusion coefficients in tungsten vs. reciprocal tcmpcrature. Y:[71Gl],Nb: [69P4],Ta: [69P4,84Al],Cr:[89Kl], MO: [89Kl], Re: [65AS, 67L2, 84Al], Fe: [55Vl], OS: [84Al], Co: [89Ll], Ir: [84Al], Ni: (79M2]. P: [7811], S: [7211], U: [68Sl]. Self-diffusion according to chapter 2 is shown for comparison.
Fig 28. Fe. Semilogarithmic plot of impurity diffusion co- b efficients for non-transition element solutes in iron vs. reciprocal temperature. Be in a- and &Fe: [68G2], Be in y-Fe: [68Gl], Cu in y-Fe: ]66Sl, 68R1,77S2,78Ml], Cu in a-p-Fe: [7782, 68Rl], Cu in a-f-Fe: [77S2], Ag in a-p-Fe: [71Bl, 73El], Ag in a-f-Fe: [73El], Au in a-Fe: [63Bl], Zn in a-pFe: [81Rl], Sn in a-f-Fe: [72T2,84Hl], Sn in a-p-Fe: [72T2], Sn in y-Fe: [75M3, 86Kl], P in a-f-Fe: [81Ll, 83Ml], P in a-p-Fe: [83Ml], P in y-Fe: [64M2], As in y-Fe: [76B4], Sb in a-f-Fe: [78M2], Sb in a-p-Fe: [75Bl], S in a-Fe: [72Gl], S in a-f-Fe: [86A2], S in y-Fe: [71H2]. Ik Claire
Land&-BBmstein New Series III;26
-T 1750 K 10-g ,, , mi/,l~i.=l~09K
1500 I‘~~~,~=1~63K( I I
I1
I1
1250 I1
,I ~~~,p=11B3K
1000 I T,= 1043K I
I;
I Be
j
lo-"0
II I I
.
I Iv-Fe/
I
I
I I
II II
900 I
800 I
Matrix : Fe
I I w-D-Fe
I I II
Be+\ Ii \
oCuI77S21 Au[63Bll
l
l/T -
I I
I
I
-.
I n-f-Fe
I
I
I
3 Diffusion of impurities in solid metallic elements(Figures)
180
[Ref. p. 203
9 - Ii!
-
sss-11 .-zzu.- 0 . a0
---
9 L
Le Claire
Land&-Bhstein New Series III/26
3 Diffusion of impurities in solid metallic elements (Figures)
Ref. p. 2031
10-1:
1200 K
1100
1000
800
900
m*/s IF"
10.1:
10-'f
10.1;
~I
IO‘"
~~-1"
lo-*(
10-2
10-2;
,o-2:
C
0.9
1.0
1.1 l/T-
1.2
1.3 .105 K-' 1.4
Fig. 30. Fe. Semilogarithmic plot of Co impurity diffusion coefficients in c1iron vs. reciprocal temperature showing the influence of the magnetic transition [63Bl, 66J1, 82M2, 89Hl]. Self-diffusion according to chapter 2 is shown for comparison.
4 Fig. 29. Fe. Semilogarithmic plot of impurity diffusion coefficients for transition element solutes in iron vs. reciprocal temperature. Hf in y-Fe: [65Sl, 70Bl], V in y-Fe: [87Gl], V in u-p-Fe: [87Gl], Nb in a-p-Fe: [85Gl], Nb in y-Fe: [85Gl], CT in or-p-Fe:[89Hl], Mn in U-p-Fe and &Fe : [73K2], Mn in a-p-Fe: [7212], Mn in a-f-Fe and y-Fe: [70Nl], Co in u-Fe: [82M2, 84Kl], Co in y-Fe: [75H2, 69B2], Co in &Fe: [63B2, 66511,Ni in a-Fe: [89Cl, 63B1, 6lHl], Ni in y-Fe: [69B2, 6lH1, 78Hl], Pd in y-Fe: [77Fl], Pt in y-Fe: [73M3]. Land&-BBmstein New Series III/26
Le Claire
181
[Ref. p. 203
3 Diffusion of impurities in solid metallic elements(Figures)
182
-T 1750K 10“ A’ ’ lm=1768K mT/
1500 I
1250 A ’ 1, = 1393K
11cIO I
MCh X ..
co
lo-
f-Co
10-l
n
lo-’ I Q
+
1o-’
lo-
10‘
lo0.60
0
0.70
0.75 l/l-
0.80
0.85
0.90 -10 K”
1
Fig. 31. Co. Semilogarithmic plot of impurity diffusion coefficients in cobalt vs. reciprocal temperature. V: [86K2], Mn: [7711], Fe: [65A7, 69B2, 74B2], Ni: [62Hl, 65H1, 69B2], Pt: [73M3], Cu: [84A2], Zn: [74B2], S: [64Pl]. Selfdiffusion according to chapter 2 is shown for comparison.
Le Claire
Landolt-Btimstein New Series III/26
Ref. p. 2031
3 Diffusion of impurities in solid metallic elements (Figures) -T 1600K
1500 I
1400 I
1300 I
I
1200 I
Matrix : Ni
2.10-;;5
I 0.60
I 0.65
I 0.70 l/T-
I 0.75
I 0.80
\ 1 0.85.lO"K-' 0.90
Fig. 32. Ni. Semilogarithmic plot of impurity diffusion coefficients in nickel vs. reciprocal temperature. S: [75Vl], Te: [89Nl], Sb: [76Vl], In: [78V2], As: [79V2], Sn: [79Vl], Ag: [78Vl], Cu: [84Tl], Ge: [83M2], Fe: [71B2], Co: [78V3], W: [78V3]. For temperature ranges of the measurementssee section 3.2.10. Selfdiffusion according to chapter 2 is shown for comparison.
Land&-Biirnstein New Series III/26
Neumann
183
3 Diffusion of impurities in solid metallic elements(Figures)
184
-1 1600K 1LOO lLO0 1200 I’ 1’ l,= 1728K
lCig lo-g d/s
800 I ,o.,o
Matrix : Ni
I 10-l’
1000
[Ref. p. 203
2000K 16001400
d/s
\ 10-13
10-16
10-M It
0.5
0.6
0.7
0.8
a9 l/T-
1.0
1.1 .lO-jK-’ 1.3
Fig. 33. Ni. Semilogarithmic plot of impurity diffusion coefficients in nickel vs. reciprocal temperature including microsectioning measurements. Al: [81G2]. Two-exponential fits for In in Ni [88N3] and Ni in Ni [86N2].
lo-LL 0.4
0.6
I ! l/T -
10-73
1.0 .105K-’ 1.2
Fig. 34. Pd and Pt. Semilogarithmic plot of impurity diffusion coefficients in palladium and platinum vs. reciprocal temperature. Fe in Pd: [77Fl], Au in Pt: [78Rl]. For temperature ranges of the measurementsseesection 3.2.10.Self-diffusion according to chapter 2 is shown for comparison. The left hand D scalerefers to Pt and the right hand D scale refers to Pd.
Neumann
htdolbB6mstein New Series III/26
Ref. p. 2031
3 Diffusion of impurities in solid metallic elements (Figures)
0.70
0.75
0.80
0.85
0.90 l/T-
0.95
1.00
.10-j K-1
185
1.10
Fig. 35. Cu. Semilogarithmic plot of impurity diffusion coefficients in copper vs. reciprocal temperature for various slow diffusing impurities. Au: [60Nl], Fe: [58Ml], Co: [58Ml], Pd: [63Pl], Ni: [58Ml], Rh: [72F2], Pt: [82Nl], Ru: [73Bl], Ir: [78Kl]. For temperature ranges of the measurementsseesection 3.2.11. Self-diffusion according to chapter 2 is shown for comparison.
Land&-BBmstein New Series III/26
Neumann
3 Diffusion of impurities in solid metallic elements(Figures)
186
-10
10 m’‘IS y-&L
10
10
-I
1000
1300K
I 1
F F --II I
[Ref. p. 203
Matrix : Cu
tPb
S ib \
\
1 2
10
10
10
I
K-’ 1 l/lFig. 36. Cu. Semilogarithmic plot of impurity diffusion coeff’cicnts in copper vs. reciprocal tempcraturc for various fast diffusing impurities. S: [69M2], Pb: [77Gl], Sb: [6011], Sn: [73Gl], Cd: (58Hl], Hg: [60Nl], Ge: [70R2], Mn: [73F2]. Be: [73F3]. For temperature rangesofthcmeasurements seesection 3.2.11. Self-diffusion according to chapter 2 is shown for comparison. I
Neumann
Land&-BBmsfein New Series Ill!26
3 Diffusion of impurities in solid metallic elements (Figures)
Ref. p. 2031
187
2x-" mVs IO-"
\ \
I
I
\
lo-li
%Zn \ \ ,o-l:
t cl
10-14
,0-l'
10-If 0.70
0.75
0.80
0.85
0.90 l/T-
0.95
1.00
.I0 K-'
1.10
Fig. 37. Cu. Semilogarithmic plot of impurity diffusion coefficients in copper vs. reciprocal temperature for various fast diffusing impurities. Bi: [77Gl], Se: [89Rl], Te: [89Rl], Tl: [63Kl], P: [76Sl], In: [7262],As: [60Nl], Si: [73F3], Ag: [60Nl], Ga: [77F2], Zn: [57Hl], AI: [73F4]. For temperature ranges of the measurementsseesection 3.2.11. Self-diffusion according to chapter 2 is shown for comparison.
LandolGB6mstein New Series III126
Neumann
188
3 Diffusion of impurities in solid metallic elements(Figures)
lo-lo In’/:
13001200K1100 1000
-T 900
800
700
[Ref. p. 203
600
10” ,o-l;
,o-l!
lo-l4 lo-l5 10-16 QI 10”’ lo-“B lo-‘9 l0-m 10-n 10-n lo-” 10-2; 0.8
0.9
1.0
1.1
1.2 l/T-
1.3
1.4
1.5 .lOJK-’ 1.7
Fig. 38. Cu. Semilogarithmic plot of impurity diffusion coefficients in copper vs. reciprocal temperature including microsectioning measurements.Au: [60Ni, 87Fl]. Two-exponential fits for In, Co, Ni in Cu: [88N3] and Cu in Cu: [86N2].
Neumann
Land&-B6mstein New Series III/26
Ref. p. 2031
3 Diffusion of impurities in solid metallic elements (Figures)
1200K
4w'
-T 3 1001
1100
T
m2h ,o":
900
800
L
10-l"
1II-l4
\
\ \
\
\ \1
aI 10-l'
1 \
IP
lo-l7
I
I
lo-'[
24-”
!L.Io-3 K-11..
0.
0.85 l/T-
Fig. 39. Ag. Semilogarithmic plot of impurity diffusion coefficients in silver vs. reciprocal temperature. Ge: [58H2], Sb: [54Sl], Al: [75F2], Hg: [57Sl], Cr: [SINI], Fe: [61Ml], Co: [73Bl], Au: [63Ml], Pd: [63Pl], Pt: [82Nl]. For temperature ranges of the measurements see section 3.2.11. Self-diffusion according to chapter 2 is shown for comparison.
LandchB6mstein New Series III/26
Neumann
189
190
3 Diffusion of impurities in solid metallic elements(Figures)
[Ref. p. 203
-1
1200K
1100
1000
900
800
2
2 10-IS 8 6 4
0
0.85
0.90
0.95
1.00 1.05 l.lO 1.15 .@K-’ 1.25 l/lFig. 40. Ag. Semilogarithmic plot of impurity diffusion coeftkicnts in silver vs. reciprocal temperature. Se: [89Rl], Te: [8762], Ga: [77F2], Tl: [5882], Sn: [54Tl], In: [54Tl, 84Ml], Zn: [67Rl], Cd: [54Tl], Cu: [57Sl]. For temperature ranges of the measurementsseesection 3.2.11.Self-diffusion according to chapter 2 is shown for comparison.
Neumann
Landoh-Bbmstein New Series III126
Ref. p. 2031
191
3 Diffusion of impurities in solid metallic elements (Figures)
0.70
0.75
0.80
0.85
0.90 l/T-
0.95
1.00
1.05 .W3 K-'
1.15
Fig. 41. Au. Semilogarithmic plot of impurity diffusion coefficients in gold vs. reciprocal temperature. Te: [89Rl], Ge: [77Cl], Al: [78F3], Sn: [72H2], Hg:.[65Ml], In: [71D2], Zn: [77Cl], Fe: [77F3], Cu: [66Vi], Ag: [74H2], Co: [78H2], Ni: [76F2], Pd: [78F2], Pt: [78F2]. For temperature ranges of the measurements seesection 3.2.11. Self-diffusion according to chapter 2 is shown for comparison.
Land&Bhstein New Series III/26
Neumann
192
3 Diffusion
of impurities
in solid metallic
elements (Figures)
[Ref. p. 203
l/IFig. 42. Zn. Semilogarithmic plot of diffusion coefficients for slow diffusing impurities parallel (II) and perpendicular (I) to the hexagonal c axis in zinc vs. reciprocal temperature. Ag: [61Rl], Cu: [66B2], Au: [6363], Ni: [67M2]. For temperature ranges of measurementsseesection 3.2.12.Self-diffusion according to chapter 2 is shown for comparison.
Neumann
Landolt-B6mstein New series III/26
3 Diffusion of impurities in solid metallic elements(Figures)
Ref. p. 2031
193 1
6.1rP m*/:
I m=
650 K ,
550
500
c 93K
+z-!T \
I
-11
IO
5 \
I
I
-Cd Ilc t
I
nlc \
In Ilc
\ \ ,pi 4
\
I Q
Golc ,p
t Snlc \ \$7 Ilc IF"
2.104 1.6 l/T-
Fig. 43. Zn. Semilogarithmic plot of diffusion coefficients for fast diffusing impurities parallel (11)and perpendicular (I) to the hexagonal c axis in zinc vs. reciprocal temperature. Sn: [7OW2], In: [61Rl], Cd: [6363], Ga: [66B2], Hg: [67B3]. For temperature ranges of the measurements see section 3.2.12. Self-diffusion according to chapter 2 is shown for comparison.
Land&-Biimstein New Series III/26
Neumann
194
3 Diffusion of impurities in solid metallic elements (Figures)
540-‘1lT?/s
550K I1 = 59 K
[Ref. p. 203
51 -
lo-” \ ih. 10-n -
*
‘blc \
% $ g IIC g
.
IC
lo-‘J-
\
\n Ilc
h s \\ $1
nlc,
\\
\
\
~I lo-‘h-
\u IIC 10‘‘5---
t
\
i
\ \\
10-K~
10-l’ -
lo-‘B1.6
2.1 .l/l-
2.2
2.3
\L 2A *ll (-1 ;
Fig. 44. Cd. Semilogarithmic plot of impurity diffusion coefficients parallel (]I) and pcrpcndicular (I) to the hexagonal c axis in cadmium vs. reciprocal temperature. Pb: [81Yl], In: [72Ml], Hg: [72Ml], Zn: [72Ml], Ag: [72Ml], Au: [72Ml]. For temperature ranges of the measurements see section 3.2.12. Selfdiffusion according to chapter 2 is shown for comparison.
Neumann
Landolf-BBmstein New Series III/26
Ref. p. 2031
3 Diffusion of impurities in solid metallic elements (Figures)
&.\..,
1.0
1.1
1.2
1.3
IA
1.5
I.6 W3K4 1.7
l/T-
Fig. 45. Al. Semilogarithmic plot of diffusion coefficients for slow diffusing impurities in aluminum vs. reciprocal temperature. Co: [7OP4], Cu: [7OP4], Ni: [78E2], Mn: [71H3], Cr: [7OP4]. For temperature ranges of the measurements see section 3.2.13. Self-diffusion according to chapter 2 is shown for comparison.
Land&-BBmstein New Series III/26
Neumann
195
196
3 Diffusion of impurities in solid metallic elements (Figures)
l.,. -,,, , 9;OK ,
8;O
,
70,D,
,
[Ref. p. 203
,
6
6
\
4
lo-l5 e 6
&lo-“6 1.05
1.15
1.25
1.35 l/1 -
1.45
1.55.10-3K-’165
Fig. 46. Al. Scmilogarithmic plot of diffusion cocfficicnts for fast diffusing impurities in aluminum vs. reciprocal tcmpcraturc. Sn: [90El], In: [71H4], Cd: [70A3], Cc: [7OP4], Ga: [7OP4], Zn: [83B3], Au: [7OP4], Ag: [7OP4], Mg: [74Rl]. Li: [87Ml]. For tcmpcraturc ranges of the mcasurcmcnts set section 3.2.13. Self-diffusion according to chapter 2 is shown for comparison.
Neumann
Landok-Rihstein New Seric~ Ill.‘26
Ref. p. 2031
3 Diffusion of impurities in solid metallic elements (Figures) -T
;
K 400 -9 425 I I ’ /s T,,=430K
197
-T
350 I
375 I
325 I
10-g m2/s
550K
FiOCI
I
-10
400 I 1
450
, ) 7K
Matrix : TI
1o“o
10.
-11 _
IO'
10-l'
10.
IO-12 ,I'
1 -10‘
~1.lo-l3
-13 _
lo-
10-14
lo--15_
10-15
IO‘-16 _
lo-l6
lo- 17 2.3[I
2 5
2.60
2.75
2.90
-IO-%’
3
IO“7 1.:
l/T-
1.85
2.1
2.15
2.30
40” K-’ 2.60
l/T -
Fig. 47. In. Semilogarithmic plot of impurity diffusion coefficients parallel (I]) and perpendicular (I) to the tetragonal c axis in indium vs. reciprocal temperature. Au: [66A2], Ag: [66A2], Tl: [52El]. For temperature ranges of the measurements see section 3.2.13. Self-diffusion according to chapter 2 is shown for comparison.
Land&-Bhstein New Series III/26
1
Fig. 48. Tl. Semilogarithmic plot of impurity diffusion coefficients in bee S-thallium and hexagonal a-thallium parallel (I]) and perpendicular (I) to the c axis vs. reciprocal temperature. Au: [68A2], Ag: [68A2]. For temperature ranges of the measurements see section 3.2.13. Self-diffusion according to chapter 2 is shown for comparison.
Neumann
198
3 Diffusion of impurities in solid metallic elements(Figures)
[Ref. p. 203
-1 500 K
10-l m’l
LOO
i0 -
I
350 I
Matrix : Sn
VI-
Sn 11 i
10‘
1 I
lo-
lgIIC \ $ 4 \k \ nlc
\ t\
I -10-
lo-
lo-
lo-
lo1.9
2.0
2s
Fig. 49. Sn. Semilogarithmic plot of impurity diffusion coefficients parallel (]I) and perpendicular (I) to the tetragonal c axis in tin vs. reciprocal temperature. In: [SSSl], Cd: [7483], Hg: [72Wl], Sb: [71H5]. For temperature ranges of the measurementsseesection 3.2.14. Self-diffusion according to chapter 2 is shown for comparison.
Neumann
Land&-B6mstein New Series III!26
Ref. p. 2031
3 Diffusion of impurities in solid metallic elements(Figures) -1 10-; m2/!
500K
450
400
350
lo-' I
IV9I-
10-"[I
10-l'I_
pI
2-
10-l': 3-
10-l'
10-l' I_
10-l'I-
,o-l; ,
1.9
2.0
2.1
2.2
2.3
2.4 2.5 2.6 2.7 .lOJK-’ ; l/T Fig. 50. Sn. Semilogarithmic plot of diffusion coefftcients for fast diffusing impurities parallel (II) and perpendicular (I) to the tetragonal c axis in tin vs. reciprocal temperature. Ni: [84Yl], Cu: [67D2], Au: [66D2], Ag: [66D2], Zn: [74H3]. For temperature ranges of the measurements see section 3.2.14. Self-diffusion according to chapter 2 is shown for comparison.
Land&-Biirnstein New Series III/26
Neumann
200
3 Diffusion of impurities in solid metallic elements (Figures)
10d1
600K
550
[Ref. p. 203
jO0
10-
\ \ 3 ?
lfi
\
1.cu
-&h
10‘
\
~t lo-
\ \ 16
t \ \
lo-’
\ \
10-l
f
Sn
\2.2 ; 26 24 .lO K-’ 2.6 l/T Fig. 51. Pb. Semilogarithmic plot of impurity diffusion cocfkients in lead vs. reciprocal temperature. Cu: [75D3], Pd: [75D2], Au: [79D3], Pt: [8OVl], Ni: [73C2], Zn: [77Dl], Ag: (82823, Cd: [77Vl], Hg: [77Vl], Sn: [77D2], Tl: (61R2]. For temperature ranges of the measurements xc section 3.2.14. Self-diffusion according to chapter 2 is shown for comparison. 10“
1.6
1.7
1.6
Neumann
Landoll-BBmslein New Series III!26
Ref. p. 2031
201
3 Diffusion of impurities in solid metallic elements (Figures) -T 10 rn;
00 K 1800
1700 I
,=2028d 1
160CI
1500 I I &=I633 K
I Matrix : Th
-Ia(fcc)
10
+I-- Fe ‘0 I
rNi
b:IO-‘“m2/s
I 10 Q
I
10-1'5
IO
\ 1O-18 0.80
0.85
4
10
0.70
0.65 . I-
0.90
.10-3K-’ 1.
0.95
0.8040-3KK“ 0.85
0.75
.I//-
Fig. 52. Th. Semilogarithmic plot of impurity diffusion coefficients in thorium vs. reciprocal temperature. a-Th: Fe: [79Wl], Co: [79Wl], Ni: [79Wl], Pa: [67Sl], U: [67Sl]. Selfdiffusion according to chapter 2 is also shown for comparison. S-Th: Zr: [84Sl], Hf: [65Rl], Nb: [78S4], Ta: [7834], MO: [84Sl], W: [84Sl], Fe: [79Wl], Co: [79Wl], Re: [84Sl], Ni: [79Wl], V: [78S4].
For Fig. 53 seenext page.
Fig. 54. Pu. Semilogarithmic plot of impurity diffusion coefficients in plutonium vs. reciprocal temperature. &Pu: Co: [75Cl], Ag: [76Cl], Au: [76Cl]. Self-diffusion according to chapter 2 is shown for comparison. a-Pu: Co: [75C2], Cu: [76Cl], Ag: [76Cl], Au: [76Cl]. Self-diffusion according to chapter 2 is shown for comparison. Land&Bhnstein New Series III/26
10
10
Le Claire
I
1.2
I
1.3 l/T-
I
1
1.4
1.5
I
.10-3K-' I:
I
202
3 Diffusion of impurities in solid metallic elements (Figures)
1300K
1Cl-!
1200
1000
1100
[Ref. p. 203
900
m2/:
10-’
Matr
10”
~t lo-
10” e , i
lo-
lo-
I
I
0.75
0.80
0.85
0.90
0.95
1.00
1.05 -110-3K-’ 1.15
l/T-
Fig. 53. U. Semilogarithmic plot of impurity diffusion coefficients in uranium vs.reciprocaltemperature.a-U: Fe: [72Sl]; 0-U: Cr: [70D2,62Rl], Fe: [62Rl], Co: [70D2]. Self-diffusion according to chapter 2 is shown for comparison. y-U: Nb: [64PZ], Cr: [64P2], Mn: [64P2], Fe: [64P2], Co: [64P2], Ni: [64P2], Cu: [64P2], Au: [61R3]. Self-diffusion according to chapter 2 is shown for
Le Claire
Landolt-B&nstein New Series III/26
3.3 References for 3
203
3.3 References for 3 52El 54Sl 54Tl 55Hl 55Kl 55Ml 55Sl 55Vl 56Al 56Jl 57Hl 57Ml 57Rl 57Sl 58Bl 58Hl 58H2 58Ml 58Sl 59Gl 5911 59Ml 59Pl 6011 60Nl 61Al 61Hl 61H2 61Ml 61Rl 61R2 61R3 61Sl 62Dl 62Hl 62Pl 62Rl 63Bl 63B2 63Fl 63Gl 6362 6303 63Kl 63Ml 63Pl 64Bl 64B2
Eckert, R.E., Drickamer, H.G. : J. Chem. Phys. 20 (1952) 13. Sonder, E., Slifkin, L.M., Tomizuka, C.T.: Phys. Rev. 93 (1954) 97. Tomizuka, C.T., Slifkin, L.M.: Phys. Rev. 96 (1954) 610. Hoffman, R.E., Turnbull, D., Hart, E.W: Acta Metall. 3 (1955) 417. Kurtz, A.D., Averbach, B.L., Cohen, M. : Acta Metall. 3 (1955) 442. Mead, H.W., Birchenall, C.E.: Trans. AIME 203 (1955) 994. Sawatzky, A., Jaumot, F.E.: Phys. Rev. 100 (1955) 1627. Vasil’ev, YP., Kamardin, V.I., Skatskii, S.G., Chermomorchenko, S.G., Schuppe, G.N. : Tr. Stredneaziat Gos. Univ. Lenina 65 (1955) 47. Ascoli, A., Germagnoli, E., Mongini, L.: Nuovo Cimento 4 (1956) 123. Jaumot, F.E., Sawatzky, A.: J. Appl. Phys. 27 (1956) 1186. Hino, J., Tomizuka, C.T., Wert, C.A.: Acta Metall. 5 (1957) 41. Mead, H.W., Birchenall, C.E.: Trans. AIME 209 (1957) 874. Reynolds, J.E., Averbach, B.L., Cohen, M. : Acta Metall. 5 (1957) 29. Sawatzky, A., Jaumot, F.E.: Trans. AIME 209 (1957) 1207. Borisov, E.V., Godin, YuG., Gruzin, P.L., Eustyukhin, A.I., Emelyanov, VS. : Met. Met. Izdatel Akad. Nauk SSSR, Moscow 1958; Translation: NP-TR-448 1960,196. Hirone, T., Kunitomi, N., Sakamoto, M., Yamaki, H.: J. Phys. Sot. Jpn. 13 (1958) 838. Hoffman, R.E.: Acta Metall. 6 (1958) 95. Mackliet, C.A.: Phys. Rev. 109 (1958) 1964. Sawatzky, A.: J. Appl. Phys. 29 (1958) 1305. Gruzin, P.L., Emelyanov, VS., Ryabova, G.G., Federov, G.B.: 2nd Geneva Conf. Proc. 19 (1959) 187. Ikushima, A.: J. Phys. Sot. Jpn. 14 (1959) 1636. MacEwan, J.R., MacEwan, J.U., Yaffe, L. : Can J. Chem. 37 (1959) 1629. Pierce, C.B., Lazarus, D.: Phys. Rev. 114 (1959) 686. Inman, M.C., Barr, L.W.: Acta Metall. 8 (1960) 112. Nachtrieb, N.H., Tomizuka, C.T., Schulz, L.G.: Report AFOSR-TR-60-23, The University of Chicago, U.S.A. 1960. Ascoli, A.: J. Inst. Met. 89 (1961) 218. Hirano, K.-I., Cohen, M., Averbach, B.L.: Acta Metall. 9 (1961) 440. Hirone, T., Miura, S., Suzuoka, T.: J. Phys. Sot. Jpn. 16 (1961) 2456. Mullen, J.G.: Phys. Rev. 121 (1961) 1649. Rosolowski, J.H.: Phys. Rev. 124 (1961) 1828. Resing, H.A., Nachtrieb, N.H. : J. Phys. Chem. Solids 21 (1961) 40. Rothman, S.J.: J. Nucl. Mater. 3 (1961) 77. Suzuoka, T.: Trans. Jpn. Inst. Met. 2 (1961) 176. DonzC, G., Le Hazif, R., Maurice, F., Dutilloy, D., Adda, Y: C. R. Acad. Sci. (Paris) 254 (1962) 2328. Hirano, K.-I., Agarwala, R.P., Averbach, B.L., Cohen, M. : J. Appl. Phys. 33 (1962) 3049. Peart, R.F., Graham, D., Tomlin, D.H.: Acta Metall. 10 (1962) 519. Rothman, S.J., Peterson, N.L., Moore, S.A.: J. Nucl. Mater. 7 (1962) 212. Borg, R.J., Lai, D.Y.F.: Acta Metall. 11 (1963) 861. Borg, R.J., Lai, D.Y.F., Krikorian, O.H.: Acta Metall. 11 (1963) 867. Federer, J.I., Lundy, T.S.: Trans. Met. Sot. AIME 227 (1963) 592. Gibbs, G.B., Graham, D., Tomlin, D.H. : Philos. Mag. 8 (1963) 1269. Gruzin, P.L., Zemskii, S.V., Rodina, I.B.: Metall. Metalloved. Chist. Met. 4 (1963) 243 (A.E.R.E. Transl. 1032, 1965). Ghate, P.B.: Phys. Rev. 131 (1963) 174. Komura, S., Kunitomi, N.: J. Phys. Sot. Jpn. 18 Supp. II (1963) 208. Mallard, W.C., Gardner, A.B., Bass, R.F., Slifkin, L.M. : Phys. Rev. 129 (1963) 617. Peterson, N.L.: Phys. Rev. 132 (1963) 2471. Bokshtein, S.Z., Bronfin, M.B., Kishkin, S.T.: Diffusion ProcessesStructure and Property of Metals, Moscow 1964, p. 16; Translation: New York: Consultants Bureau 1965. Bronfin, M.B.: Diffusion ProcessesStructure and Properties of Metals, Moscow 1964, p. 24; Translation: New York: Consultants Bureau 1965.
Land&-Biimstein New Series III/26
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204 64Ml 64M2 64M3 64M4 64M5 64Nl 64Pl 64P2 64SI 64Wl 65Al 65A2 65A3 65A4 65AS 65A6 65Al 65A8 65C1 65Dl 65Gl 65Hl 65Kl 65L1 65Ml 65Pl 65P2 65P3 65Rl 65Sl 66Al 66A2 66A3 66Bl 66B2 66D1 66D2 66J1 66Kl 66Ll 66Nl 66Sl 66Vl 66Yl 67A1 67Bl 67B2 67B3 67Dl
3.3 References for 3 Murdock, J.F., Lundy, T.S., Stansbury, E.E.: Acta Metall. 12 (1964) 1033. Mural’, V.V., Gruzin, P.L.: Fiz. Met. Metalloved. 17 (1964) 792; Phys. Met. Metallogr. (English Transl.) 17 (5) (1964) 154. Monma, K., Suto, H., Oikawa, H.: J. Jpn. Inst. Met. 28 (1964) 188. Monma. K., Suto, H., Oikawa, H.: J. Jpn. Inst. Met. 28 (1964) 192. Monma, K., Suto, H., Oikawa, H.: J. Jpn. Inst. Met. 28 (1964) 197. Naumov, A.N.: Fiz. Tverd. Tela 6 (1964) 2517; Sov. Phys. Solid State (English Transl.) 6 (1964) 1997. Pavlyuchenko, M.M., Kononyuk, I.F.: Dokl. Akad. Nauk Belorussk. SSR 8 (1964) 157. Peterson. N.L., Rothman, S.J.: Phys. Rev. A 136 (1964) 842. Sato, K.: Trans. Jpn. Inst. Met. 5 (1964) 91. Wolfe, R.A., Paxton, H.W.: Trans. Met. Sot. AIME 230 (1964) 1426. Askill, J., Gibbs, G.B.: Phys. Status Solidi 11 (1965) 557 (Contains recalculated values of D’s and Qs from the measurementson Cr, Mn, Fe, Co, Ni, Nb, and MO reported in [63Gl]. However, since these seem.in some cases,to give a much inferior representation of the original data, none is quoted). Aganvala, R.P., Murarka. S.P.; Anand, MS.: Trans. Met. Sot. ATME 233 (1965) 986. Askill, J.: Phys. Status Solidi 9 (1965) K 167. Askill, J., in: Diffusion in Body-Centered Cubic’Metals, Am. Sot. Met. 1965, p. 247. Andelin. R.L., Knight, J.D., Kahn, M.: Trans. Met. Sot. AIME 233 (1965) 19. Askill, J.: Phys. Status Solidi 9 (1965) K113. Aucouturier, M., Lacombe, P.: Cobalt No. 28 (1965) 1. Anand, M.S., Murarka, S.P., Agarwala, R.P.: J. Appl. Phys. 36 (1965) 3860. Curtin, H.R., Decker, D.L., Vanfleet, H.B. : Phys. Rev. 139 (1965) A 1552. Dupouy, J.M., Mathie, J., Adda, Y.: Proc. Int. Conf. Metallurgy of Be. Grenoble 1965, p. 159. Graham. D.,in:DiffusioninBody-CenteredCubicMetals,Cleveland,U.S.A.:Am.Soc.Met.l%S,p.27. Hassner, A., Lange, W.: Phys. Status Solidi 8 (1965) 77. Klotsman, S.M., Arkhipova, N.K., Timofeyev, A.N., Trakhtenberg, ISh.: Fiz. Met. Metalloved. 20 (1965) 390; Phys. Met. Metallogr. (English Transl.) 20 (3) (1965) 70. Lundy, T.S., Winslow, F.R., Pawel, R.E., McHargue, C.J.: Trans. Met. Sot. AIME 233 (1965) 1533. Mortlock, A.J., Rowe, A.H.: Philos. Mag. 11 (1965) 1157. Pavlinov, L.U., Nakonechnikov, A.I., Bykov, V.N.: Sov. J. At. Energy (English Transl.) 19 (1965) 1495. Pawel. R.E., Lundy, T.S.: J. Phys. Chem. Solids 26 (1965) 937. Peart. R.F.: J. Phys. Chem. Solids 26 (1965) 1853. Rothman, S.J., Peterson, N.L., in: Diffusion in Body-Centered Cubic Metals, Am. Sot. Met. 1965, p. 183. Sparke, B., James.D.W., Leak, G.M.: J. Iron Steel Inst. 203 (1965) 152. Askill. J.: Phys. Status Solidi 16 (1966) K63. Anthony, T.R., Turnbull, D.: Phys. Rev. 151 (1966) 495. Ascoli, A., Bollani, B., Guardi, C., Kustidic, D.: Phys. Rev. 141 (1966) 732. Borisov, V.T., Golikov, V.M., Sherbedinskiy, G.V.: Fiz. Met. Metalloved. 22 (1966) 159; Phys. Met. Metallogr. (English Transl.) 22 (1) (1966) 175. Batra. A.P., Huntington, H.B.: Phys. Rev. 145 (1966) 542. Dyson, B.F., Anthony, T.R., Turnbull, D.: J. Appl. Phys. 37 (1966) 2370. Dyson, B.F.: J. Appl. Phys. 37 (1966) 2375. James,D.W., Leak, G.M.: Philos. Mag. 14 (1966) 701. Kidson, G.V.: Philos. Mag. 13 (1966) 247. Lal, K., Levy, V.: C. R. Acad. Sci. (Paris) C 262 (1966) 107. Naik, M.C., Dupouy, J.M., Adda. Y: Mtm. Sci. Rev. Metal!. 63 (1966) 488. Speich, G.R., Gula, J.A., Fisher, R.M., in: The Electron Microprobe, New York: Wiley 1966,p. 525. Vignes. A., Haeussler, J.P.: M&m. Sci. Rev. Metall. 63 (1966) 1091; C. R. Acad. Sci. (Paris) C 263 (1966) 1504. Yerko, V.F., Zelenskiy, V.F., Krasnorutskiy, V.S.: Fiz. Met. Metalloved. 22 (1966) 112; Phys. Met. Metallogr. (English Transl.) 22 (1) (1966) 112. Askill, J.: Phys. Status Solidi 23 (1967) K21. Barr, L.W., Mundy, J.N., Smith, EA.: Philos. Mag. 16 (1967) 1139. Barbouth, N., Oudar, J., CabanC,J.: C. R. Acad. Sci. (Paris) C 264 (1967) 1029. Batra, A.P., Huntington, H.B.: Phys. Rev. 154 (1967) 569. De Keroulas, F., Mary, J., QuCrC,J.: J. Nucl. Mater. 22 (1967) 276. Le Claire, Neumann
3.3 References for 3 67D2 67Hl 67Kl 67K2 67Ll 67L2 67Ml 67M2 67Pl 67P2 67P3 67Rl 67% 67Vl 68Al 68A2 68Bl 68B2 68B3 68B4 68Cl 68Dl 68Gl 6862 68Kl 68Ml 68M2 6801 6802 6803 68Pl 68P2 68Rl 68Sl 68Vl 68V2 68V3 69Bl 69B2 69B3 69Cl 69Dl 69D2 69D3 69Fl 69F2 69Kl
205
Dyson, B.F., Anthony, T.R., Turnbull, D. : J. Appl. Phys. 38 (1967) 3408. Hirschwald, W., Schrodter, W.: Z. Phys. Chem. N. F. 53 (1967) 392. Kaygorodov, V.N., Rabovskiy, Ya.A., Talinskiy, V.K. : Fiz. Met. Metalloved. 24 (1967) 117; Phys. Met. Metallogr. (English Transl.) 24 (1) (1967) 115. Kaygorodov, V.N., Rabovskiy, Ya.A., Talinskiy, V.K.: Fiz. Met. Metalloved. 24 (1967) 661; Phys. Met. Metallogr. (English Transl.) 24 (4) (1967) 78. Lal, K.: CEA Report R 3136, 1967. Larikov, L.M., Tyshkevich, V.M., Chorna, L.F. : Ukr. Fiz. Zh. 12 (1967) 983. Mundy, J.N., Ott, A., LBwenberg, L.: Z. Naturforsch. 22a (1967) 2113. Mortlock, A.J., Ewens, P.M.: Phys. Rev. 156 (1967) 814. Pavlinov, L.V. : Fiz. Met. Metalloved 24 (1967) 272; Phys. Met. Metallogr. (English Transl.) 24 (2) (1967) 70. Peart, R.F.: Phys. Status Solidi (1967) 545. Peterson, N.L., Rothman, S.J.: Phys. Rev. 154 (1967) 558. Rothman, S.J., Peterson, N.L.: Phys. Rev. 154 (1967) 552. Schmitz, F., Fock, M.: J. Nucl. Mater. 21 (1967) 317. Vandyshev, B.A., Panov, A.S., Gruzin, P.L.: Fiz. Met. Metalloved. 23 (1967) 908; Phys. Met. Metallogr. (English Transl.) 23 (5) (1967) 133. Agarwala, R.P., Murarka, S.P., Anand, M.S.: Acta Metall. 16 (1968) 61. Anthony, T.R., Dyson, B.F., Turnbull, D.: J. Appl. Phys. 39 (1968) 1391. Borisov, E.V., Gruzin, P.L., Zemskii, S.V.: Zashch. Pokryt. Metal. No.2, 1968, p. 104. Translation: Protective Coatings on Metals, Vol. 2, p. 76, New York: Consultants Bureau 1970. Blechet, J.J.,van Craeynest, A., Calais, D. : J. Nucl. Mater. 28 (1968) 177. Badrinarayanan, S., Mathur, H.B.: Int. J. Appl. Radiat. Isot. 19 (1968) 353. Blechet, J.J.,van Craeynest, A., Calais, D.: J. Nucl. Mater. 27 (1968) 112. Coleman, M.G., Wert, C.A., Peart, R.F.: Phys. Rev. 175 (1968) 788. Dyment, F., Libanati, C.M.: J. Nucl. Mater. 3 (1968) 349. Grigoriev, G.V., Pavlinov, L.V.: Fiz. Met. Metalloved. 25 (1968) 836; Phys. Met. Metallogr. (English Transl.) 25 (5) (1968) 79. Grigoriev, G.V., Pavlinov, L.V.: Fiz. Met. Metalloved. 26 (1968) 946; Phys. Met. Metallogr. (English Transl.) 26 (5) (1968) 179. KuEera, J., ZemEik, T’.: Can. Met. Quart. 7 (1968) 83. Murdock, J.F., McHargue, C.J.: Acta Metall. 16 (1968) 493. Murarka, S.P., Anand, MS., Agarwala, R.P.: Acta Metall. 16 (1968) 69. Ott, A., Nordtn-Ott, A.: Z. Naturforsch. 23a (1968) 473. Ott, A.: Z. Naturforsch. 23a (1968) 1683. Ott, A.: Z. Naturforsch. 23a (1968) 2126. Pavlinov, L.V., Gladyshev, A.M., Bykov, V.N.: Fiz. Met. Metalloved. 26 (1968) 823; Phys. Met. Metallogr. (English Transl.) 26 (5) (1968) 59. Paul, A.R., Anand, M.S., Naik, M.C., Agarwala, R.P. : Int. Conf. Vat. Interstitials in Metals. Jiilich, Sept. 1968, Vol.1, p. 105. Rothman, S.J., Peterson, N.L., Walter, C.M., Nowicki, L.J.: J. Appl. Phys. 39 (1968) 5041. Schwegler, E.Ch., White, EA.: Int. J. Mass Spectrom. Ion Phys. 1 (1968) 191. Vandyshev, B.A., Panov, A.S.: Fiz. Met. Metalloved. 26 (1968) 517; Phys. Met. Metallogr. (English Transl.) 26 (3) (1968) 138. Vandyshev, B.A., Panov, A.S. : Izv. Akad. Nauk SSSR, Met. No.1 1968, 206. Vandyshev, B.A., Panov, A.S. : Fiz. Metal. Metalloved. 25 (1968) 321; Phys. Met. Metallogr. (English Transl.) 25 (2) (1968) 130. Barr, L.W, Mundy, J.N., Smith, EA.: Philos. Mag. 20 (1969) 389. Badia, M., Vignes, A.: Acta Metall. 17 (1969) 177. Bartha, L., Szalay, T.: Int. J. Appl. Radiat. Isot. 20 (1969) 825. Caloni, O., Ferrari, A., Strocchi, P.M.: Electrochim. Metall. 4 (1969) 45. Dariel, M.P., Erez, G., Schmidt, G.M.J.: Philos. Mag. 19 (1969) 1053. Dariel, M.P., Erez, G., Schmidt, G.M.J.: Philos. Mag. 19 (1969) 1045. Dariel, M.P., Erez, G., Schmidt, G.M.J.: J. Appl. Phys. 40 (1969) 2746. Federov, G.B., Smirnov, E.A., Novikov, SM.: Metall. Metalloved. Chist. Met. 8 (1969) 41. Federov, G.B., Zhomov, F.J., Smirnov, E.A.: Metall. Metalloved. Chist. Met. 8 (1969) 145. Kidson, G.V., Young, G.J. : Philos. Mag. 20 (1969) 1047.
Land&-B&n&n New Series III/26
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206 69K2 69K3 69K4 69K5 69MI 69M2 69M3 6901 6902 69Pl 69P2 69P3 69P4 69SI 69Vl 70AI 70A2 70A3 70Bl 70B2 70B3 70Dl 70D2 70Hl 70Kl 7OLI 70NI 7001 7OPl 7OP2 7OP3 7OP4 70RI 70R2 7OSl 7OS2 7OVI 7OWl 7OW2 71AI 71Bl 71B2 71B3 71Dl 71D2 71Fl
3.3 References for 3 Klotsman, S.M., Rabovskiy, Ya.A., Talinskiy, V.K., Timofeyev, A.N.: Fiz. Met. Metalloved 28 (1969) 1025; Phys. Met. Metallogr. (English Transl.) 28 (6) (1969) 66. Kaygorodov, V.N., Klotsman, S.M., Timofeyev, A.N., Trakhtenberg, J.Sh.: Fiz. Met. Metalloved. 28 (1969) 120; Phys. Met. Metallogr. (English Transl.) 28 (1) (1969) 128. Kaygorodov, V.N., Klotsman, S.M., Timofeyev, A.N., Trakhtenberg, I.Sh.: Fiz. Met. Metalloved. 27 (1969) 1048; Phys. Met. Metallogr. (English Transl.) 27 (6) (1969) 91. KuEera, J., St&sky, K.: Can. Met. Quart. 8 (1969) 91. Mundy, J.N., Ott, A., Lowenberg, L., Lodding, A.: Phys. Status Solidi 35 (1969) 359. Moya, F., Moya-Goutier, G.E., CabanC-Brouty, F.: Phys. Status Solidi 35 (1969) 893. Miller, J.W.: Phys. Rev. 181 (1969) 1095. Ott, A.: J. Appl. Phys. 40 (1969) 2395. Ott, A., Lodding, A., Lazarus, D.: Phys. Rev. 188 (1969) 1088 and Corrigendum (private communication). Pavlinov, L.V., Grigor’yev, G.V., Gromyko, G.O.: Izv. Akad. Nauk SSSR, Met. No. 3,1969, 207; Russ. Metal!. (English Transl.) No.3, 1969, 158. Pelleg, J.: Philos. Mag. 19 (1969) 25. Pelleg, J.: J. Less-Common Met. 17 (1969) 319. Pawel, R.E., Lundy, T.S.: Acta Metal!. 17 (1969) 979. Smith, EA., Barr, L.W.: Philos. Mag. 20 (1969) 205. Vandyshev, B.A., Panov, A.S. : Izv. Akad. Nauk SSSR, Met. No. 1, 1%9, 244. Anan’in, V.A., Gladkov, V.P., Zotov, V.S., Skorov, D.M.: Sov. J. At. Energy (English Transl.) 29 (1970) 941. Anand, M.S., Agarwala, R.P.: Phys. Status Solidi (a) 1 (1970) K41. Alexander, W.B., Slifkin, L.M.: Phys. Rev. B 1 (1970) 3274. Bowen, A.W., Leak, G.M.: Metal!. Trans. 1 (1970) 1695. Barreau, G., Brunel, G., Cizeron, G., Lacombe, P.: C. R. Acad. Sci. (Paris) C 270 (1970) 516. Beyeler, M., Maurice, F., Seguin, R.: M&m. Sci. Rev. Metal!. 67 (1970) 295. Dariel, M.P.: Philos. Mag. 22 (1970) 563. Dariel, M.P., Blumenfeld, M., Kimmel, G.: J. Appl. Phys. 41 (1970) 1480. Hood, G.M.: Philos. Mag. 21 (1970) 305. Klotsman, S.M., Rabovskiy, Ya.A., Talinskiy, V.K., Timofeyev, A.N.: Fiz. Met. Metalloved. 29 (1970) 803; Phys. Met. Metallogr. (English Transl.) 29 (4) (1970) 127. Lataillade, F., Despres,1, Hocheid, B.: Plutonium and Other Actinides, Nucl. Metal!. 17 (1) (1970)144. Nohara, K., Hirano, K.-I.: Proc. Int. Conf. Sci. Tech. Iron & Steel 7 (1970) 11; seealso: Trans. Iron & Steel Inst. Jpn., Suppl. 11 (1971) 1267. Ott, A.: Z. Naturforsch. 25a (1970) 1477. Pavlinov, L.V.: Fiz. Met. Metalloved. 30 (1970) 367; Phys. Met. Metallogr. (English Transl.) 30 (2) (1970) 149. Pavlinov, L.V.: Fiz. Met. Metalloved. 30 (1970) 800; Phys. Met. Metallogr. (English Transl.) 30 (4) (1970) 129. Pelleg, J.: Philos. Mag. 21 (1970) 735. Peterson, N.L., Rothman, S.J.: Phys. Rev. B 1 (1970) 3264. Roux, F., Vignes, A.: Rev. Phys. Appl. (France) 5 (1970) 393. Reinke, ED., Dahlstrom, C.E.: Philos. Mag. 22 (1970) 57. Smith, EA., Barr, L.W.: Philos. Mag. 21 (1970) 633. Saxena, M.C., Sharma, B.D.: Trans. Indian Inst. Met. 23 (3) (1970) 16. Vandyshev, B.A., Panov, A.S. : Izv. Akad. Nauk SSSR, Met. No. 1, 1970, 231. Wang, S.-J., Grabke, H.J.: Z. Metallkde. 61 (1970) 597. Warford, J.S., Huntington, H.B.: Phys. Rev. B 1 (1970) 1867. Askill, J.: Phys. Status Solidi (b) 43 (1971) K I. Bondy, A., Levy, V.: C. R. Acad. Sci. (Paris) C 272 (1971) 19. Bakker, H., Backus, J., Waals, F.: Phys. Status Solidi (b) 45 (1971) 633. Barreu, G., Brunel, G., Cizeron, G.: C. R. Acad. Sci. (Paris) C 272 (1971) 618. Darie!, M.P.: J. Appl. Phys. 42 (1971) 2251. Dreyer, K., Herzig, Ch., Heumann, Th., in: Atomic Transport in Solids and Liquids, A.Lodding, T. Lagervall (eds.), Tubingen: Verlag der Zeitschrift fir Naturforschung 1971, p. 237. Federov, G.B., Smimov, E.A., Zhomov, F.I., Gusev, F.I., Paraev, S.A.: Metal!. Metalloved. Chist. Met. 9 (1971) 30. Le Claire, Neumann
Landolt-Kmstein New Series W/26
3.3 References for 3 71F2 71F3 71Gl 71Hl 71H2 71H3 71H4 71H.5 71Kl 71Ll 71L2 71Ml 71M2 7101 71Pl 71Sl 71Wl 7121 72Al 72A2 72A3 72Bl 72B2 72Cl 72C2 72Dl 72Fl 72F2 72Gl 7202 72G3 72Hl 72H2 72H3 7211 7212 72Ml 72Nl 7201 72Rl 72Sl 72Tl 72T2 72Wl 73Bl 73B2
Federov, G.B., Smirnov, E.A., Zhomov, F.I., Gusev, V.N., Paraev, S.A. : Sov. J. At. Energy (English Transl.) 31 (5) (1971) 1280. Fogelson, R.L., Ugay, Ya.A., Pokoev, A.V., Akimova, I.A.: Fiz. Tverd. Tela 13 (1971) 1028; Soviet Phys. Solid State (English Transl.) 13 (1971) 856. Gornyy, D.S., Al’tovskiy, R.M.: Fiz. Met. Metalloved. 31(1971) 781; Phys. Met. Metallogr. (English Transl.) 31 (4) (1971) 108. Hood, G.M.: Diffusion Processes,J.N.Sherwood et al. (eds.), New York: Gordon & Breach 1971, Vol.1, p. 361. Hoshino, A., Araki, T.: Trans. Nat. Res. Inst. Met. 13 (1971) 99. Hood, G.M., Schultz, R.J.: Philos. Mag. 23 (1971) 1479. Hood, G.M., Schultz, R.J.: Phys. Rev. B 4 (1971) 2339. Huang, F.H., Huntington, H.B.: Ser. Metall. 5 (1971) 705. Klotsman, S.M., Rabovskiy, Ya.A., Talinskiy, V.K., Timofeyev, A.N. : Fiz. Met. Metalloved. 31 (1971) 429; Phys. Met. Metallogr. (English Transl.) 31 (2) (1971) 214. Lodding, A., Ott, A. : Z. Naturforsch. 26a (1971) 81. Languille, A.: M&m. Sci. Rev. Metall. 68 (1971) 435. Mulyakaev, L.M., Shcherbedinskii, G.U., Dubinin, G.N.: Metallov. Term. Obrab. Met. 8 (1971) 45. Makhlin, N.A., Ivanov, L.I.: Izv. Akad. Nauk SSSR, Met. No. 1, 1971, 222; Russ. Met. (English Transl.) No. 1, 1971, 152. Ott, A.: J. Appl. Phys. 42 (1971) 2999. Paul, A.R., Agarwala, R.P.: Metall. Trans. 2 (1971) 1691. Saxena, M.C. : Trans. Indian Inst. Met. 24 (4) (1971) 56. Weyland, J.A., Decker, D.L., Vanfleet, H.B. : Phys. Rev. B 4 (1971) 4225. Zanghi, J.P., van Craeynest, A., Calais, D.: J. Nucl. Mater. 39 (1971) 133. Agarwala, R.P., Hirano, K.-I.: Trans. Jpn. Inst. Met. 13 (1972) 425. Anusavice, K.J., de Hoff, R.T.: Metall. Trans. 3 (1972) 1279. Anand, A., Agarwala, R.P. : Philos. Mag. 26 (1972) 297. Bergner, D.: Krist. Tech. 7 (1972) 651. Badrinarayanan, S., Mathur, H.B.: Indian J. Pure Appl. Phys. 10 (1972) 512. Combronde, J., Brebec, G.: Acta Metall. 20 (1972) 37. Candland, C.T., Decker, D.L., Vanfleet, H.B. : Phys. Rev. B 5 (1972) 2085. Dariel, M.P., Dayan, D., Calais, D.: Phys. Status Solidi (a) 10 (1972) 113. Fogelson, R.L., Ugay, Ya.A., Pokoyev, A.V.: Fiz. Met. Metalloved. 33 (1972) 1102; Phys. Met. Metallogr. (English Transl.) 33 (5) (1972) 194. Fogelson, R.L., Ugay, Ya.A., Pokoyev, A.V.: Fiz. Met. Metalloved. 34 (1972) 1104; Phys. Met. Metallogr. (English Transl.) 34 (5) (1972) 198. Gruzin, P.L., Mural’, V.V., Fokin, A.P. : Fiz. Met. Metalloved. 34 (1972) 1326; Phys. Met. Metallogr. (English Transl.) 34 (6) (1972) 209. Gorbachev, VA., Klotsman, S.M., Rabovskiy, Ya.A., Talinskiy, V.K., Timofeyev, A.N. : Fiz. Met. Metalloved. 34 (1972) 879; Phys. Met. Metallogr. (English Transl.) 34 (4) (1972) 202. God&y, I., Beke, D.L., Kedves, F.J.: Phys. Status Solidi (a) 13 (1972) K 155. Hood, G.M., Schultz, R.J.: Philos. Mag. 26 (1972) 329. Herzig, Ch., Heumann, Th.: Z. Naturforsch. 27a (1972) 1109. Herzig, Ch., Heumann, Th. : Z. Naturforsch. 27 a (1972) 613. Iovkov, V.P., Panov, A.S., Ryabenko, A.V. : Fiz. Met. Metalloved. 34 (1972) 1322; Phys. Met. Metallogr. (English Transl.) 34 (6) (1972) 203. Irmer, V., Feller-Kniepmeier, M.: J. Phys. Chem. Solids 33 (1972) 2141. Mao, Ch.: Phys. Rev. B 5 (1972) 4693. Nishikawa, S., Tsumuraya, K.: Philos. Mag. 26 (1972) 941. Owens, C.W., Turnbull, D. : J. Appl. Phys. 43 (1972) 3933. Roux, R. : Thesis, Univ. Nancy, France 1972. Stelly, M., Servant, J.M.: J. Nucl. Mater. 43 (1972) 269. Tendler, R., Varotto, C.F.: J. Nucl. Mater. 44 (1972) 99. Treheux, D., Marchive, D., Delagrange, J., Guiraldenq, P.: C. R. Acad. Sci. (Paris) C 274 (1972) 1260. Warburton, W.K.: Phys. Rev. B 6 (1972) 2161. Bernardini, J., CabanC,J.: Acta Metall. 21 (1973) 1561. Bergner, D., Cyrener, E.: Neue Hiitte 18 (1973) 356.
Land&-Biimstein New Series III/26
Le Claire, Neumann
208 73B3 73Cl 73C2 73Dl 73El 73Fl 73F2 73F3 73F4 73Gl 73Kl 73K2 73K3 73Ml 73M2 73M3 73M4 73Nl 73Tl 73T2 73T3 73Wl 74Al 74A2 74B 1 74B2 74El 74Fl 74Hl 74H2 74H3 74Ll 74Ml 74R 1 74R2 74Tl 7.5Bl 75Cl 75C2 7SDl 75D2 75D3 75Fl 75F2 75Hl 75H2 75H3 75Ml 75M2
3.3 References for 3 Bergner, D., Cyrener, E.: Neue Hiitte 18 (1973) 9. Cathey, W.N., Murphy, J.E., Woodyard, J.R.: Metall. Trans. 4 (1973) 1463. Candland, CT., Vanfleet, H.B.: Phys. Rev. B 7 (1973) 575. Dariel, M.P.: Philos. Mag. 28 (1973) 915. Eguchi, T., Iijima, Y, Hirano, K.-I.: Cryst. Lattice Defects 4 (1973) 265. Federov, G.B., Smirnov, E.A., Gusev, V.N., Zhomov, F.I., Gorbenko, V.L.: Metall. Metalloved. Chist. Met. No. IO, 1973, 62. Fogelson, R.L., Ugay, Ya.A., Pokoyev, A.V. : Izv. Vyssh. Uchebn. Zaved., Chern. Metall. (9) (1973) 136. Fogelson, R.L., Ugay, Ya.A., Pokoyev, A.V., Akimova, I.A., Kretinin, V.D.: Fiz. Met. Metalloved. 35 (1973) 1307; Phys. Met. Metallogr. (English Transl.) 35 (6) (1973) 176. Fogelson, R.L., Ugay, Ya.A., Pokoyev, A.V. : Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metall. 16 (1973) 143. Gorbachev, V.A., Klotsman, SM., Rabovskiy, Ya.A., Talinskiy, V.K., Timofeyev, A.N.: Fiz. Met. Metalloved. 35 (1973) 889; Phys. Met. Metallogr. (English Transl.) 35 (4) (1973) 226. Korneluk, L.G., Mirsky, L.M., Bokshtein, B.S.: Titanium Science and Technology, Vol.11, 1973, p. 905. Kirkaldy, J.S., Smith. P.N., Sharma, R.C.: Metall. Trans. A 4 (1973) 624. Kuzmenko, P.P., Grinevich, G.P.: Metallotiz. 47 (1973) 98. Mundy, J.N., McFall, W.D.: Phys. Rev. B 7 (1973) 4363. Mundy, J.N., McFall, WD.: Phys. Rev. B 8 (1973) 5477. Million. B., K&era, J.: Kovove Mater. 11 (1973) 300. Marumo, T., Fujikawa, S., Hirano, K.-I.: J. Jpn. Inst. Light Met. 23 (1973) 17. Nohara. K., Hirano, K.-I.: Nippon Kinzoku Gakkaishi; (J. Jpn. Inst. Met.) 37 (1973) 731. Tendler, R., Varotto, C.F.: J. Nucl. Mater. 46 (1973) 107. Tiwari, G.P., Saxena, M.C., Patil, R.V.: Trans. Indian Inst. Met. 26 (1973) 55. Tiwari, G.P., Sharma, B.D.: Indian J. Technol. 11 (1973) 560. Warburton, W.K.: Phys. Rev. B 7 (1973) 1330. Albrecht, W.W., Frohberg, G., Wever, H.: Z. Metallkde. 65 (1974) 279. Ascoli, A., Filoni, L., Poletti, G., Rossi, S.L.: Phys. Rev. B 10 (1974) 5003. Biersack, J.B., Fink, D.: Proc. Symp. Fusion Technology, 8th, EUR-5182, 1974, p. 907. Bristoti, A., Wazzan, A.R.: Rev. Bras. Fis. 4 (1974) 1. Erley, W., Wagner, H.: Phys. Status Solidi (a) 25 (1974) 463. Fogelson, R.L., Ugay, Ya.A., Akimova, I.A.: Fiz. Met. Metalloved. 37 (1974) 1107; Phys. Met. Metallogr. (English Transl.) 37 (5) (1974) 201. Hood, G.M., Schultz, R.J.: Acta Metall. 22 (1974) 459. Herzig. Ch., Wolter, D.: Z. Metallkde. 65 (1974) 273. Huang. F.H., Huntington, H.B.: Phys. Rev. B 9 (1974) 1479. Lesage, B., Huntz, A.M.: J. Less-Common Met. 38 (1974) 149. Myers, S.M., Picraux, S.T., Prevender, T.S.: Phys. Rev. B 9 (1974) 3953. Rothman, S.J.,Peterson, N.L., Nowicki, L.J., Robinson, L.C.: Phys. Status Solidi (b) 63 (1974) K 29. Ross, R.A., Vanfleet, H.B., Decker, D.L. : Phys. Rev. B 9 (1974) 4026. Tendlcr, R., Varotto, C.F.: J. Nucl. Mater. 54 (1974) 212. Bruggeman, G.A., Roberts jr., J.A.: Metall. Trans. A 6 (1975) 755. Charissoux, C., Calais. D., Gallet, G.: J, Phys. Chem. Solids 36 (1975) 981. Charissoux, C., Calais, D.: J. Nucl. Mater. 57 (1975) 45. Dariel. M.P.: Acta Metall. 23 (1975) 473. Decker, D.L., Candland, C.T., Vanfleet, H.B.: Phys. Rev. B 11 (1975) 4885. Decker, D.L.: Phys. Rev. B 11 (1975) 1770. Fogelson. R.L., Ugay, Ya.A., Akimova, I.A.: Fiz. Met. Metalloved. 39 (1975) 447; Phys. Met. Metallogr. (English Transl.) 39 (2) (1975) 212. Fogelson, R.L., Ugay, Ya.A., Akimova, I.A.: Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metall. (2) 1975, 142. Hood, G.M., Schultz, R.J.: Phys. Rev. B 11 (1975) 3780. Henry, G., Barreau, G., Cizcron, G.: C. R. Acad. Sci. (Paris) C 280 (1975) 1007. Hehenkamp, Th., Wiibbcnhorst, R.: Z. Metallkde. 66 (1975) 275. Myers, S.M., Langley, R.A.: J. Appl. Phys. 46 (1975) 1034. Murphy, J.E., Adams, G.H., Cathey, W.N.: Metall. Trans. A 6A (1975) 343. Le Claire, Neumann
Landoh-BBm&n New Series 111126
3.3 References for 3 75M3 75Pl 75Sl 75Vl 75Wl 75W2 76Al 76A2 76Bl 76B2 76B3 76B4 76Cl 76Dl 76Fl 76F2 76F3 76Gl 76Ll 76Ml 76M2 76Pl 76P2 76% 76Tl 76T2 76Vl 77Al 77Bl 77B2 77B3 77Cl 77Dl 77D2 77Fl 77F2 77F3 77Gl 77Hl 7711 7712 77Jl 77Ll 77Pl
209
Marchive, D., Due, D., Treheux, D., Guiraldenq, P.: C. R. Acad. Sci. (Paris) C 280 (1975) 25. Pelleg, J.: Philos. Mag. 32 (1975) 593. Santos, E., Dyment, F.: Philos. Mag. 31 (1975) 809. Vladimirov, A.B., Kaygorodov, V.N., Klotsman, S.M., Trakhtenberg, I.Sh.: Fiz. Met. Metalloved. 39 (1975) 319; Phys. Met. Metallogr. (English Transl.) 39 (2) (1975) 82. Wu, C.H.: J. Chem. Phys. 62 (1975) 4589. Warburton, W.K.: Phys. Rev. B 11 (1975) 4945. Anan’in, V.A., Gladkov, V.P., Svetlov, A.V., Skorov, D.M., Tenishev, V.I.: Sov. J. At. Energy (English Transl.) 40 (1976) 304. Ablitzer, D., Gantois, M.: La Diffusion dans les Milieux Condenses. Theorie et Applications. CEN Saclay, Vol. 1, 1976, p. 299. Beyer, G.J., Novgorodov, A.F.: Radiochem. Radioanal. Lett. 27 (5/6) (1976) 341; seealso: ZfK-311 (Zentralinstitut fiir Kernforschung, Dresden, DDR) 1976. Beyer, G.J.: ZfK-310 (Zentralinstitut fur Kernforschung, Dresden, DDR) 1976. Beyer, G.J.: ZfK-317 (Zentralinstitut fur Kernforschung, Dresden, DDR) 1976. BoiiC, B.I., LuEiC, R.J.: J. Mater. Sci. 11 (1976) 887. Charissoux, C., Calais, D.: J. Nucl. Mater. 61 (1976) 317. Dyment, F.: J. Nucl. Mater. 61 (1976) 271. Fromont, M.: J. Phys. (Paris) Lett. 37 (1976) L117. Fogelson, R.L.,Ugay, Ya.A., Akimova, I.A.: Fiz. Met. Metalloved. 41(1976) 653; Phys. Met. Metallogr. (English Transl.) 41 (3) (1976) 180. Fujikawa, S., Hirano, K.-I.: Trans. Jpn. Inst. Met. 17 (1976) 809. Gladkov, V.P., Svetlov, A.V., Skorov, D.M., Tenishev, V.I., Shabalin, A.N. : Sov. J. At. Energy (English Transl.) 40 (1976) 306. Ladet, J., Bernardini, J., Cabane-Brouty, F.: Ser. Metall. 10 (1976) 195. Marbach, G., Charrissoux, C., Janot, C.: La Diffusion dans les Milieux Condenses - ThCorie et Applications. Proc. Colloque de Metallurgic. CEN Saclay, Vol. 1, 1976, p. 119; Report CEA-Conf.3674. Mundy, J.N., Tse, C.W., McFall, WD. : Phys. Rev. B 13 (1976) 2349. Pokoev, A.V., Mironov, V.M., Kudryavtseva, L.K.: Izv. Vyssh. Uchebn. Zadev., Tsvetn. Metall. 19 (2) (1976) 130; Sov. Non-Ferrous Met. Res. (English Transl.) 4 (2) (1976) 81. Pelleg, J.: Philos. Mag. 33 (1976) 165. Spindler, P., Nachtrieb, K.: Phys. Status Solidi (a) 37 (1976) 449. Tendler, R., Abriata, J., Varotto, C.F.: J. Nucl. Mater. 59 (1976) 215. Treheux, D., Heurtel, A., Guiraldenq, P.: Acta Metall. 24 (1976) 503. Vladimirov, A.B., Kaygorodov, V.N., Klotsman, S.M., Trakhtenberg, ISh.: Fiz. Met. Metalloved. 41 (1976) 429. Phys. Met. Metallogr. (English Transl.) 41 (2) (1976) 181. Ablitzer, D.: Philos. Mag. 35 (1977) 1239. Beyer, G.J., Fromm, WD., Novgorodov, A.F.: Nucl. Instr. Methods 146 (1977) 419. Bharati, S., Badrinarayanan, S., Sinha, A.P.B.: Phys. Status Solidi (a) 43 (1977) 653. Beke, D.L., God&y, I., Kedves, F.J., Groma, G.: Acta Metall. 25 (1977) 539. Cardis, D. : Doctoral Thesis, Univ. Miinster, FRG 1977. Decker, D.L., Ross, R.A., Evenson, W.E., Vanfleet, H.B. : Phys. Rev. B 15 (1977) 507. Decker, D.L., Weiss,J.D., Vanfleet, H.B.: Phys. Rev. B 16 (1977) 2392. Fillon, J., Calais, D.: J. Phys. Chem. Solids 38 (1977) 81. Fogelson, R.L., Ugay, Ya.A., Akimova, I.A. : Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metall. (1) 1977, 172. Fogelson, R.L., Kazimirov, N.N., Soshnikova, I.V.: Fiz. Met. Metalloved. 43 (1977) 1105; Phys. Met. Metallogr. (English Transl.) 43 (5) (1977) 185. Gorbachev, V.A., Klotsman, S.M., Rabovskiy, Ya.A., Talinskiy, V.K., Timofeyev, A.N.: Fiz. Met. Metalloved. 44 (1977) 214; Phys. Met. Metallogr. (English Transl.) 44 (1) (1977) 191. Hoshino, K., Iijima, Y, Hirano, K.-I.: Metall. Trans. A 8 (1977) 469. Iijima, Y, Hirano, K.-I., Taguchi, 0.: Philos. Mag. 35 (1977) 229. Iijima, Y, Hoshino, K., Hirano, K.-I.: Metall. Trans. A 8 (1977) 997. Jackson, M.S., Lazarus, D.: Phys. Rev. B 15 (1977) 4644. Larikov, L.N., Isaichev, V.I., Maksimenko, E.A., Belkov, B.M.: Dokl. Akad. Nauk SSSR 237 (2) (1977) 315; Sov. Phys. Dokl. (English Transl.) 22 (1977) 677. Pelleg, J., Herman, M.: Philos. Mag. 35 (1977) 349.
Landok-Biimstein New Series III/26
Le Claire, Neumann
210 17Sl r7S2 17s3 17vl 18Bl 18El 18E2 18Fl 18F2 78F3 78F4 78Hl 78H2 7811 78Kl 78K2 78K3 78Ml 78M2 78Nl 78Pl 78P2 78Rl 78Sl 7832 78S3 78S4 78Vl 78V2 78V3 79Dl 79D2 79D3 79Gl 79Kl 79Ml 79M2 79M3 79M4 79Nl 79Pl 79P2 79Sl 79S2 79Vl 19V2 79Wl
3.3 References for 3 Su, C.S.: Nucl. Instr. Methods 145 (1977) 361. Salje, G., Feller-Kniepmeier, M.: J. Appl. Phys. 48 (1977) 1833. Sudir, S., Csikai, J., Buczko, M.: Z. Metallkde. 68 (1977) 740. Vanfleet, H.B., Jorgenson, J.D., Schmutz, J.D., Decker, D.L.: Phys. Rev. B 15 (1977) 5545. Bergner, D., Schwarz, K.: Neue Hiitte 23 (1978) 210. Einziger, R.E., Mundy, J.N.: Phys. Rev. B 17 (1978) 449. ErdClyi, G., Beke, D.L., Kedves, F.J., Godeny, I.: Philos. Mag. B 38 (1978) 445. Federov, G.B., Smimov, E.A. : Diffuziya v. Reaktornykh Materialakh. Moscow: Atomizdat Publ. 1978. Translation: Diffusion in Reactor Materials. Trans. Tech. Pub!., Switzerland 1984. Fogelson, R.L., Voronina, I.M., Somova, T.I.: Fiz. Met. Metalloved. 46 (1978) 190; Phys. Met. Metallogr. (English Transl.) 46 (1) (1978) 163. Fogelson, R.L., Trotimova, N.N.: Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metal!. (4) 1978, 152. Fujikawa, S., Hirano, K.-I., Fukushima, Y: Metall. Trans. A 9 (1978) 1811. Hanatate, Y., Majima, K., Mitani, H.: Trans. Jpn. Inst. Met. 19 (1978) 669. Herzig, Ch., Eckseler, H., Bussmann, W., Cardis, D.: J. Nucl. Mater. 69/70 (1978) 61. Iovkov, V.P., Panov, A.S., Ryabenko, A.V.: Izv. Akad. Nauk SSSR, Met. No. 1, 1978, 78; Russ. Met. (English Transl.) No. 1, 1978, 68. Klotsman, S.M., Rabovskiy, Ya.A., Talinskiy, V.K., Timofeyev, A.N.: Fiz. Met. Metalloved. 45 (1978) 1104; Phys. Met. Metallogr. (English Transl.) 45 (5) (1978) 181. Krautheim, G., Neidhardt, A., Reinhold, U.: Krist. Techn. 13 (1978) 1335. Kusunoki, K., Nishikawa, S.: Ser. Metal!. 12 (1978) 615. Majima, K., Mitani, H.: Trans. Jpn. Inst. Met. 19 (1978) 663. Myers, S.M., Rack, H.J. : J. Appl. Phys. 49 (1978) 3246. Nikolaev, G.I., Bodrov, N.V.: Zh. Fiz. Khim. 52 (1978) 143. Pelleg, J.: Rev. High-Temp. Mater. IV (1978) 5. Peterson, N.L., Rothman, S.J.: Phys. Rev. B 17 (1978) 4666. Rein, G., Mehrer, H., Maier, K.: Phys. Status Solidi (a) 45 (1978) 253. Sen, S.K., Dutt, M.B., Barua, A.K.: Phys. Status Solidi (a) 45 (1978) 657. Sawanayagi, F., Hasiguti, R.R.: J. Jpn. Inst. Met. 42 (1978) 1155. Shimotomai, M., Hasiguti, R.R., Umeyama, S.: Phys. Rev. B 18 (1978) 2097. Schmidt, EA., Conzemius, R.J., Carlson, O.N.: J. Less-Common Met. 59 (1978) 53. Vladimirov, A.B., Kaygorodov, V.N., Klotsman, S.M., Trakhtenberg, I.Sh.: Fiz. Met. Metalloved. 45 (1978) 1015; Phys. Met. Metallogr. (English Transl.) 45 (5) (1978) 100. Vladimirov, A.B., Kaygorodov, V.N., Klotsman, S.M., Trakhtenberg, I.Sh.: Fiz. Met. Metalloved. 45 (1978) 1301; Phys. Met. Metallogr. (English Transl.) 45 (6) (1978) 160. Vladimirov, A.B., Kaygorodov, V.N., Klotsman, S.M., Trakhtenberg, I.Sh.: Fiz. Met. Metalloved. 46 (1978) 1232; Phys. Met. Metallogr. (English Transl.) 46 (6) (1978) 94. Dariel, M.P., Komblit, L., Beaudry, B.J., Gschneidner, K.A.: Phys. Rev. B 20 (1979) 3949. Dutt, M.B., Sen, S.K.: Jpn. J. App!. Phys. 18 (1979) 1025. Decker, D.L., Melville, J.G., Vanfleet, H.B.: Phys. Rev. B 20 (1979) 3036. Gladkov, V.P., Svetlov, A.V., Skorov, D.M., Shabalin, A.N.: Fiz. Met. Metalloved. 48 (1979) 871; Phys. Met. Metallogr. (English Transl.) 48 (4) (1979) 170. Krautheim, G., Neidhardt, A., Reinhold, U., Zehe, A.: Phys. Lett. A 72 (1979) 181. Maier, K., Mehrer, H., Rein, G.: Z. Metallkde. 70 (1979) 271. Muster, W.J.,Yoon, D.N., Huppmann, W.J.: J. Less-Common Met. 65 (1979) 211. Maier, K., Kirchheim, R., Tiilg, G.: Mikrochim. Acta Suppl. 8 (1979) 125. Makuta, F., Iijima, Y, Hirano, K.-I.: Trans. Jpn. Inst. Met. 20 (1979) 551. Nicolai, L.I., de Tendler, R.H.: J. Nucl. Mater. 87 (1979) 401. Pontau, A.E., Lazarus, D.: Phys. Rev. B 19 (1979) 4027. Pruthi, D.O., Anand, M.S., Agarwala, R.P.: Philos. Mag. A 39 (1979) 173. Shabalin, A.N., Gladkov, V.P., Gruzin, P.L., Svetlov, A.V.: Fiz. Met. Metalloved. 48 (1979) 663; Phys. Met. Metallogr. (English Transl.) 48 (3) (1979) 182. Sathyraj, K.V., Ablitzer, D., Demangeat, C.: Philos. Mag. A 40 (1979) 541. Vladimirov, A.B., Kaygorodov, V.N., Klotsman, S.M., Trakhtenberg, I.Sh.: Fiz. Met. Metalloved. 48 (1979) 352; Phys. Met. Metallogr. (English Transl.) 48 (2) (1979) 107. Vladimirov, A.B., Klotsman, S.M., Trakhtenberg, IS. : Fiz. Met. Metalloved. 48 (1979) 1113; Phys. Met. Metallogr. (English Transl.) 48 (5) (1979) 193. Weins, W.N., Carlson, O.N.: J. Less-Common Met. 66 (1979) 99. L.e Claire, Neumann
Land&-BBmstein New Series III/26
3.3 References for 3 80Dl 80Vl 81Al 8lDl 81Gl 81G2 81Kl 81Ll 81Nl 81Rl 8lYl 82Al 82Hl 82H2 82Ml 82M2 82Nl 8201 82Pl 83Al 83Bl 83B2 83B3 83Cl 83Gl 83Hl 83Kl 83Ml 83M2 83M3 83Nl 83N2 83Rl 84Al 84A2 84Dl 84Hl 84Kl 84Ml 84Pl 84Sl 84Tl 84Yl 85Gl 85Ml 85Nl 85N2
211
Dorner, P., Gust, W., Hintz, H.B., Lodding, A., Odelius, H., Predel, B. : Acta Metall. 28 (1980) 291. Vanfleet, H.B.: Phys. Rev. B 21 (1980) 4337. Ablitzer, D., Haeussler, J.P., Sathyraj, K.V., Vignes, A.: Philos. Mag. A 44 (1981) 589. Dariel, M.P., McMasters, O.D., Gschneidner, K.A.: Phys. Status Solidi (a) 63 (1981) 329. Gust, W., Hintz, H.B., Lodding, A., Odelius, H.: Philos. Mag. A 43 (1981) 1205. Gust, W, Hintz, H.B., Lodding, A., Odelius, H., Predel, B.: Phys. Status Solidi (a) 64 (1981) 187. Kidson, G.V.: Philos. Mag. A 44 (1981) 341. Luckman, G., Didio, R.A., Graham, W.R.: Metall. Trans. A 12 (1981) 253. Neumann, G., Pfundstein, M., Reimers, P.: Phys. Status Solidi (a) 64 (1981) 225. Richter, I., Feller-Kniepmeier, M.: Phys. Status Solidi (a) 68 (1981) 289. Yeh, D.C., Acuna, L.A., Huntington, H.B.: Phys. Rev. B 23 (1981) 1171. Arkhipova, N.K., Veretennikov, L.M., Klotsman, S.M., Tatarinova, G.N., Timofeyev, A.N. : Fiz. Met. Metalloved. 53 (1982) 104; Phys. Met. Metallogr. (English Transl.) 53 (1) (1982) 92. Hoshino, K., Iijima, Y, Hirano, K.-I., in: Point Defects and Defect Interactions in Metals, J.I.Takamura, M.Doyama, M.Kiritani (eds.), University of Tokyo Press 1982, p. 562. Hu, C.K., Huntington, H.B.: Phys. Rev. B 26 (1982) 2782. Manke, L., Herzig, Ch. : Acta Metall. 30 (1982) 2085. Mehrer, H:, Hopfel, D., Hettich, G.: DIMETA-82, Diffusion in Metals and Alloys, F.J. Kedves, D.L.Beke (eds.), Trans. Tech. Publ., Switzerland 1983, p. 360. Seealso [84Kl]. Neumann, G., Pfundstein, M., Reimers, P. : Philos. Mag. A 45 (1982) 499. Okafor, I.C.I., Carlson, O.N.: J. Less-Common Met. 84 (1982) 65. Pruthi, D.O., Agarwala, R.P.: Philos. Mag. A 46 (1982) 841. Akimova, LA., Mironov, V.M., Pokoyev, A.V.: Fiz. Met. Metalloved. 56 (1983) 1225; Phys. Met. Metallogr. (English Transl.) 56 (6) (1983) 175. Barr, L.W, Smith, EA., in: DIMETA-82, Diffusion in Metals and Alloys, F.J. Kedves, D.L.Beke (eds.), Trans. Tech. Publ., Switzerland 1983, p. 325. Balart, S.N., Varela, N., Tendler, R.: J. Nucl. Mater. 119 (1983) 59. Beke, D.L., GbdCny, I., Kedves, F.J.: Philos. Mag. A 47 (1983) 281. Chi, N.V., Bergner, D., in: DIMETA-82, Diffusion in Metals and Alloys, F.J. Kedves, D.L. Beke (eds.), Trans. Tech. Publ., Switzerland 1983, p. 334. Gust, W., Ostertag, C., Predel, B., Roll, U., Lodding, A., Odelius, H. : Philos. Mag. A 47 (1983) 395. Hood, G.M., Schultz, R.J., Armstrong, J.: Philos. Mag. A 47 (1983) 775. Kurokawa, S., Ruzzante, J.E., Hey, A.M., Dyment, F.: Met. Sci. 17 (1983) 433. Matsuyama, T., Hosokawa, H., Suto, H.: Trans. Jpn. Inst Met. 24 (1983) 589. Mantl, S., Rothman, S.J., Nowicki, L.J., Lerner, J.L.: J. Phys. F 13 (1983) 1441. Macht, M.P., Naundorf, V., Dbhl, R., in: DIMETA-82, Diffusion in Metals and Alloys, F.J.Kedves, D.L. Beke (eds.) Trans. Tech. Publ., Switzerland 1983, p. 516. Nakajima, H., Koiwa, M., Ono, S.: Ser. Metall. 17 (1983) 1431. Nakajima, H., Koiwa, M., Minonishi, Y, Ono, S.: Trans. Jpn. Inst. Met. 24 (1983) 655. Rockosch, H.J., Herzig, Ch.: Phys. Status Solidi (b) 119 (1983) 199. Arkhipova, N.K., Klotsman, S.M., Polikarpova, I.P., Tartarinova, G.N:, Timofeev, A.N., Veretennikov, L.M.: Phys. Rev. B 30 (1984) 1788. Arita, M., Nakamura, M., Goto, K.S., Ichinose, Y: Trans. Jpn. Inst. Met. 25 (1984) 703. Diihl, R., Macht, M.P., Naundorf, V.: Phys. Status Solidi (a) 86 (1984) 603. Hennesen, K., Keller, H., Viefhaus, H.: Ser. Metall. 18 (1984) 1319. KuEera, J., Kozak, L., Mehrer, H.: Phys. Status Solidi (a) 81 (1984) 497. Mehrer, H., Weiler, D.: Z. Metallkde. 75 (1984) 203. Pruthi, D.D., Agarwala, R.P. : Philos. Mag. A 49 (1984) 263. Schmidt, EA., Beck, M.S., Rehbein, D.K., Conzemius, R. J., Carlson, O.N. : J. Electrochem. Sot. 131 (1984) 2169. Taguchi, O., Iijima, Y, Hirano, K.-I.: J. Jpn. Inst. Met. 48 (1984) 20. Yeh, D.C., Huntington, H.B.: Phys. Rev. Lett. 53 (1984) 1469. Geise, J., Herzig, Ch.: Z. Metal&de. 76 (1985) 622. Maslov, I.A., Mironov, V.M., Pokoyev, A.V.: Fiz. Met. Metalloved. 60 (1985) 193; Phys. Met. Metallogr. (English Transl.) 60 (1) (1985) 180. Nakajima, H., Ishioka, S., Koiwa, M.: Philos. Mag. A 52 (1985) 743. Nakajima, H., Koiwa, M.: Titanium Science and Technology, Proc. 5th Int. Conf. on Ti 1985, p. 1759.
Land&-Biimstein New Series III/26
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212 35Rl 35132 36Al 36A2 36Kl 36K2 36Nl 96N2 56Pl 86Rl 87Bl B7Fl B7F2 B7Gl B7G2 B7Hl B7H2 B7H3 B7Kl 87K2 87Ml 8701 88Nl 88N2 88N3 89Bl 89B2 89Cl 89Fl 89Hl 89Kl
89Ll 89L2 89Nl 89Rl 89Tl B9Vl B9Zl 90El 9OLl 90Nl
3.3 References for 3 RIisiinen, J., Anttila, A., Keinonen, J.: J. Appl. Phys. 57 (1985) 613. Rais?inen,J., Antilla, A., Keinonen, J.: Appl. Phys. A 36 (1985) 175. Axtell, S.C., Okafor, I.C.I., Conzemius, R.J., Carlson, O.N.: J. Less-Common Met. 115 (1986) 269. Arabczyk, W., Militzer, M., Miissig, H.J., Wieting, J.: Ser. Metall. 20 (1986) 1549. Kimura, K., Iijima, Y., Hirano, K.-I.: Trans. Jpn. Inst. Met. 27 (1986) 1. Ku&era, J., Million, B., RftiiEkovl, J.: Phys. Status Solidi (a) % (1986) 177. Nakajima, H., Nakazawa, J., Minonishi, Y., Koiwa, M.: Philos. Mag. A 53 (1986) 427. Neumann, G., Tolle, V.: Philos. Mag. A 54 (1986) 619. Pelleg, J.: Philos. Mag. A 54 (1986) L21. RaisLnen, J., Keinonen, J.: Appl. Phys. Lett. 49 (1986) 773. Beke, D.L., Godeny, I., Szabo, I.A., ErdClyi, G., Kedves, F.J.: Philos. Mag. A 55 (1987) 425. Fujikawa, S., Werner, M., Mehrer, H., Seeger,A.: Mater. Sci. Forum 15-18 (1987) 431. Fujikawa, S., Hirano, K.-I.: Mater. Sci. Forum 13/14 (1987) 539. Geise, J., Herzig, Ch.: Z. Metallkde. 78 (1987) 291. Geise, J., Mehrer, H., Herzig, Ch., Weyer, G.: Mater. Sci. Forum 15-18 (1987) 443. Herzig, Ch., Neuhaus, J., Vieregge, K., Manke, L.: Mater. Sci. Forum 15-18 (1987) 481. Hood, G.M., Schultz, R.J.: Mater. Sci. Forum 15-18 (1987) 475. Herzig, Ch., Kijhler, U.: Mater. Sci. Forum 15-18 (1987) 301. Klotsman, S.M., Tatarinova, G.N., Timofeyev, A.N.: Mater. Sci. Forum 15-18 (1987) 457. Klotsman, S.M., Osetrov, S.V., Polikarpova, I.P., Tartarinova, G.N., Timofeyev, A.N., Shepatkovskiy, O.P.: Fiz. Met. Metalloved. 64 (1987) 148; Phys. Met. Metallogr. (English Transl.) 64 (1) (1987) 133. Minamino, Y., Yamane, T., Araki, H.: Metall. Trans. A 18 (1987) 1536. Okafor, I.C.I.: Acta Metall. 35 (1987) 759 (reports results that seem to be identical with those of [84Sl]!) Nakamura, Y, Nakajima, H., Ishioka, S., Koiwa, M.: Acta Metall. 36 (1988) 2787. Nakajima, H., Hood, G.M., Schultz, R.J.: Philos. Mag. B 58 (1988) 319. Neumann, G., TolIe, V.: Philos. Mag. A 57 (1988) 621. Bergner, D., Khaddour, Y., LBrx, S.: DIMETA-88, Diffusion in Metals and Alloys, F.J. Kedves, D.L. Beke (eds.); Defect and Diffusion Forum 66-69 (1989) 1407. Becker, Ch., ErdClyi, G., Hood, G.M., Mehrer, H.: DIMETA-88. Diffusion in Metals and Alloys, F.J. Kedves, D.L. Beke (eds.), Defect and Diffusion Forum 66-69 (1989) 409. Cermlk, J., Liibbehusen, M., Mehrer, M.: Z. Metallkde. 80 (1989) 213. Fujikawa, S., Hirano, K.: DIMETA-88. Diffusion in Metals and Alloys, F.J. Kedves, D.L. Beke (eds.), Defect and Diffusion Forum 66-69 (1989) 453. Hirano, K.-I., Iijima, Y: DIMETA-88, Diffusion in Metals and Alloys, F.J.Kedves, D.L. Beke (eds.), Defect and Diffusion Forum 66-69 (1989) 1039. Klotsman, S.M., Koloskov, V.M., Osetrov, S.V., Polikarpova, I.P., Tatarinova, G.N., Timofeyev, A.N.: DIMETA-88. Diffusion in Metals and Alloys, F.J. Kedves, D.L. Beke (eds.), Defect and Diffusion Forum 66-69 (1989) 439; Fiz. Met. Metalloved. 67 (1989) 767; Phys. Met. Metallogr. (English Transl.) 67 (4) (1989) 136. Lee, J.S., Klockgeter, K., Herzig, Ch., in: Proc. Int. Conf. on Intergranular and Interphase Boundaries in Materials, Paris, 1989, J. Phys. (Paris), in press; and Diploma&it K. Klockgeter, Univ. Miinster, 1989. Landolt-Bornstein, NS, Vol. 111/22b: Semiconductors, Heidelberg, Berlin, New York, Tokyo: Springer 1989. Neuhaus, P., Herzig, Ch.: Z. Metallkde. 80 (1989) 220. Rummel, G., Mehrer, H.: DIMETA-88. Diffusion in Metals and Alloys, F.J. Kedves, D.L. Beke (eds.), Defect and Diffusion Forum 66-69 (1989) 453. Tobar, G., Balart, S.: DIMETA-88. Diffusion in Metals and Alloys, F.J. Kedves, D.L. Beke (eds.), Defect and Diffusion Forum 66-69 (1989) 381. Vieregge, K., Herzig, Ch.: J. Nucl. Mater. 165 (1989) 65. Zee, R.H.: J. Phys. Condensed Matter. 1 (1989) 5631. ErdClyi, G., Freitag, C., Mehrer, H.: Philos. Mag. Lett., in press. Lee, C.-G., Iijima, Y, Hiratani, T., Hirano, K.: Materials Trans. JIM 31 (1990) 255. Neumann, G., Tolle, V.: to be published.
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4 Self-diffusion in homogeneousbinary alloys and intermediate phases Use of the tables and figures In this chapter tracer self-diffusion coefficients are presented in binary alloys, i.e. metallic mixtures of two elements. Results on diffusion in, for example, a semiconducting intermediate phase such as GaAs are not tabulated. In this chapter the tables have a central function. From these tables referencesare made to the figures. The order in which the alloy systemsare arranged is alphabetical, for example Ag - Al is tabulated before Ag - Au and V,Ga should be transformed to GaV, first and is then found after Ga - Pu. This order is exactly the same as used in collections of binary phase diagrams. Primary and terminal phasesare indicated by a hyphen between the element symbols: A - B, whereas intermediate compounds are presented by their stoichiometric formula, for example A,B. The crystal structure of thesecompounds is also given. In the various columns of the tables, a dash indicates that no data (or figures) are available (or shown) for a special composition, a blank space should be understood as a repetition of the information (immerical values, reference key) given in the line above. The full list of alloys, treated in this chapter, is presented below. In contrast to the tables, the alloys are given here both in the order A-B and B-A. In this way it is immediately clear which Ni systems,for example, occur in the tables. In a scarcenumber of casesalso isotope effectshave been measured (seechapter 10 about the mass dependenceof the diffusion coefficient for an explanation). In the list below, these are indicated by E(A), which means the isotope effect for diffusion of element A.
List of alloys, their phasesand diffusing elements System
Phase
Diffusing element
Page
Ag-Al Ag-Au
primary and terminal primary/terminal phase extending over the whole composition range in the temperature range studied primary primary intermediate, y-phase primary intermediate, B2 (CsCl) structure primary primary primary terminal intermediate, y-phase primary and terminal intermediate, B2 (CsCl) structure terminal, bee structure intermediate, B2 (CsCl) structure intermediate, rhombohedral structure intermediate, rhombic structure intermediate, monoclinic structure intermediate, B2 (CsCl) structure intermediate, Ll 2 (Cu,Au) structure primary primary/terminal phase extending over the whole composition range in the temperature range studied
Ag Ag, Au
218 218
Ag, Cd Ag Hg Ag Ag Ag Ag, Sn Ag Ag, Zn Ag, Zn Ag co Al, Fe Al, Fe Fe Al, Fe Al, Fe Ni Ni Zn Ag, Au
218 218 219 219 219 219 219 220 220 220 218 220 220 221 221 221 221 221 221f. 222 218
Ag-Cd Ag-Cu 4z,Hg, Ag-In A@fg Ag-Sb Ag-Sn Ag-Zn Ag,Zn, Al-Ag AlCo Al-Fe AlFe A&Fe AI,Fe, A&Fe AlNi AlNi, Al-Zn Au-Ag
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4 Self-diffusion in homogeneous binary alloys and intermediate phases
System
Phase
Diffusing element
Page
4uCd 4u-cu
intermediate, B2 (CsCI) structure primary/terminal phase extending over the whole composition range in the temperature range studied primary intermediate, B2 (CsCI) structure
Au, Cd Au, Cu
222 223
Au-Ta AuZn
Cu-Sb Cu,Sb Cu-Sn Cu,Sn Cu,Sn, Cu-Zn
primary primary terminal intermediate, B2 (CsCI) structure terminal intermediate, B2 (CsCI) structure primary/terminal phase extending over the whole composition range, fee, bee and ordered B2 intermediate, B2 (CsCI) structure primary primary/terminal phase extending over the whole composition range in the temperature range studied terminal intermediate, Ll 2 (Cu,Au) structure terminal primary/terminal phase extending over the whole composition range in the temperature range studied primary and terminal terminal terminal terminal primary/terminal phase extending over the whole composition range in the temperature range studied terminal primary primary primary/terminal phase extending over the whole composition range in the temperature range studied primary/terminal phase extending over the whole composition range in the temperature range studied primary intermediate, p-phase, DO, (BiF,) structure primary intermediate, p-phase, DO, (BiF,) structure intermediate, &phase, y-brass-type structure primary
CuZn
intermediate, bee, and B2 structure
Fe-Al FeAl FeAI, Fe,AI, FeA!, Fe-Co
primary, bee structure intermediate, B2 (CsCI) structure intermediate, rhombohedra! structure intermediate, rhombic structure intermediate, monoclinic structure primary/terminal phase extending over the whole composition range, fee, bee and ordered B2 primary/terminal phase extending over the whole composition range in the temperature range studied
Be-Cu Be-Ni Cd-Ag CdAu Cd-Pb CoAl Co-Fe CoGa Co-Mn Co-Ni Co-Ti Co,Ti co-u Cr-Fe Cr-Ni Cr-Zr Cu-Ag Cu-Au Cu-Be Cu-Fe Cu-In Cu-Ni Cu-Pt
Fe-Cr
Au 223 Au, Zn 223 EN4 WW Be 224 Ni 224 Ag, Cd 218 Au, Cd 222 Cd 224 co 220 224f. Co, Fe Wo), We) 225f. Co, Ga Mn 226 226f. Co, Ni Co, Ti co U Cr, Fe
221 228 228 228
Cr Ni Cr, Zr 4.z Au, Cu
228 228f. 229 218 223
Be cu cu Cu, Ni
224 229 229 229
cu, Pt
229f.
cu cu cu Cu, Sn Cu, Sn Cu, Zn Wu), Wn) Cu, Zn Wu), Wn) AI, Fe Al, Fe Fe Al, Fe Al, Fe Co, Fe E(Co), E(Fe) Cr, Fe
230 230 230 230 230 231 231f. 220 221 221 221 221 224f. 228
Land&-BCmsIein New Series 111126
215
4 Self-diffusion in homogeneous binary alloys and intermediate phases System
Phase
Fe-Cu Fe-Ge Fe-Mn Fe-MO Fe-Ni
terminal primary * primary primary primary/terminal phase extending over the whole composition range in the temperature range studied primary/terminal phase extending over the whole composition range in the temperature range studied primary, fee structure primary primary primary primary primary terminal intermediate, B2 (CsCl) structure intermediate, B2 (CsCl) structure terminal, E- and &phase intermediate, Al 5 structure terminal primary/terminal phase extending over the whole composition range in. the temperature range studied intermediate, y-phase terminal terminal terminal intermediate, B2 (CsCl) structure intermediate, B2 (CsCl) structure terminal terminal ordered phase, Ll, (Cu,Au) structure terminal terminal terminal terminal primary/terminal phase extending over the whole composition range in the temperature range studied terminal intermediate, DO, @-TiCu,) structure primary/terminal phase extending over the whole composition range in the temperature range studied primary/terminal phase extending over the whole composition range in the temperature range studied primary/terminal phase extending over the whole composition range in the temperature range studied intermediate, B2 (CsCI) structure intermediate, L 12 (Cu,Au) structure terminal primary/terminal phase extending over the whole composition range in the temperature range studied primary and terminal primary primary/terminal phase extending over the whole composition range in the temperature range studied
Fe-Pd Fe-Pt Fe-Sb Fe-Si Fe-Sn Fe-Ti Fe-V Fe-Zr GaCo GaNi Ga-Pu GaV, Ge-Fe Hf-Zr I-Q%, Hg-Pb In-Ag In-Cu InPd M&s Mn-Co Mn-Fe MnPt, Mn-Ti Mn-Zr MO-Fe Mo-Ni MO-W Nb-Ni NbNi, Nb-Ti Nb-W Nb-Zr NiAl N&Al Ni-Be Ni-Co Ni-Cr Ni-Cu
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Diffusing element
Page
cu Fe Fe, Mn Fe Fe, Ni
229 232 232 232 233
Fe, Pd
233
Fe, Pt Fe Fe, E(Fe) Fe Fe Fe, V Fe, Zr Co, Ga Ga, Ni Pu Ga, V Fe Hf
234 234 234f. 236 236 236 236 225f. 236f. 237 237 232 237
Hg Nit, Pb Ag cu In, Pd Ag Mn Fe, Mn Mn Mn, Ti Mn, Zr Fe MO, Ni MO, W
219 237 219 229 237f. 219 226 232 238 238 238 232 239 239
Ni Nb, Ni Nb, Ti
239 240 240
Nb, W
240
Nb, Zr
241
Ni Ni Ni Co, Ni
221. 221f. 224 226f.
Cr Ni Cu, Ni
228 228f. 229
:,,
216
4 Self-diffusion in homogeneous binary alloys and intermediate phases
System
Phase
Diffusing element
Page
Ni-Fe
primary/terminal phase extending over the whole composition range in the temperature range studied intermediate, B2 (CsCI) structure primary primary intermediate, DO, (B-TiCu,) structure primary intermediate, y-phase primary primary primary primary/terminal phase extending over the whole composition range in the temperature range studied intermediate, B2 (CsCI) structure primary/terminal phase extending over the whole composition range in the temperature range studied terminal, fee structure ordered phase, Ll, (Cu,Au) structure primary, E-phaseand &phase terminal terminal terminal intermediate, DO, (BiF,) structure terminal intermediate, p-phase primary/terminal phase extending over the whole composition range in the temperature range studied terminal terminal terminal terminal intermediate, DO, (BiF,) structure intermediate, y-brass-type structure terminal intermediate, p-phase primary terminal primary intermediate, L 12 (Cu,Au) structure terminal primary primary/terminal phase extending over the whole composition range in the temperature range studied primary/terminal phase extending over the whole composition range in the temperature range studied primary/terminal phase extending over the whole composition range in the temperature range studied terminal primary primary/terminal phase extending over the whole composition range in the temperature range studied terminal
Fe, Ni
232
Ga, Ni MO, Ni Ni Nb, Ni Ni Zn Cd Hg, Pb Pb, Ti Fe, Pd
236 239 239 240 241 241 224 237 241 232
In, Pd cu, Pt
237f. 229f.
Fe, Pt Mn Pu W Aiz cu cu Fe Sn Zr
232 238 237 242 219 230 230 232 242 242
Fe, E(Fe) Ni 4s Sn cu Cu, Sn Cu, Sn Fe Sn Sn, Zn Au Co, Ti co Fe Mn, Ti Nb, Ti
232 241 219 230 230 230 234 242 242 223 227 228 234 238 240
Ti, V
242f.
Ti
243
Pb, Tl U U, Zr
241 228 243
Fe, V
234
NiGa Ni-Mo Ni-Nb Ni,Nb Ni-Si Ni,Zn, Pb-Cd Pb-Hg Pb-Tl Pd-Fe PdIn Pt-Cu Pt-Fe Pt,Mn Pu-Ga Re-W Sb-Ag Sb-Cu SbCu, Sb-Fe Sb,Sn, SC-Zr Si-Fe Si-Ni Sn-Ag Sn-Cu SnCu, Sn,Cu, Sn-Fe Sn,Sb, Sn-Zn Ta-Au Ti-Co TiCo, Ti-Fe Ti-Mn Ti-Nb Ti-V Ti-Zr Tl-Pb u-co U-Zr V-Fe
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217
System
Phase
Diffusing element
Page
V,Ga V-Zr V-Ti
Ga, V V, Zr Ti, V
237 243
MO, w
239
Nb, W
240
W
Zn,Ag, Zn-Al ZnAu
intermediate, Al 5 structure primary and terminal primary/terminal phase extending over the whole composition range in the temperature range studied primary/terminal phase extending over the whole composition range in the temperature range studied primary/terminal phase extending over the whole composition range in the temperature range studied primary primary terminal intermediate, y-phase terminal intermediate, B2 (CsCl) structure
242 220 220 220 222 223
Zn-Cu
terminal
W-MO W-Nb W-Re Zn-Ag
242f.
Ag, Zn Ag Ag, Zn
Zn Au, Zn EW),
WW
Cu, Zn
231
E(Cu), E(Zn)
ZnCu
intermediate, bee and B2 structure
Zn,Ni, Zn-Sn Zr-Cr Zr-Fe Zr-Hf
intermediate, y-phase terminal primary primary primary/terminal phase extending over the whole range in the temperature range studied primary primary/terminal phase extending over the whole range in the temperature range studied primary/terminal phase extending over the whole range in the temperature range studied primary/terminal phase extending over the whole range in the temperature range studied primary/terminal phase extending over the whole range in the temperature range studied primary and terminal
Zr-Mn Zr-Nb Zr-Sc Zr-Ti Zr-U Zr-V
composition
241 242 229 234 237
composition
Mn, Zr Nb, Zr
238 241
composition
Zr
242
composition
Ti
243
composition
U, Zr
243
V, Zr
243
For figures seepage 244.
Land&-Biimstein New Series III/26
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231f.
Cu, Zn WW, -Vn) Zn Sn, Zn Cr, Zr Fe, Zr Hf
218
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) [Ref. p. 276
Zomposition It %
Temperature range [K]
ig-Al; primary and terminal phase ‘lomAg diffusion in primary phase 873 ... 1073 AI: 3.8 11.6 17.8 21.7 ‘romAg diffusion in terminal phase Al: 90.3...99 673...868
DO 10m4m’s-’
Q
Fig.
Ref.
kJ mol-’
-
185.9 256.6 180.0 114.3
-
70s
0.39
121.0
1
68H *)
‘) Remark: D is concentration independent.
Ag- Au; primary/terminal phaseextending over the whole composition range in the temperature range studied *romAg diffusion 63M 927...1218 0.52 187.5 Au: 8 0.32 184.4 17 908...1225 0.23 182.3 908...1229 35 180.5 908...1245 0.19 50 174.7 927... 1244 0.11 66 171.7 923... 1284 0.09 83 168.5 936.e.1234 0.072 94 “*Au diffusion 202.2 63M Au: 8 991... 1213 0.82 991 ..* 1220 0.48 198.0 17 0.35 195.4 991 ... 1269 35 988 ... 1274 0.21 189.5 50 186.3 988 ... 1274 0.17 66 0.12 180.2 985 ... 1274 83 176.1 991 ... 1283 0.09 94 Ag - Cd; primary phase ’ ‘OrnAgdiffusion Cd: 30.50...37.70 836,..955 11‘Cd diffusion Cd: 31.25...36.25 836...955
For D seeFig. 3
68G
For D see Fig. 3
68G
Ag - Cu; primary phase lromAg diffusion cu: 0.17 0.17 0.84 0.84 0.85 1.38 1.68 1.75 2.52 2.55 3.36 4.16 4.43 5.00 6.56 8.15
1053...1179 963 ... 1053 1053..*1179 963...1179 963...1123 883...1113 998...1179 973..*1173 926... 1091 963...1123 963...1123 973... 1173 926... 1091 998...1153 973..*1173 998.s.1103
0.65 1.06 0.68 0.08 0.39 1.04 0.07 0.66 0.63 0.30 0.26 1.84 0.57 0.06 0.51 0.04
189.2 171.6 189.2 163.3 184.2 188.9 170.0 187.5 183.2 180.4 176.6 195.1 181.3 167.0 182.1 160.3
Bakker
4
57Y, 77B2
5 6 4 7 6 5 5 7 6 4 7 4
64S, 77B2 72P, 77B2 57Y, 77B2 55H, 77B2 72P, 77B2 64S, 77B2 64S, 77B2 55H, 77B2 72P, 77B2 57Y, 77B2 55H, 77B2 57Y, 77B2
Iandolt-BBmstein New Series III/26
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Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) Composition at %
Temperature range [K]
Do 10m4m’s1l
e kJ mol-’
Fig.
Ref.
8
77s
9
85K
Ag,Hg,; intermediate phase, y-phase 203Hg diffusion Hg: 55
323...375
1.2.10-4
30.3
Ag - In; primary phase “OrnAg diffusion In: 0.151 . ..0.943 1054
For D see Fig. 9
AgMg; intermediate phase, B2 (CsCl) structure “OrnAg diffusion Mg: 41.1. 43.6 43.6, 43.8 45.0 45.8 48.5 48.7 49.8 52 52.8 57.2
773...973
0.095 0.15 0.31 0.686 1.53 0.37 0.39 0.28 0.134 0.33 0.051
139.0 147.8 154.5 165.8 172.9 165.3 166.2 170.0 159.1 153.6 120.1
0.382 0.302 2.75
182.1 178.3 175.8
10 10 10 10 10
64D 64D 61Hl 64D 64D 61Hl 61Hl 64D 64D
Ag - Sb; primary phase 1lomAg diffusion Sb: 0.53 0.89 1.42
902... 1173 842...1163 841...1164
11
55s
12 13
83H2 85K *)
14
78G
15
78G
Ag - Sn; primary phase 1lomAg diffusion Sn: 0...8.67 946... 1146 0.218 ... 0.773 1052
For D see Fig. 12 For D see Fig. 13
*) Remark: Single crystals.
Sn: 0.108 0.8 3 4.7 6
893 ... 893 ... 889 ... 893 ... 885...
l1 3Sn diffusion Sn: 0.11
893 ... 1123
1.7
Land&BBmstein New Series III/26
1042 1042 1010 1042 980
0.13 0.12 0.085 0.07 0.07
172.9 168.3 160.7 157.0 154.9
No difference with Sn impurity diffusion in pure silver 0.125 156.8
Bakker
220
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) [Ref. p. 276
Composition at %
Temperature range [K]
DO low4 rn’s-’
Q
Fig.
Ref.
16
67R
17
69s
17
69s
18
67SI,69S
18
67S1,69S
kJ mol-’
Ag - Zn; primary and terminal phase “OrnAg diffusion in primary phase Zn: 0...4.1 1020,1153
For D seeFig. 16
“OrnAg diffusion in terminal phase; diffusion in single crystals parallel to the hexagonal axis 0.42 (5) Zn: 99.11 594...686 0.35 (7) 99.32 594...690
I 10.0 (6) 109.2 (12)
1’omAgdiffusion in terminal phase; diffusion in single crystals perpendicular to the hexagonal axis 117.2 (8) 0.69 (10) Zn: 99.11 594...686 115.7 (4) 0.49 (3) 99.65 594...682 65Zn diffusion in terminal phase; diffusion in single crystals parallel to the hexagonal axis 0.17 (1) Zn: 98.6 620...690 0.14 (1) 99.43
92.4 (3) 91.9 (4)
65Zn diffusion in terminal phase; diffusion in single crystals perpendicular to the hexagonal axis 96.8 (2) 0.26 (1) Zn: 98.6 620 . . .696 96.8 (6) 0.22 (2) 99.43 Ag,Zn,; intermediate phase, y-phase “OrnAg diffusion Zn: 61 62 65Zn diffusion Zn: 61
713..*913
4.06 -
122.2 (13) -
19
71s
680...840
1.55
108.0 (11)
20
71s
21
51N
AICo; intermediate compound, B2 (CsCl) structure ‘j°Co diffusion co: 49..*57 Al-Fe;
1523
For D see Fig. 21
terminal phase, disordered bee structure
26AI diffusion in paramagnetic phase 100 Fe: 75 1173...1358
267.1
-
75L
“Fe diffusion in paramagnetic phase 32.4 Fe: 75 1173...1413
252.0
22
75L
“Fe diffusion in paramagnetic phase 0.01 Fe: 82 973... 1450 0.02 90 1156...1450 0.42 94 1088... 1478
171.7 183.5 197.7
23
81RI
“Fe diffusion in ferromagnetic phase 0.01 Fe: 82 816.a.953 0.06 90 765...941 94 953.s.991
197.7 195.9 -
23
81Rl
Landolt-BBmstein New Series III/26
I
221
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) Composition at %
Temperature range [K]
DO 10m4m2sv1
Q
Fig.
Ref.
kJ mol-’
AlFe; intermediate phase, B2 (CsCl) structure 26A1diffusion Fe: 48.8, 51.5 55Fe diffusion Fe: 47.8 48.8 51.5 59.5 65.9
1173...1358
8700
339.9
-
75L
1173.s.1423
60 170 1.82 . lo4 830 230
278.8 252.0 331.9 293.9 278.8
24
75L
180.0
-
75L
Al,Fe; intermediate phase, rhombohedral structure ’ 5Fe diffusion Fe: 33.18
-
0.02
A&Fe,; intermediate phase, rhombic structure 26A1diffusion Fe: 28.39
1173 ... 1358
1.75.10-5
106.7
-
75L
“Fe diffusion Fe: 28.39
1173 ..* 1358
0.004
141.1
-
75L
Al,Fe; intermediate phase, monoclinic structure 26A1diffusion Fe: 24.83
1173... 1358
0.012
183.3
-
75L
55Fe diffusion Fe: 24.83
1173... 1358
0.001
157.8
-
75L
0.00012 0.00104 0.00053 0.2302 4.461 0.6296 0.1504
177.9 (264) 209.7 (310) 200.5 (448) 275.9 (21) 307.3 (96) 274.2 (314) 250.3 (134)
27,28
71Hl
0.0352 0.096 0.7254
216.4 (71) 253.7 (130) 250.3 (163)
AlNi; intermediate phase, B2 (CsCl) structure 63Ni diffusion Ni: 48.3 48.6 49.0 49.2 50.0 53.2 54.5 55.5 58.0 58.5 58.7 AlNi,;
1273.‘. 1623
26,27
See Figs. 26,27
intermediate phase, Ll, (Cu,Au) structure
63Ni diffusion Ni: 73.2 74.7 74.8 76.2
Land&-BBmstein New Series III/26
1193...1553 1193... 1553 1163.~. 1477 1193... 1553
3.11 1.00 1.00 4.41
300.3 303.1 286.8 (42) 306.3
Bakker
28,29 28,29 30 28,29
71H2 71H2 75B 71H2 (continued)
222
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) [Ref. p. 276
Composition at %
Temperature range [K]
Q.
DO’
IO+ m’s-r
kJ mol-’
Dab
10e4 m2s-*
Fig.
Qb
Ref.
kJ mol-’
AINi,, continued 63Ni diffusion Analysis in terms of two exponentials: D(T) = Do" exp(- QJR T) + Dabexp(- QJR T) Ni: 14 965... 1623 105 (90) 344.9(50) 2 (3). 10-n 121.8(117) 75 965... 1623 146 (32) 347.0(29) 1.1 (4). lo-’ 141.1(33) 16 965... 1623 132 (53) 342.4 (105) 1.0 (6). lo-’ 134.8(50)
31 87H3 31, 32 31
Remark: In the high-temperature range there is a good agreement with [71H2] and [75B] (seeFig. 31).
Composition at %
Temperature range [K]
DO 10m4rn’s-’
e kJ mol-’
Fig.
Ref.
0.25 (3) 0.18 (2) 0.22 (4) 0.22 (4) 0.24 (5) 0.23 (4) 0.170 (98) 0.20 0.324 (216) 0.209 (96) 0.22 0.288 (266) 0.229 (137) 0.23
119.0 (9) 116.7 (12) 117.6 (12) 117.1 (13) 117.5 (15) 116.9 (12) 112.5 (32) 112.6 (21) 113.2 (37) 108.3 (25) 105.1 (21) 105.7 (54) 103.5 (34) 100.5 (29)
33, 34 33, 34 33, 34, 35 33, 34 33, 34 33, 34, 35 36 37 36 36
77Bl
0.162 +“‘238 -0.108 0.575 + 1.084 -0.376 0.692 (701)
100.5 (59)
-
80C
106.6 (59)
-
108.1 (54)
-
111.9 (54)
-
106.8 (25)
-
111.4 (39) 90.4 (42)
36
75Gl
117.6 (4) 125.6 (21)
38, 39 38, 39
67G 67G
116.8 (13) 109.7 (21)
-
61H2*)
38, 39
67G
129.8 (4) 130.6 (20) 117.2 (29)
38, 39 38, 39
67G 67G
-
61H2
113.4 (21)
38, 39
67G
Al - Zn; primary phase 65Zn diffusion Zn:
1.16
614...890
1.73 2.15 2.80 3.29 3.76 7.06 9.9 15.17 24.25 28.9 31.27 41.51 50.0
598...753 683...836 598...782 598...753 622...745 634...726 634...715 603...683
52.52
616...695
53.28
615...686
55.04
598...686
56.85
585...654
57.28
598...675
1 514 +2.852 -0.989 0.575 (265)
57.50 58.5
585...675 589...663
1.35 (103) 0.036
8OC 75Gl 80C 80C 75Gl 80C 8OC 75Gl
AuCd; intermediate phase, B2 (CsCI) structure lg5Au diffusion Cd: 47.5
627...871
49.0 50.0 50.5
714...822 576...877 714...822
0.23 0.61 0.17 0.12
(2) (6) (3)
(1)
*) Remark: Diffusion of rg8Au.
logCd/“sCd diffusion Cd: 47.5 646 ... 858 49.0 50.0 50.5
714...822 604 ... 893 714...822
1.36 (2) 1.5 (2) 0.23 (1) 0.22 (2)
Bakker
Landolf-Wmstein New Series Ill/26
223
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) Composition at %
Temperature range [K]
DO 10d4 rnzs-l
Fig.
Q
Ref.
kJ mol-’
Au - Cu; primary/terminal phase extending over the whole composition range in the temperature range studied lg5Au diffusion cu: 75
823...1173
0.0065 (9)
160.2 (39)
40
70. ‘. 100
1133
For D see Fig. 41
41
65B, 69A, 77B2 78H
64Cu diffusion cu: 70... 100
1133
For D seeFig. 41
41
78H
143 (10)
42
75G2
Au - Ta; primary phase lg5Au diffusion Ta: 1.2
477...669
0.0014
AuZn; intermediate phase, B2 (CsCl) structure lg5Au diffusion Zn: 49.0 50.0 51.0
701 ... 923 701 ... 923 701 ... 923
0.19 0.33 0.016
133.5 138.6 113.0
43,44
71G
65Zn diffusion Zn: 49.0 50.0 51.0
701...923 701...923 701 ... 923
0.84 1.93 0.047
144.8 148.2 115.1
43,44
71G
Composition at %
Temperature K
D 311’sl
E
Fig.
Ref.
1g5/1ggA~diffusion, Zn: 48.37 48.59 49.10 49.40 49.41 49.47 49.78 49.83 50.27 50.70 50.73 50.92 51.01
isotope effect E 876 876 878 874 878 875 757 874 757 875 875 814 875
1.620 (12). IO-l3 1.880 (13). lo-l3 1.420 (8). IO-l3 1.700 (4). 10-13 1.730 (6). lo-l3 1.650 (20) . lo- l3 1.040 (6). lo-l4 1.530 (22). 10-13 8.950 (44). lo-l5 2.000 (16). IO-l3 1.670 (15). IO-l3 6.330 (15). IO-l4 2.380 (12). IO-l3
0.22 (2) 0.30 (3) 0.41 (4) 0.24 (3) 0.32 (2) 0.21 (6) 0.37 (4) 0.20 (3) 0.23 (2) 0.25 (3) 0.29 (3) 0.35 (3) 0.36 (3)
45
83H3
0.230 (17) 0.190 (13) 0.090 (35) 0.100 (13) 0.050 (10)
46
83H3
Remark: For pressure dependence of the diffusion coefficient see [72J].
65/6gmZndiffusion, Zn: 49.18 49.35 50.21 50.43 51.85
isotope effect E 916 928 835 837 810
7.280 (64). lo-l3 1.200 (21) . lo-l2 1.330 (15). lo-l3 1.200 (16). lo-l3 3.180 (47). lo-l3
Remark: For pressure dependence of the diffusion coefficient see [725].
Land&-BGmstein New Series III/26
Ijakker
224
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) [Ref. p. 276
Q
Fig.
Ref.
9.03
195.1
47
73L, 77B2
5.99
198.0
47
73L, 77B2
Be - Ni; primary phase 63Ni diffusion Ni: 1.7 1173...1373 6.0
0.41 (16) 0.23 (12)
247.0 (109) 188.4 (17)
-
70A
Cd - Pb; terminal phase lo9Cd diffusion Pb: 99.1 . ..99.995 410.1
For D seeFig. 48
48
79Cl
Composition at %
Temperature range [K]
Be - Cu; primary phase Be tracer diffusion perpendicular to the c axis Cu: 1.6 770...1120 parallel to the c axis Cu: 1.6 770...1120
DO 10-4 m2s-’
,
kJ mol-’
Co-Fe; primary/terminal phase extending over the whole composition range in the temperature range studied “Co diffusion in the ordered B2 (CsCI) structure Fe: 50 928...995 557 (42) 70F 49 6oCo diffusion in the disordered bee structure, ferromagnetic phase Fe: 32.8
903...1153
(6.04:;:;:).
10-3
190.9 (54)
-
72H 70F ‘)
50.4 50
1023...1123 1068...1218
2.00 (50) (6.59+;:;;!
71.4
903 ... 1083
93.2
903 ... 1073
+lO-2
251.2 247.0 (84) (109)
“’
(l.25+$.
lo-’
198.0 (96)
-
(4.69;;:;;).
10-l
187.1 (121)
-
72H
‘) 5’Co diffusion.
‘j°Co diffusion in the disordered bee structure, paramagnetic phase Fe: 93.2
1153...1193
(5.72:;:;;).
lo-’
146.5 (84)
-
72H
251.2 (167)
-
72H
6oCo diffusion in the fee structure, ferromagnetic phase Fe: 10.4
1073...1283
(6.44+;:;;).
1O-2
6oCo diffusion in the fee structure, paramagnetic phase Fe: 10.4
1333... 1583
(l.61 ‘;!;i).
lO-2
234.0 (193)
-
72H
32.8
1333...1583
(3.15’;:;;).
1O-2
265.0 (117)
-
72H
50
1285...1437
1.33 (50)
290.5 (84)
49
70F ‘)
50.4
1333...1583
(1.54:;:;;).
IO-’
349.5 (42)
-
72H
71.4
1333...1583
(3.36+$
* 1O-2
266.2 (96)
-
93.2
1283...1583
(1.09$;;).
10-r
326.0 (201)
(continued)
‘) 5’Co diffusion.
Bakker
land&BBmstcin
New Series III,/26
225
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables)
Q
Fig.
Ref.
557 (42)
49
70F
59Fe diffusion in the disordered bee structure, ferromagnetic phase 230.2 (42) 1068... 1218 0.25 (10) Fe: 50
49
70F
59Fe diffusion in the fee structure, ferromagnetic phase 1081... T, 0.58 Fe: 6 10 0.68
273.3 279.2
-
74B
59Fe diffusion in the fee structure, paramagnetic phase TC... 1573 0.15 Fe: 6 10 TC... 1573 0.18 50 1285 ... 1473 1.26 (10)
261.6 263.3 286.7 (84)
49
74B 74B .70F
Temperature range [K]
Composition at %
DO
10m4m2sv1
kJ mol-’
Co -Fe, continued 59Fe diffusion in the ordered B2 (CsCl) structure 928...995 Fe: 50
Composition at %
Temperature K
D
E
Fig.
Ref.
-
70F
49
70F
49
70F
49
70F
m*s-’
57/60Codiffusion, isotope effect E in the fee structure, paramagnetic phase 0.773 (100) 1333 2.63 . lo-l6 Fe: 50 55159Fediffusion, isotope effect E in the ordered B2 (CsCl) structure 0.06 (20) 928 1.56. IO-l9 Fe: 50 0.30 (20) 956 8.68 . 10-19 0.16 (20) 975 4.79.10-18 0.30 (15) 994.5 8.70. IO-= 55/59Fediffusion, isotope effect E in the disordered bee structure 0.54 (8) 1068 1.03 . 10-16 Fe: 50 0.46 (8) 1150 1.07.10-15 0.64 (IO) 1175 1.85. 10-l’ 0.55 (8) 1218 5.12. IO-” 55/59Fediffusion, isotope effect E in the fee structure 1285 3.00.10-‘6 Fe: 50 1335 8.14. IO-l6 1400 2.28. IO-l5 1434 5.34.10-15 Composition at %
Temperature range [K]
Doa 10m4m’s’
Q.
kJ mol-’
0.67 (8) 0.71 (8) 0.65 (8) 0.61 (8) Dab 10m4m’s1r
Qb
Fig.
Ref.
80s
kJ mol-’
CoGa; intermediate phase, B2 (CsCl) structure 6oCo diffusion Analysis in terms of two exponentials: D(T) = Doa exp( - Q,/R T) + Dab exp( - QJRT) Ga: 40.0
848...1423
0.989+ o’49 -0.33
225 (10)
967+ 7oo -400
294 (21)
50
44.0
898...1423
234 (13)
51
912...1423 948 ... 1423
1450+530 -390 366 (9) 883 (14)
302(12)
50.0 52.0
0846+“‘54 . -0.33 one exponential one exponential
292 (2) 302 (1)
52 53
54.8
924... 1373
0.365 (13)
235 (2)
1160;;;
308 (2)
54
Remark: See also [79B]. (continued)
Land&-Bhutein New Series III/26
226
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) [Ref. p. 276
Composition at %
Tempcraturc range [K]
DO”
IOe4 m2s1’
Q.
kJ mol-’
Dab
Fig.
Ref.
383 (29)
50
80s
IO6
410 (29)
-
IO7
434 (45)
51
. IO4
357(50)
-
Qb
IOm4m2s11
kJ mol-’
CoGa, continued 67Ga diffusion Analysis in terms of two exponentials: D(T) = Do” exp( - Q,/R T) + Dab exp( - QJR T) 53 6+12 . -10
277 (9)
(,.I,-$IO’
Ga: 40.0
973 ... 1423
42.0
1123...1373
145+I’ -10
290
44.0
1024...1423
518+70 -80
304 (8)
46.0
1024...1373
212+380 -140
302
48.0
1198...1373
249+ 39 -34
302
(7.82;;:‘).
IO7
441 (49)
-
50.0
998...1423
292 (I I)
(I.80:;:$.
IO6
398 (18)
52
52.0
1024... 1423
303 (1I)
(4.59+::;).
IO8
462 (46)
53
53.0
1133...1323
309
1.60. IO6
394
-
54.8
923... I373
66.3+18 -14 326+50 -40 690 9410+1000 - 900
(3.26+;:‘).
IO-4 163 (IO)
328 (7)
54
Remark: See also [79B]. Composition
Temperature
at %
range [K]
Co -Mn;
DO 10m4m2s-’
Q
Fig.
Ref.
268.3 (63) 256.6 (100) 263.3 (34)
55
771
kJ mol-’
primary phase
54Mn diffusion Mn: 5.22
5.22 10.24
1141 ... 1241”)
1.38
1329...1473b) 1176... 1421
0.501
1.36
Remark: l ) Ferromagnetic phase, b, Paramagnctic phase.
Co-Ni;
primary/terminal phase extending over the whole composition range in the temperature range studied
6oCo diffusion [69M]; “Co Ni:
3.7
diffusion [72M] 1 23+1.23 1340...1579 . -06,
7.1
1349.e.1578
1 12+2.55 . -075
280.0 (142)
10.3
1358...1578
o 43 + 0.75 . -028
267.5 (126)
30.0
1362...1577
o lo+o.15 . -oo6
246.6 (113)
49.3
1366...1577
o 18+o:20 . -oo9
252.0 (88)
0.094+ o.50 -0.08 o.40+“.60 -0.25 o 98 + 0.73 . -o,41
49.3 69.7 69.7
853... 1353 1365...1574 853... 1353
56
69M
254.1 (163)
-
72M
258.7 (117)
56
69M
271.7 (50)
-
72M
283.4 (84)
(continued)
Bakker
Landolt-B6mslein New Series 111126
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) Composition at %
227
Temperature range [K]
DO 10e4 m2 s-l
Q
Fig.
Ref.
kJ mol-’
Ni: 73.7
1355...1570
o.og -oo7 + 0.26
240.3 (159)
56
69M
73.7
853*..1353
o.37 -021 +0:50
261.6 (75)
-
72M
80.1
1343...1564
o.22 -o + 0.55 16
250.7 (151)
56
69M
o.32+0.24 -o.14
259.5 (50)
-
72M
8.68 + -49.44 53
312.3 (88)
-
71M
7.1
l2 6+7:04 ’ -4.52
316.5 (54)
-
10.3
13 7+ 17.5 . -7.70
317.3 (100)
-
30.0
7 45 + 6.06 * -3.34
306.8 (71)
-
49.3
4 80+4.23 ’ -2.23
300.1 (75)
-
69.7
5 g6 + 5.63 . -2.90
298.9 (80)
-
73.7
6 13+4.87 ’ -2.72
299.7 (71)
-
80.1
3 66+ 1.65 . -1.13
293.9 (46)
-
Co - Ni, continued
80.1
853... 1353
63Ni diffusion Ni:
3.7
Composition at %
1338...1563
Temperature K
D rn2se1
Fig.
Ref.
1.92.10-12 1.15.10-‘2 1.76. IO-” 1.60. IO-l2 3.79 * lo-” 3.95 * lo-” 3.35 * IO-” 3.30.10-‘1
-
75Sl
Co - Ti; terminal phase “Co diffusion Ti: 92.6 95.1 96.7 98.4 92.6 95.1 96.7 98.4 Composition at %
1186
1478
Temperature range [K]
DO 10e4 m2 s-l
Ti: 92.6
1076... 1484
(2.50+;$.
95.1
1076..+ 1572
96.7 98.4
Q
Fig.
Ref.
lO-2
162.8 (75)
57
75Sl
(I.41 ‘i:;;).
10-Z
160.3 (50)
1166... 1617
(l.58+;$).
lO-3
140.2 (38)
1237 ... 1777
(1.26+;:;;).
lO-3
145.3 (67)
kJ mol-’
44Ti diffusion
_Lanaolt-bxlw.eln .._” New Series III/26
Bakker
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) [Ref. p. 276
228
Composition at %
Temperature range [K]
DO 10T4 m2s-’
Q
Fig.
Ref.
203 188 174
58
88N
59
64D
kJ mol-’
Co,Ti; intermediate phase, Ll z (Cu,Au) structure 6oCo diffusion Ti 21.5 22.8 24.0 Co-U;
1074.0... 1332.2 1074.0... 1322.6 1074.0... 1321.9
4.3. 10-z 1.2. 10-z 3.7. 10-3
terminal phase
235U diffusion u: X99.5...% 99.77 1095, 1113
For D see Fig. 59
Cr - Fe; primary/terminal phaseextending over the whole composition range in the temperature range studied 5’Cr diffusion in paramagnetic a-phase o *8+o.05 1073... 1673 . -o.04 Fe: 81 o 19+o.03 . -0.02 0.64 (7)
84 87
218.1 (38) 231.9 (29)
“Cr diffusion in paramagnetic y-phase Fe: 94 1073...1673 , .21 +0.73 -046
70Bl
237.3 (100)
3 21 +0.83 . -0.66
98
70Bl
216.8 (59)
244.5 (50)
s9Fe diffusion in ferromagnetic a-phase Fe: 80.25 848...919 0.65 84.78 868...950 1.25 90.87 848...999 9.27
217.3 226.5 230.6
-
68R
s9Fe diffusion in paramagnetic y-phase Fe: 90.87 1173..*1313 0.12
237.4
-
70R
s9Fe diffusion in paramagnetic a-phase Fe: 80.25 963 ... 1098 0.18 84.78 999 ... 1050 0.27 94.95 1073...1173 0.85 96.91 1040...1173 6.7 98.57 1040~~~1173 2.8 99.13 1040...1173 1.2
208.0 215.6 237.3 255.8 249.1 241.1
-
68R
Cr -Ni;
74K
primary and terminal phase
s’Cr diffusion in primary phase Ni: 18 1423.~~1688 S’Cr diffusion in terminal phase Ni: 52.3 ” 1223... 1473 61.6 65.6 70.6 76.4 78 1123...1473 85.7 1223... 1473 95.3 1223...1473 63Ni diffusion in terminal phase Ni: 52.3 1223... 1473 61.6 65.6
71A
0.28
259.5
2.64 2.16 2.42 2.91 6.10 0.61 5.66 6.37
284.2 284.0 288.0 288.5 295.5 264 293.6 292.1
-
8lR2
1.74 1.43 1.35
288.9 290.4 289.5
-
8lR2
Bakker
8lR2 79D 8lR2
(continued) Land&-B6mstein New Series 111’26
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) Composition at %
229
DO 10m4m2 s-l
e kJ mol-’
Fig.
Ref.
rangeKl
285.4 293.8 259 289.3 279.5
-
81R2
1123... 1473 1223... 1473 1223... 1473
1.02 2.95 0.15 2.31 1.32
Temperature
Cr - Ni, continued Ni: 70.6 76.4 78 85.7 95.3
79D 81R2
Cr - Zr; terminal phase ’ ‘Cr diffusion Zr: 97.4
1233... 1371
0.19
191.3
-
73Tl
g5Zr diffusion Zr: 92.14 95.92 96.51 97.95
1227... 1218 ... 1196... 1200...
1.59.10-z 1.39.10-z 2.05. IO-’ 5.16. 1O-3
173.4 (26) 169.2 (45) 169.0 (87) 165.5 (75)
60
81Pl
61
72B
62
82H
1516 1516 1518 1497
Cu -Fe; primary phase 64Cu diffusion Fe: 0 ... 2.4
1293
For D see Fig. 61
Cu - In; primary phase 64Cu diffusion In: 0.4 0.8 1.2 ., 1.7 Cu -Ni;
1005... 1145
220 200 200 190
2 0.4 0.6 0.2
primary/terminal phase extending over the whole composition range in the temperature range studied
64Cu diffusion Ni: 1
1053...1163
1.86
204.7
-
67S2
21.5
1146...1385
1.9+2.0
231.5 (80)
63
64M, 77B2
5416
1258... 1483
2.3 -lo (10,
252.4 (13)
87
1327...1632
7-03 1.5+o.4 .
263.7 (3)
64
64M, 77B2
.’
63Ni diffusion Ni: 21.5
1187... 1386
. oo63+o.012 -0.010
208.0 (21)
54.6
1298... 1476
17+11 -7
279.6 (63)
87
1379... 1618
35+17 -11
‘313.5 (71)
Cu - Pt; primary/terminal phase extending over the whole composition range in the temperature range studied ., _ 64Cu diffusion 1172...1319
1.l+1.8 -o 7
221.0 (105)
24.6
1220... 1369
. -042 053+1.01
229.0 (163)
49.4
1273 ... 1566
o.027 + 0.022 -0.012
213.5 (71)
74.5
1371...1658
37 o .67 -o + 0.83
269.6 (50)
Pt: 9.8
I&dolt-BBmstein New Series III/26
Bakker
65
77B2
(continued:
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) [Ref. p. 276
230
Q
Fig.
Ref.
oo93+“.42 . - 0.076 oo*g+o.041 . -0.013
220.2 (180)
66
77B2
1307...1560
oo66+0.126 . - 0.044
249.1 (126)
1413...1655
o.022+“~081 -0.017
252.4 (197)
0.4 0.6 0.7
200 200 200
67
82H
8.57. 1O-4 1.99.10-4 1.36. 1O-4
43.8 (56) 30.4 (42) 24.30 (364)
68,69
70H, 84B
0.4 0.07 0.06 0.03
200 180 180 170
70,71
82H
Temperature range fK1
DO lop4 m2s-’
Pt: 9.8
1179.**1331
24.6
1219..+1367
49.4 74.5
Zomposition it %
kJ mol-’
Zu - Pt, continued 195Ptdiffusion
215.2 (126)
Cu-Sb; primary phase 54Cudiffusion Sb: 0.3 0.5 0.8
1005~~~1145
Cu,Sb; intermediate phase, p-phase, DO, (BiF,) structure 54Cu diffusion Sb: 21 25 29
770 . . .900
Cu- Sn; primary phase 64Cu diffusion Sn: 0.4 0.8 1.1 1.7
1014... 1145
Cu,Sn; intermediate phase, y-phase, DO, (BiF,) structure
64Cu diffusion Sn: 16.6 18.0 19.8 20.2
811... 1008 873...998 873...998 897...992
0.0083 (17) 0.014 0.0036 0.018 (3)
83.0 (19) 74.5 84.6 82.0 (10)
72,74 73,74 73,74 72,74
80P 68E 68E 80P
1‘%n diffusion Sn: 16.6 18.0 19.8 20.2
839...998 873...998 873.e.998 903.s. 1003
0.22 (19) 0.33 0.092 0.035 (16)
117.8 (68) 122.2 113.4 107.1 (29)
72,74 73,74 73,74 72,74
80P 68E 68E 80P
129.3 (4)
75
68E
208.0 (21)
75
68E
Cu,Sn,; intermediate phase, &-phase,y-brass-type structure
64Cu diffusion Sn: 20.5
710... 850
4.7 (13)
11%n diffusion Sn: 20.5
770... 840
Bakker
Land&-BBmstein New Series III/26
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) Composition at %
Temperature range [K]
DO 10e4 m2se1
Q
231
Fig.
Ref.
76
7OP
kJ mol-’
Cu - Zn; primary phase 67Cu diffusion Zn: 0...4
I 1167,122O
For D seeFig. 76
8.6
873 .+. 1074
162.0 (84)
-
72K2
8.6
873...1074
oo57+o.100 . -0.036 o t5+0.06 . -oo5
177.0 (25)
-
72K2
10.1
1022...1252
o 64+o:07 . -oo7
190.9 (8)
-
680
14.9
783 ... 1084
160.0 (109)
-
72K2
20.5
1021...1213
176.6 (29)
-
680
28.8
873 ... 1074
133.5 (134)
-
72K2
30.2
973...1175
164.5 (25)
-
680
37.1
907... 1074
o.oo56+ 0.0100 - 0.0037
135.6 (67)
-
72K2
D
E
Fig.
Ref.
65Zn diffusion Zn:
Composition at %
Temperature K
o.075 + b.220 -0.056 o.35+o.12 -oog 0028+~.120 . - 0.023 o 32+o.10 . -oo8
m2s-l
64Cu/67Cu diffusion, isotope effect E Zn: 3.6 1169.4 29.8 1166
3.75.10-14 4.31 . 10-13
0.699 (7) 0.632 (9)
-
7OP
65Zn/6gZn diffusion, isotope effect E Zn: 4.89 1169.7 30.6 1168.8
1.31 . IO--l3 1.67. lo-l2
0.389 (10) 0.446 (8)
-
7OP
Composition at %
Temperature range [K]
DO low4 m2s-’
Fig.
Q
Ref.
kJ mol-’
CuZn; intermediate compound, disordered bee structure and ordered B2 (CsCl) structure 64Cu diffusion in the disordered structure Zn: 45.65 . ..48.00 770... 1090 0.011
92.3
77
56K
65Zn diffusion in the disordered structure Zn: 45.65 ... 48.00 772 ... 991 0.0035
78.6
77
56K
64Cu diffusion in the ordered B2 structure Zn: 45.65...48.00 654..‘715 180 565.~. 654 80
158.6 150.8
77
56K
65Zn diffusion in the ordered B2 structure Zn : 45.65 . . .48.00 649 . . .723 78000 537...649 163
185.1 152.0
77
56K
Composition at %
Temperature K
Fig.
Ref.
64Cu/67Cu diffusion, isotope effect E in the disordered structure Zn: 46.2 835.6 1.70.10-12 0.325 (9)
-
7OP
65Zn/6gZn diffusion, isotope effect E in the disordered structure Zn: 49.0 833.3 4.46. lo-l2 0.24 (1)
-
67P (continued)
Landolt-Biimstein New Series III/26
D
E
m2s-l
Bakker
232
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) [Ref. p. 276
Composition at %
Temperature K
E
D m2s-’
Fig.
Ref.
CuZn, continued 64Cu/67Cu diffusion, isotope effect E in the ordered B2 structure Zn: 46.8 683 1.77.10-‘4 0.325 (IO)
-
7OP
65Zn/6gZn diffusion, isotope effect E in the ordered B2 structure Zn: 47.2 683.6 4.38 . lo-r4 0.20 (I)
-
67P
Composition at %
Temperature range [K]
DO IOm4m2s-’
,Q
Fig.
Ref.
kJ mol-’
Fe - Ge; primary phase 5gFediffusion Ge: 4.8
1173..*1473
4.8
242.8 (42)
-
67LI
0.090 0.105 0.058 0.066 0.110 0.35 0.64 0.85 0.60
265.4 262.9 255.8 254.9 262.0 275.4 282.1 277.5 276.7
-
73N
oo55+o.014 . -0.012 0.020+ 0.0°9 -0.007 o oo96+ 0.0034 - 0.0007 oo17+o.o11 . -0.007 oo72+o.031 ’ -0.027 029+o.11 ’ -0.08 0.190 0.120 0.073
249.5 (80)
-
70N
235.3 (71)
-
222.3 (71)
-
229.4 (88)
-
248.2 (113)
-
266.6 (138)
-
261.6 251.6 242.0
-
73N
263 (11)
-
77R
257 (19)
-
266 (20)
-
264 (20)
-
Fe - Mn; primary phase “Fe diffusion in primary phase Mn: 1.04 1263...1513 2.03 2.97 4.90 7.04 10.41 18.15 25.50 33.98 54Mn diffusion in primary phase Mn:
1.04
983...1573
2.03 2.97 4.90 7.04 10.41 18.15 25.50 33.98
1263...1513
Fe-MO; primary phase sgFe diffusion in primary, paramagnetic phase MO: 0.32
0.64 0.90 1.5
953...1173
15.5+32 -10 23.6+16’ - 21 28.5+210 - 25 47.7+ 340 - 42
Bakker
Land&-BCmstein New Series III/26
Ref. p. 2761 4 Self-diffusion Composition at %
Temperature range [K]
Fe - Ni; primary/terminal 5gFe diffusion Ni: 14.9 29.7 45.3 60.5 70.0 75.3 79.8 90.0 63Ni diffusion Ni: 14.9 29.7 45.3 60.5 70.0 75.3 79.8 90.0
lo3Pd diffusion Pd: 10 20 30 40 50 55 60 70 80 90
binary
alloys and intermediate phases (Tables)
Q
DO 10m4 m’s-’
Fig.
233 Ref.
kJ mol-’
phase extending over the whole composition range in the temperature range studied
1258 -.+ 1578
2.13 9.98 8.75 28.77 11.99 20.28 12.30 17.99
286.3 305.7 301.8 311.3 302.7 309.9 304.2 307,l
(180) (105) (77) (122) (94) (72) (55) (174)
78
81M
1258 ... 1578
1.88 2.36 8.04 7.76 13.90 13.31 8.73 7.67
289.4 291.9 303.4 300.5 305.3 307.3 301.5 299.6
(139) (120) (152) (123) (62) (138) (89) (196)
79
81M
Fe - Pd; primary/terminal 5gFe diffusion Pd: 10 20 30 40 50 55 60 70 80 90
in homogeneous
phase extending over the whole composition range in the temperature range studied
1373 ... 1523
1373...1523
0.79 0.93 0.66 0.95 0.95 0.79 0.69 0.60 0.91 0.91
259.5 (130) 269.6 (134) 275.9 (147)
0.70 1.84 1.66 1.05 0.70 0.67 0.79 0.73 0.79 0.37
278.8 284.6 279.2 270.8 264.6 263.7 266.2 266.6 271.3 268.3
277.5 271.7 262.5 264.1 262.5 260.0 258.7
(110) (163) (159) (147) (130) (147) (134)
(172) (155) (167) (147) (130) (142) (142) (134) (151) (151)
80, 84
77F*)
81,84 ‘:
82, 84
77F*)
83,84
“) Remark: The values of the pre-exponential factors and activation energies(for s9Feand lo3Pd diffusion) were obtained by :omputer calculations based on the results given in Fig. 84.
Land&-Biimstein New Series III/26
Bakker
234
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) [Ref. p. 276 Temperature range [K]
Do 10e4 m2s-’
Q
Fig.
Ref.
03+0.8 . -o.22
263 (38)
-
79C2
o.1 +0.2 -0.07 o.1 +0.2 -0.07 o o4 + 0.07 . -0.04
254 (25)
-
259 (21)
-
240 (21)
-
O06+“‘3 . -o,0599
251 (71)
-
5.69
o o4 + 0.05 ’ -0.02
254 (17)
-
14.8
0.008+ “02 -0.006
224 (25)
-
1.1+26 _ 1o
264.1 (343)
-
20
0.34+ l2 - 0.33
265.0 (327)
-
25
1.17+130 - 1.16
265.4 (477)
-
30
0.28+7’1 -0.27
264.1 (335)
-
34
o.15+1.2 -0.13 1.3+1.5 -0.5 1*13+o.79 -0.47 2.1 + 3.9 -1.4 o.85 + 0.74 -0.40
264.1 (234)
-
289.7 (327)
-
284.2 (59)
-
292.2 (121)
-
286.7 (71)
-
0.34+ 3.5 -0.31
280.9 (222)
-
0.51
216.8 (84)
-
67Ll
85
75M2 *)
-
71D*) 81Rl
Composition at % Fe-Pt;
kJ mol-’
primary phase (solution in y-phase of Fe)
5gFediffusion Pt: 2.92
1386...1528
5.69 8.0 8.3 lg7Pt diffusion Pt: 2.92
15
1406.e. 1569
1173...1693
40 45 50 55 60
79C2
75K
Fe - Sb; primary phase sgFe diffusion Sb: 2.5
1169.e.1370
Fe - Si; primary phase “Fe diffusion in ferro- and paramagnetic phase Si: 7.64 806... 1366 For D see Fig. 85 *) Remark: Single crystal.
“Fe diffusion in ferromagnetic phase Si: 3 980... 1030 0.60 (30) 10 875...957 5.59
224.7 (54) 219.1
l ) Remark: Single crystal
(continued) Bakker
Iandolt-BGmstein New Series III/26
235
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) Composition at %
Temperature range [K]
DQ
10m4m’s11
Q
Fig.
Ref.
276 276 282.5 215.9 (54) 232.3
86, 87 86, 87 -
81T 81T 702 71D*) 68L
250 (11)
86
77M *)
229.8
-
68L
kJ mol-’
Fe - Si, continued 5gFe diffusion in paramagnetic phase 1.03 1063... 1373 Si: 1.48 76.7 1.87 1063... 1373 63.2 3 1173...1523 0.23 (7) 3 1030... 1173 1.63 4.7 1073... 1573 5.5
1013...1373
72+17 . _ 51
6.3
1073... 1573
1.65
6.4
1013...1373
-3,1 3.15+6.8
238 (11)
86
77M *)
6.55
1063... 1373
5.2
242
86,87
81T
7.64
1173... 1373
-028 1.38+o.35
228.1 (25)
85
751112 *)
7.8
1053...1373
86+18 . _ 58
244 (11)
86
77M *)
8.2 8.64 10
1073 ... 1573 1063 ... 1373 1005...1178
0.50 4.93 0.25
213.1 236 209.6
68L 86, 87 81T 81Rl
11.1
1173...1373
063+o.19 .
212.2 (33)
-
75M2 *)
11.3
1073 ... 1573
1.11-oll .
213.9
-
68L
11.6
1053...1373
063+1’8 .
212 (13)
86
77M *)
11.7 12.1
1073...1573 1063... 1373
1.46-047’ 0.8
216.4 213
68L 86, 87 81T
15.3
1133...1373
21+7.5 . -16
219 (16)
86
77M *)
19.2
1093...1373
-18 3.4+3.7
216 (8)
86
77M *)
’
.
*) Remark: Single crystal.
Composition at %
Temperature K
E
D
Fig.
Ref.
m2sm1
5515gFediffusion in single crystals, isotope effect E in the ferromagnetic and paramagnetic phase 71D 0.366 (48) 6.50 (32). lo-l7 980 Si: 3 0.339 (45) 1.04 (5). 10-16 996 0.336 (44) 1.35 (7). 10-16 1008 0.343 (45) 1.91 (IO). 10-16 1016 0.339 (41) 3.06 (15). IO-l6 1023 0.343 (38) 3.23 (16) * IO-l6 1039 0.346 (37) 6.18 (22). 10-16 1062 0.349 (36) 7.70 (28). lo-l6 1076 0.346 (35) 8.94 (32). lo-l6 1083 0.377 (34) 2.42 (9). 10-l’ 1128 0.397 (40) 5.77 (21) . lo- l5 1175 Remark: The Curie temperature is 1029K.
Land&-Biirnstein New Series III/26
Bakker
236
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) [Ref. p. 276
Composition 3t %
Temperature range [K]
Do 10m4m2s-’
Q
Fig.
Ref.
88
83K
kJ mol-’
primary phase
Fe-h;
5gFediffusion Sn: O... 2.7 Fe-Ti;
1168
For D see Fig. 88
primary phase
5gFediffusion Ti: 2 2
1173...1473
2.8
242.0 (42)
-
67Ll
1273... 1673
0.56+‘14 -0.12 o 27 + 0.04 . -0.03
216.4 (63)
-
70Bl
204.7 (42)
-
o.40+“.5 -0.2
208.9 (234)
-
1173...1773 1173...1466
1.4 I.87
236.9 (42) 240.3 (42)
-
67LI
1273... 1723
3 g2+0.82 . -0.68 3 ()(-)+0.49 ’ -0.42 2 28 + 0.40 . -0.34 2 12+0.25 . -0.22 , 66 + 0.49 ’ -0.38
241.1 (54)
-
70B2
238.6 (42)
-
236.1 (46)
-
236.5 (29)
-
234.0 (75)
-
4 6 primary phase
Fe-V;
“Fe diffusion V: I.8 5.3 ‘*V diffusion v:
2 5 9 14 19
Fe - Zr; terminal phase
5gFe diffusion Zr: 96.5 98.0 99.5
lOgO... 1600 1120... 1600 1120... 1580
7.4 (3) ’ 10-3
108.1 (19) same values same values
1276...1515 1188...1470 1196...1520 1218,..1515 1258...1518
5.26. lO-2 2.9. 10-3 1.62. lO-3 2.08. lO-3
155.5 (132) 140.8 (73) 146.0 (72) 150.9 (I 34)
1.52. lO-3
149.0 (65)
89
87Hl
90
81PI
91,92
76D
g5Zr diffusion Zr: 93.63
96.46 98.36 98.65 99.02 GaNi;
intermediate phase, B2 (CsCI) structure
67Ga diffusion Ni: 47.28 48.76 50.01 50.73 51.01 52.40
1085... 1384
0.1230 (2317) 0.7874 0.0010 (19) 0.0122 (329) 0.1087 (2656) 5.1430 (209524)
191.5 209.4 146.5
166.4 189.6 222.0 (continued)
Bakker
Land&BBmstein New Series 111126
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) Composition at %
237
Temperature range [K]
Do
Q
Fig.
10m4rn’s-l
kJ mol-’
978 ... 1380
0.0029 (38) 0.0126 (117) 0.0130 (192) 0.0936 (1220) 0.1353 (1187) 0.0174 (84) 0.0107 (95) 0.0121 (37)
143.1 154.3 156.0 172.5 175.3 158.2 153.7 153.9
93,94 76D
238Pu diffusion diffusion in s-phase Pu: 96.6 847...917
6.98. 1O-4
56.1
-
71w
diffusion in g-phase Pu: 96.6 613...781
76.4
152.0
-
71w
414.1 (87)
95
84V
Ref.
GaNi, continued 63Ni diffusion Ni: 47.28 48.76 49.33 50.01 50.45 50.73 51.01 52.40
Ga - Pu; terminal phase
GaV,; intermediate phase, Al 5 structure 48V diffusion V: 75.6
1298 ... 1449
15200
Hf - Zr; primary/terminal phase extending over the whole composition range in the temperature range studied ‘*‘Hf diffusion in single crystal diffusion parallel to the hexagonal axis Zr: 4.0 1493... 1883 0.86 1347... 1493 7.1. lo-”
370.0 (134) 85.0 (268)
96
72D
diffusion perpendicular to the hexagonal axis Zr: 4.0 1493 ... 1883 0.28 1347... 1493 8.9. IO-lo
348.3 (200) 104.2 (553)
97
72D
Hg - Pb; terminal phase ‘03Hg diffusion Pb: 96 “‘Pb
428.s.568
o 7g+o.17 . -0.14
90.0 (8)
98
73w
487...568
o.76 + 0.21 -0.14
105.1 (13)
98
73w
diffusion
Pb: 99 Composition at %
Temperature range [K]
DO" 10e4 m’s-’
Q.
kJ mol-’
Dab low4 m’s-’
Qb
Fig.
Ref.
314.7 (251) 318.5 (241) 293.4 (241) -
99
83Hl
kJ mol-’
InPd; intermediate phase, B2 (CsCl) structure i14”‘In diffusion Analysis in terms of two exponentials: D(T) = Doa exp( - Q,/RT) + Pd: 49 1094...1270 0.0084 (44) 192.1(125) 50 996... 1326 0.0050 (27) 181.5(106) 53 996... 1417 0.016 (8) 191.1(116) 56 1039... 1472 0.14 (3) 215.3 (29)
Dabexp(- QJR T) 5.0 (39). IO2 10.6 (62). IO2 20.0 (ill) -
-
(continued)
Land&-Bhstein New Series III/26
Bakker
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) [Ref. p. 276
238
Composition at %
Temperature range [K]
DQ
Q
Fig.
Ref.
lop4 m*s-’
kJ mol-’
1056... 1274 1098... 1326 1122...1424 1056...1379
0.12 (2) 2.30 (55) 0.60 (13) 0.20 (4)
207.5 (29) 243.3 (29) 222.0 (19) 205.6 (19)
99
83Hl
57.0 222.0 53.1
100 101 102
79A
Fig.
Ref.
-
75Sl
Q
Fig.
Ref.
103
75Sl
InPd, continued ro9Pd diffusion Pd: 49 50 53 56
MnPt,; ordered phase, Ll z (Cu,Au) structure s4Mn diffusion Pt: 65 75 82
1026... 1284 1026... 1283 1020... 1284
2.3.10-r’ 3.10-2 2.1 * 10-10
Composition at %
Temperature K
D
Mn -Ti;
m*s-’
terminal phase
54Mn diffusion Ti: 79.4 82.1 86.7 90.3 86.7 90.3
1171
1513
8.83. IO-l4 9.67. IO-l4 1.54.10-13 1.86.10-‘3 1.44.10-11 5.64. IO-”
Temperature range [K]
DO
Ti: 79.4
1083... 1525
(5.47;;:;).
IO-’
208.0 (75)
82.1
1070... 1570
(2.60+;:;;).
lo-*
176.2 (42)
86.7
1076... 1617
(2.06+;:;;).
lo-*
172.0 (54)
90.3
1137...1720
(1.90’;:;;).
lo-*
171.2 (96)
Composition at %
10m4m*s-l
kJ mol-’
44Ti diffusion
Mn -Zr;
terminal phase
54Mn diffusion Zr: 98 98.5 99 99.5 “Zr diffusion Zr: 98 98.5 99 99.5
1173...1473
0.08 (3) +10-j 0.46 (12). IO-’ 1.38 (41). lO-3 2.92 (73). lO-3
104.6 (27) 120.1 (30) 129.5 (37) 135.7 (27)
104
79P2
1173...1473
3.36 (97). 2.17 (61). 1.20 (30). 0.71 (20).
125.3 (35) 121.8 (28) 116.7 (34) 112.3 (27)
105
79P2
lO-4 lO-4 10-4 10-a
Bakker
land&-Btimsfein New Series III/26
239
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) Composition It %
Temperature range [K]
Do 10m4rn’s-l
Q
Fig.
Ref.
207.2 210.6 218.5 228.6
-
71F
229.8
-
198.4
-
kJ mol-’
MO- Ni; terminal phase )gMo diffusion Ni: 77 80 82 84 92
63Ni diffusion Ni: 77 80 82 84
0.20 0.25 0.45 1.30 1.31
1373...1573
0.12 0.19 0.34 0.63 2.55
1223...1573 1223 ... 1623 1223 ... 1623 1273 ... 1673
92 MO-W; studied
1373 ... 1573 1223 ... 1573 1223 '.* 1623 1223 ... 1623 1273 ... 1673
204.3 211.0 218.5 236.1
71F
primary/terminal phase extending over the whole composition range in the temperature range -
ggMo diffusion w: 0.1 15 20 25 35 45 50 56 65 75 80 85
99.9 la5W diffusion w: 0.1 15 20 25 35 50 65 75 80 85
99.9
2073 ‘.. 2673 1673 . ..2673 1673...2673 1673...2673 1773...2673 2173...2673 1973... 2773 2173 ... 2573 2073 ... 2873 2073 .*. 3073 2073 *.. 3073 2073 . . .3073 2473 +.. 3073 2073.‘.2673 1673...2673 1673 ... 2673 1673 ... 2673 1773 ... 2673
1973...2773 2073 ... 2873 2073 ... 3073 2073 ... 3073 2073 ... 3073 2473 ... 3073
468.8 443.7 427.0
142 265 146 47 28 0.12 12 0.17 1.3 0.2
397.6 385.1 431.2 368.4
447.9
0.11
360.0 353.7 343.3
0.08 0.0025
326.5
-
69F
-
69F
-
68s
67L2 69F 67L2 69F
334.9
297.2
0.0085 1.4 1.7 2.2
305.6 312.3 322.3 355.8
6.9
397.7
14 16 20 22 25 24
427.0 485.6
498.1 510.7 544.2
Nb - Ni; terminal phase 63Ni diffusion Ni: 90 92 98.8
Land&-Bknstein New Series 111126
1303 ... 1503
281 260 255
1.80 0.20 0.12
Bakker
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) [Ref. p. 276
240
Zomposition 1t %
Temperature range [K]
DO 10m4m2s-’
Q
Fig.
Ref.
kJ mol-’
VbNi,; intermediate phase, DO, (P-TiCu,) structure “Nb diffusion in single crystals Ni: 75 1543.s.1623
240
447.9
-
75Ml
“Ni diffusion in single crystals Ni: 75 1363.s.1643
0.18
304.7
-
75Ml
Vb-Ti;
primary/terminal phase extending over the whole composition range in the temperature range studied
“,‘95Nb diffusion fi: 10 35 50
2000.‘.2473 1773. ..2273 1473...2073
SeeFig. 106 SeeFig. 106 SeeFig. 106
64.3
1279...1657
70
1373.e.2073
o.29*+o.195 -0.117 SeeFig. 106
80.4
1222... 1565
(1.18+;:;;).
85 90
1150~~*1515 1230...1515
SeeFig. 106 SeeFig. 106
94.6
1222...1784
(l.79+;$.
95
1230...1573
See Fig. 106
1279.e. 1657
(2.51:;:;;).
80.4
1222...1565
94.6
1222... 1784
106,107 106,107 106,107
63G 63G 63G
106,108
79Pl
106,107
63G
106,108
79Pl
106,107 106,107
63G 63G
106,108
79Pl
106,107
63G
247.1 (43)
108
79Pl
(3.15~;:~~)~ 1O-3
175.6 (52)
108
79Pl
(l.27+$.
149.1 (24)
108
79Pl
258.4 (61)
lO-2
1O-3
198.1 (67)
160.0 (33)
“4Ti diffusion Ti: 64.3
10-l
lO-3
Nb- W; primary/terminal phase extending over the whole composition range in the temperature range studied p5Nb diffusion w: 5 IO 30
1873... 2273
Composition at % W
Temperature K
psNb diffusion w: 2 5 10
2680 (20)
‘*‘W diffusion w: 2 5 10
2680 (20)
2334 164 0.0257
544.2 489.8 355.8
-
67L3
Fig.
Ref.
1.277 (7). IO-l2 1.065 (4). lo-l2 0.760 (4) . lo- l2
-
86M
4.35 (20). lo-‘3 3.30 (8). IO-l3 2.38 (6). IO-l3
-
68M
D
m2s-’
Bakker
Landolf-BBmstein New Series III/26
242
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) [Ref. p. 276
:omposition 1t %
Q
Fig.
Ref.
373.0 (234)
-
72Kl
344.5 (540)
-
(.46+5.1 -2.4 > ’ lo-*
469.7 (151)
-
633.e.673 633...663 613...653
0.871 . 1O-7 0.923.10-* 0.929. lo-’
83.7 67.0 46.0
-
72s
Temperature
DO
Fig.
Ref.
range[Kl
10m4m*s-l
Temperature range [K]
DO 10v4 m*s-l
kJ mol- ’
ae- W; terminal phase “W diffusion ii’: 78
2208...2773
89 94 Sb,Sn,; intermediate phase, p-phase ‘r3Sn diffusion jn: 41 43 45 Composition at % SC-&;
Q
A
kJ mol-’
kJ mol-‘K-l
primary/terminal phase extending over the whole composition range in the temperature range studied
)5Zr diffusion The following measurementsare analyzed by D(T) = Do exp (- Q/R T) exp (A/R T*) Zr: 86.4 1400... 1900 1.3 341.7 17.18. lo4 111 93.3 1280... 1900 1.0 335.9 16.31 . lo4 Composition at %
87H2
Temperature
DO
Fig.
Ref.
low4 m*s-l
Q
range[Kl
kJ mol-’
Sn- Zn; primary phase 1‘3/‘23Sn diffusion Zn: 0.9
420...490
89+7.3 . -4.0
104.6 (23)
112
66B
65Zn diffusion Zn: 0.9
350...455
20+1.0 ’ -0.5
71.0 (15)
112
66B
Ti-V;
primary/terminal phase extending over the whole composition range in the temperature range studied
44Ti diffusion v: 10 20 30 40 50 60 70 80 90
1173...1875 1173.s.1796 1223... 1848 1273... 1848 1273.e.1849 1273...1874 1373... 1918 1373... 1941 1423... 2023
Arrheniusplot is curved
113
68M
48V diffusion v: 10 20 30 40
1173.s.1823 1173...1848 1223...1846 1223... 1848
Arrheniusplot is curved
114
68M
(continued) Bakker
Land&-Bknslein New Series III/26
243
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Tables) Composition at %
Temperature range [K]
DO
10e4 m2 s-l
Q
Fig.
Ref.
114
68M
kJ mol-l
Ti - V, continued v: 50 60 70 80 90
1323... 1846 1323... 1845 1373... 1875 1423... 1923 1423..’ 2020
Ti - Zr; primary/terminal phase extending over the whole composition range in the temperature range studied 44Ti diffusion Zr: 49
1060... 1920
I15
Arrheniusplot is curved
87H2
U - Zr; primary/terminal phase extending over the whole composition range in the temperature range studied 235U diffusion Zr: 41 61 73 89
1173 ... 1325 1173 ... 1338
8.96 0.007 0.00365 7.5. 10-4
245.3 168.7 160.7 141.9
-
68F
1173...1338
7.5. 10-7 3.8 . 1O-6 2.4. IO-’ 3.9. 10-4 0.028 0.12
83.7 99.2 118.5 146.5 190.5 205.5
-
68F
1428...2047
064+I.20 ’ -0.42
312.6 (153)
II6
81P2
1578 ... 1888
86 (25) 72 (22) 68 (22) 58 (15)
383.2 (109) 379.4 (110) 376.7 (106) 373.0 (105)
117
84P
48V diffusion in terminal phase 1166... 1480 Zr: 98.0 98.5 99.0 99.5
0.7 (2). 10-5 1.5 (3). 10-5 3.0 (6). IO-5 5.5 (11). 10-5
94.2 (10) 100.6 (18) 106.9 (21) 112.5 (24)
118
82P
g5Zr diffusion in primary phase 1578...1883 Zr: 0.5 1.0 I.5 2.0
115 (38) 153 (52) 195 (64) 242 (80)
373.0 (100) 376.0 (103) 378.6 (107) 380.8 (112)
119
84P
“Zr diffusion in terminal phase 1167... 1476 Zr: 98.0 98.5 99.0 99.5
14.0 (40). 10-5 9.3 (25) . IO-’ 5.9 (15). 10-5 4.5 (13) * 10-5
120.8 (33) 116.8 (31) 112.0 (29) 109.0 (26)
120
82P
g5Zr diffusion Zr: 15 22 41 61 73 89
V - Zr; primary and terminal phase 48V diffusion in primary phase Zr: 0.5 0.5 1.0 1.5 2.0
Land&-Biimstein New Series III/26
Bakker
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures)
[Ref. p. 276
Figures for 4 10 m2 6 4 2
10
-I
10 6 6 4 2
10-15 1.00
1.05
1.10
1.15
1.20
.lOJK-’ 1.30
Fig. 3. Ag-Cd (30 ... 38 at % Cd). “OrnAg diffusion coeflicient (full lines) and “‘Cd diffusion coefficient (dashedlines) vs. reciprocal temperature [68G]. 0
1
2
3
4
5
6
Ag-
7
8 ot% -
Fig. 1. Ag-AI (90.3...99 at % Al). ‘romAg diffusion coefficient vs. Ag concentration at various temperatures [68H].
1.6 .10-“3 mvs
6 6
1.2
I 4 m
I 0.8 a
2
0.1
01 0
10-14 I 20
I 40
I 60
I I 80 at% 100
Au Fig. 2. Ag-Au (8...94 at % Au). “OrnAg diffusion coeflicient (open circles) and 198A~diffusion coefficient (full circles) vs. Au concentration at 1148K [63M].
0.85
0.89
0.93 0.97 1.01.10-3K-‘1.05 l/lFig. 4. Ag-Cu(0.17...8.15at %Cu). “omAgdiffusioncoefkicnt vs. reciprocal temperature [77B2].
Bakker
Landoh-BBmstcin New Series 111i26
245
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures) 2d3 m2/sI 1ll-'2
m2/5
I
I
I
A-
P..
I
h
An
r-t,
I
lo-l3 8
I
6
4 4
2
I
~hI lo-" 8 6 4
4\ 2
2
I
I
0.85
0.90
I
I
I
\\
1Pl
0.80
0.95
1.00
W3 K-'
1.10
0.85
0.90
0.95
1.00 l/T-
l/T-
Fig. 5. Ag-Cu (0.85 ... 3.36 at % Cu). “omAgdiffusion co-
efficient vs. reciprocaltemperature[77B2].
1.05
.10-3K'
1.15
Fig. 6. Ag-Cu (1.38 ... 4.43 at % Cu). “OrnAg diffusion coefficient vs. reciprocal temperature [77B2].
lo-‘-‘2
I”
m2/s
m2/s 6 4
I
I
I
3.0
.10-3,(-l
64
Q 2
I
10-13 B
Q
lo-l3 2.6
6
2.7
2.8
2.9 l/T-
4
3.2
Fig. 8. Ag,Hg, (55 at % Hg). ‘03Hg diffusion coeffkient vs. reciprocal temperature [77S].
2
1.25,
I
I
0.95 0
0.2
0.4
I
I
I
10-14 a
$15
0.
j
0.88
0.91
0.94 l/T -
0.97
.,0-3K-l
1.03
Fig. 7. Ag-Cu (1.75 ... 6.56 at % Cu). llomAg diffusion coefficient vs. reciprocal temperature [77B2].
Fig. 9. Ag-In (0.151. ..0.943 at % In). “OrnAg diffusion coefficient relative to the silver self-diffusion coefficient vs. In concentration at 1054 K [85K]. Different symbols correspond to two runs of measurements. Land&-B6rnstein New Series III/26
Bakker
0.6 In -
0.8 at%
1.0
4 Self-diffusion in homogeneousbinary alloys and intermediate phases(Figures)
246
[Ref. p. 276
10-12 _ m7/s .
-13 >
10
\
1o-l3
I -14 _ a 10 lo-‘& 10-15 I Q 10-16
48
45
40
52
56
lo-l5
ot% 60
MgFig. 10. AgMg (41.l ... 57.2at % Mg). “OrnAg diffusion co:flkient vs. Mg concentration at various temperatures [64D]. lo-l6
I
Ag - Sn
10-l’ 0.8
0.9
1.1 1.0 l/l -
1.2.10-3K-’1
Fig. 11. Ag-Sb (0.53...1.42 at % Sb). “OrnAg diffusion coefficient vs. reciprocal temperature [55S].
8 at% 10 6 SnFig. 12. Ag-Sn (1 . ..8.67 at % Sn). “OrnAg diffusion coefficient relative to the silver self-diffusion coefficient minus 1 vs. Sn concentration at various temperatures [83H2]. 2
4
0.8 at% 1.0 0.6 0.4 Sn Fig. 13. Ag-Sn (0.218...0.773 at % Sn). “OrnAg diffusion coeffkient relative to the silver self-diffusion coeflicient vs. Sn concentration at 1052K [85K]. Different symbols correspond to two runs of measurements.
Bakker
0
0.2
Landolf-BBmstein New Series III!26
247
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures) 10-12 m2/S
I
Ag - Sn
13
10-12 m2/s 14 -13
IO jot% Sn I
4.1 3 15 _
a
0.8 lo-l4
0.108
I6
1.1540JK-' 1.20
1.9:
Fig. 14. Ag-Sn (0.108... 6 at % Sn). rromAg diffusion coefficient vs. reciprocal temperature [78G].
0.85
0.90
0.95
1.00 l/T-
1.05
@K-'
1.15
Fig. 15. Ag-Sn (0.11, 1.7 at % Sn). rr3Sn diffusion coefticient vs. reciprocal temperature [78G].
10-12 m2/s 6
I
I
Ag -Zn
, 2.8
28.
2
1o-13 8 6
I
I a
4
2.2
22
2
I a
a
2.0
20
'T 6
1.8
18
4
1.6
16 14 0
2
1.1, 1
2
3
4 at%
1.65 40-3K-'
5
Fig. 16. Ag-Zn (1.1...4.1 at % Zn). ‘lomAg diffusion coefficient vs. Zn concentration at various temperatures [67R].
Land&-Biirnstein New Series III/26
1.75
l/T -
Zn -
Fig. 17. Ag-Zn (99.11 ... 99.65at % Zn). ‘romAg diffusion coefficient vs. reciprocal temperature parallel (D,,) and perpendicular (D,) to the c axis [69S].
Bakker
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures)
248
[Ref. p. 276
10-“[
KS/s
2
10-12
\ 2 \
10-l’
I el
I 6 ,o-li Q6 4
-13 10 1.0
2
1.1
1.2 l/l-
1.3
1.4.lO-‘K-’ 15
Fig. 19. AgxZn, (61,62 at % Zn; y-phase). “OrnAg diffusion coefficient vs. reciprocal temperature [71S]. lo-‘) l.LO
1.45
1.50
1.55 l/l -
1.60
.10-JK“
1.70
Fig. 18. Ag-Zn (98.6,99.43 at % Zn). 6sZn diffusion coefficient vs. reciprocal temperature parallel (D,,) and perpendicular (D,) to the c axis [69S].
10‘‘amk
10-n 2.5 48
54 56 01% 58 co Fig. 21. AlCo (49 ... 57 at % Co). “Co diffusion coefficient vs. Co concentration at 1623 K [51N].
I Q
50
52
10-u 10-l’ m2/s
I
Al - Fe
10-u 10-n 1.0
14 .1O-3K-’ 1.5 1.3 l/l Fig. 20. Ag,Zn, (61 at % Zn; y-phase). 6sZn diffusion coefficient vs. reciprocal temperature [71S]. 1
1.2
I ~ 10-u
lo-l4
Fig. 22. AI-Fe (75 at % Fe). “Fe diffusion coeflicient vs. b reciprocal temperature [75L].
lo-l5 0.65
0.70
0.75
0.80
0.85.10-‘K-’ 0.90
l/T-
Bakker
Land&-BBmstein New Series III/26
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures) 10-12_ m21s
10-13
IO‘"
Y
_
249
I
m2/s
AlFe
.
i L
t
82ot%Fe o 90ot%Fe ,94ot% Fe
Y 10-14 _ ?I 10-15 _
I
\
I a
0.85.1O-3 K-’I 0.75 0.80 l/T Fig. 24. AlFe (51.5 ... 65.9 at % Fe). 55Fe diffusion coefficient vs. reciprocal temperature [75L]. 0.65
10
0.70
10
10
2
1o-13 8 6
10-19 0.7
4
- .
0.9 1.0 1.1 .lO-‘K-’ 1.3 l/l Fig. 23. Al-Fe (82 .. .94 at % Fe). “Fe diffusion coeffcient vs. reciprocal temperature [81Rl]. Arrows indicate Curie temperatures. 0.6
0.8
2
I
10-l'"
a*
6 4 2
2
lo-l5 8 6
10-l'" 6 6 4
4
2
1o-gIl;
I
-2
0.80 l/TFig. 26. AlNi (50.0 ... 58.7 at % Ni). 63Ni diffusion coefficient vs. reciprocal temperature for various Ni concentrations (in at %): Curve f: 50.0; 2: 53.2; 3: 54.5; 4: 55.5; 5: 58.0; 6: 58.5; 7: 58.7 [71Hl].
11-1, 6 4
2
6 I
I
I
I
0.64
0.68 l/l-
0.72
/Jo-17
0.60
Landok-BBmstein New Series III/26
I
14
Fig. 25. AlNi (48.3 ... 50.0 at % Ni). 63Ni diffusion coefficient vs. reciprocal temperature for various Ni concentra0.76.10-3K-’ 0.80 tions(inat%):Curve1:48.3;2:48.6;3:49.0;4:49.2;5:50.0 [71Hl].
Bakker
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures)
250
[Ref. p. 276
Fig. 28. AINi, (73.2...76.2 at % Ni). “3Ni diffusion coeffi- b cient vs. reciprocal temperature for various Ni concentrations (in at %): Curve I: 76.2; 2: 74.7; 3: 73.2 [71H2].
2.11f2I
m’/s 1;-‘2
1
AlNi I
A, //
2
10-15 8 6 I 4
4
1i-‘6 6 4
6
I
1
4.1o-l* 0.60 1;-‘5
10'.Dm2,‘s
6
I
0.65
0.70
I
I
0.75
I 0.90
0.80
40JK-’
I
AINi3
4
1557K A 1
10-“6 8 6
4.10-"7 66
, II
,y -1
I
I
48
50
I
I
I
I
I
I
52 54 Ni -
56
lo- 14 _
I I
L 1427
58 at % 60
Fig. 27. AlNi (48.3 ... 58.7 at % Ni). 63Ni diffusion coefficient vs. Ni concentration (48.3 ... 58.7 at % Ni) at various temperatures: Curve I: 1623K; 2: 1573K; 3: 1523 K; 4: 1473K; 5: 1423K; 6: 1373 K; 7: 1323K; 8: 1273 K [71Hl].
oc 1471 L27 -? 394 -v -v 374
t I I5 _ 1394 ~ lo-
318 9
1290 L-
290 9
lo- 16 _
1190 LFig. 29. AINi, (73.2 ... 76.2 at % Ni). 63Ni diffusion coefli- b :ient vs. Ni concentration at various temperatures [71H2].
10-lI7 73.1 3
Bakker
73.5
7
74.tj Ni -
75.0
75.5 0
251
Ref. p. 2761 4 Self-diffusion in homogeneousbinary alloys and intermediate phases(Figures) lom2/
IO+ m2/s
i.”
I
Al Ni,
lo-’
IO-
a
I a
A
10-1’8 IO-‘91 0.6
lo-’
P * 0.7
1.0 .IO’K-’ 1.1
0.9
0.8 1/T-
Fig. 31. AlNi, (74 ... 76 at % Ni). 63Ni diffusion coefficient vs. reciprocal temperature for various Ni concentrations (in at %): Open circles: 74; triangIes: 75; full circles: 76. Solid line: result from [75B] for 75 at % Ni; dashed line: result from [71H2] for 75 at % Ni.
10-l
10“ [
0.90 l/T-
Fig. 30. AINi, (74.8 at % Ni). 63Ni diffusion coefficient vs. reciprocal temperature [75B].
Y
10-12-
o
0
8L2.5
10-L
m2/s
792.2
!,Io-13~
I o-l3
10-l 4 10-14 , ~I lo-‘! 10-'5 0
1
2
3
4 ot%
Zn -
lo-l6
Fig. 33. Al-Zn (1.16 ... 3.76 at % Zn). 65Zndiffusion coefficient vs. Zn concentration at various temperatures [77Bl]. 10-l
10-l’1 23.5
Landok-B&stein New Series III/26
24.0
24.5
25.0 Al -
25.5
at%
;!6.5 4 Fig. 32. AINi, (z 74 ... x 76 at % Ni). 63Ni diffusion coef-
ficient vs. Al concentration at various temperatures [87H3].
Bakker
4 Self-diffusion in homogeneousbinary alloys and intermediate phases(Figures)
[Ref. p. 276
10' m*/
lo>
4 .l(p I lo-' a
ml/s 3 2 I a
10-l \ \
11 0
I 1
I
I
I
I
2
3
4 at%
5
lo-' 1.1
1.2
1
1.4
1.5
h
*l[ i-‘K 1
l/1 __)
ln -
Fig. 34. Al-Zn (1.16...3.76 at % Zn). Linear plot of the 65Zn diffusion coefficient vs. Zn concentration at various temperatures [77Bl].
Fig. 35. Al -Zn (2.15,3.76 at % Zn). 65Zn diffusion coefficient vs. reciprocal temperature [77Bl].
1P m2/s 10-”
,0-x
I a ,pI
10-l’
10-p 50 at% 60 Zn -
Fig. 36. Al-Zn (lo... 58.5 at % Zn). “5Zn diffusion coeflicient vs. Zn concentration at various temperatures [7X1].
Fig. 37. AI -Zn (24.25 at % Zn). 65Zn diffusion coefficient vs. reciprocal temperature [SOC].
Bakker
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures) &lo-"2 m2/s
mVs 6
lo-l2 8
253
I
AuCd I .
I
I
I I
/I ,
_
821.7K_,A --&---
6
_-/ /
10 8 6 4
46
L7
48
49
50 at%
51
Cd -
Fig. 39. AuCd (47.5 ... 50.5 at % Cd). “‘Au diffusion coefficient and “‘Cd diffusion coefficient vs. Cd concentration at various temperatures [67G]. Full symbols: Au diffusion; open symbols: Cd diffusion. , o-l;
m2/s
10-y\
I 1.2
1.3
1.4 1/T -
1.5
1.6~10-3K-'1.7 ,o-lZ
Fig. 38. AuCd (47.5 ... 50.5 at % Cd). rg5Au diffusion coefficient, “‘Cd and ‘r5Cd diffusion coefficient vs. reciprocal temperature [67G]. Open triangles: “‘Cd diffusion in the 47.5 at % Cd compound; full triangles: “‘Cd diffusion in the 47.5 at % Cd compound; open circles: Au diffusion in 47.5 at % Cd compound; open squares: “‘Cd diffusion in the 49.0 at % Cd compound; full circles: Au diffusion in the 49.0 at % Cd compound; diamonds: “‘Cd diffusion in the 50.5 at % Cd compound; full squares: Au diffusion in the 50.5 at % Cd compound. 10-1’3 m2/s
I 6
TX-j-
Au-Cu I
1o-l4 1 Q , o-l!
1 I lo-"
,i-‘44 0
5
IO
15 Au -
20
25 at% 30
Fig. 41. Au-Cu (72.5 ... 97.5 at % Cu). rgsAudiffusion coefficient and Wu diffusion coeftkient vs. Au concentration at 1133 K [78H]. Full circles: Au diffusion; open circles: Cu liffusion. Landolt-Biimstein New Series III/26
lo-l7 C
0.9
1.c l/T -
Fig. 40. Au-Cu (75 at % Cu). lg5Au diffusion coefficient vs. reciprocal temperature [77B2]. Open circles: [65B]; full circles: [69A].
Bakker
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures)
254 10-l’ m2/s ml/s
[Ref. p. 276
lo-11 m21 5
Au -To
1\
10’-12
b c\
oI 10’.13 -
10‘” a lo-‘3 1.k
10.14 _
2.0 alO-‘K-’ 2.2 1.8 l/T Fig. 42. Au-Ta (1.2 at % Ta). lg5Au diffusion coeftkient vs. reciprocal temperature [75G2]. [X(32]. 1.6
10-15 1.05
10“ m21
1.15
1.25 l/T-
1.35.lO-“K-l 1.
Fig. 43. AuZn (49.0 ... 51.Oat % Zn). “‘Au diffusion coefficient and 65Zn diffusion coefficient vs. reciprocal temperature [71G]. A: Au diffusion in the 49.0 at % Zn compound; A: Zn diffusion in the 49.0 at % Zn compound: o: Au diffusion in 50.0 at % Zn compound; l : Zn diffusion in the 50.0 at % Zn compound; V: Au diffusion in the 51.0 at % Zn compound; V: Zn diffusion in the 51.0 at % Zn compound.
lo-’
~I 10“
10“
OS 10-l
69
50
0 48.0
51 ot%
2nFig. 44. AuZn (49.0 ... 51.8 at % Zn). “‘Au diffusion coefticient and 6SZndiffusion coeflicient vs. Zn concentration at various temperatures [71G]. Open circles: Au diffusion; full circles: Zn diffusion.
48.5
49.0
49.5 50.0 Zn -
50.5 at%
51.5
Fig. 45. AuZn (48.37...51.01 at % Zn). ‘95”99Au isotope effect Efor diffusion vs. Zn concentration at various temperatures [83H3]. Full triangles: 757 K; open triangle: 814 K; circles: 876 K.
Bakker
Land&-BBmsfein New Series III!26
Ref. p. 2761 4 Self-diffusion in homogeneousbinary alloys and intermediate phases(Figures) 0.3
1 o-li
I
mVs
255
‘
Be-Cu \
I 0.2 ,o-l: u 0.1 I
0
49.0
49.5
50.0
50.5 Zn -
51.0
at%
52.0
?ig. 46. AuZn (49.18...51.85 at % Zn). 65/6gmZnisotope :ffect E for diffusion at various temperatures (see table) ac:ording to [83H3].
-14
10
Q , 0 -l!
10-16
1.i
1 1.1
t
10-17L
2
0.7
3 I.( --, 2
0.9
1.0 l/T-
1.1
0.2
0.6
0.4
0.8 at%
1.0
1oq3 m2/s
Cd -
?ig. 48. Cd-Pb (99.1 . ..99.995 at % Pb). “‘Cd diffusion :oefficient relative to the lead self-diffusion coefficient vs. Cd :oncentration at 470.7 K [79Cl].
I f-o-~e
730°C I
9iO°C
IO.14 10-15 1o-16 I Q
10-1'1 10-18 10-19
0.6
Fig. 49. Co -Fe (50 at % Fe). Upper part: “Co diffusion coeffkient (full circles) and s9Fe diffusion coefficient (open circles) vs. reciprocal temperature [70F]. Full triangle: “Co diffusion [68w]; open triangles: s9Fediffusion [68w]. Lower part: ss’5sFeisotope effect E for diffusion vs. reciprocal temperature [70F]. Land&-B&m&n New Series III/26
1.240"K-'1.3
Fig. 47. Be-Cu (1.6 at % Cu). Be tracer diffusion coefficient vs. reciprocal temperature parallel (I]) and perpendicular (I) to the c axis according to [77B2] based on [73L].
a o.! 0.E 0
0.8
Bakker
-0.2 I 0.6
0.7
0.8
0.9 l/T-
1.0
256
4 Self-diffusion in homogeneousbinary alloys and intermediate phases(Figures)
10’ ml/
[Ref. p. 276
10-l’ m2/s
10-12
10 lo-’
I a
10“
10-l‘ a
10-’
lo-l5
lo-’
\ ‘,
lolo-
0.8
0.9
1.0
1.1.lo-)KJ 1.2
0.7
0.8
l/1Fig. 50. CoGa (40.0 at % Ga). 6oCo diffusion coefficient (full circles) and 67Ga diffusion coeflicient (open circles) vs. reciprocal temperature [8OS].
0.9 l/l -
1.0
1.1.10-3K-’1.2
Fig. 51. CoGa (44 at % Ga). 6oCodiffusion coefficient (full circles) and 67Gadiffusion coefficient (open circles) vs. reciprocal temperature [SOS].
lo-” m2/s
mVs
lo-‘j
10-12
10-l‘
10-l)
10-l'
I lo-l5 a
I a
10-1’6
lo-‘& lo-‘5
1.1.1W3K-1.2 1.0 0.9 l/1Fig. 53. CoGa (52.0 at % Ga). 6oCo diffusion coefficient (full circles) and “‘Ga diffusion coefticient (open circles) vs. reciprocal temperature [8OS]. 0.7
Fig. 52. CoGa (50.0 at % Ga). 6oCo diffusion coefficient (full circles) and 67Ga diffusion coefficient (open circles) vs. reciprocal temperature [8OS].
Bakker
0.8
257
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures) 10. m2/ 10-1'2 10-1'2, mVs
1
\: lo-
IO-l3 lo-l3
IOP lo-l4 I -10-
I a 10-1'5 lo-"6
IO-l7 t IO-'* 0.7
lo0.8
0.9
1.0
1.1 40" K“ 1.2
j
t
0.
0.75
l/T -
Fig. 54. CoGa (54.8 at % Ga). 6oCo diffusion coefficient :full circles) and 67Ga diffusion coefficient (open circles) vs. :eciprocal temperature [8OS].
0.80 l/T -
0.85 *10-3K-'
O.!
Fig. 55. Co-Mn (5.22, 10.24 at % Mn). 54Mn diffusion coefficient vs. reciprocal temperature [771].
10-l' m2/s 6
\3\
I
\\
.
Co-P I A 92.6 at% Ti
1o-l2 m2/s '1
1723K
IO 8
Co-Ni
I Q 6
1o-l3
4
2
I -14 Q Q IO
IO 8 6
IO-15 -15 IO
I 10-161 lo-'6 0
4
I
I
20
40
I co-
60
I\d
Fig. 56. Co -Ni (3.7. .. 80.1 at % Ni). 6oCodiffusion coefticient vs. Co concentration at various temperatures [69M].
Land&-Biimstein New Series 111126
0.5
80 at% 100
0.6
0.7 l/T-
0.8
0.9 .W3K-' 1.0
Fig. 57. Co-Ti (92.6...98.4 at %). 44Ti diffusion coefficient vs. reciprocal temperature [75Sl].
Bakker
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures) I
I
I
I
I
I
I
I
I
I
I
I I
I I
0.80
0.85 l/l-
m”sl Co?Ti
[Ref. p. 276
-15
‘P t 6 I 1 I
I I
!
!
I
I I I I FH
10-166 0.70
0.75
01 0
0.90 -10-3K-’ 1.00
Fig. 58. Co,Ti (21.5 ... 24.0 at % Ti). 6oCo diffusion coeflicient vs. reciprocal temperature [88N]
I 0.1
I 0.2 co-
I 0.3
I I 0.4 ot % 0.5
Fig. 59. Co-U (x 99.5 ... x 99.7 at % U). 235U diffusion coefficient vs. Co concentration at various temperatures
WPI.
1.00
10‘ t 0.95 z 0 :a90 0
10‘ 0.60
0.65
0.70
0.75 l/l-
0.85 0
0.80 alO-‘K-’ 0
0.5
1.0
1.5
2.0 ot% 2.5
Fe -
Fig. 60. Cr-Zr (92.14...97.95 at % Zr). g5Zr diffusion coefficient vs. reciprocal temperature [81Pl].
Fig. 61. Cu - Fe (0.2 ... 2.4 at % Fe). 64Cu diffusion coefficient relative to the copper self-diffusion coefficient vs. Fe concentration at 1293K according to [72B].
Bakker
Land&-Bctnmfein New Series 111’26
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures) 4s .10-1” m2/s 3.5
10. m,2
259
I
L Cu-Ni
3.0 I 2.5 Q 2.0 1.5 IO' 1.0
I
0.5
I
I
I1005K
/
1.5 2.0 2.5 at% 3.5 In Fig. 62. Cu - In (0.4 ... 3.1 at % In). @Cu diffusion coefficient vs. In concentration at various temperatures [82H]. 0.5
1.0
I
0.65
0.70
87.0at%Ni 54.60i
IOAl-LLLL
-II
I
0.60
0.75 0.80 .lo”K-“- 0 l/7Fig. 63. Cu-Ni (21.5 ... 87 at % Ni). 64Cudiffusion coefficient vs. reciprocal temperature according to [77B2], based
,o-l;
-r-l-
m2/s 10-l m2/I 5
I
9.8at%Pt
Cu-Ni ,o-l:
I m
1o-14 Pt ?BSot%Pt 1 ,o-l5
0. l/T-
0.65
0.70
0.75
0.80 -lo-3K-’ 0.90
l/T-
Fig. 64. Cu-Ni (21.5 ... 87 at % Ni). 63Ni diffusion coefficient vs. reciprocal temperature according to [77B2], based on [64M]. Land&-Bijmstein New Series III/26
0.60
Fig. 65. Cu - Pt (9.8 . .74.5 at % Pt). 64Cudiffusion coeffcient vs. reciprocal temperature [77B2].
Bakker
4 Self-diffusion in homogeneousbinary alloys and intermediate phases(Figures)
260 ‘C?
[Ref. p. 276
I
d/s cu- Pt
10”
I Q
0
III
l
0.55
~~~~!
0.60
0.65
0.70 l/l-
0.75
0.80 .10-3K-’ 0.90
Fig. 66. Cu -Pt (9.8 . ..74.5 at % Pt). ‘gsmPtdiffusion coefficient vs. reciprocal temperature [77B2].
I
6
I
I
SbFig. 67. Cu-Sb (0.3 ... 1.7 at % Sb). 64Cu difl‘usion COGcient vs. Sb concentration at various temperatures [82H].
!
25ol%Sb
t
10-1’1 lo-‘01
I
I
I
I !
Zlot% Sb
1.10
1.14
1.22
1.18 l/l
1.26@K-’ 1.30
-
Fig. 68. Cu,Sb (21 . ..29 at % Sb). 64Cu diffusion cocfficicnt vs. reciprocal tcmperaturc [7OH].
29 ot% 27 25 Sb Fig. 69. Cu,Sb (21 ...29 at % Sb). 64Cu diffusion coefficient vs. Sb concentration at various temperatures [70H].
Bakker
‘9
21
23
Landolt-BCmslein New Series 111’26
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures)
261
IO.'3 m2/s
3.0
lo-l4
I
Q I a
1.7ot% Sn
2.0
l.lot% Sn 0.8 at% Sn
,o-l'
1
2.5
I.5
0.4ot% Sn
10-b'
i
0
1.00
40‘3K-'
1.
I/T-
Sn-
Fig. 70. Cu- Sn (0.4 ... 1.7 at % Sn). 64Cu diffusion coeffi:ient vs. reciprocal temperature [82H].
Fig. 71. Cu - Sn (0.4 .. .3.0 at % Sn). 64Cu diffusion coefficient vs. Sn concentration at various temperatures [82H].
10-1tl r m2
10-l’ m2h
I 10-l a
I :r16.6at% Sn
I do
latO/oSn
,o-l;
0.95
1.00
1.05
1.10 I/T-
1.15
.IO-jK-'
Fig. 72. Cu,Sn (16.6, 20.2 at % Sn). Yu diffusion coefticient (full circles) and l13Sn diffusion coefficient (open circles) vs. reciprocal temperature [8OP].
Land&-Biirnstein New Series III/26
IO'.12 1.000
1
1.025
1.050
1.075 I/T-
1.100 dK-'
1.150
Fig. 73. Cu,Sn (l&19.8 at % Sn). Wu diffusion coefficient (no symbols) and l13Sn diffusion coefficient (open circles) vs. reciprocal temperature [68E].
Bakker
4 Self-diffusion in homogeneousbinary alloys and intermediate phases(Figures)
262
c
Cu3Sn
I
I
[Ref. p. 276
I 10.11 m2/‘s i
lo-
10-l’ 8 j.lO-“l
I
I
I
4
I
I
I
I
T-l
I 10’ Q
lo-
10-“1 15
I 17
I 19
21
10‘
I I 23 ot% 25
,
1 i
1.20
1.30
Fig. 74. Cu,Sn (16.6...20.2 at % Sn). 64Cudiffusion coefli:ient (full circles) and ‘13Sn diffusion coefficient (open cir:les) vs. Sn concentration at various temperatures [68E, 8OP].
6.0t 3.7 JO-‘4
I
I
1
2
I
I
1.35
.@K-’
1)
l/l -
Sn -
Fig. 75. &Cu,Sn, (20.5 at % Sn). 64Cu diffusion coefficient (open circles) and l13Sn diffusion coefficient (full circles) b‘S. reciprocal temperature [68E]. I
I
1.0
1.2
I
I
I
d/s I 3.3 Q 2.9 2.5 0
3 4 01% 5 ln Fig. 76. Cu-Zn (0.6...4.2 at % Zn). 67Cu diffusion coeficient vs. Zn concentration at various temperatures [7OP].
0.8
1.4 1.6 1.8 .10-3K-’ 2.2 l/T Fig. 77. CuZn (45.46... 48 at % Zn). 64Cu diffusion coefficient (full circles) and 65Zndiffusion coeffkient (open circles) vs. reciprocal temperature [56K].
I Bakker
Landok-ESmstein New Series III!26
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures)
263
Fig. 79. Fe-Ni (z 0 ... 90 at % Ni). 63Ni diffusion coefticient vs. Ni concentration at various temperatures [81M]. Open circles: [81M]; open squares: [76Z]; full circles: [7532]; full squares: [63F]; open triangles: [67D], full triangles: mean values.
1o-l5
lo-"1 I a
10-1’5
1 4 1o-14
1Cl-l3 m2/s
lo-l5 mVs
lo-‘6
IP
10-"5
I a
aI 10-16
10-17 I
0
I
I
I
20
40
60
Fe
0 lo-l5
0
m2/s
0
NI-
I
I
80 at% 100 Ni
lo-l6
“A”
I
1o-l6
a
lo-l7
10-181 0 Fe
20
40
60 NI-
80 at% 100 Ni
4
Fig. 78. Fe-Ni (5 ... 90 at % Ni). 5gFediffusion coefficient vs. Ni concentration at various temperatures [81M]. Open circles: [81M]; open squares: 16601;full circles: [55N]; full squares: [63F]; open triangles: [72K3], full triangles: mean values.
I
2
a
10 6
Fig. 80. Fe-Pd (lo...50 at % Pd). “Fe diffusion coefficient vs. reciprocal temperature [77F]. The Arrhenius curves were obtained by computer calculations based on the results given in Fig. 84. Land&-Biirnstein New Series III/26
Bakker
0.600
0.625 0.650
0.675 l/T-
0.700 .lOJK’
0.7:
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures)
264 2*10ml/
[Ref. p. 276
4 Fig. 81. Fe-Pd (55...90 at % Pd). 59Fe diffusion coeficient vs. reciprocal temperature [77FJ.The Arrhenius curves were obtained by computer calculations based on the results given in Fig. 84.
Fe- Pd
10’ 8 6 4
I el
2
1tY 8
4
6 4
2
10-l 0.
2*10-n,
625
0.650
0.675) l/1-
1
1
m2’slFe-Pd 1
1
4
0.700 .lO-‘K-’ 0.750
2
10-1’5
0.600
0.625
0.650
0.675
0.700 W3K”
0.750
Fig. 82. Fe-Pd (lo...50 at % Pd). lo3Pd diffusion coefficient vs. reciprocal temperature [77F]. The Arrhenius curves were obtained by computer calculations based on the results given in Fig. 84.
For Fig. 83 see next page.
Pd-
4 Fig. 84. Fe-Pd (lo...90 at % Pd). 59Fe diffusion coefftcient (full lines) and ro3Pddiffusion coefticient (dashed lines) vs. Pd concentration at various temperatures [77F].
Bakker
Land&BBmstein New Series Ill/26
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures)
265
4 Fig. 83. Fe-Pd (55 ... 90 at % Pd). lo3Pd diffusion coeff, cient vs. reciprocal temperature [77F]. The Arrhenius curve> were obtained by computer calculations based on the result5 given in Fig. 84.
10-l' m2/s IO-l2
0.600
0.625
0.650
10 m2
0.675
0.700
.10‘3K-' 0.750
I
Fe-S
10 0.7 b
0.8
0.9
1.0
1.1 l/T -
1.2
I.3 40-3lc'
1.5
Fig. 85. Fe-Si (7.64 at % Si). “Fe diffusion coeffkient vs. reciprocal temperature [75M2]. Full circles: mechanical sectioning; open circles: chemical sectioning; open triangles: Zener relaxation; full triangles: magnetic Zener relaxation. The dashed line is the high-temperature extrapolation.
I 10 a
10
lo0.75
Landolt-tlknstein
New Series III/26
0.80
0.85 0.90 1/T-
0.95 *lo-
4 Fig. 86. Fe-Si (1.87 ... 19.2 at % Si). 59Fediffusion coefficient vs. reciprocal temperature for various Si concentrations (in at %): Curve 1: 0; 2: 1.87; 3: 6.55; 4: 8.64; 5: 12.1; curve a: 5.5; b: 6.5; c: 7.8; d: 11.6; e: 15.3;f: 19.2. Curves I...5 1.05 from [81T], curves a.. .f from [77M].
Bakker
4 Self-diffusion in homogeneousbinary alloys and intermediate phases(Figures)
266
[Ref. p. 276
10“’ m>/s 1173 K I’ 1ll23K
r’
10”
11073K *
/’
I Q 10-‘5
0
20 .,p mVs 15
I 10 Q
2.5
5.0
7.5 Si -
10.0
12.5of% 15.0 .
Sn -
Fig. 87. Fe-Si (1.4... 12.1 at % Si). “Fe diffusion coeflicient vs. Si concentration at various temperatures [81T].
Fig. 88. Fe-Sn (0.2...2.7 at % Sn). “Fe diffusion coefficient vs. Sn concentration at 1168 K (83K].
lo-l0
I Q
.
L A
10-l’
T-
Ao. ----SC ” A
l- .. *
10‘” 0.5
0.6
0.7
0.8 l/T-
0.9 .lO-‘K“ 1.0
Fig. 89. Fe - Zr (96.5 ... 99.5 at % Zr). “Fe diffusion coefficient vs. reciprocal temperature [87Hl]. Full triangles: 96.5 at % Zr; open triangles: 98 at % Zr; open circles: 99.5 at % Zr; full circles: 100 at % Zr.
98.65 I 0.60
0.65
0.70
0.75 l/T -
0.80
.10-3K-’
a
Fig. 90. Fe-Zr (93.63...99.02 at % Zr). gsZr diffusion coefficient vs. reciprocal temperature [81Pl].
Landolt-BCmstein New Series III!26
267
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures)
=-l--l-
1-11
IO-”
I
2/s
m2/s
GaNi
3-12
o-13
IO" mvs
. .a I a
VI-'
o-l"1
10“
p5
47
I a
48
49
50
51
52 at%
:
NIFig. 92. GaNi (47.28. .. 52.40at % Ni). 67Gadiffusion toe ficient vs. Ni concentration at various temperatures [76D]
o-16
10-l
IO"' m2fs
,p
I
GaNi 1380K I
lo-" 0.7
I
0.8
*
f
la-l2 IT
1285
0.9 l/l -
Fig. 91. GaNi (47.28. ‘52.40 at % Ni). 67Gadiffusion coefficient vs. reciprocal temperature [76D].
For Fig. 93 see next page.
1o-l5
Fig. 94. GaNi (47.28*.. 52.40 at % Ni). 63Ni diffusion coef- b ficient vs. Ni concentration at various temperatures [76D]. Landolt-Bbmstein New Series III/26
Bakker
47
f
48
49
N50w51
[Ref. p. 276
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures)
268
c
10“ r m2k
IV3 GC 0
10-l
I=2
\
I Q
1 n
0 \
lo-
\
1
0
lo0.68 1
0.70
0.72 l/l-
0.74
0.7640°K' 0.78
Fig. 95. GaV, (75.6 at % V). 48V diffusion coefficient vs. reciprocal temperature [84v].
1
t
10“‘
\\
lo-"
t
l/l
0.9 -
1.0 JO-jK-' 1.1 l/l-
Fig. 93. GaNi (47.28... 52.40at % Ni). 63Ni diffusion coefficient vs. reciprocal temperature [76D].
Fig. 96. Hf-Zr (2.1 at % Zr). ls’Hf diffusion coefficient vs. reciprocal temperature in single crystals, parallel to the c axis [72D].
Bakker
Landok-B6mstein New Series III!26
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures) IV" m2/s
T0
IO-13 m2/S
I
Hf- Zr
r
-
-
K-r
-
10-14
IO“!
269
I m
-
IO‘-15 _ I IO-'" m
--
10-16 a 10-12 m2/S
,o-l;
-13 _
IO
\ 4
I
1-c
-
I:
-
-
li+
0.50
0.55
0.60 l/T-
0.65
0.7040" K“ 0.75
Fig. 97. Hf-Zr (2.1 at % Zr). isiHf diffusion coefficient vs. reciprocal temperature in single crystals, perpendicular to the c axis [72D].
I 10-14 _ m
IO-15 _
IO-16 c 0.65
10-1'2 m2/s
0.85 .I0
0. l/T-
I-
d I5 0.65 0.75 0.85 ~10. l/T-
Fig. 99. InPd (49 ... 56 at % Pd). “4mIn diffusion coefficient (open circles) and iosPd diffusion coefficient (full circles) vs. reciprocal temperature [83Hl]. Fig. (a): 49 at % Pd, (b): 50 at % Pd, (c): 53 at % Pd, (d): 56 at % Pd.
1o-l3
10'5 mVs
\
I -IO-l4
\
\ ~I lo-l6
I
MnPt,
=-
10-1'5
lo-l6 0.17
0.18
0.19
0.20 l/T-
0.21
l-.-2 .. .10-JK-'
Fig. 98. Hg-Pb (96 and 99 at % Pb). 203Hgdiffusion coeficient (open circles) and ‘i”Pb diffusion coefficient (full cirdes) vs. reciprocal temperature in Hg-Pb with 96 at % Pb md 99 at % Pb, respectively [73w]. Land&-Bhstein New Series III/26
lo-l7 0.75
0.23
0.80
0.85
O!
Fig. 100. MnPt, (65 at % Pt). 54Mn diffusion coeflicient vs. reciprocal temperature [79A].
Bakker
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures)
270 10-l’ m’/s
[Ref. p. 276
lo-l5 ml/s
I
MnPt3
,p!
~I lo-l6
I a
lo-l1 0.75
10-”
0.90 0.95 .,o”K-’ 1.05 l/T Fig. 102. MnPt, (82 at % Pt). 54Mn diffusion coefficient vs. reciprocal temperature [79A].
\
\_
,(p; 0
0.80 0
0.80
0.85
.95
Fig. 101. MnPt, (75 at % Pt). S4Mndiffusion coefficient vs. reciprocal temperature [79A].
lomZI
Mn-Ti
10’
tr
:
.
10”
I Q 10-l 0.66
0.70
0.74 l/T-
0.78
0.8240” K-’0.86
Fig. 104. Mn-Zr (98...99.5 at % Zr). 54Mn diffusion coefficient vs. reciprocal temperature [79P2]. 10-l’
,o-l!
0
A
0.f
A 0.i
l/l-
0.l
4 Fig. 103. Mn -Ti (79.4 ... 90.3 at % Ti). “Ti diffusion coefficient vs. reciprocal temperature for various Ti concentrations (in at %): full triangles: 79.4; open triangles: 82.1; full circles: 86.7; open circles: 90.3 [75Sl].
Bakker
Land&-BBmstein New Series III/26
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures)
271
IO-’ 8 6 I 4 Q
’ 250 CI
2
I
I
20
40
\I.
I
IO-’ 8 6 4.1o-1” 0.66
0.70
0.74 l/T-
0.78
0.82.10-dK’I1.86
Fig. 105. Mn-Zr (98 ... 99.5 at % Zr). g5Zr diffusion coefficient vs. reciprocal temperature [79P2].
60 80 at% 100 Ti Fig. 106. Nb-Ti (lo...95 at % Ti). Activation energy and pre-exponential factor for g4/g5Nbdiffusion vs. Ti concentration. Open circles: [63G]; full circles: [79Pl]. 0
10-l m2/1
10-l
10-l
k0
I Q 10-l
10-l
0.8.10-jK-’ l/T-
Fig. 107. Nb-Ti (10 1..95 at % Ti). 95Nb diffusion coefti:ient vs. reciprocal temperature [63G]. Fig. 108. Nb-Ti (64.3...94.6 at % Ti). g4/g5Nb and 44Ti p liffusion coefficient vs. reciprocal temperature [79Pl]. Land&-Blirnstein New Series III/26
Bakker
10-l’ 0
I 0.60
0.65
0.70 l/T-
0.75 -lOJK-’
0
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures)
272 10-10
10.”
rnzfs
m2k
[Ref. p. 276
I
9
Pb-T1
10“’ 1o-l4
lo-” ~I lo-l5 I ~I lo-l3
I lo-‘6
lo-”
10-17. 0
60 80 ot% II TLFig. 110. Pb-TI (5...87 at % Tl). zl”Pb diffusion coeflicient (circles) and 204TIdiffusion coefficient (triangles) vs. TI concentration at various temperatures [61R].
lo-l5
10-1’6 0.5
10-l
0.8 0.9 .10-K-’ 1.1 l/lFig. 109. Nb-Zr (71.9...94.5 at % Zr). g5Zr diffusion coeficicnt vs. reciprocal tempcraturc for various Zr conccntrations (in at %): open circles: 71.9; full circles: 83.7; triangles: 94.5 [8782].
a6
0.7
2.10.’
m2/5
40
Sn-;n
10-l
-r
m2/:
10-l
10-l
I Q 0
10-l
\
9
,o-l"
10-l” 2.6 2.4 2.8.lO”K-’ 3.0 l/TFig. 112. Sn-Zn (0.9 at % Zn). 1’3”*3Sn diffusion coeflicicnt (lower curve) and 65Zn diffusion cocflicient (upper curve) vs. reciprocal temperature [66B]. 2.2
I 0.7 l/l-
0.8
0.9 *lO”K-’1.0 4 Fig. 111. SC- Zr (86.4,93.3 at % Zr). “Zr diffusion coeflicient vs. reciprocal temperature [87H2]. Bakker
land&B6mstein New Series 111’26
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures) 4.10-11m21s
4.10.11 II12/s
Ti-V
IO--11 _
IO-
12-
II
]-11 _
II
)42 _
-13 _
10.
II
]-l3-
\\ $
I Q
I Q
‘\
14 _
lo-
273
1C,-14
_
-30
0
10
-20
'40
I5 _
lo-
IO-15
lo-' 16 0.4
0.5
0.7
0.6
IC,-16
0.8 .10-3K-'I
0.4
l/T-
Fig. 113. Ti-V (10 ... 90 at % Ti). 44Ti diffusion coefficient vs. reciprocal temperature [68M]. 10-l'I m2/5
_
0.b
u.7
0.8 WK-'
l/T-
Fig. 114. Ti - V (10 . . .90 at % Ti). 48V diffusion coefficient vs. reciprocal temperature [68M].
,
Ti -Zr
;r
lo-"
10-l I a lo-':
IO-'4
1oP5 1.7
Land&-BBmstein New Series III/26
Fig. 115. Ti - Zr (49 at % Zr). 44Ti diffusion coefficient vs. reciprocal temperature [87H2].
Bakker
4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures)
274
[Ref. p. 276
10
10
10
10
0.8+lO”K-’0.9 0.6 0.7 l/T Fig. 116. V-Zr (0.5 at % Zr). 48V diffusion coefficient vs. reciprocal temperature[81P2]. 0.1
0.5
lom2/ 6 0.58 0.60 40-3K-’ 0.6L l/7Fig. 117. V-Zr (0.5...2 at % Zr). 48V diffusion coeflicient vs. reciprocal temperature for various Zr concentrations (in at X): open circles: 0.5; open triangles: 1.0; full triangles: 1.5; full circles: 2.0 [84P]. 0.52
i
0.68
0.71
0.76 l/l-
0.77
0.54
0.56
0.80 .lO”K-’ 0.86
Fig. 118. V-Zr(98.0...99.5 at % Zr). 48Vdiffusion cocfficient vs. reciprocal temperature for various Zr concentrations (in at %): full triangles: 98.0; open triangles: 98.5; full circles: 99.0; open circles: 99.5 [82P].
Bakker
Land&-BGmstein New Series Ill!26
Ref. p. 2761 4 Self-diffusion in homogeneous binary alloys and intermediate phases (Figures) 10-l
275
I
m2/5
- V-Zr
I
I
\I -7r
10-l13_ 9 8 1 6
4.10-‘51 0.52
5100.54
0.56
0.58 l/T-
0.60
~10-~K-’ O.Ei$
Fig. 119. V-B (0.5 ... 2.0 at % Zr). g5Zr diffusion coefficient vs. reciprocal temperature for various Zr concentrations (in at %): open circles: 0.5; open triangles: 1.0; full triangles: 1.5; full circles: 2.0 [84P].
Land&-Biimstein New Series III/26
14
I3.67
0.71
0.75 l/T-
0.79
3W3K-’ 0.8i 0.8:
Fig. 120. V-Zr (98.0...99.5 % Zr). “Zr diffusion coefficient vs. reciprocal temperature for various Zr concentrations (in at %): Curve I: 98.0; 2: 98.5; 3: 99.0; 4: 99.5 [82P].
Bakker
276
References for 4
References for 4 51N 55H 55N 55s 56K 57Y 61Hl 61H2 61R 63F 63G 63M 64D 64M 64P 64s 65B 66B 660 67D 67G 67Ll 67L2 67L3 67P 67R 67Sl 6782 68E 68F 68G 68H 68L 68M 680 68R 68s 68W 69A 69F 69M 69s 70A 70B 1 70B2 70F 70H 70N 7OP 70R 70s 702
Nix, EC., Jaumot, FE.: Phys. Rev. 83 (1951) 1275. Hoffman, R.E., Turnbull, D., Hart, E.W.: Acta Metall. 3 (1955) 417. Neiman, M.B., Shinyaev, A.Ya.: Dokl. Akad. Nauk. SSSR 102 (1955) 969. Sonder, E.: Phys. Rev. 100 (1955) 1662. Kuper, A.B., Lazarus, D., Manning, J.R., Tomizuka, C.T: Phys. Rev. 104 (1956) 1536. Yanitskaya, M.E., Zhukovitskii, A.A., Bokshtein, S.Z.: Dokl. Akad. Nauk. SSSR 112 (1957) 720. Hagel, W.C., Westbrook, J.H.: Trans. AIME 221 (1961) 951. Huntington, H.B., Miller, N.C., Nerses, V: Acta Metall. 9 (1961) 749. Resing. H.A., Nachtrieb, N.H.: J. Phys. Chem. Solids 21 (1961) 40. Fraden, E: B.S. Thesis, Massachusetts: Inst. of Technology, 1963. Gibbs, G.B., Graham, D., Tomlin, D.H.: Philos. Mag. 8 (1963) 1269. Mallard, WC., Gardner, A.B., Bass, RX, Slifkin, L.M.: Phys. Rev. 129 (1963) 617. Domian, H.A., Aaronson, HI.: Trans. AIME 230 (1964) 44. Monma, K., Suto, H., Oikawa, H.: Nippon Kinzoku Gakkaishi 28 (1964) 192. Peterson, N.L., Rothman, S.J.:Phys. Rev. 136 (1964) A 842. Sato, K.: Sci. Rep. Fat. Lit. Sci., Hirosaki Univ. 11 (1964) 9. Benci, S., Gasparrini, G., Germagnoli, E., Schianchi, G.: J. Phys. Chem. Sol. 26 (1965) 687. Bergner, D., Lange, W: Phys. Status Solidi 18 (1966) 67. Okada, T: Radioisotopes 15 (1966) 169. De Reca, E.W, Pampillo, G.: Acta Metall. 15 (1967) 1263. Gupta, D., Lazarus, D., Lieberman, D.S.: Phys. Rev. 153 (1967) 863. Lai, D.A.E, Borg, R.J.: US A.E.C. Report: UCRL-50314 (1967). Larikov, L.N., Tyshkevich, VM., Chorna, LX: Ukr. Fiz. Zh. 12 (1967) 983. Lyubimov, VD., Geld, P.V, Shveikin, G.P., Sutina, Yu.A.: Izv. Akad. Nauk. SSSR,Met. (1967) 84. Peterson, N.L., Rothman, S.J.:Phys. Rev. 154 (1967) 558. Rothman, S.J.,Peterson, N.L.: Phys. Rev. 154 (1967) 552. Santoro, C.J.: Bull. Am. Phys. Sot. 12 (1967) 104. Smirnov, O.A., Ivanov, L.I., Abramyan, E.A.: Izv. Akad. Nauk. SSSR,Met. (1967) 168. Ebcling, R., Wcver, H.: Z. Metallkd. 59 (1968) 222. Fedorov, G.B., Smirnov, E.A., Zhomov, EL: Metall. Metalloved. Chist. Met. 7 (1968) 124. Gardner, A.B., Sanders, R.L., Slitkin, R.L.: Phys. Status Solidi 30 (1968) 93. Heumann, Th., Biihmer, H.: J. Phys. Chem. Solids 29 (1968) 237. Lai, D.YE, Borg. R.J.: UCRL Report No. 50 516 (1968). Murdock, JE, McHargue, C.J.: Acta Metall. 16 (1968) 493. Oikawa, H., Anusavice, K.J., DeHoff, R.T, Guy, A.G.: ASM Trans. Q. 61 (1968) 354. Ray, S.P.,Sharma, B.D.: Acta Metall. 16 (1968) 981. Shinyaev, A.Ya.: Izv. Akad. Nauk. SSSR,Met. (1968) 109. Wanin, M., Kohn, A.: C. R. Acad. Sci., Ser. C 267 (1968) 1558. Alexander, WB.: Studies on Atomic Diffusion in Metals, Ph. D. Thesis, Univ. of NC., USA (1969), cited in [77B]. Frantsevich, I.N., Kalinovich, DE, Kovenskii, I.I., Smolin, M.D.: J. Phys. Chem. Solids 30 (1969) 947. Million, B., Kucera, J.: Acta Metall. 17 (1969) 339. Santoro, C.J.: Phys. Rev. 179 (1969) 593. Ananin, VM., Gladkov, VP., Zotov, VS., Skorov, D.M.: At. Energ. 29 (1970) 220. Bowen, A.W, Leak, G.M.: Metall. Trans. 1 (1970) 2705. Bowen, A.W., Leak, G.M.: Metall. Trans. l(l970) 2767. Fishman. S.G., Gupta, D., Lieberman, D.S.: Phys. Rev. B2 (1970) 1451. Heumann, Th., Meincrs, H., Stiier, H.: Z. Naturforsch. 25a (1970) 1883. Nohara, K., Hirano, K.: Proc. Int. Conf. Sci. and Technol. Iron and Steel, Tokyo, Sept. 1970,Section 6 (1970) 1267. Peterson, N.L., Rothman, S.J.:Phys. Rev. B2 (1970) 1540. Ray, S.P.,Sharma, B.D.: Trans. Indian Inst. Met. 23 (1970) 77. Spasov, A., Ivanov, G.: God. Solii. Univ. Khim. Fak. 65 (1970/1971) 39. Zemskii, S.V.,Grigorkin, VI., Moskaleva, L.N.: Izv. Vyssh. Ucheb. Zaved., Chern. Metall. 13 (1970) 106.
References for 4 71A 71D 71F 71G 71Hl 71H2 71M 71s 71w 72B 72D 72H 72J 72Kl 72K2 72K3 72M 72P 72s 73L 73N 73Tl 73T2 73w 74A 74B 74K 75B 75Gl 75G2 75K 75L 75Ml 75M2 75Sl 7582 7533 76D 762 77Bl 77B2 77F 771 77M 77R 77s 78G 78H 79A 79B 79Cl 79c2 79D Landolt-Bihstein New Series III/26
277
Askill, J.: Phys. Status Solidi (a) 8 (1971) 587. DeCormales, C.O., DeReca, N.E.W: .I Phys. Chem. Solids 32 (1971) 1067. Frantsevich, I.N., Kalinovich, DX, Kovenskii, II., Smolin, M.D.: Proc. Europhysics Conf., Lodding, A., Agarwall, ‘I: (eds.),Verlag Z. Naturforsch., 1971, p 100. Gupta, D., Lieberman, D.S.: Phys. Rev. B 4 (1971) 1070. Hancock, G.E, McDonell, B.R.: Phys. Status Solidi (a) 4 (1971) 143. Hancock, G.E, McDonell, B.R.: Phys. Status Solidi (a) 7 (1971) 535. Million, B., Kucera, J.: Czech. J. Phys. B 21 (1971) 161. Seith, W, Heumann, Yh., Wever, H.: Z. Metallkd. 62 (1971) 294. Wade, WZ.: J. Nucl. Mater. 38 (1971) 292. Bocquet, J.L.: Acta Metall. 20 (1972) 1347. Davis, B.E., McMullen, WD.: Acta Metall. 20 (1972) 593. Hirano, K. and Cohen, M.: Trans. Jpn. Inst. Met. 13 (1972) 96. Jeffery, R.N., Gupta, D.: Phys. Rev. B 6 (1972) 4432. Korolev, A.A., Pavlinov, L.V, Gavrilguk, M.I.: Fiz. Met. Metalloved. 33 (1972) 295. Kucera, J., Million, B., Peskova, J.: Phys. Status Solidi (a) 11 (1972) 361. Kutnetsov, E.V: Uch. Zap. Gor’k. Gos. Univ. 148 (1972) 38. Million, B.: Z. Metallkd. 63 (1972) 484. Patil, R.V., Sharma, B.D.: Trans. Indian Inst. Met. 25 (1972) 1. Shcherbedinskii, G.V, Ipatova, VM., Grechnyi, Ya.V, Yakovlev, S.G.:Dopov. Akad. Nauk. Ukr. RSR. Ser. A 34 (1972) 759. LeHazif, R., Edelin, C., Dupouy, J.M.: Metall. Trans. 4 (1973) 1275. Nohara, K., Hirano, K.: J. Jpn. Inst. Met. 37 (1973) 51. Tiwari, G.P., Saxena, M.C., Patil, R.R: Trans. Indian Inst. Met. 26 (1973) 55. Tiwari, G.P., Sharma, B.D., Raghunathan, VS., Patil, R.R: J. Nucl. Mater. 46 (1973) 35. Warburton, WK.: Phys. Rev. B 7 (1973) 1330. Assassa,W, Guiraldenq, P.: C. R. Acad. Sci. Ser. C 279 (1974) 59. Bristotti, A., Wazzan, A.R.: Rev. Bras. Fiz. 4 (1974) 1. Kucera, J., Million, B., Ruzickova, J., Foldyna, V, Jakobova, A.: Acta Metall. 22 (1974) 135. Bronfin, M.B., Bulatov, G.S., Drugova, LA.: Fiz. Met. Metalloved. 40 (1975) 363. Gbdeny, I., Beke, D., Kedves, EJ., Groma, G.: Phys. Status Solidi (a) 32 (1975) 195. Gupta, D., Rosenberg, R.: Thin Solid Films 25 (1975) 171. Kucera, J., Million, B.: Phys. Status Solidi (a) 31 (1975) 275. Larikov, L.N., Geichenko, VV, Fal’chenko, VM.: Diffusion Processesin Ordered Alloys, Naukova Dumka Publ., Kiev 1975, Nat. Bur. Stand. New Delhi: Amerind. Publ. Co., 1981. Maramatsu, EI: Trans. Nat. Res. Inst. Met. 17 (1975) 21. Mirani, H.VM., Harthoorn, R., Zuurendonk, TJ., Helmerhorst, S.J.,De Vries, G.: Phys. Status Solidi (a) 29 (1975) 115. Santos, E., Dyment, E: Philos. Mag. 31 (1975) 809. Shinyaev, A.Ya.: Diffuzionnye Processy v Splavach, Nauka, Moscow, 1975, p. 100. Shinyaev, A.Ya.: Izv. Akad. Nauk. SSSR Met. (1975) 162. Donaldson, A.T., Rawlings, R.D.: Acta Metall. 24 (1976) 285. Zemskii, S.V, Lvov, VS., Makashova, L.S.: Fiz. Met. Metalloved. 41 (1976) 775. Beke, D.L., Godeny, I., Kedves, EJ., Groma, G.: Acta Metall. 25 (1977) 539. Butrymowicz, D.B., Manning, J.R.,Read, M.E.: Diffusion Rate Data and Mass Transport Phenomena for Copper Systems,INCRA Monograph V, Washington: Nat. Bur. Stand., 1977. Fillon, J., Calais, D.: J. Phys. Chem. Solids 38 (1977) 81. Iijima, Y, Hirano, K.: Philos. Mag. 35 (1977) 229. Million, B.: Czech. J. Phys. B 27 (1977) 928. Ruzickova, J., Million, B.: Kovove Mater. 15 (1977) 140. Shires, P.J.,Hines, A.L., Okabe, T: J. Appl. Phys. 48 (1977) 1734. Gas, P., Bernardini, J.: Ser. Metall. 12 (1978) 367. Heumann, Th., Rottwinkel, T: J. Nucl. Mater. 69-70 (1978) 567. Ansel, D., Barre, J., Meziere, C., Debuigne, J.: J. Less Common Met. 65 (1979) Pl. Bose, A., Frohberg, G., Wever, H.: Phys. Status Solidi (a) 52 (1979) 509. Carlson, P.T, Padgett jr., R.A.: Ser. Metall. 13 (1979) 355. Cermak, J., Kucera, J.: Kovove Mater. 17 (1979) 3. Dehaunay, D., Huntz, A.M., Lacombe, P.: Ser. Metall. 13 (1979) 419. Bakker
References for 4
278 79Pl 79P2 8OC 8OP 80s 81M 81Pl 81P2 81Rl 81R2 81T 82H 82P 83Hl 8382 83H3 83K 84B
Pontau, A.E., Lazarus, D.: Phys. Rev. B 19 (1979) 4027. Pruthi, D.D., Anand, MS., Agarwala, R.P.: Philos. Mag. A 39 (1979) 173. Cermak, J., Ciha, K., Kucera, J.: Phys. Status Solidi (a) 62 (1980) 467. Prinz, N., Wever, H.: Phys. Status Solidi (a) 61 (1980) 505. Stolwijk, N.A., Van Gend, M., Bakker, H.: Philos. Mag. A 42 (1980) 783. Million, B., Ruzickova, J., Velisek, J., Vrestal, J.: Mater. Sci. Eng. 50 (1981) 43. Patil, R.V, Tiwari, G.P., Sharma, B.D.: Philos. Mag. A 44 (1981) 717. Pelleg. J.: Philos. Mag. A 43 (1981) 273. Raghunathan, VS., Sharma, B.D.: Philos. Mag. A 43 (1981) 427. Ruzickova, J., Million, B.: Mater. Sci. Eng. 50 (1981) 59. Treheux, D., Vincent, L., Guiraldenq, P.: Acta Metall. 29 (1981) 931. Hishino, K., Iijima, Y,‘Hirano, K.: Acta Metal!. 30 (1982) 265. Pruthi, D.D., Agarwala, R.P.: Philos. Mag. A 46 (1982) 841. Hahn, H., Frohberg, G., Wever, H.: Phys. Status Solidi (a) 79 (1983) 559. Hehenkamp, T, Faupel, E: Acta Metall. 31 (1983) 691. Hilgedieck, R., Herzig, C.: Z. Metallkd. 74 (1983) 38. Kumagai, A., Iijima, Y, Hirano, K.: DIMETA 82, Kedves, EJ., Beke, D.L. (eds.),Trans. Tech. Publ., Switzerland, 1983, p. 389. Bakker, H.: Diffusion in Crystalline Solids, Murch, G.E., Nowick, AS. (eds.),Academic Press, 1984, p. 250.
84P 84V 85K 86M 87Hl 87H2 87H3 88N
Pruthi, D.D., Agarwala, R.P.: Philos. Mag. A 49 (1984) 263. Van Winkel, A., Lemmens, M.P.H., Weeber,A.W, Bakker, H.: J. Less Common. Metals 99 (1984)257. Kiihler, U., Neuhaus, P., Herzig, C.: Z. Metallkd. 76 (1985) 170. Mundy, J.N., Ockers, S.T, Smedskjaer,L.C.: Phys. Rev. B 33 (1986) 847. Herzig, C., Neuhaus, J., Vieregge, K., Manke, L.: Mat. Science Forum 15-18 (1987) 481. Herzig. C., Kiihler, U.: Mat. Science Forum 15-18 (1987) 301. Hoshino, K., Rothman, S.J.,Averback, R.S.:Symp. Diffusion Processesin High Technology Materials, Cincinnati, Ohio, Oct. 12-14, 1987. Nakajima, H., Nakamura, Y., Koiwa, M., Tagasuki, T, Izumi, 0.: Scri. Metall. 22 (1988) 507.
Land&-B6mstein New series III,/26
Ref. p. 3661
5.1 Introduction
279
5 Chemical diffusion in inhomogeneousbinary alloys 5.1 Introduction In this chapter are listed data on chemical diffusion processesin inhomogeneous binary alloys. Only data for essentially ‘bulk’ samples (5 2um) are given, thus ‘thin-film’ data are not presented. Use of tables For a given metal pair, the metal having the chemical symbol earlier in the alphabet always comes first. All alloy concentrations are expressedin atomic percentagesunless specifically given as otherwise e.g. weight percent. The tables give data for the interdiffusion coefficient d, sometimes also called the chemical diffusion coeficient or mutual diffusion coefficient, see section 1.4.3. In many casesthe interdiffusion coefficient 0” is conveniently expressed by an Arrhenius equation: 6=D” exp(- Q/RT)
(5-l) where Do is the pre-exponential, Q is the activation enthalpy, R is the gasconstant (R = 8.3145J mol-’ K- ‘) and Tis the absolute temperature. Long extrapolations beyond the temperature range given are not generally recommended. In some cases,intrinsic, sometimes known as partial, diffusion coefficients are also given in the tables. These are denoted by, for example D,, and D,,. The intrinsic diffusion coefficients are related to b, see Eq. 1.30 in 1.4.4.The intrinsic diffusion coefficients can also be conveniently expressedby an Arrhenius equation, e.g. D,,=Dk ew(- Q&T) (5.2) At the limit of the concentration of one metal component approaching zero, the interdiffusion coefficient approaches the impurity diffusion coefficient, see Chapter 3. Ideally, in an impurity diffusion experiment, the impurity is present at very low concentration, so low that it does not chemically affect the host. When these conditions are obviously not met, the experiment is strictly a chemical diffusion experiment and the data are presented in the tables here. The following methods for measuring interdiffusion coefficients are used in the tables. Method A Use of the Boltzmann-Matano analysis gives the concentration dependence of the interdiffusion coefficient 8, see section 1.6.1.2.2.(The Hall analysis [53H2] is sometimes used near terminal concentrations). Method A is by far the most common and reliable method. Early work used sectioning and chemical analysis but since about 1965 most concentration profiles have been obtained with the electron microprobe. Method B When it is evident or assumedthat the interdiffusion coefficient d is not a function of concentration an analytical solution is used, the usual one is Eq. 1.47 in 1.6.1.2.2. Method C The interdiffusion coefficient is calculated by using measurements on rates of migration of phase boundaries, typically using the Wagner equation of parabolic growth kinetics [69W2]. Method D The interdiffusion coefficient is determined by an electrochemical method. There are several variations of such a method, all of them indirect and relaxational in nature. Method E The interdiffusion coefficient is determined by in-diffusion and out-diffusion followed by determination of concentration profile, and use of the Boltzmann-Matano analysis or Eq. 1.47 of the General Introduction, see also section 1.6.1.2.4. Method F The interdiffusion coefficient is determined by total gain or loss of material or rate thereof, this is really an indirect form of Method E. Method G The interdiffusion coefficient is determined by ferromagnetic relaxation, seesection 1.6.2.1.a. Method H The interdiffusion coefficient is determined by X-ray diffraction analysis, see section 1.6.1.2.3. Method I The interdiffusion coefficient is determined by a resistometric method, see section 1.6.1.2.3.
Landolt-B6mstein New Series III/26
Murch, Bruff
280
5.1 Introduction
The full list of alloys, treated in chapter 5, is presented below. In contrast to the tables in section 5.2, the alloys are given here in the order A - B and B-A. In this way it is immediately clear which Ni systems,for example, occur in the tables.
List of alloys System
Page
System
Page
System
Page
System
Page
Ag-AI Ag-Au Ag-Cd Ag-Cu Ag-Ga Ag-Hg Ag-Mn Ag-Pb Ag-Pd Ag-Zn
282f. 283 283 283f. 284 284 284 284 285 285
Ce-Mg Ce-Pu Ce-U
294 294 294
284 288 297 302f. 31Of. 321 321
282 f. 285 285 286f. 287 287 287f. 288 288 288 288 f. 289 289 290 290 f. 291
285 291 295 295 295 ff. 297 297 297 298 298 298 298 298
301 31Of. 311 312f. 314 314 315 315f. 316 316f. 317 317 317 317f.
Mn-Ag Mn-AI Mn-Co Mn-Cu Mn-Fe Mn-Ni Mn-Ti
AI-Ag Al-Be Al-Co AI-Cu Al-Fe AI-Li Al-Mg Al-Mn AI-Na AI-Nb AI-Ni AI-Pu AI-Si AI-Ti Al-Zn Al-Zr
Co-Al Co-Au Co-Cr co-cu Co-Fe Co-Mn CO-MO Co-Ni Co-Pd Co-Pt Co-Ti co-v co-w
Fe-Cu Fe-Mn Fe-MO Fe-Ni Fe-Pd Fe-Sb Fe-Si Fe-Sn Fe-Th Fe-Ti Fe-U Fe-V Fe-W Fe-Zn
Cr-Co Cr-Fe Cr-Mo Cr-Ni Cr-Ti Cr-U
295 299f. 300 300 301 301
Ga-Ag Ga-Cu Ga-Pu Ga-Ti
284 301f. 318 319
Ge-Nb
319
Hf-Ti Hf-W Hf- Zr
319 319 319
MO-CO Mo-Cr MO-Cu MO-Fe Mo-Nb Mo-Ni MO-OS Mo-Pd Mo-Pt Mo-Re Mo-Ta Mo-Ti MO-U MO-W Mo-Zr
297 300 302f. 311 107f. 322 322 322f. 323 323 323 323 324 324 325
Na-AI
288
284
291
Au-Ag Au-Co Au-Cu Au-Fe Au-In Au-Ni Au-Pd Au-Pt Au-Sn
283 291 291 292 292 292 293 293 293
In-Au In-Cu In-Ni In-Pb
292 302 319 320
La-Mg La-U
320 320
Be-AI Be-cu Be-Fe
285 293 294
287 294 294 320 320 320 320
288 319 321f. 325 325 325 325f. 326f. 327 328 328 329
293
Li-AI Li-Bi Li-Cd Li-Mg Li-Sb Li-Si Li-W
Nb-Al Nb-Ge Nb-Mo Nb-Ni Nb-Pd Nb-Sn Nb-Ta Nb-Ti Nb-U Nb-V Nb-W Nb-Zr
Ba-U
283 f. 286f. 291 293 294 295 301 301f. 302 302f. 303 303f. 304 304 305 305 305ff. 307 307ff.
Hg-Ag
As-Fe
Cu-Ag Cu-AI Cu-Au Cu-Be Cu-Cd cu-co Cu-Fe Cu-Ga Cu-In Cu-Mn Cu-MO Cu-Ni Cu-Pd Cu-Pt Cu-Sb Cu-Si Cu-Sn Cu-Ti Cu-Zn Fe-Al Fe-As Fe-Au Fe-Be Fe-Co Fe-Cr
287 291 292 294 295 ff. 299 f.
Mg-AI Mg-Ce Mg-La Mg-Li Mg-Ni Mg-Pu Mg-U
287 f. 294 320 320 320 321 321
Ni-AI Ni-Au Ni-Co Ni-Cr Ni-Cu Ni-Fe Ni-In Ni-Mg Ni-Mn Ni-Mo Ni-Nb Ni-Pd
288f. 292 297 300 303f. 312f. 319 320 321 322 325 329f.
Bi-Li
294
Cd-Ag Cd-Cu Cd-Li
283 294 294
Murch, Bruff
Landok-Bhstein New Series III/26
5.1 Introduction
281
System
Page
System
Page
System
Page
System
Page
Ni-Pt Ni-Si Ni-Sn Ni-Ta Ni-Th Ni-Ti Ni-U Ni-V Ni-W Ni-Zn
330 330 33Of. 331 331 331 331 332 332 333
Pu-Ga Pu-Mg Pu-Ti Pu-u Pu-Zr
318 321 334 334 335
Ta-Ti Ta-W
336 337
Th-Fe Th-Ni
316 331
U-Sm U-Sr U-Ti u-w U-Zr
336 336 337 339 339
Re-Mo Re-Pt Re-W
323 334 335
Rh-W
336
298 328 332 334 337f.
322
Pb-Ag Pb-In Pb-Sn Pb-Tl
284 320 333 334
Sb-Cu Sb-Fe Sb-Li
305 314 320
Pd-Ag Pd-Au Pd-Co Pd-Cu Pd-Fe Pd-Mo Pd-Nb Pd-Ni Pd-Ti Pd-V
285 293 298 304 314 322f. 325 329f. 334 334
Si-Al Si-Cu Si-Fe Si-Li Si-Ni Si-U
289 305 315 320 330 336
Sm-U
336
290 298 301 307 316f. 319 319 321 323 326f. 331 334 334 336 336 337 337f. 339
v-co V-Nb V-Ni V-Pd V-Ti
OS-MO
Ti-Al Ti-Co Ti-Cr Ti-Cu Ti-Fe Ti-Ga Ti-Hf Ti-Mn Ti-Mo Ti-Nb Ti-Ni Ti-Pd Ti-Pu Ti-Sn Ti-Ta Ti-U Ti-V Ti-Zr
w-co W-Fe W-Hf W-Li W-MO W-Nb W-Ni W-Re W-Rh W-Ta w-u
298 317 319 320 324 328 332 335 336 337 339
334
336
Pu-Al Pu-Ce
289 294
Ta-Mo Ta-Nb Ta-Ni
323 325f. 331
293 294 301 317 320 321 324 327 331 334 336
285 290f. 307ff. 317ff. 333
Sr-U
U-Ba U-Ce U-Cr U-Fe U-La U-Mg U-MO U-Nb U-Ni u-Pu U-Si
Zn-Ag Zn-Al Zn-Cu Zn-Fe Zn-Ni
293 298 304 323 330 334
293 305ff. 315f. 325 330f. 333 336 336
Tl-Pb
Pt-Au Pt-Co Pt-Cu Pt-Mo Pt-Ni Pt-Re
Sn-Au Sn-Cu Sn-Fe Sn-Nb Sn-Ni Sn-Pb Sn-Ti Sn-Zr
Zr-Al Zr-Hf Zr-Mo Zr-Nb Zr-Pu Zr-Sn Zr-Ti Zr-U
291 319 325 329 335 336 339 339
Landolt-Biimstein New Series III/26
Murch, Bruff
5.2 Chemical diffusion tables Composition at.%
A&! 0.5 1.0 1.5 2.0 2.5 3.0 3.5 6.5 8.5 1.76 3.98 0.869 1.76 4.0 0.518 1.84 0.86 1.85 4 7 64 g:,
61.90
DO
Q
d
Dl
D2
10S4 m*s-r
kJmol-’
rn*s-l
m*s-’
m*s-’
0.21 0.30 0.33 0.55 0.78 1.5 3.0 11.0 16.0 0.21 0.21
121 124 125 129 131 136 141 155 159 113 113
7.3.10-14 1.8. lo-l3 3.8 . IO- l4 1.16.10-13 1.73.10-‘2 9.2 . IO- l2 -
1.22.10-13 7.87. lo-l4 3.20 . lo- l3 2.75 - lo- l3 1.85 . IO- l3 7.78 . IO- l3 6.61 . 10-13 11.22. 10-13 9.94.10-13 1.22.10-12 5.01 - 10-12 -
-
773 ..a 868
;0.10-‘4 4.9. 10-14 1.6. lo- l3 1.6. lo-l3 1.2. 10-13 3.9 * 10-13 4.1 * 10-13 5.3 * 10-13 5.0.10-13 -
773
1.3
121
-
Temperature range K
AI
;02.10-‘2 1.141 . lo-” -
DL =
D;, =
2.2 * 10-s QA, = 113
2.4. 1O-4 QA, = 124
Method/Remarks
Fig.
Ref.
l=Ag,2=Al Method A
-
57H
Method A
-
70K2
Method C
-
75Y
Method A Further data at pressures up to 3 GPa given in reference.
-
84M
808
845 868 770 808 770 808 770 808 633...713 753.a.833 731... 828
1.63
1.53
-
-
-
648...793
0.14 2.42. IO-’ -
175 155 -
See Fig. 1.
-
-
1036... 1238 1079e.. 1290 1173
-
-
See Fig. 2. 3.8. lo-l3
7.3.10-13
1.7.10-13
1213 1213
4.7. 10-3
131
-
-
-
923... 1168
0...25 5.5 8.0 9.8 14.8 18.9 24.8 27.7 32.7 33.8
-
See Fig. 3. 3.4. lo-” 5.2. IO-” 7.4.10-11 1.2.10-‘0 1.7 * lo-‘0 7.3 . 10-10 8.04. 10-I’ 4.7. 10-g
-
-
2.14. IO-” 2.72. IO-” 3.29. IO-” 5.62.10-l’ 9.12.10-‘I 1.91 . lo-I0 2.78. IO-” 5.53 . 10-10 6.61 * 10-10
2.9. IO-” 3.97. IO-” 5.07.10-‘I 1.04. 10-10 1.89~10-10 4.61 . IO-” 7.31 . 10-10 1.66.10-g 2.09. lo-’
900..* 1053 873
-
-
CL
6...30 =O... 6 zo...17 zO...24
-
-
See Fig. See Fig. See Fig. See Fig.
&
CU 1.2. 10-z 0.52
149.0 183.8
-
0...20
Ag
Au
50.8 0 . . .8.77 xO...lOO 5O.e.85 63.5
Ag
Cd o... 5
1
0...2
4. 5a. 5 b. 5c.
883...933 1179 1087 1073
990... 1140 1023 .... 1073
-
87C
-
2
425 50E 52S, 53Hl 54B
-
50K
3 -
59Ml 731
4 5a 5b 5c
73U2 78B
-
50K 67C2
Method D Data listed are for 15at.% Al. Slight dependence on concentration, see reference. l=Ag,2=Au Method A Method A Method A
1
Method A l=Ag,2=Cd Reanalysis of earlier data Method B Method A Method A 0” determined from intrinsic diffusion coefficients.
Method A Method A Many intrinsic diffusion coefficients given in reference. 1 =Ag,2=Cu Method B Method B
(continued)
Composition at.%
AlZ
0.**2
DO
Q
10m4m’s-’
kJmol-’
Cu (continued) 1.2 0.1 1.7 1 2 2.5 3.1 4 6.8 6 98.5 6.8 99 3.1 99.5 1.6 99.9 0.88 0.21
1.1 xo...3 go--- loo
m2s-’
-
192 196 200 203 210 216 208 201 195 184.5 143c*, G,: atomic fraction Ag) SeeFig. 6. See Fig. 6.
Method/Remarks
m2s-’
Temperature range K
-
818.e. 1043
-
Method A b available at higher concentrations, e.g. up to 18 at.% Cu at 1043 K and down to 95 at.% Cu, see reference.
974*** 1273
Method A
0.28 . lo- l3 -
1174 1023 1193
D,
D2
m2s-’ -
1.56. lo-t3 -
-
Fig.
Ref.
71B
-
7302
Methods A. H 6 Concentration profiles determined from microprobe and X-ray intensity bands. See figure for effect on b(C).
76U
Ag
Ga 1.9..- 3.5
0.42
163
-
873 --. 1213
Method B
77B2
Ag
Hg 56
3.181 . IO-”
32.5
-
313.e.388
Method A
86L
Ag
Mn 0 . . a8.5
0.18
180
-
849... 1206
Method A
69B1
-
63 -
1.5 - 10-12 3.13 * 10-12 5.43 * 10-12 9.14 * 10-12
493 ... 558 493 538 518 493
Method B Do not reported.
32s
Pb Ag 0.**0.12
-
Pd In solid solution 50
6.36. 1O-4
85
-
-
-
7ooe.e 1000
Method B
-
335
1.5. 10-6
103
-
-
-
898... 1198
Method A
-
7ON2
1.64. lo-’ -
69 -
See Fig. 7. 2.45 . IO-l3 8.75. IO-l3 1.7.10-13 1.7. IO-” See Fig. 8.
-
-
673..*883
l=Ag,2=Zn Method A
7
55Hl
923 973 873
Method E
-
59G
Method A
-
70Hl
8.1 . IO-” -
2.3. IO-” -
823 ... 1023
Method A
8
73U2
See Fig. 9.
See Fig. 9.
-
-
583...673
9
78Sl
-
-
See Fig. IOa.
Method A Do and Q depend on couple used, see figure. Method C
IOa
81W
-
-
See Fig. lob.
lob
-
-
See Fig. 10~.
IOC
See Fig. 11.
See Fig. 11. -
52 126
163 169
-
550
180
-
10.5
295
-
Zll 50 40 . . .55 26.5 26.5 u P CL
40 4.e. 30
CL
74 to sfq phase boundary 31..*39 wt. %(P) 46...51 wt. %(y) 55...81 wt. %(&) 0.e. 18
Al
Al 0...5
Be 0.005 wt.% 0.0075 wt. % 0.91 wt.%
673
823 ... 1023
Method A
11
86S2
773...908
Methods B and C
-
51B
1273 -.. 1473
Method A
-
85G
co
Composition at.% Al
Q
d
D,
D2
10s4 m’s-’
kJmol-’
m*s-l
m*s-*
rn*s-l
0.29 0.19 0.131 0.231 0.287 0.364 0.588 1.033 1.293 0.85 2.1 1.6. IO6 2.2 0.56 0.18 0.432 0.306 0.425 0.393 0.424 0.556 0.13
130 115 185 188 188 187 189 194 191 136 138 231 149 128 126 194 187 187 183 181 179 113
-
-
-
-
SeeFig. 12. 0.65
SeeFig. 12. 177 -
-
-
-
-
D'&=
D& =
0.13.10-4 Q,,, = 163
2.2.10-4 Qc. = 182
cu 0..*0.215
z25
DO
P 2.5 *** 5.0
0 2 4 6 8 10 12 Y2
6 ”
L2 Jl2
0 0 . . . x2
X0 2 4 6 8 10 74 . . +80
6.0. lo-l4 1.31 .10-9 -
-
-
Temperature range K 778...908 923 ... 1023 782 814 985 -.a 1270
Method/Remarks
1 =Al,2=Cu Method B Method C Method B
Fig.
Ref.
-
61Ml 64A 70H2
Method A Empirical equations for Do and Q given in in reference.
700
673 ... 808
Method C
71F
977-e. 1277
Method A
72C 75M2
823.a.1113
Method A Slight dependence of B on concentration. Method A Method A
853-e. 1273 1073 a.. 1223
-
75Pl
12 -
75P2 83R
I I I$
I I IZ
5.2 Chemical diffusion in inhomogeneous binary alloys (Tables)
I I I I I I I
Ref. p. 3661
I I I I I I
%a 1ddd
Murch, Bruff
$1 .Y F4
I I I I I I I
I I I I IIS
I I I I I I
I I I I I I
Land&-B6mstein New Series III/26
287
Composition at.% Al Y
Al
Method/Remarks
-
690...818
Method A Further data at pressures up to 3.3 GPa given in reference.
83M
-
-
873.e.923
Method A
15
43B
Q
B
Dl
D2
10m4rn’s-’
kJmol-’
m2s-l
m2s-’
m2s-’
125 124 127 122 122
-
-
-
See Fig. 15.
Mg (continued) ZO 0.42 1.0 0.49 2.0 0.61 3.0 0.32 4.0 0.45 Mn
0.02~~~0.15 Al
Temperature range K
DO
Na
Fig.
Ref.
0.*.0.002
1.1
134
-
-
-
823.0.923
Method F
-
50R
33 25
Nb Nb,AI Nb,AI
2.0. 10-3 2.5
230 366
-
-
-
1473-e. 1773
Method C
-
75A
Al
Ni
1.87 1.5 4 10 -
268 197 172 50 201 230 268 272 -
-
-
-
1372+..1553 701... 883 928..- 1273 928..- 1273 928 ..a 1273 1533
Method B Method C
16
56s 675
Method A
-
72W
1273 ... 1573
Methods A, C
735
1143 1203 1273 1143 1203 1273
Method C
75H
Al
0..*0.7 Y 6 ; 2 4 6 8 NiAl N&Al
62 86
See Fig. 16. See Fig. 16. See Fig. 16. See Fig. 16. 1.2 * 10-13 1.5.10-‘3 1.5.10-13 1.1 . 10-13 2.1 . 10-12 6.0. IO-l2 1.1 . 10-11 1.5 . lo- l4 6.3. IO-l4 3.5. lo-”
NiAI(G) (36 . . .54) N&AI(s)
3.7. 10-z
See Fig. 17 See Figs. 18a...d. 5.0.10-l5 6.3. IO-” 2.95 . IO- l4 3.6 . lo- I4 1.16. lo-l3 266 24 . IO-l5 3.8.10-l’ 11.5.10-15 24.0. IO-l5 55.0.10-‘5 234 1.5. 10-15 3.0.10-15 7.9.10-15 16.0. IO-l5 37.0.10-‘5 234 See Fig. 19. 123
1.3
257
2.25. 1O-4
107
-
-
1 ... 19 Ni,AI, w 0...5
Al
Pu
3...9.1
6
Al
Si wO...O.48
See Fig. 20.
~0~~~0.5
0.346
124
xo...o.5
2.02
136
wo.31 ... 0.51
-
-
-----------
-
-
-
-
D;, =
D$ =
5.07.10-4 QA, = 143
3.95.10-4 Qsi = 140
1223 ... 1423
Method A
17, 18
7835
1223 1273 1323 1373 1423 1273 ... 1223 1273 1323 1373 1423 1223 ... 1223 1273 1323 1373 1423 1223 ... 1323...
1423 1573
Method A
SOY2
1073 ... 1273
Method C
19 -
1323 ... 1473
Method A
-
85G
623...790
Method B
-
69T
743...853
1 = Al, 2 = Si Method B
43B 79F
1423
1423
617...904
Method B
20 -
753 ... 893
Method A
-
82s
73Bl
Composition at.%
Al 2 12.0 10.0 3.8 TiAl, Al
DO
Q
iJ
Dl
D2
lob4 m2s-’
kJmol-’
m2s-’
m2s-’
m2s-’
Temperature range K
1.4. 10-5 9.0. 10-5 1.6. 1O-5
92 107 99
-
-
1256.e. 1523
1 = Al, 2 = Ti Method A
60G
8.10-’
95
-
1.411~10-* -
4.61.10-’ -
1107...1173 1523 789.e.915
Method C
73v
-
128
1.84 . IO- l5 3.98 . IO- l5 12.7 . IO- I5 4.92. IO-l4 1.49 * 10-13 6.1 . IO-r3 1.95.10-1s 4.85 . IO- l5 19.3.10-15 6.96 . IO- l4 1.74 * 10-13 6.1 - lo- l3 3.64 . lo- *s 6.12. lo-l5 21.6. lo-l5 6.92. lo-l4 2.12.10-13 3.64.10-15 6.12 . IO- l5 2.0.10-‘4 7.48. IO-l4 2.2. 10-15 6.66.10-1s 7.08 - lo-l4 1.10. to-15 5.1 * to-14 -
-
-
Method A
59H
Ti i u B
Zn x0
9
9.1
18.1
18.2
37.6 x0*** x 3.1
1.33
603 633 673 713 758 1086 603 633 673 713 758 1086 603 633 673 713 758 603 633 673 713 758 633 713 633 713 673.e.868
Method/Remarks
Method I
Fig.
-
Ref.
80M
X0 Al
AU
-
1373*.. 1573
Method A
78G
4.3 0.58
220 247
-
1223 a.. 1653
Method A
0.22
183
-
973 ..* 1323
Method H
5.7. 10-4 -
115 -
-
700 ... 1000
Method B
1006+.. 1130
Method A
50 50
2.36 +1O-6 7.94 * 10-E -
57 45 -
823.e.973 573...723 323 ... 1023
Method A Method A
0.5 4.2 7.2 11.2 14.6 21.8 28.3 38.6 55.3 63.9 79.0
8.99 . IO- 3 12.4. 1O-3 15.6. 1O-3 21.7. 1O-3 29.9f10-3 53.6. 1O-3 89.1 . 1O-3 0.214 0.828 1.69 6.092
133 136 138 141 144 149 154 161 173 179 191
-
659..-827
Method D
Fe cf. Y co X0 CU In solid solution lo.*.90
AuCu (disorordered) (ordered) IO...90 wt.%
82M
169 179 189 192 192 283 272 382
A1,Zr 3 Al,Zr,
AU
Method A Data at pressures up to 3GPa given in reference.
9.2.10-3 2.3. 1O-2 5.2. IO-’ 7.6. IO-’ 8.0. IO-’ 9.2 3.4 1.6. lo5
-
-
Zr
M3Zr5
0.6 . . .4.6
757...881
124 121
8 10 12 14 16
As
-
0.406 0.28
3.5
-
-
-
-
See Fig. 21.
-
-
-
See Fig. 22.
-
-
-
-
-
-
-
-
-
-
-
1473 **. 1573 1373 ... 1573 1273 ... 1573 1273 ... 1573 -
76B2
77F 335 21
69B3,69B4 70Kl
22 -
71P 81L
Composition at.% Fe 0.~.15.6 X0 5***40 AU 3
In
33
AuIn,
50
AuIn
69
Au,In,
80
Au.&
91 Ni 2 IO 20 30 40 50 55 60 65 70 75 98 0-e. 100
DO
Q
d
Dl
D2
10m4 m’s-’
kJmol-’
m’s-’
m2s-’
m2s-’
See Fig. 23.
-
4.7 * 10-l’ 9.9 * 10-l’ 7.0 * 10-16 1.8 - IO-” 2.6. IO-l6 3.6. IO-l6 5.8. IO-l6 5.8. IO-” 4.9 * 10-l’ 7.8. IO-” 2.4 1 10-l’ 6.2. IO-”
-
2.4. 10-l’ 5.0.10-15 2.9. IO-l5 7.4.10-1s 6.6.10-16 9.1 . 10-16 9.8. IO-l6 9.8. IO-l6 6.8 * 10-l’ 1.1 . 10-16 2.8.10-” 7.1 . 10-l’
415 424 415 424 415 424 415 424 415 424 415 424
-
-
1123...1198
1198
l.157.10-4
102
0.19 -
172
4.3. 10-2 3.9. 10-2 9.5. 10-2 7.8. IO-* 2.2. 10-2 1.3. 10-2 5.9. 10-3 6.8. 10-2 1.4. 103 2.0 . IO’ 6.1 . 10s 1.8. lo4 -
173.3 173.8 183 183.8 175.9 177.5 174.6 204.3 305.6 402.8 439.6 356.7 -
See Fig. 24.
Temperature range K
Method/Remarks
Fig.
Ref.
1026... 1276
Method B
-
44K
973 .a. 1323
Method H
-
77F
973 ... 1273
Method A
23
831
l=Au,2=In Method A
-
64P
Method A
-
57R
Method A
24
67L5
D,, calculated assuming
Au
Pd In solid solution
1.11.10-3
157
-
3.2. 1O-4
153
-
1.23. 1O-3
163
-
-
98 ‘. 96 .. 94 92 90 ‘~ 88 .86 84 -. 82 80 2...8
0.62 1.0 0.73 0.67 0.60 0.58‘ 0.53 0.52 0.47 0.43 0.37
229 234 232 232 231 231 231 231 231.. 230. 262
-
-
94.9
-
-
-
D;,=O32 QAu= I&
D;t=9.0.1d-2
Sn 0 ... 1.75 o... 1.4
-
-
See Fig. 25. See Fig. 25.
-
-
Ba o...solubility limit
U Y
0.112
171
Be o...x15 x33 ~48 75
CU u P
174 115 130 138
-
-
i
1.9. 8.4. 5.4. 1.2.
-
P
-
-
-
D;, =
50 Au
Pt In solid solution
Au
33
’
-
-
IOOO... 1250
Method B
-
335
-
899 ... 1313
Method A
-
70N2
-
1000... 1250
l=Au,2=Pt Method B
-
1198..+ 1328
-
-
--
Method A Data for 0” resulting from rolled Pt used in couples are also given in reference.
61B
-
-
335
.’
:
QR = 226 :
10-l 1O-2 10-z 10-3
3.5.10-6 QBe = 121
Method A
-
1090 1129
25
72H2
-
1123 ... 1313
Method C
-
64T
-
823...1113 923...1113 823.e.1113 823...1113
-
63R
-
D& =4.5. IO-’ Qcu = 105
‘l=Be,2=Cu Method A
’
Composition at.% Be
Bi
Ref.
-
-
1073 .** 1373
Method A
-
64L
See Fig. 26.
-
-
653-a-873
Method D Seereference for 6(T) details.
26
77W2
27
38R
6;
D,
4
10s4 m2s-r
kJmol-’
m2s-*
m2s-’
Fe 0 . . .0.2
1.0
226
-
Li Li,Bi
-
Cll
Cd
Li 35 **e47.5 Mg
Pu Ce 3.74 *** 7.17wt.% Ce O.**solubility limit
Fig.
Q
Cd 0.075 . . . 0.525 0.5
Ce In solid solution
Method/Remarks
m2s-’
Temperature range K
DO
U y
-
-
See Fig. 27.
-
-
773.0.853
Method A
3.5 * 10-3
122
-
-
-
773...1123
Method B Data from A. Klein presented by 0. Kubaschewski [50K]
-
-
See.Fig. 28.
-
-
774-e. 802
Method D
450
176
-
-
-
823...871
Method C
1.31 .10-t
124
-
-
-
676.e. 801
Method B
3.92
278
-
-
-
1073 ..a 1273
Method C
50K
28
84L
co
co 0.1
C-3 0...40
0...15.2wt.% 0...28.3wt.% 0...25 CU
2 1.12 1.75 2.02 2.20 0.98 1.35 1.63 3.21 4.12 4.92 co o..* 100 10 20 30 40 50 60 70 80 90
Fe
0.443
266
-
-
-
1273... 1633
8.4. 1O-2 8.0 ’ IO-’ 0.14
254 250 253
-
-
-
1273... 1573
Method A (0” reported to be a function of concentration but dependence is very slight) Method B
1273 ... 1573
Method A
0.6 5.7
214 243
-
-
-
1073.** 1346
see remarks
seeremarks 6.8 . 10-l’ 1.5.10-l’ 2.2.10-l’ 9.0.10-18 5.1 . 10-16 6.4. IO-l6 3.8 . lo-l6 4.5.10-16 9.6. lo-l6 3.6 . lo- l6
-
-
1158
1273
Method A Data for intermediate compositions are also given in reference. Method B Do = 1.0 * 10m4m2sm1 and Q = 275 kJmol-’ calculated from 2 points only.
-
-
See Fig. 29.
-
-
1409..+ 1629
1.5. 10-3 2.9 * 10-3 4.4. 10-3 5.8. 1O-3 7.0. 10-3 8.8. 10-3 11.5.10-3 12.0.10-3 13.1 .10-3
219 215 212 216 215 217 218 218 219
-
-
-
1273... 1673
-
52W
63D1,63D2 73Gl 73B2
-
84A
l=Co,2=Fe Method A
29
Method A
-
69B3, 69B4 73Ul
(continued)
Composition at.%
co 3 5 15 20 25 30 3.5 40 45 50 55 60 65 5 10 15 20 25 30 35 40 45 50 55 60 65 70 80 85 90 95 45 52
Fe CL
Y
DO
Q
b
D,
4
10S4 m2s-’
kJmol-’
m*s-*
m*s-’
m*s-’
-
-
3.01 .10-‘5 1.76.10-”
1.33 * 10-14 4.18.10-”
(continued) 3.02 . 10’ 4.13 * lo4 1.15. 10s 1.52. 10’ 3.02 - 10’ 5.89. IO’ 1.4 * 10s 1.54 * 104 4.34 * 103 1.02. 103 3.67 . lo* 84.4 30 45.2 21.6 10.5 5.33 2.54 1.01 4.21 5.67 2.5 2.7 1.53 5.75 0.871 0.783 1.37 2.11 5.01 5.72 -
318 343 361 366 373 378 363 339 323 306 292 274 261 329 319 319 303 293 276 270 273 276 277 281 294 276 273 281 291 306 318 -
-
Temperature range K
Method/Remarks
Fig.
Ref.
1123...1168
Method A
-
77H
1073***1168 1073+.. 1228
993... 1228
993 *a* 1141 1323-e. 1573
1273 .a. 1573
1228 1168
-
56 i7 io ZO
Mn 5 5 10 20 30 40
7.79 0.78 3.07 0.70 0.721 0.627
296. 273 284 257 248 241
-
33 :0
:0
-
MO o..* 15 wt.%
0.23
263
3
2.48
295 See Fig. 30.
xo*..go
-
szo... 100
-
-
10 20 30 40 50 60 70 80 90 zo-..
1.76 1.61 1.89 1.50 0.48 0.166 0.140 0.725 1.94 -
299 295 295 290 273 258 254 273 285 -
-
Ni 10 . . .90
IO...90
100
-
-
See Fig. 31. See Fig. 32.
See Fig. 33. See Fig. 34.
9.0.10-‘6 5.5.10-16 8.2. 10-l’
2.09 * 10-15 1.45. 10-lS 5.29.10-16
1141 1123 1073
-
-
1133 ... T, (ferro) T,.-. 1150 (para) 1133...1423
-
-
1273 .-. 1573
Method B
-
63Dl
1273 ... 1573
Method A
-
74H
1428... 1673
Method A
30
53H
1423 ... 1578
Method A
31
67B2
1409 ... 1629
Method A
32
67B3, 69B4
1153...1573
Method A
-
711
7711
-
D& =
Do
2.2 * 10-s Q, = 263
9.8. 1O-s QMn = 229
-
-
-
-
-
l=Co,2=Mn Method A
-
Mn
=
1373
Method A
33
73H
1373... 1673
Method A
34
73Ul
Composition at.%
co
Pd
10 20 30 40 50 60 70 80 90 IO***90 co
co Co,Ti Co,Ti CoTi
DO
Q
b
Dl
4
10-4mZs-1
kJmol-’
m2se1
m2s-*
mzs-*
-
Pt 0.e. 100 5 10 20 30 40 50 60 70 80 90
-
-
0.872 1.27 0.887 0.746 0.667 0.639 0.536 0.447 0.465 0.516
286 288 279 275 274 274 272 272 274 277
21
-
-
Ti 4.s.8 21 30 . . a32 46.e. 50 90***95(L3)
15.0 5.3 * 10-z 0.28 4.4 * 10-4 67
281 167 218 173 207
13.7 * 10-15 25.6. IO-” 55.0 * 10-15 12.0 * 10-14 14.5 * 10-14 12.0 - 10-14 70.7.10-14 28.2. lo-l4 13.9.10-14 See Fig. 35.
-
See Fig. 36. -
-
Ok=
Temperature range K
Method/Remarks
Fig.
Ref.
1423
Method A
-
66B
1153*.. 1466
Method A
35
721
1398..*1573 1271... 1673
1 =co,2=Pt Method A Method A
36 -
67B2 801
Method C
-
76V
D;=
2.25. 1O-4 8.09. 1O-4 1473 e-e1673 Qc, = 278 QR = 291 -
1173***1413
973 .a. 1123
co co Cr IO...20 o..-11 11 15 5.4 37 42 52 62 72 81 91 0...7.1 13.7 15.5 16.8 18.2 19.3 20.7 12.1 13.9 15.3 16.8 18.0 19.1 O.e.28.3
V 0...14.8wt.%
2.1 . IO-’
222
W 0...14.6wt.%
8. 1O-3
238
1.48 7.1 . 10-5 1.2. 10-3
230 170 219 240 252
Fe u y u u u u u
y See remarks
u Y
2.4 6.27
-
-
1373 **. 1573
Method B
-
-
-
1373 ... 1573
Method B
-
-
-
-
I =Cr,2=Fe Method A
-
1.7. IO-” 1.42. IO-’ 1.22 * lo-’ 1.53 * 10-7
0.8. IO-” o.95.1o-g 0.9.10-7 l.o~Io-’ -
1096... 1713 1223 ... 1423 1096 1323 1688 1713 1523
Method A
-
6OPl
1173...1473
Method B
-
63D1,63D2
1473
Method A Fe samples are actually steels with 0.014 % C, 0.18 % Mn, and O.l6%Si.
70s
948-e. 1758
Method B
-
74A
8.0. IO-” 5.6. 10-l’ 2.78.10-l’ 1.17.10-‘I 7.1.10-‘0 4.9.10-10 4.64. 10-l’ 1.1 . 10-12 1.16. 10-l’ 1.30.10-‘2 1.23. IO-” 1.20 * 10-12 1.14 * 10-12 3.5.10-12 3.76. IO- I2 3.76. IO-” 3.68. IO-” 3.68. IO-l2 3.56. IO-l2 -
-
-
-
63DI,63D2 63D1, 63D2
(continued)
L
Composition at.% Cr
I7 20 22 24 26 28 30 32 34 36 38 40 42 44 46 47.8 X0 5 10 I5 20 25
MO
Cr
Ni
o*** 10.3 wt. % s-.-45 5 ... 20
Method/Remarks
Fig.
Ref.
1453
Method A
-
74c
1044... 1124 1049... 1124 1039... 1124 984-e. 1124 974-e. 1124 974.e. I124
Method A
-
85B
-
1323 ... 1473
Method B
-
71HI
-
-
1373 *** 1573
Method B
SeeFig. 37. SeeFig. 38. -
-
1268 ... 1573 1268-e. 1573
Method A
Q
b
D,
D2
IOm4m2s-t
kJmol-’
m2s-l
m2s-*
m2s-’
299 292 279 280 269 269
7.5 . IO- 1X 7.5 . IO- 1X 7.0.10-*3 6.4. IO-l3 5.8. IO-l3 5.2 . IO- l3 4.8 . IO- l3 4.3 * 10-13 4.1 . 10-13 3.8 . IO- l3 3.4 . IO- l3 2.8 . IO- l3 2.3 . IO- l3 2.0.10-13 1.7.10-‘3 1.5.10-‘3 -
2.27. lo-” -
0.66 * lo-” -
2.9. 1O-3
257
-
0.6
257
SeeFig. 37. SeeFig. 38.
Fe (continued) CL 1.69. IO3 8.24 . IO2 2.21 . 102 2.56. IO2 60 15
Cr SoIid solution range
Temperature range K
DO
37 38
63D1, 63D2 67U
Cr 9
Ti P
-
-
3.6. IO-’
Cr 0. . . solubility limit
U y
0.7
142
-
3.7. 10-g
2.8. IO-’
1258
Method A
-
62P
-
1173...1273
Method C
-
60M
l=Cu,2=Fe
Fe xO...6
-
See Fig. 39.
-
-
See Fig. 39.
D&= 6.1 . 1O-4 Qn, = 268
21.0 1.3.103 300.0 0.19 0.091
251 301 284 273 193
-
0.504
208
-
1073 ... 1323
Ga CuGa,
1.34.1o-2
43
-
2.5 4.9 7.6 10.3 13.1 15.9
3.0. 10-4 1.8. 1O-3 1.6. IO-’ 1.8. IO-’ 1.3. 10-l 8. IO-’
134 142 153 167 157 146
DoGa = 11.1 .10-5 QGa = 155
0.5 1 CL k-
cu
0;. = 2.7. 1O-4 QFe = 266
-
Y
97 *-. 99.5(E)
0.**7.4wt.% O...2wt.%
0;. = 8.9 +1O-4 QFe = 314
0;” = 3.6 1 1O-4 Qc, = 274
2.6 wt. %
12.5
-
-
-
-
I
D& = 6.5. IO-’ Qcu = 140
1173 ... 1323
Method A
39
71K
1133 ... 1283
Method A
-
74Tl
1045 **. 1153 1198 ... 1323 923 ... 1073
Metliod
B
-
77s
Method B.
-
7883
313 . ..433
1 =Cu,2=Ga Method C
-
70T2
773...973
Method A
-
74Wl
(continued)
Composition at.%
DO
Q
10m4m2sS1 kJmol-’
cu
cu
cu
Ga (continued) 16.3
d
Dl
D2
m2s-’
m2s-i
m2s-r
D& = 1.2. 1O-6
0;. = 8.6. 1O-6
-
-
18.4
-
-
-
X0... 0.3 In 1 2 3 4 5 6 7
0.58
194
-
0.93 1.2 1.8 5.8 9.8 11.0 18.0
188 188 189 195 198 196 198
-
Mn O.e.28 3.3 6.0 6.85 9.0 10 20 30 40 50 72 76 80
0.52 5.66 17.5 4.62 9.22 2.11 * 102 1.4 * 106 2.42 . 10’ 2.78 . 10’
177 207 211 198 209 241 366 400 408
0.54.10-‘3 0.61 . lo- l3 0.71 . 10-13 1.18. lo-l3 -
Qcu = 135
D& = 6.3. IO+
Qcu = 136 -
QGa= 135 -
-
Method/Remarks
Fig.
Ref.
74Wl
Method A
Qo.= 14
D& = 4.7. 1O-6
-
Temperature range K
973... 1323
Method B
-
77B2
-
949***1119
Method A
-
81H2
-
913.e. 1093 1123
l=Cu,2=Mn Method B Method A
-
67C2 7ow
1021... 1203
Method A
-
7714, 7712
949.a. 1089
Much data on intrinsic diffusion coefficients are given in reference from 0.6 at.% In to 4.6 at.% In and at temperatures x lOOOK.
408 397 397
-
-
-
29
-
-
D& = 12.0.10-4 Q, = 210
0;” = 1.7.10-4 QMn = 190
1043 ... 1118
77
-
-
Dk = 1.3. IO7 Q, = 490
0;” = 1.4. 10’
1171... 1203
0.37 0.56 0.51 0.53 0.66 1.17 1.33 2.34 10.7 93.6 41.0 2.1 0.14 7.0. 10-z 0.16
187 187 183 181 181 186 189 197 216 241 239 218 198 195 204
0.6. IO-l3 0.8.10-13 0.88 . IO- l3 1.04.10-‘3 -
-
Qm = 40 -
2.82. 1O-6
146
-
-
-
82 84 86
3 5 6.0 6.85 9.0 10 15 20 25 30 35 40 45 50 55 60 65 70 75 CU MO 0.016.. .5.45 CU 70*.* 100
2.11 . 107 7.12. IO6 6.06 * IO6
-
85A
1173...1548
Method B
-
55B 52T
-
-
1196..* 1322
-
See Fig. 40. -
3.7.10-14
1.7.10-14
1333
Method A
40 -
-
See Fig. 41.
See Fig. 41.
See Fig. 41.
1273
Method A
41
o... 100
Method A
1 =Cu,2=Ni Method A
Ni
83
850 750-s. 850 850 850 850 750s.. 850
54B 67L3 (continued)
Composition at.%
CU Ni O***loo o... loo o*** loo
DO
Q
d
Dl
D2
10m4m*s-l
kJmol-’
m*s-r
m*s-’
-
See Fig. 42. See Fig. 43. See Fig. 43.
-
-
See Fig. 44. See Fig. 44. 6.09. IO-l4 2.3 . IO- l3 .exp(-5.94X,,) .exp(-6.13X,3 Xni is mole fraction Ni See Fig. 44. See Fig. 44.
(continued) . -
0..- loo o-.. 5 -
o*** 100 CU IO*..90 10 20 30 40 50 60 70 80 90 O.--l00
Pd
-
50 6 a.. 95
-
-
-
-
-
-
-
0.48 -
224 -
See Fig. 47.
4.2. lo3 0.67
233 233
-
Pt
0..*‘13.9 1.5 ... 2.5
See Fig. 45. 2.7. lo-l5 4.9.10-15 8.5 . IO- Is 1.53.10-14 4.01 . 10-14 8.88 . lo- I4 1.54. 10-13 1.65 . IO- l3 1.28 . lo- l3 See Fig. 46.
Method/Remarks
Fig.
Ref.
m*s-i
Temperature range K
-
983-s. 1339 1273 1193
Method A Method A b(c) near 100% Cu depends on calculational method used, see figure.
42 43
69B2 71M2
See Fig. 44. 6.11 . lo-l4 =exp(-9.08X,3
1273 1273
Method A Method A
44 -
72Hl 78H
See Fig. 44.
1273
Method A
44
8212
-
-
1151... 131 1292
Method A Method A
45 -
52T 66B
1204.e. 1334
46
69B3, 69B4
.-
-
1048...1313 1173
Method A See figure for d(C) at 1204 and 1334K. Method A Method A
-
70N2 74T2
-
-
1314...1674 1023... 1348
Method B Method B
47 -
44K 72F2
Sb
1.0 2.0 3.0 1.0
CU
0.32 9.4. 10-Z 3.0. 10-2 -
1.7
.-
0.6
-
Si ~0~~~10 a/a+K boundary
11.4
CU 6
Sn w37wt.%
Y & rl
28 ... 33 wt.% -
Cu,Sn
(4
1
o... 33 wt.%
-
”
C!u,,Sn,
-
‘-
.I74 160 147 -
1.3. IO-” 6.9. lo-‘* -
-
-
663
1 =Cu,2=Sb Method A
-
56H
‘, 949 -:‘1040
Method A
-
81Hl
2.9 . IO- l4 6.1 . lo-l4 2.15. IO-l4 4.05.10-14 7.8. IO-l4 2.5. lo-l4
1005 1040 970 1005 1040 1005 Method A Method C
48 -
38R 68A
l=Cu,2=Sn Method C d values in 6 phase are averaged.
64s 49, 50a,b
-
-
1.8. IO-l4 3.7.10-14 0.5.10-14 1.85 . IO- l4 3.7.10-14 1.3.10-14
-
See Fig. 48. L
-
-
973 ... 1075 938 ... 1048
7.7.10-14 3.6 . IO-l3 1.0.10-l* 1.1 . lo-” 1.65. lo-‘1 1.3. 10-l’ See Fig. 50a. 4.3.10-16 3.7.10-15 2.7. lo-l6 2.2.10-15 See Fig. 51.
See Fig. 49. See Fig. 50b. -
See Fig. 49. See Fig. 50 b. -
701 714 731 780 818 845 979 453 483 453 483 523...623
199
78
2.4. lo-” 1.0.10-14 2.2 ’ 10-14 1.6. IO-l4 3.0 . lo- l4 2.9’. IO-‘*
473 573 673 723 673 723
Method C Do not given. Method A Activation energies for interdiffusion of Cu,Sn and Cu,Sn, given in reference.
51
70F
-
75L
(continued) i ,’
Composition at.%
DO
Q
10s4 m2sw1 kJmol-’ CU
Sn (continued) 34***38wt.% Cu,Sn Cu,Sn, 62~~~lOOwt.% 00.07 2.10-2
40.--bowt.%
a
90 87 156
6
Dl
D2
m2s-’
m2sv1
m2s-*
2.4. lo-” 1.0 * lo-t4 2.4. IO-l4 5.1 * lo- l4 9.0 * lo- l6 3.5 * lo- *s 1.2 * lo- *z 3.8. lo-l2 3.0 * 10-l’ 7.5 * 10-15 3.0.10-1s 4.0.10-‘5 3.1 . 10-1s 3.0.10-13 2.0 * 10-12 5.2. IO-‘* 2.0. IO-” 3.4.10-1s 4.0.10-‘5 -
-
-
-
-
-
-
-
-
-
-
-
-
Temperature range K
Method/Remarks
473 573 673 723 473 573 673 723 473.0.723 473 573 673 723 473 573 673 473... 673 473 573 673 723 lOOO*.*1100
Method A
Method A
-
7501
-
7502
Fig.
Ref.
75L
. 1013.3Ns.
(IV,,: atomic fraction Sn) 1.43 * 10-4 70 1.55. 1O-4 65
E rl
1 2 3 4 5 6 0.6
0.295 0.240 0.313 0.265 0.666 1.02 -
177 173 173 169 174 175 -
-
-
463e.0493
Method C
-
9.3 * 10-14
973...1101
Method A
6.1 . lo-l4
973 ... 1057 1089
80H
0.9
-
14.5(P)
9.11
134
Y
-
-
1.25 . lo- I4 3.7 * 10-14 4.1 .10-‘4 1.35.10-14 4.9.10-14 6.5 . IO- l4 1.5. 10-14 5.2. IO-I4 5.5 . lo- I4 2.1 . 10-14 Docu = 2.58. 1O-4 tmQcu = 103 See Fig. 52. 1.10-‘5
-
-
3.10-15
-
-
0.693 0.934 1.41 1.92
196 199 204 208
-
-
-
7.1 . 10-14 3.7.10-12 9.1 . 10-13 See Fig. 53. See Figs. 54a... c.
4.7.10-12 1.2.10-12 See Figs. 54a...c.
1.0.10-13 6.3 +IO-I2 See Figs. 54a...c.
2.6 3.1
4.9
Cu,Sn (E) Cu,Sn 6-l)
Ti ZO 0.5 1.0 1.5
Cu
Zn P Y E
cf.
-
-
1.4 1.7
Cu
-
-
84 2...28 28 1 5 10 16 20 25 28
-
-
5.6. IO-’ 6.2. IO-’ 8.3 . lo-’ 9.5. 10-2 9.0. 10-2 3.1 . 10-2 1.6. 1O-2
167 167 165 158 152 136 124
-
2.4 . IO- I4 1.0~10-13 1.1 . lo-‘3 2.9 . lo-l4 1.2.10-13 1.5. 10-13 4.3 . lo- I4 1.8. IO-I3 2.0.10-13 6.5 . IO-I4
Dzn = 3.05. 1O-3 Qsn = 144 -
1014 1089 1014 1089 1014 1089 1101 1014 874. . . 993
Method A
52
8OYl
493
Method C Non-parabolic growth, possible grain boundary diffusion dominated.
-
84C
Method A
-
7713
668
1 =Cu,2=Zn Method C
-
53Hl
1163
Method A
53
54B
1053 ... 1188
Method A
54a . ..c
55H2
973 ... 1283
997... 1188 (continued)
Composition at.% CU u
g (disordered) Y
S (disordered) P (ordered)
Zn 10 15 20
DO
Q
B
Dl
D2
10m4m2s-’
kJmol-’
m2s-’
m2s-’
m2s-’
170 170 170
-
-
-
D!?"= 0.81
D& = 2.1
Qcu = 178 -
Q& = 178 1.4.10-12 1.5. lo-” 6.7 . lo- l2 1.1 * lo-‘0 4.6 . IO- lo 1.8 . IO- lo -
648 753.e.983
SeeFig. 58.
(continued) 0.13 0.21 0.36
28
1.7
172
-
4.4..-48
1.8.e. 1.3. 10-2 2.45. lO-2 2.44.10-2 1.71 * 10-2 2.45. lO-2 l.14.10-2 0.99.10-2 0.62. lO-2 0.19.10-2 0.28. lO-2 -
83 . . .76
-
98 95 91 91 84 80 74 65 64 -
-
See Fig. 55a.
1.4.10-13 1.6. IO-l2 7.2 . lo- l3 9.5.10-12 8.1 . IO- *’ 2.1 . lo-” -
800.. 85(~) 48 6.9. 1O-2
78
See Fig. 55 b. -
-
48
1.4. IO3
150
M... 47.5 (p’)
-
SeeFig. 59. SeeFig. 57.
59 60 61 62 63 64 65 65.5 66.5 65.3 65.7 65.7 67.2 68.2 68.2 62*.*66(y)
-
SeeFig. 58.
Temperature range K
Method/Remarks
Fig.
Ref.
973...1183
Method E
-
55R
773.e. 1073
Method A
56L
648 . . .923
Methods A and C
6lM2
698.0. 923 798-e. 923 648 748 698 798 923 848 648
Method A
55 ab
69U
56
71Ul
591 .*a720
Method A Seefigure for b dependence at 877 K.
734-e. 924
Method A
57.e. 75F 59
41.5...
-
See Fig. 59. See Fig. 57.
See Fig. 58.
See Fig. 58.
602...718
-
-
523...673
Method A
60
76F
-
-
-
-
-
748.e.827
Method C
61,
76s
48.5 (P) 79 ... 86(E) 45 . ..49(P) 55...
E
66.5 (Y)
6 0.9
-
-
-
See Fig. 60. See Fig. 61. See Fig. 62. 2.5. IO-” 3.0.10-12 4.6. 10-l’ x1.0~10-‘0 9.7 . lo- l4 1.1 . 10-13 1.2. lo-‘3 1.2.10-13 1.4.10-13 1.4.10-13 -
-
-
-
-
4.10-14 9.10-14
2.3 3.2 3.5 4.6 4.7 5 9 15
0.412 0.285 0.614
196 182 184
X0
0.966
201
-
2
1.10
200
-
4
1.14
198
-
6
1.15
196
-
8
1.13
194
-
10
1.02
191
-
;: : :;I:: ; : g::: -
9.6. IO-l4 1.1 . 10-13 1.2.10-13 1.2.10-1: 1.4.10-13 1.4.10-13 -
0;" =
62
748 768 827 842 1168
1105... 1213
966... 1183
-
82H
Method A Data at pressures up to 3 GPa also given in reference. Method A
84T
Method A 0” = 8.9. IO-l4 * exp(8.9AJz,)m2s-’ @L : mole fraction Zn)
87s
11.3.10-5 Qz,, = 203 DoZn = 15.3.10-S Qz,, = 203
Do Zn=
19.0.10-5 I c+ I 203 Z” 20.2. 1o-5 i Qz,, = 201 DoZn = 22.1 * 1o-5 i Qz,, = 200
D;, = 21.8. 1O-5 Qz,, = 198
(continued)
Composition at.% CU
Fe Y
Y CL CL
Zn
DO
Q
d
D,
D2
10e4 m2s-’
kJmol-’
m2s-’
m2s-r
(continued)
I
Method/Remarks
m2s-l
Temperature range K
D,o,=
966.a. 1183
Method A
12
0.957
188
-
-
14
0.920
186
-
-
16
0.671
181
-
-
12.6. lO-5 i Qzm= 185
18
0.518
176
-
-
I
20
0.346
170
-
-
22 24 26 28 30
0.228 0.14 0.0796 0.0366 0.0128
164 157 150 140 128
-
-
-
4 + 0.02 wt. %C 14 + 0.02 wt. %C
0.57
276
-
-
-
0.54
273
-
-
-
xo***o.59 1.9.e. 3.6 In solid solution 5 10 15 20
6.8 * 10-2 3.467 IO
246 241 250
-
-
-
1423 ..a 1533 1203...1533 1063 a.*1458
5.95 3.04 3.37 2.89
314 303 305 301
-
-
-
1363.v.1523
Mn
Fig.
Ref.
87s
17.3 * 10-s Qzn = 193
0;" =
14.0~10-~ I Qzn = 189
0;. =
0;. = 10.1.10-S
1323 ..a 1723
1 =Fe,2=Mn Method A An empirical eqn. for d is given in reference. Further d data at 1.25wt.% C and also at 1473K are given. Method B
4lWl
45H
Method C
-
69P
Method A
-
70Tl
25 30 35 40 45 50 55 38 41.2 38.0 36.4 5 10 15 20 25 30 24
2.83 2.53 3.12 2.44 2.17 1.96 2.04 7.2.10-’ 1.75.10-Z 0.3 0.163 7.2. 1O-2 0.12 -
297 295 299 294 291 286 289 -
251 264 270 262 249 251 -
-
9.07. lo-‘5 3.36. lo-l5 5.29.10-16 3.48. IO-l6 -
D;, = 0.27 QFe= 269
Fe CL
MO 0 **. 5.05
;0 95 95...97 2.5 (u) 4.1 5.0 5.7 7.5 8.3 4.4 4.4 4.4 & R CF
0.785 3.6 2.29 2.19 18.1 3.6 4.2 4.0 4.8 3.8 4.0 73.2 62.3 2.35 . lo2
226 240 238 236 256 257 260 262 263 268 270 336 346 380
-
6.03. IO-l5 3.52 +IO- l4 1.68 * 10-13 -
2.42 . IO- l4 8.04. IO-l5 1.55. lo-‘5 6.22. lo-l6
-
Do = ?.26. 1O-2 QMn = 241
-
1.78. lo-l4 9.24.10-14 3.87. lo-l3
1523 1443 1363 1283 1123 ... 1573
Method A
-
73N
948 ... 1758
l=Fe,2=Mo Method B
-
74A
1373 ... 1573
Method A
-
74H
1073 *.. 1573
Methods A and C B values extend to 15 at.% at 1300°C in ref. d for y phase (estimated from growth rate of E) given in reference.
-
77N2
1273 ... 1473
1373 1473 1573 1265e.. 1635 1515.e. 1673 1515 ... 1673
DO
Q
b
Dl
D2
10-4m2s-1
kJmol-’
m*s-’
rn*s-l
m*s-’
Temperature range K
Ni o*** loo
-
-
-
1423-e. 1583
1
-
10
5.3 8.9 15.0 24.5 41.5 58.5 38.5 44.5 49.5 -
See Fig. 65. See Figs. 63, 64. 2.9. lo-‘* 2.75 . lo- l6 318 317 316 316 316 316 306 308 312 -
-
973 1073 1273-a. 1561
-
-
1.1 .10-‘5 2.5.10-l’ 4.6. lo-l5 -
0.25. lo-l5 1.2 * 10-15 6.7. IO-” -
1373
-
DFe=
Dii =
-
QNL=
Composition at.%
Fe u Y
20 30 40 50 60 70 80 90 12 37 76 O***lOO
See Fig. 66.
1409...1629
Fig.
Ref.
53H
Method A
63... 65 -
Method A
66
67B1, 6984
Method/Remarks
1 = Fe, 2 = Ni Method A
65G
1.6. 1O-4 304
5*.*95
-
-
See Fig. 67.
3.6. 1O-4 QFc = 274 -
1373.e. 1578
Method A
67
67B2
O.-e loo
-
See Fig. 68.
See Fig. 68.
See Fig. 68.
1473
Method A
-
5.0 * 10-15 7.8. IO-l5 1.2 * 10-14 1.8 . lo- l4 2.6 - lo- l4 3.6 - lo- l4 4.6 + lo- l4 4.8. lo-l4 4.2. lo-l4
1.0. 10-14 1.9. 10-14 2.8 . lo- l4 3.8. IO-l4 4.8. IO-l4 5.6. IO-l4 6.2. lo-l4 5.6. lo- l4 4.4.10-14
3.0 * 10-15 3.6. 10-l’ 4.2.10-” 5.2. 10-l’ 6.2.10-” 8.0.10-” 9.6 . IO- l5 1.2 * lo- l4 1.6. IO-l4
1473
Method A
68 -
67L4
10 20 30 40 50 60 70 80 90
-
0.32
-
70K3
10 20 30 40 50 60 70 80 90 0 ... 100
0.2 0.15 0.26 0.30 0.38 0.41 0.56 0.71 0.63 See Fig. 69.
264 263 262 258 256 254 254 255 254
-
-
-
-
-
923 ... 1223
Method A
69
74B3
IO...90 wt. % 7.5 wt.% 7.5 wt.% 12.5 wt.% 12.5 wt.%
-
-
See Fig. 70.
-
-
1223 ... 1373
Method A
70
84G
-
-
2.7. 10-l’ 4.4.10-19 3.6. 10-l’ 2.3. IO-”
-
-
86D
-
1184 1124 1075 1030
Method B
-
83N
1.6. IO-” 1.2.10-21 4.0.10-22 9.0.10-16 1.5.10-16 1.1 . 10-18 3.3 . 10-20 6.8.10-21 1.1 . 10-21
-
-
Method B (Reference [83N] is closely related to [86D]) Method B
978 923 883 1126 paramagnetic 1078 > 978 927 ferromagnetic 877 827
17.5 wt.% 22.5 wt.% 27.5 wt.% 0.5 wt.% 0.5 wt.% 1.0 wt.% 1.0 wt.% 1.0 wt.% 1.0 wt.%
-
-
978 .-. 1699
Method A
908 ... 1699
86D
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
5.2 Chemical diffusion in inhomogeneous binary alloys (Tables)
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
Murch, Bruff
[Ref. p. 366
Iandolt-Btimsrcin New Series III./26
Fe Y
Si O...lwt.%
a
3 wt.% 5 wt.% 8.5 wt.% 4 5 8 18
u
17 17 35
249 247 249
4.10-‘0 1.7.10-g 2.67 . ;;I:: 7.87 . 2.66 . 10-12 -
1.8
209
-
-
-
-
-
7 ... 21
See Fig. 71. -
18 u
CL
Fe
0 . . .4.7 + 1.8% V to stabilize u phase 8.35 8.69 9.04 9.38 9.73 10.07 10.41 SIR xl wt.% 3 wt. % . . . solubility limit - e.g. 17 wt.% at 1123K
_ -
-
-
0;. =
Dzi = 2.2
5.6. 1O-4 QFe = 226 -
Qsi = 209 -
0;. =
D,91 = 2.2. 10-4 Qsi = 209 -
I -
l=Fe,2=Si Method B
-
52B
Method C
-
53F
1073 ... 1673
Method A
-
67V
1423 ... 1473
Method C
-
67M
1403 ... 1493
Method A
71
680
1173...1673
Method A
-
70B
1479 1566 1423
0.735.(1 + 12.4X,,) (Xsi: atom fraction Si)
219
-
5.6. 1O-4 QFe = 226 -
1403 ... 1493
1.82 1.87 1.77 1.62 1.52 1.55 1.66
215 214 213 212 211 211 211
-
-
-
1173 ... 1373
Method A
-
72M
12.9. 10 3.16. IO6 1.59. 106
345 356 356
-
-
-
1003...1173 1003~~-1113 1113...1173
Method A
-
73T
(continued)
Composition at.%
Fe
CL Y c?
Fe ci Y
Y CL
Q
0
Dl
D2
10-4m2s-1
kJmol-*
m2s-’ .
m2s-’
-
Sn (continued) 0...80 wt. % Sn FeSn, 81...100 wt. % Sn 0...9 -
0.3 ..+ 1.6 wt. %
Y Fe
DO
-Ill Th,Fe, Ti 0.7 * ** 3.0 o.e.o.7 2 85 90 95 0 *. .0.4 wt. %
-
Method/Remarks
Fig.
Ref.
m2s-’
Temperature range K
3.0 * lo-l9
-
473
Method A
-
75L
1.0 * 10-16 9.3 * 10-16 1.2 * 10-16 2.1 * 10-16 1.9 * 10-14 9.1 * 10-14 2.4. 10-l’ 2.0 * 10-l”
-
573 673 723 473 573 673 723 473
Method A
81Y
Method E
72 -
Method B
-
86Sl
-
-
-
0.931 5.04.10-5 0.8
221 136 160
4.4*10-‘7 6.2 . lo- l6 3.6 . lo- *’ See Fig. 72. -
2.32
185
-
-
-
1235-e. 1473
1.34.102
207
-
-
-
823 ... 1073
Method C
-
7834
3.15 0.15 68 3.6 0.77 0.6 8.5. IO’
247 250 260 213 192 188 377
-
-
1348-a. 1498
Method A
-
59M2
-
973.e.1573 973-e. 1323 973-e-1573 1173.e. 1573 1423 a.. 1573
Method A
-
68H3
Method B
-
6882
2.89 . IO2
274
-
-
1123...1323
Method C
79 -
-
573 673 723 473e.o 723 1073*** 1373
-
1183... 1680 1273-e. 1580 1033... 1235
81A
76T
-
-
-
-
222 252 217
-
P
4.41 .10-Z 2.08 3.23
Fe O**.solubility limit
U y
1.3
133
-
1063 ... 1273
Method C
-
60M
Fe u
V 0.7 5.0 10.0 15.0 20.0 25.0 30.0 In solid solution
0.61 3.9 1.1 0.7 0.71 0.63 0.59 3.4
266 237 223 219 220 220 221 221
-
1223 ... 1523
Method A Atmospheric pressure data only. Reference contains data up to 40 k bar pressure for the y phase.
-
65Hl
973 ... 1273
Method C
-
7886
11.52
592
-
2473 ... 3073
Method F
-
45v
1.6 0.13
244 268
-
948 ... 1758
Method B
-
74A
-
-
5.2. IO-l6 6.1 . IO- l6 1.14.10-‘5 1.44.10-15 6.78. IO-” 6.0 . IO- l6 7.9 . lo- l6 1.41 .10-‘5 1.75.10-15 8.39. IO-” -
1273 1289 1322 1333 1425 1273... 1425 1273 1289 1322 1333 1425 1273 ... 1425
Method A
Fe,Ti FeTi
Fe 0...0.026 wt. % ct Y
W
Fe Y
Zll
0...2.9
1
1 2
2
257 -
260
-
-
-
-
-
-
-
-
-
-
-
-
-
73B3
(continued) L
Composition at.% Fe CL
L
6.8.e.9.9 8.5 9.0 9.5 10.0 10.5 11.0 II.5 12.0 12.5 13.0 21.5...22.5 31 ... 32 Ga 3.o.s.7.9
0.48 . ‘. 2.6 0.73 - *. 1.97wt. %
Zn
Temperature range K
Method/Remarks
-
1223 1282 1333 1368 1424 1223.m.1425 513...593 513***595 741 .a. 798
Method A
-
623 .+. 790
DO
Q
d
Dl
D2
IOm4rn*s-l
kJmol-t
m*s-’
m*s-*
m*s-’
226 75 75 64 72 80 79 80 78 74 75 75 78 80 92
5.7 . IO- l4 1.4. 10-13 3.82 . IO- ” 5.81 . lo-‘* 1.37 * lo-‘* -
-
156 55 138
-
-
(continued) 4.25 . IO-’ 3.99 * 10-3 2.97 * 10-3 7.88. 1O-3 1.39. lo-* 5.53.10-3 2.82. IO-’ 1.02. 1O-3 5.81 . 1O-4 6.98. 1O-4 1.26. 1O-3 8.21 . 1O-3 2.04. 1O-4 1.05.10-J I.3 5.3 * 10-4 9.8. lo-*
833.e.913 673 ..a 807
Fig.
Ref.
73B3
Method C Method C Method A
-
7303 7301 77WI
Method B Method A Method A
-
68E 7lH2 67R
Ref. p. 3661
Land&-Biimstein New Series III/26
I
I
8 29 r.k 8 VI
I
I
5.2 Chemical diffusion in homogeneous binary alloys (Tables)
I
I I I I I I I I I I I I I I I I I
G8: l I lItihlc.4
I I I I I I I I I I I I I I I I I
IIIIIIIIIl
Murch, Bruff
I
319
Composition at.% In
Method/Remarks
Fig.
Ref.
m2s-*
Temperature range K
-
388.e.446
Method A
76
76Cl
-
388.e.446
DO
Q
b
D,
D2
low4 m*s-’
kJmol-’
m2s-*
m2s-’
2.9. 1O-3
57
Pb Dp. =
41 x20*.*50
1.1.10-6
-
-
t Q,. = 61 SeeFig. 76. -
2.2. 10-2
102
-
-
-
813.e.871
Method C
-
66L
La In solid solution
Mg
La In solid solution O*..solubility limit
U y
117
233
-
-
-
1123.a.1363
Method C
-
59A
y
118
233
-
-
-
1123...1363
Method C
-
64T
Li 34*** 50
Mg
-
-
SeeFig. 77.
-
-
768...800
Method D
77
84L
Li Li,Sb
Sb -
x 19 **a29 SeeFig. 78.
-
633...900
Method D
78
77W2
Li X0
Si 2.5. 10-s
63.2
-
-
-
1073 ... 1623
Method F
-
6OP2
Li !ZO
W 5.0
174
-
-
-
1365 a.. 1500
Method B Li concentration not given but probably small.
63L
Mg O...l
Ni 0.44
234
-
-
-
1323s.. 1573
Method B
-
57s
Mg
PU 0.01
0.562 1.124 1.686
Mg Mn 0 ... 4
U 0.025
-
-
2.45. IO-’ 1.05.10-2 3.6. 1O-4
119 118 94
6.1 . 10-l’ 2.5. lo-l4 1.3~10-13 -
-
-
1.2.10-1s 3.3 . 10-15
7.5
281
-
-
-
693 748 807 693...807
Method A
-
63C, 65C
-
673 773
Method A
-
63C
-
1376... 1570
l=Mn,2=Ni Method B
-
56s
1073 ... 1323 1173 1223 1273 1323
Method A
79
79Yl
Method A
-
60G
-
65H2
Ni
-
-
See Fig. 79. -
4.62 . IO- l5 10.4.10-‘5 32.4.10-l’ 66.3. IO-”
1.4 . 10-15 4.83. lo-l5 12.2 * 10-15 27.5. IO-”
1 .10-3
147
-
-
-
1103...1463
1 . IO3 1 . IO3 1 .I03
553 573 578
-
-
2073 ... 2436
X0
-
-
-
DoMO= 9.2. 10-z QMo= 549
19.9
-
-
-
5...25 19.7
Mn 8
Ti P
MO WO 50 ~100
Nb
16.2
~100
-
-
-
-
-
-
DoMO= 1.4. 10-l 1 QMo= 571 DoMa= 1.1 . 10-l i QMo= 563 D;, = 4.0 . 10-4 QM,,= 481
l=Mo,2=Nb Method A Values of Do and Q taken from smoothed curves given in reference.
Dib = 1.3 QNb = 586 DR = 1.9 . 10-l QNb = 548 D&, = 1.0 . 10-l QN,, = 582
(continued)
Composition at.% MO 20 40 60 80 20 . . .80 10
Nb
DO
Q
b
D,
4
low4 rn’s-’
kJmol-’
m2sTt
m2s-’
m2s-’
429 413 411 345 399 -
8.75. IO-r6
-
-
-
1.67. lo-l6 SeeFig. 80. SeeFig. 81. SeeFig. 82.
-
-
(continued) 13.5 3.8 2.1 5.2 * 10-2 1.5 -
90 IO...80 x10***90
-
See remarks
x10..*90
MO 0 . . .0.93 0-m.13.5 wt. % 5 15
Ni
MO OS lo... 100 vol. % MO
Pd 61 66 71 75 80 85
3.0 0.853
288 270
-
1.56 0.97
283 278
-
-
-
SeeFig. 83.
5.5 * 10-s 4.0 - 10-s 5.0 * 10-s 2.4. 1O-4 1.6. 1O-3 1.6. 1O-2
188 165 178 201 219 253
-
-
-
-
-
-
-
-
Temperature range K
Method/Remarks
Fig.
Ref.
1673-a-2648
Method A
-
66W
1573
Average of data given. Method A
67P1, 67P2
1253 1373-e. 1773 1473...2173
Method A Method A Method A Curved Arrhenius plots, see reference.
80 81 82
69s 7ov 73B4
1423 ... 1673 1373...1573
Method B Method B
-
1273 ... 1568
Method A
-
57s 63D1, 63D2 74H
2147...2450
Method A
83
73E
1273 ... 1873
1 =Mo,2=Pd Method A
-
722
90 95
0.9 0.14
293 283
-
85 MO
MO MO
MO O...lO solid solution range 0 10 20 30 40
-
-
DL = 1.5. 1O-6 Dgd = 1.2 . 1O-7 QMo= 260 QPd = 193
Pt u P E rl Y
-
8.0. lo-l6 1.63. IO-” 3.59.10-15 6.27. IO-l5 1.05.10-‘4
-
-
1773
Method C
-
77M
Re 0 ... 100
-
See Fig. 84.
-
-
1773
Method A
84
77M
Ta Ta rich MO rich
4.68. IO-’ 4.16. IO-’
251 234
-
2173...2573
Method A
-
701
Ti p CL
1.23. 1O-4 3.42. IO-*
139 119
-
1173 ... 1973 873 ..+ 1073
l=Mo,2=Ti Method B
-
62E
w2.10-2 x2.10-2 z2.10-2 w9.10-2 z 10-2
197 209 218 264 255
1483 ... 1873
Method A Further data for Do and Q are given in reference but the scatter is large.
-
65H2
1173 1773 1623 1373 ... 1673
Method A
85 86 87 -
69F
P
tzlO0
-
11.1
-
X0
-
20...50 30...50 30...50
1.64. 1O-4
0 ... x 40
-
-
-
-
-
D;,=40 QMo= 481
Dii =6.3. 1O-3 QTi = 211
-
Die = 1.0. 1O-2 D$ = 1.8 . 1O-3 QMo= 204 QTi = 161
205
See Fig. 85. See Fig. 86. See Fig. 87. -
D;, = 2.5.10-2 QMo= 197 - -
-
Method B
73s
Composition at.% MO 2 4 6
U Y
8 IO I2 I6 20 24 26 MO
DO
Q
10m4m2s-’
kJmol-’
2.2 0.58 20 I6 28 3.2 9.6. IO-2 3-10-3 4.5.10-4 2.1 . Io-4
IO wt.% 20 wt.% 30 wt.% 40 wt.% 50 wt.% 60 wt.% 70 wt.% 80 wt.% 90 wt.% IO wt.% 20 wt.% 30 wt.% 40 wt.% 50 wt.% 60 wt.% 70 wt.% 80 wt.% 90 wt.%
4.48 2.41 0.64 0.48 0.30 0.17 0.14 8.0. IO-2 5.0.10-2 0.52 0.24 5.6. IO-2 1.1 * 10-3 3.8 . 1O-3 7.5 * 10-3 4.0 * to-3 1.7 * 10-4 4.6. IO-4
3.4. lo-l3 1.4.10-'2 1.6. IO-l2 3.4.10-12 -
1123...1323
Method A
-
2273...2773
Method A
-
71N
1973.e.2673
Method A Polycrystalline data given here. Single crystal data also given in reference.
76KI
m2s-’
m2s-’
m2s-’
199 192 222 230 238 219 191 165 162 142
-
5.2. lo-l4 2.1 . 10-13
491 481 459 458 451 441 438 430 422 448 425 405 394 382 372 386 355 344
-
-
W
Ref.
Method/Remarks
02
-
Fig.
Temperature range K
D,
58Al
1123 1223 1123...1323 1273 1123...1323 1323 1123...1323
MO
Zr O...lO
Mo,Zr Nb
449 233
-
3.3. 10-8 3.0. 10-5
71 163
Pd
Nb
2.2. 10-z
Ta 10 90 x10...90 10 20 25 35 40 45 55 60 65 70 75 90
!O wt. %
-
65H2
-
-
-
1173...1303
Method C
-
75Ml
See Fig. 88. See Fig. 88. See Fig. 88.
-
-
88
71U2
-
1473 1473 1473
Method A
232
-
-
-
1573 ... 1623
Method C
-
71Rl
-
1.58. IO-l7 2.76 .+,-Is
-
1573
Method A
-
67P1, 67P2
-
See Fig. 89. -
-
1573...2073
Method A
2273 ... 2653
Method A
89 -
7ov
-
1673 1773 1873 1973 2073 2173 1673...2173
Method A Values of d and Q extrapolated to 0 and 100 wt.% Nb are given in reference.
-
74W2
Sn
Nb,Sn
Xb
1923...2108 1098... 1718
Method B and C
-
-
;d,Nb P
1.1 . 10-z 1.34.1o-2 1.0. 10-z 9.3. 10-3 1.0. 10-2 1.56. lo-’ 1.26. 1O-2 2.0. 10-z 3.16. IO-’ 4.4. 10-z 5.6. lo-’ 1.24. IO-’
-
-
Ni
NbNi, NbNi Nb
1.6 1 .10-3
343 352 343 347 352 360 364 373 385 394 398 414 293
6.0. lo-l6 1.77.10-15 1.6 . IO-l4 4.3.10-14 7.7.10-14 1.8. IO-l3 -
-
-
-
-
74s
-
(continued)
Composition at.% Nb 40 wt.%
60 wt.%
80 wt. %
Nb
DO
Q
B
Dl
D2
10T4 m2sm1
kJmol-’
m2sS1
m2s-’
7.6. lo-l6 2.3.10-" 2.3. IO-l4 6.1 . IO-l4 1.12 * lo-‘3 2.8. IO-l3 9.4*10-'6 3.1 . 10-15 3.1 . 10-14 8.7. lo-l4 1.63 . IO- l3 4.2. IO-l3
-
313
-
1 -
322
l.18~IO-15 4.1*10-'5 4.4.10-14 I.25 -10-13 2.4. IO-l3 6.2.10-13 -
Ta (continued) -
308
-
-
-
1 -
-
-
-
Method/Remarks
m2s-’
Temperature range K
-
1673 1773 1873 1973 2073 2173 1673...2173 1673 1773 1873 1973 2073 2173 1673...2173 1673 1773 1873 1973 2073 2173 1673...2173
Method A
Ti
Ref.
74W2
74W2
1 =Nb,2=Ti
D;, = X0
2.5 -10-j
293
-
20 40 60 80
2.5.10-3 3.2. lo-’ 3.8. lo-’ 3.8. 1O-3
263 239 209 184
-
Xl00
Fig.
3.8. lo-’
167
-
3.8. IO-’ QNb = 164 -
-
-
Dsf = 5.0. IO-' Qr,= 259
1273.a.1863
Method A Values here taken from smoothed plots given in reference.
-
65H2
DoNb =
81.1 -
-
3.48 . 10-15 3.9.10-14
-
See Fig. See Fig. See Fig. See Fig.
~0~~~100
-
See Fig. 92.
IO...90
See Fig. 93. -
10 90
-
lo...60 IO..*70 40..*90 x10...90
Nb
U(Y) 2 12 18 22 28 38 46 54 62 68 74 78 82 93
2.8 . IO’ 2.3 . IO’ 9.6. lo6 9.1 . 10-z 0.113 0.149 6.4. lo-’ 0.45 0.84 1.94 0.82 1.16 1.19 * 10-4 1.63. 1O-4
623 604 586 308 305 305 285 293 287 292 253 252 140 126
97
2.31 . 1O-4
125
-
85. 90. 87. 91.
2.2. 10-7 QN,, = 177 -
-!
Dii = 1.7. IO-’
( QTi = 164
D;, = 7.1 . 10-7 Qm= 39
0; = 3.82. lo-’ Qu = 30
1573
Method A
1173 1273 1623 1373 ... 1573
Method A
Method A
85 90 87 91
1273 ... 1473
Method B
92
71P
1273 ... 1673
Method A
93
75u
-
63P
1773 ... 1923
1673 ... 1873 1573 ... 1423 ... 1423 ... 1348 ...
1773 1673 1663 1573
1223 ... 1448 1165s.. 1398 966... 1298
l=Nb,2=U Method A Further data are available in the reference.
67P1, 67P2 69F
7ov
Composition at.% Nh
DO
Q
d
D,
D2
10v4 m’s-’
kJmol-’
m2s-’
m2sS1
m2s-’
--
V
X0
1.6. IO-*
410
20 40 60
1.95 * 10-2 2.3. 1O-2 2.8. IO-’
343 293 268
80
3.3 * 10-2
264
-
-
85
DE, =
Temperature range K
Method/Remarks
Fig.
Ref.
1 =Nb,2=V
D;= 2.9. 1O-4 ( Qv = 405 -
1678.a.2023
Method A Values have been taken from smoothed plots given in references.
65R, 65H2
67P1, 67P2
D;= I
4.9 * 10-6 QNb = 278
4.2 - IO+ QV = 253
D;= 2.6. 10-j QV = 247
DE, = 100
-
1573
Method A
10 90
1.4.10-15 2.3. IO-l4
xlO***90
See Fig. 94.
-
-
1573 a** 1773
Method A
94
7ov
See Fig. 95.
-
-
1473
Method A
95
7lU2
1.39 * 10-1s
-
-
1573
Method A
3.74 . lo- l9
-
-
See Fig. 96. -
-
-
1573e.02073
Method A
-
-
2273 ... 2673
Method A
-
o*.-90 Nb
8.6. 10-6 QNb = 275 -
W 10
-
-
90 xlo*~*90
-
-
10 20 30 40 50 60 70 80 90
81.45 22.2 1.97 1.4. 10-2 7.4. 10-J 3.0. to-3 1.8. IO-’ 1.0 * 10-3 6.0. lO-4
440 419 376 280 272 255 247 236 228
wt.% wt.% wt.% wt.% wt.% wt.% wt.% wt.% wt.%
-
---
67P1, 67P2 96 -
7ov 71N
Nb X0
197
-
4.0. 10-z
209
-
23
-
-
40 60 80
0.1 0.3 2.0
255 301 347
10.0 10 90 ~10~~~90 x5...85
Ni
-
20
-
30
40
50
-
-
1.74.10-15 2.5. lo-l4
-
-
10
-
-
-
-
See Fig. 97. 0.68 .10-15 1.30.10-‘5 1.79.10-15 1.86.10-14 1.03~10-15 2.01 . 10-15 3.37.10-15 3.0. 10-14 1.52. IO-l5 3.54.10-15 7.39.10-15 7.04 . lo- l4 1.72. IO-l5 5.37.10-15 1.17.10-14 9.82. lo--l4 1.97.10-15 6.61 * 10-15 1.61 . IO-l4 1.58. IO-l3
-
1718.+.1963
Method A
1573
Method A
1373 ... 1573
Method A
97
7ov
1173...1973
Method A
98
73R
1132 1223 1292 1423 1132 1223 1292 1423 1132 1223 1292 1423 1132 1223 1292 1423 1132 1223 1292 1423
Method A
-
66B
65H2
D;, = 3.8 ’ 1O-7 Qzr = 185 -
389
See Fig. 98 b. See Fig. 98a.
Pd
-
l=Nb,2=Zr
DO Nb = 1.1 . 10-6 QNb = 191
-
D;, = 2.2. 10-4 Qzr = 415 -
-
67P1, 67P2
(continued)
Composition at.% Ni
Pd
60
70
80
90
O...lOO Ni o-.- 14.9
Ni
Q
b
Dl
D2
low4 m*s-*
kJmol-’
m2s-’
m2s-’
-
1.40 * 10-15 5.42 . IO- I5 1.56 1IO-l4 1.31 * 10-13 0.84. IO-l5 3.06 . IO- l5 1.13.10-‘5 1.04.10-‘3 0.56 . IO- l5 1.90.10-‘s 5.58 . IO-” 5.87 . IO- l4 o.s.lo-‘s 1.25.10-1s 2.30. IO- l5 3.50. lo-l4 SeeFig. 99.
68 -
180 -
SeeFig. 100.
1.5
258
-
-
-
4.5.10-14 4.8. IO-l4 5.0. lo-‘4 5.5 * lo-‘4 5.8. IO-l4 6.0. lo-l4 6.5 3IO- l4 7.0.10-‘4
(continued) -
Pt
0.e. loo Ni
DO
Si o*** < 1 Sll 0
1 2 3 4 5 6 7
Method/Remarks
m2sv1
Temperature range K
-
-
1132 1223 1292 1423 1132 1223 1292 1423 1132 1223 1292 1423 1132 1223 1292 1423 1385
Method A
Method A
-
-
1316... 1674 1223 ... 1573
-
1393 .-. 1573 1373
Fig.
Ref.
66B
99
69B4
Method A Method A
100
44K 67B2
Method B
-
57s
-
8211
1 =Ni,2=Sn Method A Data determined from figure in reference. Some intrinsic data also given at 1373 K.
-
1 2 3 4 5 6 7 0.8 1.5 2.2 4.5
-
259 257 255 251 253 251 250 -
-
1.9.10-14 2.2.10-14 1.8 . lo- l4 3.0 . IO- l4
2.6 . lo- 3 2.1 0.1 1.7. 10-5 0.9 . 10-z
231 307 250 134 334
-
-
2.5 2.3 2.3 1.9 2.5 2.4 2.3
Method A
-
841
1423 ... 1573
Method C
-
77P
-
823 ... 1073
Method C
-
7884
-
1377... 1555
Method B
56s
773 **. 1173
Method C Phase growth data for TiN, and Ti,Ni given in reference. Method C
68H4
-
1223 ... 1423
;4.10-14 3.7. 10-14 4.2 . lo-l4 6.0. IO-l4
1373
-
-
-
1223 ... 1473
Ni Ta,Ni TaNi TaNi, TaNi, TaNi,
Ta
Ni
Th ThNi
1.6. IO-’
74
Ti 0 . . .0.9
0.68
61
-
-
5.48. IO-’
103
-
-
141 142 137 138
-
-
-
193
-
-
-
1123 ... 1273
Method C
180 222 130
-
-
-
803 ... 1003 803 ... 1003 803 ... 1003
Method C Do is multiplied by 6,, where 6, is the range of solubility in the phase.
Ni
TiNi
6 50 51 52
P TiNi
Ni 0 . . . solubility limit
UY U,Ni U,Ni, mi5
2.5 . lo2
s:e marks
8.5 . IO2 7.4.10-3
-
1073 ... 1213 923 ... 1213
-
74B4
Composition at.% Ni
V 0.~. 14.8 wt. % 5*..95 25 33 60 65 In solid solution
Ni
w 0.v. 1.5 O.-e14.6 wt. % 1 2 3 4 5 6 7 8 9 10 11 12
Method/Remarks
Fig.
Ref.
m2s-’
Temperature range K
-
-
1273...1573
Method B
-
1083 ... 1448 1343 ... 1448 1083 ... 1293 1223... 1448 1083...1163 1253 ..- 1448 1083 ... 1223 1253 ... 1448 1083 ... 1223 773 ... 1273
Method A Method A
101
-
-
63D1, 63D2 78Kl 78K2
Method C Limited data on d for other VfNi phases given in reference.
-
7836
-
1426-v. 1562 1273 ... 1573
Method B Method B
-
-
1273-e. 1589
Method A
-
56s 63D1, 63D2 69Wl
DO
Q
B
D,
D2
10v4 m2s-r
kJmol-’
m2s-’
m2s-’
0.287
248
-
36 4.2. 1O-6 1.2 * 10-3 2.0 - 10-s 0.2 7.0 * 10-4 6.8 * 10-2 6.0. 1O-4 1.6. 1O-4
301 87 165 117 234 167 227 172 132
SeeFig. 101. -
11.1 0.862
322 295
-
2.24 2.16 2.11 2.07 2.04 2.01 1.98 1.95 1.94 1.92 1.90 1.89
303 303 304 304 304 305 305 306 306 306 307 307
-
-
Ni
Zll Is...95
1.05. IO3
180 .exp(-14.24X,,) (XNi: mole fraction) 15 255 20 255 6 75 u 79 :6-.90(y) 243 P 55 . ..6O(B) 6 7.1 . 10-z 85 1.2. 10-l 91 Y’,,, 3.0. 10-z 97 Y l.e.40 Pb
Sn
1.82.10-” 2.63. 10-l’ 1.35.10-14 2.29.10-14 1.0. 10-13 3.31 . 10-15 4.68. IO-l5 2.45 . lo- I4 4.16. lo-l4 1.86. IO-l3
I SeeFig. 102a. SeeFig. 102b. SeeFig. 102~. SeeFig. 103.
-
1 -
In solid solution (PI u solid 7.0 solution
99 101
3.12. lo-l5 6.9. IO-l5 1.96. IO-l4
O...lO
-
SeeFig. 104.
-
-
-
-
-
-
882... 1281
Method A
-
69A
1169 1203 1266 1293 1373 1169... 1373 1169 1203 1266 1293 1373 1169...1373 700..*758 1203 790... 1073 883 1173...1273 1203 483...873
Method A
-
74B5
Method A and C Do values not given.
77B3 102a
Method C
102c 7882
1073 -.. 1323
Method A
103
518...558 518 538 558 443...454
Method B Do not reported.
32s
Method A B increases with concentration. Equation for Do(C) given in reference. Method A 104
60C
523
102b
79Y2
87M2
DO
Q
B
D,
D2
10s4 m’s-’
kJmol-’
m2s-’
m2sW1
m2s-’
-
87 -
2.7. IO-” 1.5. to-14 3.13.10-‘4
-
1.26 alo-’ 1.6.10-* 3.6. lO-4 1.6. 1O-6 6.4. 1O-4
132 45 129 84 145
-
-
-
-
Temperature range K
Method/Remarks
Fig.
Ref.
-
493.a.558 493
Method B Do not reported.
-
32s
-
-
973 ... 1273 973...1173
Method A Several intrinsic diffusion coefficients given in reference.
-
73L
SeeFig. 105.
-
-
1473
Method A
105
7lU2
-
SeeFig. 106.
-
-
1773
Method A
106
77M
9.4. 10-4 2.3. 1O-3
124 128
-
1173.0.1373
Method B
-
71L
Pu U 0.35 wt.%
0.17.10-7
57
-
683.e.813
Method A
-
1.75wt.% 3.50wt.% 5.25wt.% 7.0 wt.% 8.75wt.% 10.50wt.% 12.25wt.% 14.0wt.% 15.75wt.% 17.15wt.%
0.14. IO-’ 0.15.10-7 0.18. IO-’ 0.28 . IO-’ 0.44.10-7 0.88.10-7 1.18. IO-’ 2.0. IO-’ 2.57. IO-’ 1.83. lo-’
56 57 59 64 68 75 79 84 86 84
-
65D, 65C, 67D
Composition at.% Pb
TI
In solid solution (Iv Pd
Ti B Y 6 E rl
Pd 2..-98
V
Pt
Re 0-a. loo
Pll
2 15
Ti B
-
-
538 558
Ref. p. 3661
I I I I I
I
I
I
I
I
Murch, Bruff
I
5.2 Chemical diffusion in homogeneous binary alloys (Tables)
I I I I I I I
I I I I I I I
I I I I I I I
Land&-Biimstein New Series III/26
335
Composition at.% Rh 3 6o
Method/Remarks
Fig.
Ref.
-
1573+..2073
Method A
-
64R
-
-
1123...1323
Method C
-
60M
-
-
-
1073 *** 1313
Method C
-
64T
64 125 -
-
9.18 . IO- *’
2.65 - 10-l’
1277... 1523 1363-v. 1523 1523
1 =Sm,2=Ti Method A Between 1.0 and 8.0 at.% Sn, d increases linearly.
-
60G
3.0. 10-4
92
-
-
873...1123
Method B
-
53R
6.9. 1O-4
153
-
-
1373 ... 1573
2.38
197
-
-
1073 ... 1273
Method C
-
59A, 64T
8.62. IO-’
202
SeeFig. 85. SeeFig. 90. -
-
1173 1273 1373 ... 1673
Method A
85 90 -
69F
Q
I3
Dl
4
10s4 m’s-’
kJmol-’
m’s-’
m2s-’
m*s-l
1.3. 10-6 1.5 * to-6 2.5. 3.1 . 10-6
243 175 182 174
-
-
20
188
-
4.08 . IO’
229
8.4. IO-’ 2.7. 1O-4 -
W
CL
Zi( 1) E Si Gzo...
Temperature range K
DO
U y
solubility limit Sm U 0 .. . Y solubility limit Sn
1.0 8.0 2.0
Ti B
Zr Sn In solid CL solution 0...3.9 p
Sr U y zo*.. solubility limit Ta IO*** 35 IO.-* 55
Ti 0 ... z30
Method B
73s
Ta
W 10 wt.% 20 wt. % 30 wt. % 40 wt. % 50 wt. % 60 wt. % 70 wt. % 80 wt. % 90 wt. %
10 20...80 90 30 Ti 10 20 30 40 50 60 70 80 90 95 16.5 18.0
U Y
Ti
V 2.0 3.5 Solid solution range o... 10
7.0. 10-4 1.0. 10-4 1.22.10-5 6.08.10-6 3.34.10-6 1.66.10-6 1.5. 10-6 1.23. lO-‘j 2.2. 10-7 1.0 1.0 1.0
309 302 262 254 245 231 232 229 198 544 553 502
-
-
1.1 . 10-Z 1.4. 10-3 1.6. 1O-3 4.0. 10-3 9.5. 10-3 2.6. 1O-3 2.6. 1O-3 2.2. 10-3 1.1 . 10-3 4.6. 1O-4 -
153 138 146 161 176 165 165 157 142 126 -
6.0. 1O-3 -
166
1.25. IO-’
173
-
2273 . . .2673
1 = Ta, 2 = W Method A
-
71N
1573...2373
Method A
-
85R
-
6OAl
-
-
D;a = 1.8. 1O-4 QTa = 554
D;= 1.7. 10-S Q, = 511 1223 ... 1348
-
-
-
-
-
-
-
-
-
5.8. IO-l3 1.2.10-13 2.9. IO-l3 4.1 . 10-13
2.2.10-12 4.7. lo-‘3 9.5 . lo- l3 1.6. lo-l2
1348 1223 1273 1323
-
-
L9l . 10-19 4.7. lo-l9 -
1.31 .10-g -
14.9.10-g -
1173...1521 1523 873 973 1173... 1573
1 = Ti, 2 = U Method B Q values (but not Do values) for intrinsic diffusion coefficients are given in reference.
1 = Ti, 2 = V Method A Method B
60G -
62E (continued)
Composition at.%
DO
Q
IO 20 30 40 50 60 70 80 90
V (continued) 15***90 10**~90 so***90 50***90 8.3. lO-4 1.5. 10-3 4.4. 10-J 1.3. 10-2 2.4. lO-2 1.1 . 10-2 8.1 . lO-2 4.1 * 10-4 1.6. lO-4 -
68
11.1
-
20.2 36.0 38.0 55.1 76.4 88.0
-
20 . . .80
Fig.
Ref.
-
1173 1273 1623 1773 923e.a1083
Method A
85 90 87 86
69F
1.23. IO-’ QTi = 158
-
923 ... 1083
-
1273...1673
Method A
-
-
1623
Method A Extensive intrinsic diffusion data given in this reference and also in [78C] for 1173Kto 1773K.
1177.e. 1476
-
1173.e.1573
m2s-’
m2s-’
m2s-’
198 199 204 207 203 187 153 140 124
SeeFig. 85. SeeFig. 90. SeeFig. 87. SeeFig. 86. -
-
-
-
SeeFig. 107. -
lo**.90
Method/Remarks
4
10v4 m2sw1 kJmol-’ Ti
Temperature range K
Dl
-
3.1 .10-‘2 2.82. IO-l2 1.64. lo-l2 1.06. lo-l2 4.61 . IO-l3 1.54 * 10-13 1.64. IO-l4 SeeFig. 108. SeeFig. 109. -
-
74Bl
Method A Data should not be extrapolated outside temperature range.
923.e.1323
Dti =
-
107 -
75u
Method A
108
76K2
Method A Data should not be extrapolated outside temperature range.
109
77Bl
76C2
Ti cf. P 10 25
Zr O...lO o... 10
-
3.2 . lo- I4 -
5.1 . IO- l4 -
1 = Ti, 2 = Zr 873 .-. 1073 Method B 1173.*.1573 1103...1323 Method A Two regions in 1103...1323 923...1103 Arrhenius plots 1103 1.. 1323 Two regions in 923...1103 Arrhenius plots 1 Two regions in 1103 ... 1323 923...1103 Arrhenius plots 1 1103...1323 Two regions in 923...1103 Arrhenius plots 1 1103...1323 Two regions in 923...1103 Arrhenius plots 1103...1323 1073 1173.e.1573 Method A
389
-
-
-
2243 . . .3003
Method F
68Sl
134 120 110 115 124 124 124 144 172 197 -
Method A
57A
1223 ... 1313
Method A
1 3 5 7 9 11 13
1.82. 1O-4 1.78. 1O-4 2.95. 1O-4 8.72. 1O-4 1.07.10-3 1.0. 10-3 9.35.10-4
119 123 131 146 149 149 149
-
See Fig. 111. -
1223 ... 1348
-
-
5 ... 90
9.5 * 10-4 1.3. 10-4 3.5. 10-s 4.0. 10-s 8.0. lo-’ 6.3. lo-’ 5.5. 10-s 3.2. 1O-4 7.8. 1O-3 8.7. 1O-2 -
-
1223 ... 1723
Method A
40 50 65 80 90 50.5 20...80 U zlo-3
W
U Y
Zr 10 20 30 40 50 60 70 80 90 95
1.6. 10-l’ 1.8. IO-’ 1.4. 10-Z 3.3 . 10-3 5.10-7 2.7 . 1O-3 1.2. IO+ 2.4 . 1O-3 1.7.10-6 1.6 . 1O-3 2.0.10-6 1.5 . 10-3 2.2.10-6 1.3. 10-3 -
49 168 165 147 66 143 72 141 74 137 75 135 75 132 See Fig. 110.
1.8. IO-’
-
-
-
-
62E
-
74B2
110
76Bl
111 -
60A2 67P3
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
340
[Ref. p. 366
Figures for 5
ml/s 4 3 I .10-1: m’/s 2
3
I
la
2
I 1
IQ 1
0 0 Ag
20
60 Au -
Fig. 1. Ag-Au. 53Hl]. 10-lI1 mv!j
40
0
80 at% 100 Au
Interdiffusion coefficient at 1173 K [52S,
20
80 at% 100 60 Ag AgInterdiffusion coefficient at 1213 K [54B].
Au Fig. 2. Ag-Au.
40
I r
AS-Cd 053K
10-l
. b.
‘.
,0-l';
I7
;OOO K
:. l . .
0
,~t 10-l
m?s
0 n
+
7 900K
,0-K
v v 10-l
0
I IQ
v
10-l’
,o-l!
10’
25of% 30
0 Ag
CdFig. 3. Ag-Cd. Interdiffusion coeffkicnt from 900... 1053 K [59Ml]. Different symbols denote different starting
5
10
15 Cd-
20
25 at% 30
Fig. 4. Ag-Cd. Interdiffusion coefficient at 883 and 933 K [73U2].
couples.
Murch, Bruff
Land&-BBmstein New Series III,/26
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
Ref. p. 3661
Fig. 6. Ag-Cu.
Interdiffusion coefficient at 1023 K [76U].
-y---i.-+_ ‘\.,. \ ‘1. ----
20 Xl-'3 m% 0 CU
10 8 6
2
92
4 Ag -
probe X-roy 96 at% 100 Ag
I 14 4 2
a
0 Ag
1
2
3
4
5
at%
//
7
883 K I
0
Cd-
Zn Fig. 7. Ag - Zn. Interdiffusion coefficient from 673 .883 K [55Hl]. 10-12 m2/s
b 4
Cd-
10 15 20 at% 25 5 Cdc A; Fig. 5. Ag-Cd. Interdiffusion coefficient at 1179.5 K (a), 1087 K (b) and 1073 K (c) [78B]. Different symbols denote different samples. Lmdolt-Biirnstein New Series III/26
25 at% 30 10 15 20 0 5 ZnAg Fig. 8. Ag - Zn. Interdiffusion coefficient from 823 . 1023 K [73U2].
Murch, Bruff
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
342
[Ref. p. 366
120 kJ Et 100 I 5
30
32
34
a 10-l’-
lo-’ 0* e,-Zn 6~ y-Zn I 76
38 wt%
40
I
I
m2’s Ag-Zn (~1 I
60 73
36
Zn -
79
82
85 at%
I b
8
ZnFig. 9. Ag -Zn (E).Activation energy Q and pre-exponential Do for interdiffusion [78Sl].
b
I
‘tr ia
1
Ag-Znia)
160
j
I
I
I
Ag-Zn(c)
lo-' 12
IIo-( nII/S
D
Zn 10" I1 m2/!
I 14 r5 I %2
120 0 4
5
10 Zn -
15
ot%
IICT6 20
10-l 111; C
Fig. 11. Ag -Zn (a). Activation energy Q and pre-exponential Do for interdiffusion [8682]. 10‘; m2/
10-l
0 ln -
Fig. 10. Ag-Zn. Interdiffusion coefficient at 673 K in Ag -Zn (fi) (a), in Ag -Zn (r) (b) and in Ag-Zn (E) (c) alloys [81w].
AI-CU
0 cu
5
10 Al-
15 ot%
20
4 Fig. 12. AI-CL Activation energy Q and pre-exponential Do for interdiffusion [75P2].
Murch, Bruff
Landolt-BBmsfein New series III/26
Ref. p. 3661
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
loml/
lo4;
lo-7 T m2/1 j
Li -
v
53
at%
55
Al Li,+s
10'
-T-r
t !Q
A 1=873 K 833 778 733 688K
10-1 10.'
I 1Q
10-g 10“
10“
10" -0.12
-0.06
0
Al-
Fig. 13. Al-Fe. 1373 K [70Nl].
0.06
0.12
0.18
0
S-
Interdiffusion coefficient from 1073..’
Fig. 14. AI-Li.
Interdiffusion coefficient from 688 ... 873 K
[79W
m2/s
1 AI-Ni
I.
I
I
I
lo-l4
a
I 10-15 10-16
o S-phasein -phasein S-Nicouples~ S-Nicouple
0
01
0.4 wt%
0.5
jig. 15. Al-Mn. Interdiffusion coefficient from 873 ... 123K [43B]. im’day-’ = 1.16~10-5mZs-‘.
Fig. 16. Al -Ni. Interdiffusion coefficient vs. reciprocal temperature [67Jl.
Murch, Bruff
0.8
1.2
J 1.4W3 K' 1.6
Mn -
LandolGB6mstein New Series III/26
0.3
10-201 0.6
1.0 l/T-
Al
0.2
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
[Ref. p. 366
For Fig. 17 see next page 10"
10-l
rn'h
mk
Al-ii
(6)
1373K
I
n
VI-'
10-l
10"
10-l
I '.a
I 'Q 10'
10'
10-l
10'
10-l 10-l rnV
lo-'
lo-'
I g10-'
I ,olo-
\ \ K, .
d !d 10-l
10'
10‘
C
lo-'
40
50
45
55 at%
I
40 Al -
Al -
Fig. 18. AI-Ni (6). Interdiffusion coefficient at 1273 and 1373 K(a), at 1223and 1423 K(b) and at 1323 K (c). Fig. (d) shows interdiffusion coefficient and intrinsic diffusion coeffL cients at 1373 K [ 78851.Different symbols indicate different starting
couples.
Murch, Bruff
LandoM36mstein New Series III/26
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
Ref. p. 3661
10-l’ d/S
,o-li
I ,Q1o-‘:
10-l”
,o-l~
36
39
Fig. 17. Al-Ni
42
45 Al-
48
0
51 at% 54
4
(6). Activation energy Q for interdiffusion
[7835].
12
8
Ni
16 at%
20
Al -
Fie. 19. Al-Ni. Interdiffusion coefficient from 1323... 1573 K [8OY2]. 10-1'2
d/s 1130K \
1o-l3
I
1Al - Si
day
1aI 1o-l4
6
4 laI
lo-‘5
2’ ---
0.1
783 743K
-
0
0 Al
F
0.2
0.3
0.4 wt % 0.5
Si -
Fig. 20. Al- Si. Interdiffusion coefficient from 743 ... 853 K [43B]. Im’day-’ = 1.16~10-5mZs-‘. Land&-Biimstein New Series III/26
10-16 0 cu
20
60
40 Au -
at%
1 Au
Fig. 21. Au- Cu. Interdiffusion coefficient from 1006. . . 1130K [69B4].
Murch, Bruff
5 Chemical diffusion in inhomogeneousbinary alloys (Figures)
346
[Ref. p. 366
m2
Au-
,0-l'!
10 10‘” 10-l’
I b 1123
lo-“B
1098 lo-‘9
10
10-20
1048
10-2’ lo-” 10-233
0
cu Fig. 22. AU-CL 1023 K [71P].
lo-” m2/r
,o-l:
20
10 40 ot% ! 30 80 wt% 100 10 20 FeAu Au Au Fig. 23. Au-Fe. Interdiffusion coefficient from 973 ... Interdiffusion coeffkient from 323.‘. 1273 K [831]. 60
40
yT--r
f &O-l’
,o-l!
lo-” 0 Au
20
40
60 Ni -
80 ot% 100 Ni
Fig. 24. Au-Ni. Interdiffusion coefticicnt at 1198 K [57R]. Different symbols denote diffcient starting couples.
0.4 Au Fig. 25. Au-Sn. 1129 K [72H2].
Murch, Bruff
1.2
0.8
1.6 ot% 2.0
SnInterdiffusion coefficient at 1090 and
LandoMi6mstein New Series III,/26
341
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
Ref. p. 3661
,igL!I!EEU -18
-12
-15
-9
-6
-3
0 1o-23
Fig. 26. Bi - Li. Interdiffusion coeffkient at 653 K [77W2]. 2.5 40-e m2/s 2.0
0.10 0
cu
0.15
Fig. 27. Cd-Cu. 853 K [38R].
. 0 34
802K I 38 36
m2/s
0.45 at%
0.60
Interdiffusion coefficient from 773 ...
10-13
44 at% 48 42 Li Fig. 28. Cd-Li. Interdiffusion coefficient at 774 and 802 K [84L]. 8 .10-‘5
0.30 Cd-
40
I
ml/s 6
44 2
Co-Ni lo-l4
I1 8 la 66 la 4
240130
2
10-1'5 8
I
1001
I
0 20 40 60 80 at% 100 Ni Ni co Fig. 30. Co -Ni. Interdiffusion coefficient from 1428..’ 1673 K [53Hl]. Landolt-BBmstein New Series III/26
4wl6~ n
I
I
I
80 at% lO[ CO Fig. 29. Co-Fe. Interdiffusion coefficient from 1409.. 1629 K [69B3, 69B4].
Murch, Bruff
Fe
20
40
co-
60
5 Chemical diffusion in inhomogeneousbinary alloys (Figures)
348 7
A!;:
I
2xl-'3 mvs
1578K 0,
Co-Ni
[Ref. p. 366
I
Co-Ni
1529K
10-l’ 8 6
lo-‘& 6 6
1 0 0 20 60 80 _~ 01% 100 Ni co Ni Fig. 31. Co-Ni. InterdiRusion coeflkient from 1423... 1578 K [6782]. 10-l’” m%
l:-ls5” n
m-l NiNi Fig. 32. Co-Ni. Interdiffusion coefficient from 1409... 1629 K [6783,6984]. 7n
LO
co
6 I
lo-12 ‘S m21
4
I
Co- Pd
14 2
lo10-15 0 20 LO 60 80 ato/0 100 co Ni NI Fig. 33. Co-Ni. Interdiffusion coeflicient at 1373 K (73H]. 10-12 m2/s
13
I4 _
lo-'
I I b
Co-Ni I
lo-
15 _
lo- 16 _ !C
10-l‘
.I7
10“
0
co
Fig. 35. Co-Pd. 1466 K [721]. 10-15 0 co
20
LO Ni -
60
80 ot% 11 4 Fig. 34. Co-Ni. 1673 K (73UlJ.
Murch, Bruff
20
40
60 t PdInterdiffusion coefficient from 1153...
Interdiffusion coeffkient from 1373...
Land&-BBmslein New Series III/26
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
Ref. p. 3661
Co-'Pt
I
I
I
I
2.0 40-4 mvi
290 kJ ii
1.5
280
-21.5
270 I o
I 1.0 =& I -22.5 a -23.0 -c
a5
-23.5
0 0 Ni
10
20
250 40 ot% 50
30 Cr -
Fig. 37. Cr. -Ni. Activation energy Q and pre-exponential Do for interdiffusion in Cr-Ni alloys (Ni base) [67U].
-24.5 -25.0 0 co
260
10-13 mz/s 20
40
60
80 at%
Pi -
100 Pt
Fig. 36. Co-Pt. Interdiffusion coefficient from 1398... 1573K[67B2].D”incm2s-‘.
IO-14
I a
10-1'5
lo-l6 0 Fe
2
4
6 cu -
96
98
100 cu
Fig. 39. Cu-Fe (E and y). Interdiffusion coefficient from 1173...1323 K[71K]. z-10-'3 m2/s IO-13
0
5
10
15
20 at% 25
8
Ni -
6
Fig. 38. Cr-Ni. Activation energy Q and pre-exponential Do for interdiffusion in Cr-Ni alloys (Cr base) [67U].
4
Cr
I
2
Ia I;-'" 6 4
2
Fig. 40. Cu-Ni. 1322 K [52T]. Landolt-Biirnstein New Series III/26
Interdiffusion coefficient from 1196...
,
10-15 70
Murch, Bruff
75
80
85 cu-
90
95 IIt% 100 cu
[Ref. p. 366
5 Chemical diffusion in inhomogeneousbinary alloys (Figures)
350 10-l3m*1s
10-1'2 m*fs
10’lb _
lo-l3
I
I Q
---
10-’I5
(1
Cu-Ni
Hall method
lo-"
I 1-a
10-“60
40
80 at% 100 Ni Fig. 41. Cu-Ni. Interdiffusion coeffkient and intrinsic difhsion coefficients at 1273 K [67L3]. 20
CU
60
10-l'
NI-
lo-'
10-l
20
0 Ni
i&f
0.20
.10-‘4
Cu-Ni
P
4
10-l m2/s
60 cu -
Fin. 42. Cu-Ni. 1339 K [69B2].
8
40
Interdiffusion coefficient from 983...
T
cu-$i
m*/s
80 ot% 100 cu
0.16 10-13
I lo-l4 Q
d
0
20
Ni
Fig. 43. Cu-Ni. 1193 K [71M2].
40
60 cu -
80 ot% 100 cu
10-v
,
lo-"
,
Interdiffusion coefficient at 1273 K and
Fig. 44. Cu-Ni. Interdiffusion coeffkicnt and intrinsic dif- ä fusion coefficients at 1273 K (72H1, 82121.
Murch, Bruff
0 Ni
LL 40
cu-
80 at%
100
cu
Landolt-B6msfein New Series III,/26
351
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
Ref. p. 3661
1O-12
I
m2’s Cu- Pd
10-12 10-'2 m%
l33(K cl326 "a, e dl241 -. -
2
10-1'5 0 Pd
Fig. 45. Cu-Pd. 1311 K [52T].
80 ai% II
Fie. 46. Cu-Pd. Interdiffusion coefficient from 1204... 13?4 K [69B3,69B4].
Interdiffusion coefficient from 1151 ..
, o-l:
16
m2/s
I
.10-'4
m2/s CU- Si I 12
‘aIIYl
’
1023K
41
\
12 /
m2/s 8
0 3 .lly4
40
ai%
60 Pd -
II f
.10-'4
I --
,A
mVsI
I
I
I
0 cu
2
4
6 SI -
Fig. 47. Cu -Pd. Interdiffusion coefficient at 1173K [74T2]. 1O-10 m2/s
10-l' 7.
I
8
10 at% 12
Fig. 48. Cu- Si. Interdiffusion coefficient from 973 ... 1075 K [38R].
. 0
c 0" 10-12 3 el
lo-l3
10-14. 11.5
:
12.0
13.5
12.5 l/T -
Land&BBmstein New Series III/26
4 Fig. 49. Cu-Sn (6). Intrinsic diffusion coefficients in alloys with sz37 wt._._% Sn from 701 ... 845 K [64S]. Different symbols denote different starting couples.
14.5
Murch, Bruff
5 Chemical diffusion in inhomogeneousbinary alloys (Figures)
352 10”ImVs
[Ref. p. 366
I
Cu-Sri(y)
lo-‘3, 10-l lo-! mV
I
m2kcu: n
2a I lo-l4
t CYp” 4”
\
, \
10-l1 I 25
28
31
34
37 wt% 40
Sn Fig. 50. Cu-Sn (r). Interdiffusion coeffkient (a) and intrinsic diffusion coeflicient (b) at 979 K [64S]. Different symbols denote different runs.
10-151 14
17 l/l-
18
19 *lo-’ 1 i
Fig. 51. Cu,Sn. Interdiffusion coefficient vs. reciprocal tern perature [7OF].
10“ m’/l 6 4
5 .,o-1 2
m2A;i
4
1
I j
1 b;-$
I j
I ;rEi(K
15
16
I
1
1
10.li
13
1L
0 0 CU
17 al% 18
Sn?g. 52. Cu-Sn (B and v). Interdiffusion coefficient from 174...993 K (SOYl].
Fig. 53. Cu-Zn [54B].
Murch, Bruff
5
10
15 20 25 at % ln (a). Interdiffusion coefficient at 1163 K
Landolt-Kmstein New Series 111126
Ref. p. 3661
353
5 Chemical diffusion in inhomogeneous binary alloys (Figures) 2*10-1’ d/s IO-11 8
1 I
I
lllS3K
I
IDU I
64
b 2
lo-‘*
58
55
61
a
64
67 at% 70
90
95 at% 100 Zn
Zn-
12.5
I
=I
10.0 15
1o-~3 b
75
i
I
I 80
85 Zn-
I
Fig. 55. Cu - Zn. Interdiffusion coefkient in Cu-Zn (r) (a) and Cu-Zn (E) (b) alloys at 648 K [69u]. Different symbols refer to different starting couples.
I 20
//
Q
I
I
20
at%
15 IO 5 0 0
cu
10
30
43
49
46
52 at% 55
Zn-
Fig. 54. Cu - Zn. Interdiffusion coefficient and intrinsic diffusion coefficient at 1053 K (a), 1128 K (b) and 1188 K (c) [55H2]. Solid lines are from smoothed Arrhenius plots. Land&-Biirnstein New Series III/26
40
Zn-
Fig. 56. Cu-Zn (S). Interdiffusion coefficient at 877 K [71Ul]. Different symbols denote different starting couples.
Murch, Bruff
[Ref. p. 366
5 Chemical diffusion in inhomogeneousbinary alloys (Figures) 10” m'l
lo10’
-12
t 10 6
10’
-2 c!?
I b
-13
10 -
10‘ 10-14 -
O01, l
10’
10‘
DC”
-15
10 1.0
1.2
10‘-11 m21s
I
1.4 1.6 1.8 .lO”K-’ 2.0 l/lFig. 58. Cu-Zn (b and p’). Intrinsic diffusion coeffkients vs. reciprocal temperature [75F]. 40
42
44
46
48 at%
50
ln Fig. 57. Cu-Zn (p and p). Interdiffusion coefficient from 602 . ..924 K [75FJ.
r
Cu-Zn
10
160 !!! mol
I 10 kl
140
I D 120
10
100
80 40
42
44
46
48
ot% 50
10
84
87
at%
ln Fig. 59. Cu-Zn. 175Fl.
Activation energy Q for interdiffusion
Fig. 60. Cu-Zn. 673 K [76F].
Murch, Bruff
Interdiffusion coefficient from 523 ...
Land&B6mstein New Series III,/26
Ref. p. 3661
5 Chemical diffusion in inhomogeneous binary alloys (Figures) IO-'0 m2/s
1P 59 Zn(b). Interdiffusion coefficient from 748. ..
Fig. 61. Cu-Zn 827 K [76S].
60
Fig. 62. Cu-Zn 827 K [76S].
.,$ mVs
61
62
63 64 65 66of%67 Zn(y). Interdiffusion coeffkient from 748 1..
I Fe-Ni
I 20 .1p m% 3-
’
Fe-Ni
Ia 10 0 0 Fe
I 2
la
20
Fig. 64. Fe-Ni. [53Hl]. 01 0 Fe Fig. 63. Fe-Ni. [53Hl].
I 20
40
60 80 at% 100 NI Ni Interdiffusion coefficient at 1583 K
I 40
60 80 at% 100 Ni Ni Interdiffusion coefficient at 1423 K
300 %I 275 5I 250 225 200 0 20 40 60 80 at% 100 Fe NI Ni Fig. 65. Fe-Ni. Activation energy Q for interdiffusion :53Hl].
0 Fe Fig. 67. Fe-Ni. 1578 K [67B2].
For Fig. 66 seenext page. La”aolt-Bornstel”
New Series III/26
Murch, Bruff
20
40
60 80 at% IC NiL Interdiffusion coefficient from 1373...
356
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
[Ref. p. 366
A be 00” v DNi 80 at% 100
60 Ni Fig. 68. Fe-Ni. fusion coefficients 10’
40
60
of%
Ni -
Fig. 66. Fe-Ni.
lntcrdiffusion coefticicnt from Diffcrcnt symbols rcfcr to diffcrcnt
1629 K [67Bl]. :ouples.
Interdiffusion coeflkient at 1473 K [67L4].
and intrinsic
dif-
I
m2/ 10-16. 0 Fe
Ni
Fe- Ni
1.
100 Ni
1409 ‘.. starting
lo-’
I
Fe-Ni
m2/s
0
I
I
I
20
40
60
I
Fe -
Ni Fix. 70. Fc-Ni. 1373 K [84G].
I
80 wt%
Interdiffusion
coeflkicnt
‘\
from
100 Fe
1223...
10‘3 m2/s
\
DO \
200 0 Fe
‘1
20
40
60 Ni -
80 at%
100
.
Ni
Fig. 69. Fe-Ni. Activation D” for intcrdiffusion [74B3].
energy
Q and pre-exponential
Fig. 71. Fe-Si. Activation D” for interdiffusion [680].
energy
Q and prc-exponential
b
Murch, Bruff
il 17
01%
10.‘ I G
10-s 21
Ref. p. 3661
5 Chemical diffusion in inhomogeneous binary alloys (Figures) lo-’
I
m2/!>
Fe-Sn
1o-12
I_ ,aI 10-11
10-11
1 3
1o-15 I
L _1
Fe Fig. 72. Fe-k 1373 K [MY]. 10. m2/
4
8 at%
b
IO
Sn -
Interdiffusion coefficient from 1073...
Hf -Ti
I
I
11
1 17 77
I2
3 !
I JL!
: Hall method
0 Hf
Fig. 73. Hf-Ti. Land&-BBmstein New Series III/26
60
80
at%
TI -
Interdiffusion coefficient from 1273... 2273 K [87L].
Murch, Bruff
100 Ti
357
358
5 Chemical diffusion in inhomogeneous binary alloys (Figures) 250
$
I a
11 4o-7 m2/s
I
Hf-Zr
/
Q
200 --=.\
/
/
/
/
\
10-13
d/s
I 100 a
/ y
[Ref. p. 366
In- Ni
0
(aI 1o-'C
" \
150_ U
9
.~
20
60
40
a0 at%
10-15 .;1
0.70
100 Hf
lr HfFig. 74. Hf-Zr. Activation energy Q and pre-exponential Do for interdiffusion [75B]. 10-1:
0.82
0.78
0.86*0.90
l/T -
Fig. 75. In-Ni. Interdiffusion coefficient vs. reciprocal temperature [80B]. 10 .,o -10
/
m2h
0.71,
C46K
mV5 8
G
G2
6 I
10-l'
aa &K
4
I la
lo-" Li -
Fig. 77. Li -Mg. [84L]. lo-"
I
20
Ot%
In
In -
I
Fig. 76. In -Pb. 446 K [76Cl].
coefficient at 768 and 800 K
Interdiffusion
Interdiffusion coefficient from 388 ... -7.2
I
Mn-Ni
I \I 280 m'/s 6
I.1' 3+6
I
4 I Ia i
270
26 I & 7.8 .E
a 260
/
a 1
I.6
kJ mol
10-e
8.0
250
00
8.2
240 -1.0
0
-0.5
0.5
*lo-'
0 Ni
1.0
6-
Fig. 78. Li-Sb. Interdiffusion coefficient at 633 K [77W2].
5
10
15 Mn -
20
25 at%
30
Fig. 79. Mn -Ni. Activation energy Q and pre-exponential Do for interdiffusion [79Yl]. Do in m*s-I.
Murch, Bruff
Ref. p. 3661
m2/s 6
4 2 I lo-'* 1~ 0
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
I
I
I
10-l' m2/s
I
Mo-Nb 10-l
,~I 10-l'
6
lo-"9
10-d/ 0 MO
20
40
60
80 at%
Nb-
100 Nb
IO‘*[
Fig. 80. Mo -Nb. Interdiffusion coefficient at 1253K [69S].
Nb 10-l" mVs
Mo-
Fig. 81. MO-Nb. 1773 K [7Ov].
10-l' m2/s
MO
Interdiffusion coefficient from 1373...
I
MO-OS I
lo-'"I1 0 MO
20
40
60 Nb -
Fig. 82. MO-Nb. 2173 K [73B4].
80 at%
,o-l;
Nb
Interdiffusion coefficient from 1473...
t '~I 1o-l3
I -k--!-k 2450K I
\
10-l'" -25/~+
-261 0 MO
lo-l5 20
40
60 Re-
Fig. 84. MO-Re. Interdiffusion 77M]. 0” in cm’s-‘. Land&-Bihstein New Series III/26
80 at% 100 Re
coefficient at 1773 K
40
60 Mo-
80 ~01% 100 MO
Fig. 83. MO-OS. Interdiffusion coefficient from 2147... 2450 K [73E].
Murch, Bruff
[Ref. p. 366
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
360 2w’ m7/! 10-l
Me=V
_/
80 01% 100 ME MeFig. 86. Interdiffusion coeffkient in MO-Ti and Ti -V allays at 1773 K [69F]. a
I 10-l’ m2/s
60 MeFig. 85. Interdiffusion coefficient in Mo-Ti, ‘fa--Ti, and Ti -V alloys at 1173 K [69F]. 20
40
Me
10-1'5
Nb-Ti,
f~I 10‘”
, o -1;
10-l"
80 ot% 100 60 ToTo Interdiffusion coefficient at 1473 K
20 2*10-‘3r m% 10-1’3
Me- Ti
I
I
I
I
40
Nb Fig. 88. Nb-Pd. [71U2]. lo-l3 m2/s
10-l’ I kl 1o-l!
’ I’ 1 I’ ---I$ PdlHb/ I /4[I 7-: Od‘III I’11 -11 III 11 -p-k III III III
lo-‘6 0 Ti
40
60
MeFig. 87. Interdiffusion coefficient in Mo-Ti, Ti-V alloys at 1623 K [69F].
80 at% 100 Me Nb-Ti,
and
10-l” 0 Pd Fig. 89. Nb-Ta. 2073 K [7Ov].
Murch, Bruff
1 II II II II
60
20 Nb-
80 ot% Nb
Interdiffusion coefficient from 1573..
Iandolt-BMnsfem New Series III/26
Ref. p. 3661
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
361
I
Me-Ti
Ti -
Nb Fig. 91. Nb-Ti. 1573 K [7Ov].
60
40
Ti
Me-
Fig. 90. Interdiffusion coefficient Ti-V alloys at 1273 K [69F]
in Nb-Ti,
Interdiffusion
coeffkient
at 1373 and
80 at% 100 Me Ta-Ti,
and
10-4 m2/s
I
kJ mol
Nb- Ti
10-5 I % U6
10-1
I50020
Nb
I
0
Ti -
ri
Fig. 93. Nb -Ti. Activation energy Q and pre-exponential Do for interdiffusion [75UJ.
IO,
m2/s
6
1473K
I
P
0
20
40
Ti
Fig. 92. Nb-Ti. 1473 K [71P]. Land&-Biirnstein New Series III/26
60 Nb-
Interdiffusion
coefficient
80 at% 1 Nb at 1273 and
lo-l5 0 Nb Fig. 94. Nb-V. 1773 K [7Ov].
Murch, Bruff
20
40
60 v-
Interdiffusion
coefficient
80 at% 100 V at 1573 and
[Ref. p. 366
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
362
zq.
,p!
mVs
1P ml/s
1
l *. 0.
.
(,
..-
.
1o-‘5
.
.
.
t~ lo-”
10‘‘6 I b 10-‘7
.
lo-’
60
40
20 V
10-‘*
at% Nb
Nb-
Gg. 95. Nb-V. InterdifTusion coefficient at 1473 K [71U2]. 10-‘9
lo- 13 IT?/s
0
Nb Fig. 96. Nb-W. 2073 K [7OVJ.
LO
80 ot% 100
60
W
w-
Interdiffusion coeflicient from 1573...
lo- lb 1 m
250 lo-
15 _
0 I -
P 12/S
Lr7
10‘M
0
Nb Fig. 97. Nb-Zr. 1573K [7Ov].
20
I 0 Q
60
40
Zr Intcrdiffusion cocflicicnt at 1373 and
o4
0-9
ot% 100 Nb
Zr Nb Fig. 98. Nb-Zr. Activation energy Q and pre-exponential Do for interdiffusion [73R].
Pd
Ni-
80 at% 1004 Fig. 99. Ni -Pd. Interdiffusion coefficient at 1385 K [69B4] Ni Different symbols refer to different starting couples.
Murch, Bruff
LandolbB6mstein New Series 111126
363
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
Ref. p. 3661
I Ni-Zn (a)
$ji
I
-22
?Q
2 1
-23
a
Zn-
aI -24 c
-2:
0 75
78
81
84
87 at % 90
Zn-
b -2E
-2;
80 at% 100 60 20 40 Pt Ni Pt Fig. 100. Ni-Pt. Interdiffusion coefficient from 1223. I573 K [67B2]. d in cm2sm1.
44 O-l3
m2/s
T-
I
Ni-V
<
lo-l3
1 0
Ni Fig. 101. Ni-V. 1448 K [78Kl]. Land&-BBmstein New Series III/26
20
40
60
54
56
60 at% 58 Zn Fig. 102. Ni-Zn. Interdiffusion coefficient in Ni-Zn (a: alloys at 1203 K (a), Ni-Zn (y) alloys at 883 K (b), ant Ni-Zn (p) alloys at 1203 K (c) [77B3].
c
h-
0 52
80 at%
vInterdiffusion coefficient from 1083...
Murch, Bruff
364
5 Chemical diffusion in inhomogeneous binary alloys (Figures) 1C1.12r Ill’f/s
10-0
[Ref. p. 366
“r
_
10-14 I ‘a
:
0
/
Pb
10-15 -
2
4
6
8
01% 10
Sn -
Fig. 104. Pb-Sn. Interdiffusion coefficient at 523 K for two runs [87M2].
;
10-12
4
10-16 -
m2/s
4
lo-”
10’-17 0 10 20 30 50 at% 50 Ni ln Fig. 103. Ni-Zn. Interdiffusion cocflicicnt from 1073... 1323 K [79Y2].
Fig. 105. Pd-V. [71U2].
Interdiffusion
coefficient at 1473 K b
1 kl 10-14
lo-15)
0
20
40
V
60
Pd -
80 ot%
100 Pd
300 kJ mol
lo-'
I 250
ml/s
0 -25
I ‘a +
200
I 1U5&
-5
-26
-27
0
Pi
20
150
40
60 Re -
Fig. 106. Pt-Re. Interdiffusion [77M]. din cm%-‘.
80 ot%
0
100 Re
coefficient at 1773 K
V
20
40
60 Ti -
10-f 80 at% 100 Ti
Fig. 107. Ti-V. Activation energy Q and pre-exponential Do for interdiffusion [75u].
Murch, Bruff
5 Chemical diffusion in inhomogeneous binary alloys (Figures)
Ref. p. 3661 1O-1' ml/s
lo-‘?
r
365
300
I
10”
kJ iii
Ti -V
m2/s
250
1o-4 I %
I a
10-5
200
T
,g:
I el
150 -
0
10-"
20
40
Ti
10-6 80 at% 100 V
60 V-
Fig. 109. Ti-V. Activation energy Q and pre-exponential Do for interdiffusion [77Bl].
,0-l'
2
Ti-Zr
40-6 m2/s
00 A
190
I
1o-“t
60 Ti -
Fig. 108. Ti-V. 1476 K [76K2].
1.9
L
0
/
80 ot % 1 Ti
Interdiffusion coefficient from 1177...
Ti -
Fig. 110. Ti-Zr. Activation energy Q and pre-exponential Do for interdiffusion [76Bl].
4-l o-l2 ml/s
x
U -Zr
lo-li
IL CT a=
l
ou
0
DZr
A
ou
A
OZr
‘223
K
‘273
K
I
1
lo-l3
Fig. 111. U - Zr. Intrinsic diffusion coefficients at 1223 and b 1273 K [60A2]. Land&BBmstein New Series III/26
lo-l4
Murch, Bruff
I
0
Zr
20
40
60 U-
80 at%
1 u
366
5.3 References for 5
5.3 References for 5 32s 335 38R 41M 41Wl 41W2 425 43B 44K 45H 45v 50E 50K 50R 51B 52B 52s 52T 52W 53F 53Hl 53H2 53R 54B 55B 55G 55Hl 55H2 55R 56H 56L 56s 57A 57H 57R 57s 58Al 58A2 59A 59G 59H 59Ml 59M2 6OAl 6OA2 60C 60D 60G 60H 60M 6OPl 6OP2 61B 61Ml 61M2
Seith, W., Land, J.G.: Z. Metallkd. 24 (1932) 193. Jost, W.: Z. Phys. Chem. B21 (1933) 158. Rhines, EN., Mehl, RF.: Trans. Am. Inst. Min. Eng. 128 (1938) 185. Mehl, RF., Rhines, EN., Von den Steiner, K.A.: Met. Alloys 13 (1941) 41. Wells, C., Mehl, RF.: Trans. Am. Inst. Min. Eng. 145 (1941) 315. Wells, C., Mehl, RF: Trans. Am. Inst. Min. Eng. 145 (1941) 329. Johnson, WA.: Trans. Am. Inst. Min. Eng. 147 (1942) 331. Buckle, H.: Z. Electrochem. 49 (1943) 238. Kubaschewski, O., Ebcrt, H.: Z. Electrochem. 50 (1944) 138. Ham, J.L.: Trans. Am. Sot. Met. 35 (1945) 331. Van Liempt, J.A.M.: Rec. Trav. Chim. Pays-Bas 64 (1945) 239. Ebert, H., Trommsdorf, G.: Z. Electrochem. 54 (1950) 294. Kubaschewski, 0.: Trans. Faraday. Sot. 46 (1950) 713. Ransley, C.E., Neufeld, H.: J. Inst. Met. 78 (1950) 25. Buckle, H., Descamps,J.: Rev. M&tall. 48 (1951) 569. Boltz, W, Mead, H.W., Birchenall, C.E.: Trans Metal. Sot. AIME 194 (1952) 1070. Seith, W, Kottmann, A.: Angew. Chem. 64 (1952) 379. Thomas, D.E., Birchenall, C.E.: J. Met. 4 (1952) 867. Weeton, J.W.:Trans. Am. Sot. Met. 44 (1952) 436. Fitzer, E.: Z. Metallkd. 44 (1953) 462. Heumann, T., Kottmann, A.: Z. Metallkd. 44 (1953) 139. Hall, L.D.: J. Chcm. Phys. 21 (1953) 87. Resnick, R., Balluffi, R.: U.S. Report S.E.P. 118, August 1953. Ballufi, R.W, Seigle, L.L.: J. Appl. Phys. 25 (1954) 607. Byron, E.S., Lambert, XE.: J. Electrochem. Sot. 102 (1955) 38. Grobner, P: Hutn. Listy 10 (1955) 200. Heumann, T., Lohmann, P.: Z. Electrochem. 59 (1955) 849. Horne, G.T, Mehl, RF.: Trans. Am. Inst. Min. Eng. 203 (1955) 88. Resnick, R., Balluffi, R.W: Trans. Am. Inst. Min. Eng. 203 (1955) 1004. Heumann, Von Th., Heinemann, E: Z. Electrochem. 60 (1956) 1160. Landergren, U.S., Birchenall, C.E., Mehl, RF.: Trans. Am. Inst. Min. Eng. 206 (1956) 73. Swalin, R.A., Martin, A.: J. Metall. Trans. AIME 206 (1956) 567. Adda, Y, Philibert, J., Faraggi: Rev. Metall. 54 (1957) 597. Heumann, Th., Dittrich, S.: Z. Electrochem. 61 (1957) 1138. Reynolds, J.E., Averbach, B.L., Cohen, M.: Acta Metal!. 5 (1957) 29. Swalin, R.A., Martin, A, Olsen, R.: Trans. Am. Inst. Min. Eng. 209 (1957) 936. Adda, Y, Philibert, J.: C.R. Acad. Sci., Paris 246 (1958) 113. Adda, Y, Philibert, J.: Rep. CEA-880, March, 1958. Adda, Y, Levy, X, Hadari, Z., Tournier, J.: Mem. Sci. Rev. Metall. 57 (1959) 278. Guy, A.G.: Trans. Metall. Sot. AIME 215 (1959) 279. Hilliard, J.E., Averbach, B.L., Cohen, M.: Acta Metall. 7 (1959) 86. Manning, J.R.: Phys. Rev. 116 (1959) 69. MO!!, S.H., Ogilvie, R.E.: Trans. Metall. Sot. AIME 215 (1959) 613. Adda, Y, Philibcrt, J.: Acta Metall. 8 (1960) 700. Adda, Y, Mairy, C., Andreu, J.L.: Rev. Metall. 57 (1960) 550. Cordus, H., Kakuk, M.: Z. Anorg. Allg. Chem. 306 (1960) 121. DeLuca, L.S.: U.S. Rep. KAPL-M-LSD-1 August 1960. Goold, G.: J. Inst. Met. 88 (1960) 444. Heumann, T, Bohmer, H.: Arch. Eisenhiittenwes. 31 (1960) 749. Moss& M., Levy, V, Adda, Y: CR. Acad. Sci. Paris 250 (1960) 3171. Paxton, H.W, Pasierb, E.J.: Trans Metall. Sot. AIME 218 (1960) 794. Pell, E.M.: Phys. Rev. 119 (1960) 1014. Balk, A.: Acta Metall. 9 (1961) 643. Murphy, J.B.: Acta. Metall. 9 (1961) 563. Mehl, RF, Lutz, C.E: Trans Metal!. Sot. AIME 221 (1961) 561. Murch, Bruff
5.3 References for 5 62C 62E 62P 63C 63Dl 63D2 63L 63P 63R 64A 64L 64P 64R 64s 64T 65C 55D 55G 55Hl 55H2 55R 56B 56L 56W 57Bl 57B2 57B3 57Cl 57C2 57C3 57D 57J 57Ll 57L2 67L3 67L4 67L5 67M 67Pl 67P2 67P3 67R 67U 67V 68A 68E 68Hl 68H2 68H3 68H4 68K 680 68R 68Sl
367
Costas, L.P.: USA Rep. TID-16676, 1962. Elliot, R.P.: USA Rep. AD290336 March 1962. Peart, R.E. Tomlin, D.H.: J. Phys. Chem. Solids 23 (1962) 1169. Calais, D., Beyeler, M., Mouchnino, M., van Craeynest, A., Adda, Y: C.R. Acad. Sci. Paris 257 (1963) 1285. Davin, A., Leroy, V, Coutsouradis, D., Habraken, L.: Rev. Metall. 60 (1963) 275. Davin, A., Leroy, V, Coutsouradis, D., Habraken, L.: Cobalt 19 (1963) 51. Love, H.M., McCracken, G.M.: Can. J. Phys. 41 (1963) 83. Peterson, N.L., Ogilvie, R.E.: Trans. Metall. Sot. AIME 227 (1963) 1083. Reinbach, R., Krietsh, E: Z. Metallkd. 54 (1963) 173. Asundia, M.K., West, D.R.E: J. Inst. Met. 92 (1964) 428. LeHazif, R., Donze, G., Dupouy, J.M., Adda, Y: Rev. Metal1 61 (1964) 467. Powell, G. W, Braun, J.D.: Trans. Metall. Sot. AIME 230 (1964) 694. Rapperport, E.J., Merses, V, Smith, M.E: U.S. Rep. MI-TDR-64-61, March 1964. Starke, E., Wever, H.: Z. Metallkd. 55 (1964) 107. Tournier, J.: Rep. CEA-R-2446, October 1964. Calais, D., Dupuy, M., Mouchnino, M., Portnoff, A.Y, Van Craeynest, A.: in: Plutonium 1965, Kay, A.E., Waldron, M.B., (eds.),London: Chapman and Hall, 1965, p. 358. Dupuy, M., Calais, D.,: Mem. Sci. Rev. Met. 62 (1965) 721. Goldstein, J.I., Hanneman, R.E., Ogilvie, R.E.: Trans. Metall. Sot. AIME 233 (1965) 812. Hanneman, R.E., Ogilvie, R.E., Gatos, H.C.: Trans Metall. Sot. AIME 233 (1965) 691. Hartley, C.S., Steedly, J.E., Parsons, L.D.: ‘Diffusion in BCC Metals’, Am. Sot. Met. 1965, p. 51. Reiss, R.C., Hartley, C.S., Steedly, J.E.: J. Less-Common Met. 9 (1965) 309. Borovsky, LB., Marchukova, I.D., Ugaste, Yu.E.: Phys. Met. Metallogr. 22 (1966) 43. Lal, K., Levy, W: C.R. Acad. Sci. Paris 262 C (1966) 107. Wyatt, B.S., Argent, B.B.: J. Less-Common Met. 11 (1966) 259. Badia, M., Vignes, A.: C.R. Acad. Sci. Paris 264 (1967) 1528. Borovskiy, I.B., Marchukova, I.D., Ugaste, Yu.E.: Phys. Met. Metallogr. 24 (1967) 51. Badia, M., Vignes, A.: C.R. Acad. Sci. Paris 264 (1967) 858. Caloni, O., Ferrari, A.: Z. Metallkd. 58 (1967) 892. Cahoon, J.R., Youdelis, WV: Trans. Metall. Sot. AIME 239 (1967) 127. Caloni, O., Ferrari, A.: Trans. 2nd Nat. Conf. Electron Microprobe Analysis, Boston, 1967, Paper No. 21. Dupuy, M.: CEA Rep. R3439 1967. Janssen,M.M.P., Rieck, G.D.: Trans. Metall. Sot. AIME 239 (1967) 1372. Lal, K.: CEA Rep. CEA-R-3136, 1967. Lauthier, J.C., Van Craeynest, A., Calais, D.: J. Nucl. Mater. 23 (1967) 111. Levasseur, J., Philibert, J.: CR. Acad. Sci. Paris 264 (1967) 277. Levasseur, J., Philibert, J.: C.R. Acad. Sci. Paris 264 (1967) 380. Lifshin, E.: Trans. 2nd Nat. Conf. Electron Microprobe Analysis, Boston 1967, Paper No. 23. Mitani, H., Onishi, M., Kawaguchi, M.: J. Jpn. Inst. Met. 31 (1967) 1341. Prokoshkin, D.A., Vasil’yeva, E.V, Vergasova, L.L.: Fiz. Met. Metalloved. 23 (1967) 1134. Prokoshkin, D.A., Vasil’yeva, E.R, Vergasova, L.L.: Metalloved Term. Obrab. Met. 12 (1967) 44. Pavlinov, L.V.: At. Energ. 22 (1967) 290. Rafalski, A.L., Harvey, M.R., Reifenberg, D.H.: Trans. Am. Sot. Met. 60 (1967) 721. Ugaste, Yu. E.: Fiz. Met. Metalloved. 24 (1967) 442. Vignes, A., Philibert, J.,Badia, M., Levasseur,J.: Trans. 2nd Nat. Conf. Electron Microprobe Analysis, Boston, 1967, Paper No. 20. Aaronson, H.I., Domian, H.A., Brailsford, A.D.: Trans. Metall. Sot. AIME 242 (1968) 738. Edwards, G.R., Tate, R.E., Hakkila, E.A.: J. Nucl. Mater. 25 (1968) 304. Harvey, M.R., Rafalski, A.L., Reifenberg, D.H.: Trans. ASM 61 (1968) 629. Hirano, K., Hishunima, A.: J. Jpn. Inst. Met. 32 (1968) 516. Hirano, K., Ipposhi, Y: J. Jpn. Inst. Met. 32 (1968) 815. Hirano, K., Ouchi, K.: J. Jpn. Inst. Met. 32 (1968) 613. Kimmel, G., Bar-Or, A., Rosen, A.: Trans. ASM 61 (1968) 703. Onishi, M., Mitani, H.: Kinzoku Hyomen Gijutsu 19 (1968) 146. Remy, C.: CEA-R-3573,1968. Schwegler, E.C.,: Intl. J. Mass Spec.: Ion Physics 1 (1968) 191.
Land&-Bhstein New Series III/26
Murch, Bruff
368 68S2 652 69A 69B 1 69B2 69B3 69B4 69F 69H 69P 69s 69T 69U 69Wl 69W2 70B 70F 70Hl 70H2 701 70Kl 70K2 70K3 70Nl 70N2 700 70R 70s 7OTl 70T2 7OV 7OW 71B 71F 71Hl 71H2 711 71K 71L 71M1 71M2 71N 71P 71Rl 71R2 71s 71Ul 71U2 72C 72Fl 72F2 721 72Hl 72H2
5.3 References for 5 Swisher, J.H.: Trans. Metal]. Sot. AIME 242 (1968) 2433. Zelikman, A.N., Kotlyar, A.A., Kznetsov, Yu G.: Izv. Akad. Nauk SSSR, Met. 1 (1968) 197. Andreani, M., Azou, P., Bastien, P.: MCm. Sci. Rev. Metal]. 66 (1969) 21. Barclay, R.S., Niessen, P.: Trans. ASM 62 (1969) 721. Brunel, G., Cizeron, G., Lacombe, P.: C.R. Acad. Sci., Paris 269C (1969) 895. Badia, M., Vignes, A.: Rev. Met. 66 (1969) 915. Badia, M.: Thesis, University of Nancy, 1969. Fedetov, S.G., Chudinov, M.G., Konstantinov, K.M.: Fiz. Met. Metalloved 27 (1969) 873. Harvey, M.R., Rafalski, A.L., Reifenberg, D.H.: Trans. ASM 62 (1969) 1014. Pivot, J.P.,Van Craeynest, A., Calais, D.: J. Nucl. Mater. 31 (1969) 342. Steeb, S., Keppeler, R.: Z. Naturforsch. 24A (1969) 2607. Tate, R.E., Edwards, G.R., Hakkila, E.A.: J. Nucl. Mater. 29 (1969) 154. Ugaste, Yu.E.: Fiz. Met. Metalloved. 27 (1969) 663. Walsh, J.M., Donachie, M.J.: Met. Sci. J. 3 (1969) 68. Wagner, C.: Acta Metal]. 17 (1969) 99. Borg. R.J., Lai, D.YE: J. Appl. Phys. 41 (1970) 5193. Fidos, H., Schreiner, H.: Z. Metallkd. 61 (1970) 225. Hurley, A.L., Dayananda, M.A.: Metal]. Trans. 1 (1970) 139. Hall, M.G., Haworth, C.W.: Acta Metall 18 (1970) 331. Ivanov, A.N., Krasilnikova, G.B., Mitin, B.S.: Phys. Met. Metallogr. 29 (1970) 204. Khobaib, M., Gupta, K.: Ser. Metall. 4 (1970) 605. Kaekonen, H., Syrjaenen, E.: J. Mater. Sci. 5 (1970) 710. Kohn, A., Levasseur, J., Philibert, 1, Wanin, M.: Acta Metall. 18 (1970) 163. Nishida. K., Yamamoto, T, Nagata, T: J. Jpn. Inst. Met. 34 (1970) 595. Neukmann, 0.: Galvanotechniek 61 (1970) 626. Oikawa, H., Obara, T, Karashima, S.: Metall. Trans. 1 (1970) 2969. Remy, C., Dupuy, M., Calais, D.: J. Nucl. Mater. 34 (1970) 46. Sulaev, E.T, Kurasov, A.N., Karpov, N.A., Rabinovich, A.V.: Izv. Akad. Nauk SSSR,Met. 4 (1970) 209. Tsuji, A., Yamanaka, K.A.: Nippon Kinzoku Gakkaishi 34 (1970) 486. Tikhomirova, O.I., Ruzinov, L.P., Pikunov, M.V, Marchukova, I.D.: Fiz. Met. Metalloved. 29 (1970) 796. Vergasova, L.L., Prokoshkin, D.A., Vasileva, E.V.: Izv. Akad. Nauk SSSR,Met. 4 (1970) 198. Whittenberger, J.D., Dayananda, M.A.: Metall. Trans. 1 (1970) 2023. Barreau, G., Brunel, G., Cizeron, G., Lacombe, P.: Mem. Sci. Rev. Metal]. 68 (1971) 357. Funamizu, Y., Watanabe, K.: Trans. Jpn. Inst. Met. 12 (1971) 147. Holloway, P.H., Mohanty, G.P.: J. Phys. Chem. Solids 32 (1971) 2656. Harvey, M.R., Doyle, J.H., Rafalski, A.L., Reifenberg, D.H.: J. Less-Common Met. 23 (1971) 446. Iijima. Y, Hirano, K.: J. Jpn. Inst. Met. 35 (1971) 511. Krishtal, M.A., Mokrov, A.P., Belobragin, Yu.A.,Volkov,K.V: Fiz. Khim. Obrab. Mater. 3(1971) 109. Languille. A.: Mem. Sci. Rev. Metal]. 68 (1971) 435. Moreau, G., Carnet, J.A., Calais, D.: J. Nucl. Mater. 38 (1971) 197. Marchukova. I.D., Miroshkina, M.I.: Fiz. Met. Metalloved. 32 (1971) 1254. Nechiporenko, YP., Krivoruckko, XM., Mitrofanov, AS., Kondratov, YT.: Phys. Met. Metallogr. 32 (1971) 86. Polyanskii, VM., Podgorskii, B.N., Makarovets, O.D.: Svar. Proizvod. 3 (1971) 9. Ronami, G.N., Gryzunov, VI., Baranov, LA., Konovalov, N.T, Sokolov, VI., Vorob’eva N.S.: Izv. Akad. Nauk SSSR,Neorg. Mater. 7 (1971) 1490. Ronami, G.N., Gryzunov, VI., Sokolov, VI., Vorob’eva, N.S.: Issled. Mater. Novoi. Tekh. (1971) 36. Shamblen, C.E., Rosa, C.J.: Metal]. Trans. 2 (1971) 1925. Ugaste, Yu E., Pimcnov, VN.: Phys. Met. Metallogr. 31 (1971) 140. Ugaste, Yu E., Lazarev, E.M., Pimenov, VN.: Izv. Akad. Nauk SSSR,Met. 2 (1971) 211. Cahoon, J.R.: Metall. Trans. 3 (1972) 1324. Funamizu, E Watanabe K.: Trans. Jpn. Inst. Met. 13 (1972) 278. Fogelson, R.L., Ugai, YA., Pokoev, A.V: Phys. Met. Metallogr. 33 (1972) 194. Iijima. Y, Hirano, K.: Trans. Jpn. Inst. Met. 13 (1972) 419. Heumann, Th., Grundoff, K.J.: Z. Metallkd. 63 (1972) 173. Herzig. Chr., Heumann, Th.: Z. Naturforsch. A27 (1972) 1109. Murch, Bruff
Landolt-Kmstein Nen Series 111’26
5.3 References for 5 72M 72P 72W 722 73Bl 73B2 73B3 73B4 73E 73Gl 7362 73H 731 73J 73L 73N 7301 7302 7303 73R 73s 73T 73Ul 73U2 73v 74A 74Bl 74B2 74B3 74B4 74B5 74c 74H 74s 74Tl 74T2 74Wl 74W2 75A 75B 75F 75H 75L 75Ml 75M2 7501 7502 75Pl 75P2 75u 75w 75Y 76Bl 76B2 76Cl
369
Mirani, H.VM., Maaskant, P.: Phys. Status Solidi Al4 (1972) 521. Pinnel, M.R., Bennet, J.E.: Metall. Trans. 3 (1972) 1989. Whittenberger, J.D.: Metall. Trans. 3 (1972) 2010. Zaiss, W., Steeb, S., Krabichler, T: Z. Metallkd. 63 (1972) 180. Bergner, D., Cyrener, E.: Neue Huette 18 (1973) 356. Bruni, F.J.,Christian, J.W: Acta Metall. 21 (1973) 385. Buduvov, S., Kovatchev, P., Kamenova, Z.: Z. Metallkd. 64 (1973) 652. Brunsch, A., Krabichler, T, Steeb, S.: High Temp.-High Pressures5 (1973) 199. Erley, W, Wagner, H.: Phys. Status. Solidi. A 19 (1973) 23K. Green, A., Whittle, D.P., Stringer, 1, Swindells, N.: Ser. Metall. 7 (1973) 1079. Gomez, J.P.,Remy, C., Calais, D.: Mem. Sci. Rev. M&tall. 70 (1973) 597. Hirai, Y, Tasaki, Y, Kosaka, M.: Nagoya Kogyo Gijutso Shikensho Hokoku 22 (1973) 125. Iorio, N.R., Dayananda, M.A., Grace, R.E.: Metall. Trans. 4 (1973) 1339. Janssen,M.M.P.: Metall. Trans. 4 (1973) 1623. Lamparter, P., Krablicher, T, Steeb, S.: Z. Metallkd. 64 (1973) 720. Nohara, K., Hirano, K.: J. Jpn. Inst. Met. 37 (1973) 51. Onishi, M., Wakamatsu, Y: J. Jpn. Inst. Met. 37 (1973) 1279. Oikawa, H., Takei, H. Karashima, S.: Metall. Trans. 4 (1973) 653. Onishi, M., Wakamatsu, Y, Sasaki, T: J. Jpn. Inst. Met. 37 (1973) 724. Ronami, TN., Gryzunov, VI.: Vestn. Mosk. Univ. Fiz. Astronomiya 14 (1973) 367. Shapovalov, VP., Kurasov, A.N: Izv. Akad. Nauk SSSR,Met. 2 (1973) 234. Treheux, D., Giuraldenq, P.: C.R.Acad. Sci. Paris C277 (1973) 1299. Ustad, T, Sorum, H.: Phys. Status. Solidi A20 (1973) 285. Ugaste, Yu E., Pimenov, VN., Khlomov, VS.: Fiz. Met. Metalloved. 36 (1973) 211. Van Loo, EJ.J.,Rieck, G.D.: Acta Metall. 21 (1973) 61. Alberry, P.J.,Haworth, C.W: Metal. Sci. 8 (1974) 407. Brunsch, A., Steeb, S.: High Temp.-High Pressures 6 (1974) 155. Brunsch, A., Steeb, S.: Z. Naturforsch. A. 29 (1974) 1319. Balakir, E.A., Zotov, Yu. P., Malysheva, E.B., Panchishniyi, VI.: Russ. Metall. 5 (1974) 198. Bastin, G.E, Rieck, G.D.: Metall. Trans. 5 (1974) 1817, 1827. Budurov, S., Kovatchov, P.: Z. Metallkd. 65 (1974) 435. Carter, G.E: J. Less-Common Met. 37 (1974) 189. Heijwegen, C.P., Rieck, G.D: Acta Metall. 22 (1974) 1269. Shinyayev, A.Ya, Kopaleishvili, N.T: Phys. Met. Metallogr. 38 (1974) 212. Tsuji, S., Yamanaka, K.: J. Jpn. Inst. Met. 38 (1974) 415. Tenney, D.R., Talty, P.K.: Metall. Trans. 5 (1974) 241. Wilhelm, M.: Z. Naturforsch. A 29 (1974) 733. Weisweiler, W., Nageshwar, G.D.: High Temp.-High Pressures.6 (1974) 229. Agafonov, V, Sokolovskaya, E.M., Kulakov, VI., Gapeev, A.K.: Vestn. Mosk. Univ. Khim. 16 (1975) 121. Balakir, E.A., Zotov, Yu. P., Malysheva, E.B. Panchischnyi, VI., Podgorskii, B.N., Sharapov, 88: Izv. Vyssh. Uchebn. Zaved. Tsvetn. Metall. 4 (1975) 162. Funamizu, Y, Watanabe, K.: J. Jpn. Inst. Met. 39 (1975) 1087. Hickl, A.J., Heckel, R.W: Metall. Trans. A 6A (1975) 431. Lubyova, Z., Fellner, P., Matiasovsky, K.: Z. Metallkd. 66 (1975) 179. Muramatsu, P.Y, Roux, E, Vignes, A.: Trans. Jpn. Inst. Met. 16 (1975) 61. Matsuno, N., Oikawa, H.: Metall. Trans A 6A (1975) 2191. Oikawa, H., Hosai, A.: Ser. Metall. 9 (1975) 823. Onishi, M., Fujibuchi, H.: Trans. Jpn. Inst. Met. 16 (1975) 539. Pimenov, VN., Akkushkarova, K.A., Ugaste, Yu E.: Fiz. Met. Metalloved. 39 (1975) 821. Pimenov, VN., Akkushkarova, K.A., Gurov, K.P.: Fiz. Met. Metalloved. 39 (1975) 328. Ugaste, Yu E., Zaikin, Yu A.: Fiz. Met. Metalloved. 40 (1975) 567. Wakamatsu, Y, Onishi, M., Miura, H.: J. Jpn. Inst. Met. 39 (1975) 903. Yamane, T, Takahashi, J., Yashiki, H.: Keikinzoku 25 (1975) 167. Balakir, EA., Zotov, Yu P., Malysheva, E.B., Panchishnyi, VI., Voevodin, VP.: Izv. Vyssh. Uchebn. Zaved. Tsvetn. Metall. 3 (1976) 152. Bozic, B.I., Lucic, R.J.: J. Mater. Sci. 11 (1976) 887. Campbell, D.R., Tu, K.N., Robinson, R.E.: Acta Metall. 24 (1976) 609.
Land&-Blirnstein New Series III/26
Murch, Bruff
370 76C2 76D 76F 76K 1 76K2 76s 76T 76U 76V 77Bl 77B2 77B3 77F 77H 7711 7712 7713 7714 77M 77Nl 77N2 77P 77s 77Wl 77W2 78B 78C 78G 78H 78Kl 78K2 78Sl 78S2 7833 78S4 7885 7836 79F 791 79N 79w 79Yl 79Y2 80B 80F 80H 801 80M 80W 8OYl 8OY2 81A 81Hl 81H2 81L
5.3 References for 5 Carlson, P.T: Metal!. Trans. A 7A (1976) 199. Dainyak, B.A., Kostikov, VI.: Izv. Vyssh. Uchebn. Zaved. Chern. Metal!. 11 (1976) 15. Funamizu, Y.F., Watanabe, K.: Trans. Jpn. Inst. Met. 17 (1976) 59. Krishtal, M.A., Rykova, L.L.: Fiz. Khim. Obrab. Mater. 3 (1976) 120. Kale, G.B., Khera, SK., Tiwari, G.P.: Trans. Indian Inst. Met. 29 (1976) 422. Sorensen, O.B., Maahn, E.: Met. Sci. 10 (1976) 385. Tsuji, S.: J. Jpn. Inst. Met. 40 (1976) 844. Unman, J., Houska, CR.: J. Appl. Phys. 47 (1976) 4336. Van der Straten, P.J.M., Bastin, G.E, van Loo, EJ.J.,Rieck, G.D.: Z. Metallkd. 67 (1976) 152. Balakir, E.A., Zotov, Yu. P., Malysheva, E.B., Panchishnyi, VI., Voevodin, VP.: Izv. Vyssh. Uchebn. Zaved. Chern. Metall. 3 (1977) 5. Borovskiy, I.B., Marchukova, I.D., Ugaste, Yu E.: Izv. Vyssh. Uchebn. Zaved. Tsvetn. Metall. l(l977) 172. Budurov, S., Wassilew, G., Thi Kuk, N.: Z. Metallkd. 68 (1977) 226. Fogelson, R.L., Kazimirov, N.N., Sochnikova, 1.V: Phys. Met. Metallogr. 43 (1977) 1105. Hirano, K., Iijima, Y., Araki, K., Homma, H.: Trans. Iron Steel Inst. Jpn. 17 (1977) 194. Iijima, Y, Taguchi, O., Hirano, K.I.: Metall. Trans. A 8A (1977) 991. Iijima, Y, Hirano, K.I., Sato, K.: Trans. Jpn. Inst. Met. 18 (1977) 835. Iijima, Y, Hoshino, K., Hirano, K.I.: Metal! Trans. A 8A (1977) 997. Iijima, Y, Hirano, K.I., Sato, K.: J. Jpn. Inst. Met. 41 (1977) 142. Matveyeva, M.P., Volkova, R.M., Marchukova, I.D., Boshenov, VA.: Phys. Met. Metallogr. 43 (1977) 179. Nishida, K., Murohashi, H., Yamamoto, T: J. Jpn. Inst. Met. 41 (1977) 1101. Nohara, K., Hirano, K.: Tetsu To Hagane 63 (1977) 926. Pimenov, V.N., Ugaste, Yu E., Akkushkarova, K.A.: Russ. Metal!. 1 (1977) 155. Salje, G., Feller-Kniepmeier, M.: J. Appl. Phys. 48 (1977) 1833. Wakamatsu, Y, Samura, K., Onishi, M.: J. Jpn. Inst. Met. 41 (1977) 664. Weppner, W, Huggins, R.A.,: J. Solid State Chem. 22 (1977) 297. Butrymowicz, D.B., Manning, J. R.: Metall. Trans. A 9A (1978) 947. Carlson, P.T: Metall. Trans. A 9A (1978) 1287. Gukelberger, A., Steeb, S.: Z. Metallkd. 69 (1978) 255. Heumann, Th., Damkiihler, R.: Z. Metallkd. 69 (1978) 364. Khlomov, VS., Pimenov, VN., Ugaste, J., Gurov, K.P: Fiz. Met. Metalloved. 46 (1978) 668. Khlomov, VS., Pimenov, VN., Gurov, K.P.: Fiz. Met. Metalloved. 46 (1978) 199. Shimozaki, T., Onishi, M.: J. Jpn. Inst. Met. 42 (1978) 1083. Shimozaki, T, Onishi, M.: J. Jpn. Inst. Met. 42 (1978) 402. Salje, G., Feller-Kniepmeier, M.: J. Appl. Phys. 49 (1978) 229. Scheidler, G.P., Osthoff, W, Singh, S.P.: Z. Metallkd. 69 (1978) 591. Shankar, S., Seigle, L.L.: Metall. Trans. A 9A (1978) 1467. Scheidler, G.P., Osthoff, W: Z. Metallkd. 69 (1978) 495. Fujikawa, S., Hirano, K., Fukushima, Y: Metal!. Trans. A 9A (1979) 1811. Iijima, Y., Igarashi, T., Hirano, K.: J. Mater. Sci. 14 (1979) 474. Nishida. K., Murohashi, H., Yamamoto, T: Trans. Jpn. Inst. Met. 20 (1979) 269. Wen, C.J., Boukamp, B.A., Huggins, R.A., Weppner, W: J. Electrochem. Sot. 126 (1979) 2258. Yokota, M., Harada, R., Mitani, H.: J. Jpn. Inst. Met. 43 (1979) 793. Yamamoto, T, Takashima, T, Nishida, K.: J. Jpn. Inst. Met. 43 (1979) 1196. Budurov, S.J.,Boshinov, W.S.,Kovatchev, P.D.: Krist. Tech. 15 (1980) K22. Fujiwara, Y, Katayama, M., Hara, K., Osugi, J.: High Temp.-High Pressures.12 (1980) 643. Hoshino, K., Iijima, Y, Hirano, K.: Trans Jpn. Inst. Met. 21 (1980) 674. Iijima, Y, Taguchi, O., Hirano, K.: Trans. Jpn. Inst. Met. 21 (1980) 366. Minamino, Y, Yamane, T, Tokuda, K.: Z. Metallkd. 71 (1980) 90. Wen, C.J.,Weppner, W, Boukamp, B.A., Huggins, R.A.: Metall. Trans. B 11B (1980) 131. Yokota, M., Nose, M., Mitani, H.: J. Jpn. Inst. Met. 44 (1980) 1007. Yamamoto, T, Takashima, T, Nishida, K.: J. Jpn. Inst. Met. 44 (1980) 294. Arita, M., Ohyama, M., Goto, KS., Somero, M.: Z. Metallkd. 72 (1981) 244. Hoshino, K., Iijima, Y, Hirano, K.: Trans. Jpn. Inst. Met. 22 (1981) 527. Hoshino, K., Iijima, Y, Hirano, K.: Philos. Mag. A 44 (1981) 961. Lantelme, E, Belaidouni, S.: Electrochim Acta 26 (1981) 1225. Murch, Bruff
Land&El6mslein New Series 1111’26
5.3 References for 5 81N 81W 81Y 82H 8211 8212 82M 82s 831 83M 83N 83R 84A 84C 84G 841 84L 84M 84T 85A 85B 85G 85Ml 85M2 85R 86D 86L 86Sl 8632 87C 87L 87Ml 87M2 87s
Land&-Bijmstein New Series III/26
371
Nanba, M.: J. Electrochem. Sot. 128 (1981) 420. Williams, D.S., Rapp, R.A., Hirth, J.P.: Metall. Trans. A 12A (1981) 639. Yamamoto, T., Takashima, T., Nishida, K.: J. Jpn. Inst. Met. 45 (1981) 985. Hoshino, K., Iijima, Y, Hirano, K.: Metall. Trans. A 13A (1982) 1135. Iijima, Y, Kikuchi, M., Hoshino, K., Hirano, K.: in: Yamada Conf. on Point Defects and Defect Interactions in Metals, Takamura, J., Doyama, M., Kiritani, M., (eds.)Amsterdam: North Holland, 1982, p. 566. Iijima, Y, Hirano, K., Kikuchi, M.: Trans. Jpn. Inst. Met. 23 (1982) 19. Minamino, Y., Yamane, T, Koizumi, M., Shimada, M., Ogawa, N.: Z. Metallkd. 73 (1982) 124. Sarkhel, A.K., Seigle, L.L.: Metall. Trans. A 13A (1982) 1313. Iijima, Y., Hirano, K., Ohzeki, T., Suzuki, K.: in: Diffusion in Metals and Alloys, Kedves, EJ., Beke, D.L., Switzerland: Trans Tech, 1983, p. 401. Minamino, Y, Yamane, ‘I, Shimomura, A., Shimada, M., Koizumi, M., Ogawa, N., Takahashi, J., Kimura, H.: J. Mater. Sci. 18 (1983) 2679. Narayan, C., Goldstein, J.I.: Metall. Trans. A 14 (1983) 2437. Romig, A.D.: J. Appl. Phys. 54 (1983) 3172. Arita, M., Nakamura, M., Goto, KS., Ichinose, Y: Trans. Jpn. Inst. Met. 25 (1984) 703. Cogan, SF, Kwon, S., Klein, J.D., Rose, R.M.: J. Mater. Sci. 19 (1984) 447. Ganesan, V!, Seetharaman, V, Raghunathan, YS.: Mater. Lett. 2 (1984) 257. Iijima, Y, Hoshino, K., Kikuchi, M., Hirano, K.: Trans. Jpn. Inst. Met. 25 (1984) 234. Langen, G., Schwitzgebel, G., Ruppersberg, H.,: Mater. Res. Bull. 19 (1984) 1141. Minamino, Y, Yamane, T, Ueno, S., Koizumi, M., Ogawa, N., Shimada, M.: Metal Sci. 18 (1984)419. Takahashi, T, Kato, M., Minamino,Y, Yamane,T., Azukizawa, T, Okamoto., T., Shimada, M., Ogawa, N.: Z. Metallkd. 75 (1984) 440. Aubin, J.L., Ansel, D., Debuigne, J.: J. Less-Common Met. 113 (1985) 269. Braun, R., Feller-Kniepmeier, M.: Phys. Status Solidi A 90 (1985) 553. Green, A., Swindells, N.: Mater. Sci. Technology 1 (1985) 101. Minamino, Y, Yamane, T, Takahashi, T: J. Mater. Sci. Lett. 4 (1985) 797. Moreau, C., Allouche, A., Knystaustas, E.J.: J. Appl. Phys. 58 (1985) 4582. Romig, A.D., Cieslak, M.J.: J. Appl. Phys. 58 (1985) 3425. Dean, D.C., Goldstein, J.I.: Metall. Trans. A 17 (1986) 1131. Lee, K.H., Shin, M.C., Lee, J.Y: J. Mater. Sci. 21 (1986) 2430. Sarafianos, N.: Mater. Sci. Eng. 80 (1986) 87. Shimozaki, T, Ito, K., Onishi, M.: Trans. Jpn. Inst. Met. 27 (1986) 160. Chryssoulakis, Y, Lantelme, I?, Alexopoulou, A., Kalogeropoulou, S.,Chemla, M. : Electrochim. Acta 32 (1987) 699. Le Gall, G., Ansel, D., Dubuigne, J.: Acta Metall. 35 (1987) 2297. Minamino, Y, Yamane, T, Araki, H.: Metall. Trans. A 18 (1987) 1536. Mei, S., Huntington, H.B., Hu, C.K.: Ser. Metall. 21 (1987) 153. Shimozaki, T, Shuto, H., Onishi, M.: Trans. Jpn. Inst. Met. 28 (1987) 191.
Murch, Bruff
312
6.1 Fick’s law, ternary interdiffusion
and intrinsic diffusion coefficients
[Ref. p. 435
6 Diffusion in ternary alloys In this chapter diffusion data are compiled for ternary alloys. Becauseternary diffusion is not treated in the General Introduction the main concepts and methods employed in ternary diffusion studies are briefly covered below.
6.1 Generalized forms of Fick’s law, ternary interdiffusion and intrinsic diffusion coefficients An extended form of Fick’s law, as proposed by Onsager [310,450], is employed for the general treatment of diffusion in multicomponent systems.For a unidirectional diffusion in a 3-component system,the interdiffusion flux ji of component i referred to a laboratory fixed frame of referenceis expressedas a linear function of two independent concentration gradients by
Since the interdiffusion fluxes of only two of the components are independent in a ternary alloy, only 4 interdiffusion coefficients, I?:, , B:, ai,, a:, are needed.The superscript 3 in @ refers to the component taken as the dependent concentration variable. a:, and & are referred to as the main or diagonal interdiffusion coefficients, while a:, and a:, correspond to the cross or nondiagonal coefficients. The laboratory coordinate is equivalent to the volume fixed frame, if there are no volume changes on mixing. Similarly, the intrinsic diffusion flux Ji of component i relative to a lattice-fixed frame (Kirkendall frame) is expressedby J,=-$Di% j=1
(i=l,2,3)
where Dz are the ternary intrinsic diffusion coeflicients. Since the interdiffusion and intrinsic fluxes are related through the lattice or marker velocity u, the interdiffusion coefficients can be expressedin terms of the intrinsic coefficients by [62G] d,!j=L$-Xi
i
k=l
Dzj
(i,j=l,2)
(6.3)
where the molar volume, V,, is assumedconstant (Xi: molar fraction ofcomponent i). In general, all the diffusion coeficients are functions of composition. The D: are inter-related through 3 atomic mobilities and thermodynamic data (see6.5).
6.2 Solutions of diffusion equations for constant ternary interdiffusion coefficients The differential equations corresponding to Fick’s second law are obtained by the substitution of Eq. (6.1) in the continuity equation (1.6) of chapter 1 and for the case where & can be assumed constant over a composition range of interest, they are given by
acizbs ,, a% s+Bf2 at
3
(i=1,2).
(6.4)
For ternary systems involving interdiffusion of substitutional and/or interstitial elements, Eq. (6.4) has been solved for selected boundary conditions corresponding to experimental diffusion couples.
Dayananda
Landolt-B6mstein Nea Series Ill’26
Ref. p. 4351
6.2 Solutions of diff. equations for constant ternary interdiff. coefficients
313
6.2.1 Infinite, solid-solid diffusion couple An infinite solid-solid couple is assembledwith disks of terminal alloys of compositions CT and C; and diffusion annealed isothermally at temperature T for time t. The concentrations of the components initially exhibit a step function at the plane of contact of the alloys (Matano plane) at t = 0, and the concentration profiles developed within the diffusion zone can be expressedin terms of error functions by [56F, 58K] C,=a erfX 2&G
where u&
[
+b erf x+c q/G
(6.5a)
C,=d erfz +e erfX+f 2Ju,t. L/G
(6.5b)
o”:,(c: -c;)-{(B;,-D:,)-d}
b=; [cc-c;
cc: y
1
-2a]
c=$ [Cl +CJ
d=&~:,(c:-c;,-{(a:,-a:,,-a)(cyiq e=; [c; -c; j=;
-2d]
EC: +c;1
Based on the thermodynamic requirements and the stability of solutions of the diffusion equations, the four interdiffusion coefficients satisfy the relations [63Kl, 70K] a:,+0”2,>0 (b:,+o”~,)z~4(~::,~::,-6:,b~,) (a:,a;,-s:,b:,)~o.
(6.6) (6.7) (6.8) Eqs. (6.6) through (6.8) assure that no negative values of concentrations appear as solutions of the diffusion equations. The &s as constants can be evaluated from the experimental ternary concentration profiles on the basis of method of moments [55B]. An alternative and easier procedure is first to evaluate the main coefficients, o”:, and o”,“, with binary couples involving 1-3 and 2-3 components, respectively, and employ these values to determine the cross-coefficients from ternary couples [63K2].
Land&-BBmstein New Series III/26
Dayananda
374
6.2 Solutions of diff. equations for constant ternary interdiff. coefficients
[Ref. p. 435
6.2.2 Darken-type couple The solution in Eq. (6.5) can be further simplified [57K] for a solid-solid couple referred to as Darken-type [49D], if component 1 is initially uniform and the concentration of component 2 has a step function at the a2c, . Matano plane (x=0) at t=O. For such a couple, one may neglect the term a:, axz m (6.4) and the approximate solutions become: Cl=!
(CT +C;)+A
where
[
erfX2m
(
2A-~j+c’)
erf*]
(6.9)
(G-G)
&2
*=(6:,--a;,)
(6.10)
2
and C,=Cl
+i (C; -C,‘)
I-erfX [
295
1 .
6.2.3 Semi-infinite, vapor-solid diffusion couple For a ternary vapor-solid couple set up with a semi-infinite sample of composition CT in contact with a vapor source such that at t > 0 the surface concentrations are maintained at Cf, the solution for the concentration profiles is expressedby Eqs. (6.5a) and (6.5b) with the following relations for the various constants.
a=;[q,(c;-c;)-(jj;,-@, -6)y6’) 1
b=i[c,,(C;-C:)-(d:,-d:,+~) yc:)1 c=c: d=; ol:,(c:-c;)-(6:,-6:,-6) yci) 1 [
u,, u2 and b are given by the samerelations as indicated earlier. The above solution is basedon the assumption that the diffusion disk shows negligible expansion due to mass input from the vapor phase. However, such expansions can be taken into account [65D, 68Dl] in the determination of interdiffusion coefficients.
6.2.4 A layered couple with one-dimensional periodic boundary condition or a finite diffusion couple A layered couple with alternating layers of two alloys is considered. The initial conditions correspond to a uniform concentration of component 1 at CT and to a periodic step-function of wavelength 2L for the concentration of component 2 varying between Ci and C;. The boundary condition also represents an impervious walled finite system lying between - L and + L. For such a system,the cross-effectof component Y -0 1 on component 2 may be ignored by setting D,, - and the solutions [65K] are given by:
c
m (-Um+l -&e:~-,-a:,cr m?l (2m-1) cos6mx[e
=c++~G-c;m2
1
1 II (a:, -a:,,
I
(6.12)
and
c JG 2
+w+; 2
(C’-C-) 7-t 2
2 (- urn+’ e-6:,5~rcos~ x ’ m=~ (2m-1)
m
(6.13)
where r
=(2m-Un m
L
Dayananda
.
(6.14)
Land&-B6mstein New Series lllf26
6.3 Concentration-dependent
Ref. p. 4351
ternary interdiffusion
375
coefficients
6.2.5 Transient equilibrium or quasi-steady state solution The concept of quasi-steady state or transient equilibrium was used by Kirkaldy and coworkers [62K, 64B] in the study of interdiffusion in ternary austenites with finite couples consisting of a layer of a binary substitutional Fe-base alloy welded between two layers of an Fe-base plain carbon alloy. If 8:, a@, (1 =carbon, 2=substitutional element), component 1 may reach a quasi-steady state with respect to a slowly diffusing component 2 after a period of time and
or (6.15) where Cp and CF refer to the concentrations in the outside and middle layers of the couple. The ratio of the coefficients in Eq. (6.15) is assumed to be evaluated at the mean concentrations, (Cy + Cy)/2 and (Cy)/2. For dilute alloys, &/@, may be estimated from thermodynamic data on the basis of the relation [64B]:
0”:2 e12xl s:,=- l+ellxl where e,, and e,, refer to Wagner’s thermodynamic interaction parameters [52w].
6.3 Concentration-dependent ternary interdiffusion coefficients 6.3.1 Interdiffusion
data at composition points of intersection of diffusion paths
The Boltzmann-Matano analysis described in chapter 1 for binary couples is extended [57K, 672, 65D] to ternary solid-solid and vapor-solid couples to yield:
Cl d1’xdCi
2). ci(i=ly
= - 2t
(6.17)
The molar volume is assumed constant in the diffusion zone and (x=0) is identified at the common Matano plane identified on the basis of Eq. (1.44)of chapter 1 for any of the components. Since there are 4 concentrationdependent &‘s, they cannot be determined from a single couple; in fact, two couples chosen to have a common composition developed in their diffusion zones are needed. Such a common composition can be identified as a point of intersection (C,, C,) of the composition paths or diffusion paths for a pair of couples shown schematically on a ternary isotherm in Fig. 1. The four equations set up from the two couples by evaluating the integrals and derivates in Eq. (6.17)at (C,, C,) are solved to evaluate o”:, , B:,, a;, and o”:, at the composition (C,, C,).
a
b
Fig. 1. Schematic diffusion paths (composition paths) for (a) a pair of solid-solid diffusion couples, A vs. B and C vs. D and (b) a pair of vapor-solid diffusion couples, A vs. B and C vs. pure 3 component. The diffusion paths of each pair intersect at a common composition (C, , C,) where Eq. (6.17) can be employed to evaluate the four ternary interdiffusion coeffkients, i?:, , o”:,, o”il, and o”:, . Land&-Bhstein New Series III/26
Dayananda
6.3 Concentration-dependent
376
ternary interdiffusion
coefficients
[Ref. p. 435
The four ternary coeflicients 6;‘s can be transformed to alternative setsof four coefficients depending on the choice of the component employed for the dependent concentration variable. The transformation relations [67Z, 70K] are expressedby +f&-pj =&-a/, = - aj, .
(6.18) (6.19) (6.20)
The limiting values of the ternary coefficients on the three binary sides and three corners of the ternary diagram have been established [63S, 70K]. The limiting values of the major coefficients sFi are (6.21)
lim GFi=fii-, c, - 0 where &,
is the binary interdiffusion coefficient for i-k
system. Also, (6.22)
where DFu-L, is the tracer diffusion coeflicient of component i in a binary j - k alloy. The limiting values of the cross-coefficients a: are (6.23)
lim Q=O. ci+o
6.3.2 Interdiffusion coefficients at maxima and minima in concentration profiles If the concentration profile of a component (say 1) develops a maximum or minimum, as normally encountered in Darken-type couples, z=O
at such sections, and Eq. (6.17) yields:
Cl xdC, I
I+
[ 1Cl(i=‘72).
= - 2t 6,5, 2
(6.24)
Eq. (6.24)allows the determination of two of the coefficients directly at the compositions of the extrema in the profile of component 1. An expression similar to Eq. (6.24) is used to calculate partial interdiffusion data at extrema for component 2.
6.3.3 Ratio of 6i3i/B~i at a zero-flux plane for component i During isothermal diffusion in a ternary or multicomponent diffusion couple the interdiffusion flux of a component can go to zero at a section within the diffusion zone and exhibit a change of flux direction from one side of the section to the other [79D]. Such a plane where z=O is referred to as a zero-flux plane (ZFP) for component i. For ternary solid-solid and vapor-solid couples, z at any section x can be determined [83D, 85D2] directly from the concentration profiles by ~(x)=~c,~~~-xdCI I
(i=l,2,3)
without the knowledge of interdiffusion coefficients. At a ZFP for component i, CdZFP)
ct .f,- xdCi=o
(6.26)
and it follows from Eq. (6.17) ai3, ac, ac, 1ZFplo,, = - a:, .
(6.27)
Hence, the ratio of the cross to the main interdiffusion coefficients can be directly determined from the slope of the ternary diffusion path at a ZFP composition. A ZFP developed for a component in an experimental ternary diffusion couple is shown in Fig. 2. The ZFP phenomenon has been identified in several multicomponent systems[83K, 84K, 85D2,85K]. A ZFP for a component normally develops in an “isoactivity couple” characterized by similar thermodynamic activities for the component in the terminal alloys.
Dayananda
Landott-BBmsfein New Series III/26
Ref. p. 4351
6.4 Determination
of ternary intrinsic diff. coefficients with inert markers
377
0.6 I q
0.4
- 0.5
-200
-150
-100
-50
0
50
100 pm 150
Fig. 2. Concentration profiles and profiles of interdiffusion fluxes ji” calculated from Eq. (6.25) for a single phase c(~ (30.10 at.% Cu-44.70 at.% Ni-25.20 at.% Zn) vs. cllz (80.61 at.% Cu-19.39 at.% Ni) ternary diffusion couple annealed at 1048K for 2 days. Ni exhibits a zero-flux plane (ZFP) located by the requirement that area A = area B and area C = area D on the basis of Eq. (6.26). Note that the directions of .& are different on the two sides of the ZFP for Ni [84K].
6.4 Determination of ternary intrinsic diffusion coefficients with inert markers A direct integration of Eq. (6.2) with respect to t yields [52H, 63PJ ,+‘.li&=-2t; d
D;z j=l
1
marker
(6.28) plane
(i =
”
2’
3,
where Ai refers to the cummulative intrinsic flux of component i past a marker plane identified at a constant composition and moving parabolically with time. The gradients X,/ax and X,/ax are evaluated at the marker plane and Ai can be determined graphically from appropriate areas under the profiles (Heumann’s method [52H]). To determine the six Dz’s two independent couples characterized by marker planes of identical or similar compositions are needed; such a pair of couples have their diffusion paths meet or intersect at the composition point (C,, C,), the common composition of the marker planes. Practically it is difficult to set up a pair of solid-solid couples with identical marker composition. However, it is easier to realize this requirement with vapor-solid couples set up with two different alloys exposed to the same vapor source. Inert markers placed initially at the vapor-solid interfaces get embedded in the diffusion disks, remain close to the interface and are found at compositions close to that of the interface. In Fig. 3 are shown schematic concentration profiles for a vapor-solid couple with inert markers employed in the determination of intrinsic diffusion coefficients. From the intrinsic coefficients, the interdiffusion coefficients can be calculated from Eq. (6.3). Land&-Biirnstein New Series III/26
Dayananda
378
6.5 Lij phenomenological coefficients, atomic mobilities, vacancy wind parameters
[Ref. p. 435
Fig. 3. Schematic concentration profiles for a ternary vaporsolid couple with inert markers; x, and x, refer to the positions of the vapor-solid interface and the marker plane at time 1.The cumulative intrinsic fluxes, A,, A, and A,, past the marker plant can bc determined directly from the profiles [65D].
6.5 Lij phenomenological coefficients, atomic mobilities and vacancy wind parameter The general flux-force relations for an n-component alloy is given by [310,70K]
II-l Ji = - c L,, 2 ]=I
(6.29)
where the (n-l) independent forces are defined in terms of gradients of chemical potentials, pj. If the cross interactions between i and j are ignored in the lattice-fixed frame, Eq. (6.29) is simplified to (6.30) where fli refers to the atomic mobility. On the basis of this simple atomic mobility model the intrinsic coetlicients Dl?jare expressedby [65Z, 68D2] Q+cipi
-g
(6.31) J Dayananda [68D2] has shown that the three atomic mobilities for a ternary system can be experimentally determined from values of cumulative intrinsic fluxes Ai past a marker plane with a single couple on the basis of the relation
/+Ai
plnnc 1marker
(6.32)
2tC.?!5 1ax
provided the thermodynamic data are available. An alternate procedure is to set up steady-state diffusion profiles in a thin membrane of a solvent metal exposed to vapors of the diffusing species [7Ow]. Under steady-state conditions .Jiin Eq. (6.30) becomesconstant and /& can be evaluated over the entire composition range of the diffusion membrane with the knowledge of Ji and thermodynamic data. Dayananda
Landok-B6mstein New Series 111126
Ref. p. 4351
6.6 Tracer diffusion coefficients; 6.7 Use of the tables and figures
379
If the diffusional interaction between the components on the lattice-fixed frame cannot be ignored, Eq. (6.32) is modified to [71D]. Ai = - 2tcipi $+apixi
5 Aj j=l
1
(6.33)
marker plane
where c(is a vacancy wind parameter describing the interactions in terms of the vacancy wind effect [68M, 70M]. The three pi and the parameter a in Eq. (6.33) can be determined with a pair of independent ternary diffusion couples characterized by marker planes of similar composition. Such experimental data currently available are limited.
6.6 Tracer diffusion coefficients Tracer diffusion measurementsin ternary alloys with the techniques discussedin chapter 1 are also limited. Expressions are available for the calculation of ai and L,, coefficients from tracer data or atomic mobilities [67Z, 70M]. The expressions for & in terms of the & on the basis of atomic mobility model are:
o”:1=xIwI-xI(~1-8311
~-x,x,@&-P,)
2
D”:,=x,[P,-x,(P1-&)1
g-X,XAkP,)
2
1
2
(6.34)
1
(6.35)
2
(6.36)
~,32=X2[P2-Xz(P2-/L)l g-X,X,W,)~. 2
(6.37) 2
6.7 Use of the tables and figures The order in which the alloy systemsare arranged in this chapter is alphabetical. For a given ternary system, the element having the chemical symbol earlier in the alphabet always comes first. For example AgAlZn is tabulated before AgCdZn and NiFeAl must be transformed into AlFeNi and is then found after AlCuZn. The alloy compositions are expressedin atomic percentages,unless indicated otherwise. The data are distributed into four sections (tables) with the titles of -
Ternary interdiffusion coefficients (Sect.6.8.1) Ternary intrinsic diffusion coefficients (Sect.6.8.2) Atomic mobilities and vacancy wind parameters (Sect.6.8.3) Tracer diffusion coefficients for ternary alloys (Sect.6.8.4). The tables have a central function. From the tables referencesare made to the figures.
Land&-B&stein New Series III/X
Dayananda
6.8.1 Ternary interdiffusion
380
[Ref. p. 435
coefficients (Tables)
6.8 The diffusion tables 6.8.1 Ternary interdiffusion coefficients Composition at. %
T
81 Ag 0.49 0.57 0.78 0.91 1.0 1.1 1.3 I.3 1.5 1.6 1.8 2.0 2.1 2.3 2.5 3.0 3.0 3.7 4.0 4.8 0.44 0.58 0.64 0.83 0.95 1.1 1.3 1.4 1.4 I.4 1.7 2.0 2.0 2.2 2.6 2.7 3.0 3.8 3.9 5.1 0.45 0.59 0.75 0.92 0.95 0.98 1.3 1.3 1.4
Al Zn (fee) 2.8 3.2 2.5 2.9 4.9 2.2 2.5 6.1 1.9 4.3 2.2 1.5 5.4 3.8 1.7 3.3 4.6 3.9 2.4 2.8 (fee) 2.7 3.3 2.4 3.0 4.7 2.1 2.5 1.9 4.2 6.2 2.3 1.4 5.4 3.5 1.7 3.1 4.6 3.9 2.3 2.8 (fee) 2.8 3.4 2.5 4.7 3.0 2.2 2.8 6.2 1.9
765
785
796
Remarks
2s-,
K
1.5 1.5 1.6 1.4 1.4 1.4 1.2 1.3 1.3 1.1 1.0 1.0 1.2 1.2 0.79 1.1 1.1 0.96 0.65 0.67 2.6 2.6 2.1 2.5 2.4 1.7 I.7 1.7 2.3 2.2 I.7 1.6 2.0 2.0 1.4 1.7 1.7 1.2 1.2 0.85 2.8 3.8 2.8 3.1 2.9 2.5 2.5 3.0 2.2
o”:,
o”:,
Fig.
Ref.
a
In units of lo-l3 mzsP1 1.8 -0.05 -0.65 1.8 -0.07 -0.79 1.7 -0.10 -0.59 1.8 -0.09 -0.60 1.7 -0.09 -0.74 2.0 -0.24 -0.34 2.0 -0.10 -0.33 2.2 -0.10 -1.4 1.9 -0.20 -0.44 1.9 -0.11 -0.60 1.9 -0.24 -0.35 2.0 -0.28 -0.28 2.0 -0.09 -1.3 2.1 -0.12 -0.51 I.9 -0.30 -0.26 2.1 -0.17 -0.60 2.7 -0.24 -0.67 2.5 -0.25 -0.76 2.2 -0.43 -0.44 2.4 -0.37 -0.61 3.1 -0.13 -0.58 3.1 -0.15 -0.42 2.8 -0.08 -0.73 2.9 -0.26 -0.61 3.6 -0.27 -2.0 2.8 -0.64 2.9 -0.09 -0.62 2.9 -0.14 -0.63 3.6 -0.52 -1.8 3.5 -0.18 -2.3 3.0 -0.11 -0.60 3.2 -0.70 -0.47 3.6 -0.41 -2.4 3.9 -0.57 -1.6 3.4 -0.44 -0.60 4.2 -0.50 -1.2 4.0 -0.21 -1.7 4.2 -0.59 -1.4 3.9 -0.81 -0.89 4.5 -0.90 -1.1 3.5 -0.22 -2.1 3.6 -0.45 -2.0 3.8 0.03 -1.2 4.1 -0.23 -2.9 4.1 -0.07 -1.0 3.6 -0.03 -1.1 3.8 -0.01 -1.0 4.6 -0.32 -2.9 4.2 -0.20 -0.84 Dayananda
1 = Ag; 2 = Zn; 3 = A! Solid-solid couples with intersecting diffusion paths; the interdiffusion fluxes of Zn and Ag are reduced down each other’s gradient; the negative &s indicate Zn and Ag attract each other in Al. Bf, increaseswith Zn concentration and decreaseswith Ag.
84Ml
4 Solid-solid couples with intersecting diffusion paths; &, is more sensitive to Ag content than to Zn; @, is more influenced by Zn.
84M
Solid-solid diffusion couples with intersecting diffusion paths; the cross coefficient B:, becomes appreciable in magnitude compared to B:, .
84Ml
(continued) Landolt-BCmstein New Series 111126
6.8.1 Ternary interdiffusion
Ref. p. 4351
T
Composition It. %
Remarks
Al
Zn (continued) 4.1 3.1 1.6 2.2 2.3 2.4 3.7 2.8 5.4 2.6 1.9 2.1 3.1 2.2 4.8 2.3 2.5 1.9 4.0 2.0 3.0 1.5
R2
El
Q2
-0.42 -0.06 -0.40 -0.60 -0.42 -0.51 -0.46 -0.64 -0.50 -0.68 -0.74
-1.9 -0.69 -0.88 -2.2 -2.4 -0.77 -1.6 -2.7 -1.0 -2.2 -0.98
4.9 4.3 4.4 4.7 5.1 4.6 4.9 4.6 4.9 5.0 6.0
808
3.7 4.4 3.0 3.4 3.4 2.9 3.0 3.2 3.5 4.0 3.1 2.7 3.1 4.1 2.6 2.6 2.9 2.1 2.4 3.0
-0.02 -0.16 -0.11 -0.18 -0.10 -0.29 -0.60 -0.29 -0.09 -0.29 -0.74 -0.61 -0.53 -0.69 -1.2 -1.1 -0.77 -0.75 -1.1 -0.85
-0.81 -2.5 -1.5 -1.7 -2.2 -0.71 -0.78 -1.3 -2.7 -2.4 -1.3 -0.88 -1.7 -3.2 -1.85 -2.0 -2.3 -1.1 -2.3 -1.6
5.5 5.4 4.3 4.6 5.8 5.5 5.8 5.2 5.3 7.1 5.5 5.7 6.7 6.6 5.8 6.3 6.7 6.7 6.7 7.6
0.46 (fee) 2.75 832 3.23 0.56 2.49 0.69 2.93 0.85 4.65 0.92 2.15 1.01 2.57 1.27 6.22 1.33 1.85 1.35 4.15 1.37 2.19 1.76 1.36 1.96 5.31 1.99 2.09 3.55 2.49 1.67 3.01 2.73 4.39 2.85 3.68 3.60 3.66 2.25 2.62 4.62
6.5 6.8 6.6 6.4 7.3 6.5 6.1 7.7 5.4 5.6 5.9 5.2 6.5 5.4 5.4 5.3 5.7 4.7 4.3 3.3
-0.17 -0.29 -0.26 -0.31 -0.39 -0.68 -1.1 -0.76 -1.2 -0.60 -1.9 -0.44 -1.4 -1.2 -1.1 -1.5 -0.87 -1.3 -1.1 -2.4
-1.8 -2.8 -0.98 -2.4 -4.2 -2.1 -3.3 -6.4 -1.7 -3.3 -2.7 -0.85 -4.1 -3.4 -1.9 -2.5 -3.5 -3.0 -1.8 -1.9
7.9 8.7 8.9 9.1 10.0 8.7 9.4 10.0 9.3 10.0 11.0 8.7 12.0 11.0 11.0 12.0 11.0 12.0 12.0 13.0
0.43 (fee) 2.7 3.3 0.55 2.4 0.74 2.8 0.90 4.7 0.91 2.3 0.93 1.2 2.6 1.9 1.3 4.2 1.4 6.5 1.4 2.3 1.6 1.5 1.9 2.1 3.6 2.1 5.7 2.4 1.7 2.8 3.1 3.1 4.7 2.3 3.8 4.0 3.9 2.8 4.9
Land&B6mstein New Series III/26
Fig.
Ref.
K R
Ag 1.5 1.9 1.9 1.9 2.1 2.5 2.8 2.8 3.7 3.8 4.9
381
coefficients (Tables)
Dayananda
84Ml
Solid-solid couples with intersecting diffusion paths; the @s increase with T. Approximate Q values over T-range 765...832 K determined for average values of each coefficient : Q for 8:,=126kJmol-’ Q for &, = 126kJmol-’ Q for ~~,=115kJmol-1 Q for 8:, = 128kJmol-‘.
84Ml
Solid-solid couples with 5 intersecting diffusion paths; the negative cross-coefficients indicate that the interdiffusion fluxes of Ag and Zn are reduced down each other’s gradient; B:, varies little with Zn and 8& varies little with Ag.
84M1, 84M2
6.8.1 Ternary interdiffusion
382 Composition at.%
Remarks
T
Cd
r(fcc) 2.9 3.0 3.1 3.3 3.5 3.8 3.8 4.2 4.4 6.5 6.7 7.0 7.1 8.5 9.0 9.8 10.2 10.5
2.1 0.43 0.73 3.2 1.8 3.1 0.61 0.93 3.0 2.3 1.11 2.4 I.3 2.3 2.5 0.99 0.89 1.9 0.53 1.0 0.86 1.2 1.1 2.1 2.3 0.74 1.7 I.2
Zn 10.8 873 11.4 11.8 12.3 13.1 14.4 14.7 16.3 18.1 Il.6 12.1 12.8 13.3 16.4 11.3 12.0 12.5 13.0
0’:2
&
Ref.
a:2
In units of IO-i4 m2 s-i
Cu
0.7 a(fcc) 66.3 998 2.1 90.1 2.4 81.6 44.6 2.5 2.7 66.6 41.8 3.0 3.0 88.6 81.0 3.9 35.1 4.2 58.5 4.8 79.8 5.9 62.9 9.5 11.8 6.1 12.9 60.3 18.0 35.1 34.0 13.1 36.6 6.3 14.0 15.7 56.2 1.2 58.6 7.5 6.2 59.3 59.3 7.3 59.5 6.0 Il.2 71.9 72.7 3.6 78.1 13.8 34.5 5.9 2.1 36.9
4g
Fig.
K a:,
Au
[Ref. p. 435
coefficients (Tables)
2.4 0.04 -0.21 0.04 0.11 -0.01 0.73 0.81 0.20 0.18 0.75 0.29 -0.03 0.08 0.20 0.17 1.7 0.57 0.53 0.81 0.28 0.42 1.04 1.9 0.73 1.11 I.8 I.6 2.8 0.09 1.7 0.86 1.1 2.1 0.39 0.22 0.96 0.57 0.28 0.83 0.77 0.21 0.50 0.70 -0.28 0.81 0.04 0.19 0.07 -0.60
1 = Cu; 2 = Ag; 3 = Au 1.8 0.85 1.3 3.3 1.5 2.0 0.93 1.4 2.8 3.0 I.5 3.6 3.1 4.0 I.3 2.4 0.91 0.76 1.3 0.63 I.6 1.4 0.42
In units of lo-l4 m2s-* 0.74 0.82 0.91 1.0 I.2 I.5 1.4 I.6 3.3 1.4 1.7 2.4 2.3 4.4 2.3 4.0 4.5 4.9
0.77 0.80 0.67 0.71 1.3 1.0 2.0 4.8 2.4 0.98 0.90 0.71 I.4 4.5 2.2 1.4 1.9 2.6
0.01 0.06 0.10 0.11 0.13 0.24 0.13 0.03 0.60 0.18 0.36 0.61 0.50 I.4 0.50 2.5 2.8 2.9
0.98 0.86 0.79 0.89 1.2 1.1 1.7 3.7 2.1 I.5 I.4 I.5 2.0 5.5 3.3 2.2 2.9 4.1
Dayananda
6 Solid-solid diffusion couples; intersecting diffusion paths; compositions where only b:, and @, are reported correspond to extrema in Ag concentration profiles; Bf, is nearly independent of Ag content for low Ag alloys; Bz, correlates with thermodynamic properties and Ag exhibits up-hill diffusion down a Cu gradient.
672
l=Zn;2=Cd,3=Ag Vapor-solid diffusion 7, 8 couples with intersecting diffusion paths; Ag-Cd-Zn alloy chips used as vapor sources in contact with Ag or Ag-8.7 at.% Zn alloy disks; appreciable cross effect between Zn flow and Cd gradient resulting in up-hill diffusion of Zn up its own concentration gradient in several couples; d:, and @, show maxima when plotted against Ag concentration at C,,/C,, = 3.8.
72C
Land&-BCmstein New Series III,/26
6.8.1 Ternary interdiffusion
Ref. p. 4351 Composition at. %
s;
rn’s-l Ql
Al
Remarks
T
K
Co Cr [wt.%]
0.3 (fee) 5.1 1373 4.0 11.1 2.4 0.3 4.9 4.9 1.5 8.7 3.3 1.7 6.5 4.4 1.9 7.1 3.3 1.9 7.9 4.3 2.0 7.8 4.2 2.1 11.4 5.4 2.1 7.4 4.6 2.2 12.1 4.9 2.2 12.5 5.2 2.3 11.4 5.2 2.4”) 11.5 5.6 2.4”) 11.5 5.6 2.4 11.5 5.7 2.5 11.8 5.9 2.5 2.2 7.1 2.6 13.4 5.5 2.6 9.9 5.2 2.8=) 9.9 5.5 2.8a) 9.1 6.1 2.9 9.2 5.8 3.0 3.3 10.0 4.1 2.9 9.4 4.2”) 2.9 6.8 4.2”) Ni
0”:2
El
-0.2 1.0 0.009 0.47 0.043 2.5 1.4 1.8 1.9 0.88 2.4 4.1 0.45 1.2 1.3 1.4 2.7 0.04 4.7 1.0 2.5 1.7 0.5 0.62 0.45 0.084
Fig.
Ref.
62 1 = Al; 2 = Cr; 3 = Co
In units of 10-15m2s-1 -1.5 8.7 0.14 0.3 0.43 0.61 0.51 0.44 0.19 0.52 0.51 0.56 0.65 0.74 0.61 0.63 0.68 0.09 1.3 0.7 0.57 0.64 0.85 1.7 1.4 0.73
383
coefficients (Tables)
2.4 2.6 1.9 1.1 1.6 1.4 1.6 1.7 1.7 1.4 2.3 2.3 2.0 2.2 2.0 1.7 1.9 3.0 2.6 2.4 1.8 1.7 2.2 2.1 2.1 2.0
Solid-solid diffusion 9 couples with intersecting diffusion paths. Several of the reported data are not included here due to large errors arising from small concentration gradients or small angles between diffusion paths at the common composition point of couple pairs; Cr interdiffusion is enhanced down an Al gradient and vice versa, as indicated by mostly positive crosscoefficients. “) Two runs
80Rl
1 = Al; 2 = Cr; 3 = Ni
Al
Cr
In units of lo-l4 m2s-’
3.21 3.59 3.77 3.83 4.49 5.16 5.33 5.72 6.71 7.66 8.46
6.74 (fee) 1373 1.61 1.27 19.90 9.22 1.67 1.34 20.83 1.53 24.05 16.70 1.70 1.92 29.17 1.96 17.21 2.58 18.23 2.07 13.54 2.47 13.66
0.35 0.29 0.44 0.29 0.33 0.56 0.43 0.58 0.80 0.58 0.81
1.02 1.46 0.94 1.12 1.14 0.91 1.34 0.55 0.73 0.73 0.90
0.89 0.89 1.05 1.02 1.05 0.23 1.15 0.81 0.97 0.99 1.00
Solid-solid diffusion couples with intersecting diffusion paths; both cross coefficients are positive; o”,“, can be larger than o”,“, .
87Nl
2.45 2.46 2.62 2.65 2.80 2.84 2.90 2.96 3.23 4.38
14.65 (fee) 1473 7.61 8.21 14.61 14.04 5.97 13.90 6.75 7.13 13.36 13.25 6.40 13.05 6.30 33.49 7.16 7.50 33.31 10.40 32.36
1.40 1.57 0.97 1.18 1.31 1.11 1.13 0.39 0.66 2.85
4.66 4.58 3163 3.61 3.70 2.97 3.68 4.96 5.74 5.09
3.96 3.94 3.67 3.66 3.68 3.47 3.71 4.81 5.94 4.96
Solid-solid diffusion 10 couples with intersecting diffusion paths; o”Tl is approximately 4 times greater than o”:,, while o”& and o”;, are of the same magnitude.
87Nl
(continued)
Land&-Biirnstein New Series III/26
Dayananda
6.8.1 Ternary interdiffusion
384 ,Composition at.%
Remarks
T K o”:,
Al 4.40 4.40 4.46 4.49 4.53 4.55 4.56 4.64 4.72 4.80 4.83 4.90 4.92 4.93 4.97 4.97 5.01 5.24 5.46 5.62 5.70 5.79 5.94 5.97 5.98 5.99 6.11 6.13 6.17 6.18 6.22 6.74 6.86 6.89 7.01 7.06 7.10 7.78 8.08 8.10 8.12 8.12 8.24 8.32 8.33 8.40 9.31 9.42 9.55 9.66
Ni Cr 31.53 31.63 34.31 34.58 15.38 25.61 15.20 14.70 14.19 13.80 25.46 13.26 24.55 24.68 2.48 12.77 24.46 1.93 1.58 18.00 9.05 3.32 15.92 15.58 2.70 15.40 14.14 13.94 13.39 2.10 12.33 4.41 3.85 16.35 16.11 2.88 15.96 5.65 27.40 17.21 14.10 17.15 13.86 31.44 13.72 16.54 29.05 14.34 14.08 10.89
(continued) 10.94 11.41 13.05 10.87 11.63 8.62 12.73 8.41 7.91 9.39 9.00 7.84 10.88 8.55 8.43 8.07 11.77 10.75 10.76 9.36 12.44 8.73 15.96 16.83 13.18 9.60 9.55 11.20 8.97 11.66 9.79 9.16 15.94 11.31 11.15 12.72 11.15 2.73 10.93 13.14 14.62 14.61 12.75 15.98 11.60 13.89 7.70 17.68 11.10 15.72
a2 2.74 2.55 2.80 2.83 2.26 2.01 2.44 1.73 1.64 1.89 2.15 1.69 2.37 2.02 1.89 1.68 3.31 3.18 3.31 2.57 2.91 2.37 3.44 3.42 3.78 2.77 2.86 3.00 2.78 3.34 3.05 2.89 4.28 3.45 3.25 3.66 3.25 8.84 1.31 4.22 5.14 4.88 4.10 3.83 3.49 4.60 0.16 6.62 3.50 3.15
o”:, 4.02 4.82 7.02 8.35 6.14 8.44 6.04 3.98 3.70 4.23 7.48 3.85 5.94 2.91 1.32 2.45 6.93 1.49 1.08 3.33 -0.11 2.03 8.19 7.62 3.00 4.31 3.86 4.58 4.40 1.88 2.49 1.86 5.44 5.47 4.52 3.49 5.17 2.30 1.20 4.95 4.91 6.76 4.40 10.31 6.43 5.97 7.41 5.20 7.61 2.69
[Ref. p. 435
coefticients (Tables) Fig.
Ref.
& 4.79 4.78 4.63 3.89 3.84 5.86 3.81 3.47 3.37 3.43 4.24 3.95 4.09 3.71 3.59 3.05 5.33 3.56 3.30 3.86 3.01 3.20 4.32 4.12 3.36 3.86 3.71 3.74 3.60 2.94 3.40 3.80 3.05 5.43 4.55 2.18 4.91 4.39 1.23 5.13 4.91 5.95 4.62 7.67 5.82 5.65 6.61 5.55 6.71 4.30
The large positive o”:, implies enhancement of Cr interdiffusion down an Al concentration gradient. Both o”:, and a:, increase with increasing Al concentration but show little dependenceon Cr.
87Nl
(continued)
Dayananda
Landok-BBmstein New Series III/26
Ref. p. 4351
6.8.1 Ternary interdiffusion
T
Composition at.% Al
Cr
9.75 9.76 9.77 9.78 10.17 10.18 10.21 10.28 10.31 10.34 10.34 10.40 10.41 10.43 10.46 10.53 10.56 10.57 10.58 10.64 10.64 10.65 10.70 10.74 10.76 10.76 11.03 11.24 11.24 11.25 11.34 11.38 11.38 11.39 11.45 11.47 11.59 11.60 11.78
19.72 13.63 19.70 11.31 10.73 20.80 12.73 18.37 20.66 14.69 19.12 13.56 13.55 21.60 12.22 20.41 10.62 10.16 18.89 8.05 8.07 8.05 21.18 14.88 21 .lO 22.84 19.86 20.38 22.02 9.34 21.86 18.16
0.19 0.51 0.82 0.93 0.94 1.48 1.48 1.57 1.62
coefficients (Tables) Remarks
385
Fig.
Ref.
K Ni
10.50 20.81 20.08 19.37 21.42
10.10 10.51 34.50 (fee) 25.30 46.37 35.15 35.43 33.95 46.96 35.73 35.92
(continued) 20.01 16.10 21.73 12.43 19.08 21.80 13.02 19.94 21.17 21.85 24.37 18.25 18.02 21.83 15.52 23.58 19.44 13.86 24.05 10.17 21.03 12.33 21.82 26.58 23.30 25.70 25.07 24.14 24.91 17.15 28.11 29.11 23.97 9.60 31.51 30.83 29.14 20.54 26.90 3.01 3.84 4.33 4.77 6.21 6.09 4.87 6.03 5.87
4.31 5.97 5.84 4.27 9.04 6.45 4.56 6.84 5.52 6.15 6.64 6.09 3.50 7.04 5.88 7.07 5.69 5.62 5.63 10.90 5.53 5.40 6.95 2.02 7.87 7.52 6.77 7.78 6.32 9.52 7.95 6.39 11.22 13.44 13.20 10.22 7.93 9.74 8.14
-
5.89 4.99 7.42 3.24 2.46 10.05 2.80 5.04 8.51 5.64 8.30 5.54 5.21 5.71 7.65 12.50 2.93 6.14 6.48 2.88 5.88 3.46 5.34 8.00 8.61 9.57 9.81 3.60 11.52 6.08 9.33 3.69 2.42 12.10 -2.86 8.39 6.91 7.43 1.70 -2.79 2.36 4.67 1.92 5.65 4.24 2.60 11.71 6.35
87Nl
6.05 5.52 7.41 4.22 3.72 6.77 4.52 8.12 5.33 6.52 8.44 7.12 3.93 8.54 6.99 8.84 5.77 6.40 7.31 7.25 5.78 5.75 8.80 3.35 11.05 8.43 6.17 8.62 9.90 7.08 8.75 4.63 4.55 5.74 4.55 4.73 7.68 7.59 10.91
-
At maxima of Cr concentration profiles.
87Nl
(continued)
Land&-BBmstein New Series III/26
Dayananda
6.8.1 Ternary interdiffusion
386 Composition at. %
Remarks
T
Al 1.79 2.02 2.22 4.65 4.05 4.38 6.24 7.34 10.65
Ni Cr 13.33 26.36 25.74 14.19 19.52 32.61 11.56 0.87 7.31 -
1.2 1.2 1.3 1.8 1.3 3.4 7.1 11.8
10.9 (fee) 1373 24.3 35.4 11.7 24.9 1473 33.6 27.6 8.8
Al
(continued) 5.65 5.67 6.91 7.82 -
1.2 Cu
Cu
0”:2
s:,
s:,
1.86 2.90 3.18 2.69 5.36
3.30 9.15 6.04 3.65 -
2.82 5.01 3.26 3.84 5.54
~:,I~:*
Fig.
Ref.
In units of IO-r4 rn’s-’ -8.0
-
1 = Cu; 2 = Mn; 3 = Al 0.09
In units of lo-r3 m2s-’ 777
87N2
At ZFP for Al.
0.30
Zn
At maxima of Al concentration profiles.
At ZFP’s for Cr.
~:,I~:,
Mn
87Nl
Determined at compositions corresponding to ZFP’s for Cr.
1.73 1.79 1.13 1.07 0.81 1.42 1.16 0.78
829.5 17.8
Al
[Ref. p. 435
K &I
6.4
coefficients (Tables)
2.91
1.65
-
3.4
1.65
-
Darken-type couple: Al-3.8 wt.% Cu-1.15 wt.% Mn vs. Al-3.7 wt.% Cu; Cu interdiffuses up a Mn cont. gradient; @, taken as zero and the remaining coefficients obtained from a best fit to the cont. profile ofCu.
61K
l=Zn;2=Cu;3=Al 1.23
Darken type couple; Al-l 1.8 wt.%Zn-3.66 wt.%Cu vs. Al-12.6 wt.%Zn; with o”:, assumedzero, the other coefficients calculated from a best tit to the experimental concentration profile of Zn. (0.454+ Darken-type couple: 0.067% Al-l 1.8 wt.%Zn-3.66 wt.%Cu vs. Zn) Al-3.32 wt.%Cu; based on a tit to the experimental concentration profile of Cu.
63K2
(continued)
Dayananda
Landolt-BBmstein New Series 11I,f26
6.8.1 Ternary interdiffusion
Ref. p. 4351
T
Composition at. %
o”:, Al
CU
Zn
o”:,
0”:1
o”,“,
1.4 0.8 2.1 4.4 0.2 0.2 9.0 12.8 -6.003 0.06 0.01 0.3 0.3 0.5 1.3 0.06 1.0 1.0 0.08 1.1 0.05 1.3 0.1 0.1 0.04 2.2 2.0 0.5 0.8 0.1 0.2 0.02 1.0 0.03
0.003 0.01 0.1 0.2 0.1 0.2 0.3 0.4 0.07 0.3 0.3 0.2 0.3 0.5 0.6 0.01 0.8 0.9 0.5 1.0 0.5 0.7 0.4 0.7 0.8 1.7 0.9 0.8 1.3 1.0 2.7 2.1 1.3 -0.03
1.1 1.2 2.3 2.8 1.1 1.2 5.1 5.9 0.8 1.2 1.2 1.5 1.5 2.4 3.3 1.3 2.4 4.4 1.8 5.5 1.8 3.2 1.6 1.9 2.0 5.3 5.1 2.9 3.4 3.6 4.7 4.1 4.5 2.5
Fig.
Ref.
(continued)
0.4 a(fcc) 5.7 1173 1.6 1.9 0.5 6.7 1.3 3.7 13.3 1.4 4.5 14.8 1.0 1.5 2.5 1.7 2.0 1.0 10.1 1.9 19.4 11.3 1.9 20.2 2.1 0.7 0.9 2.2 0.8 0.5 2.3 0.8 0.3 2.5 1.4 4.6 3.3 1.5 3.9 2.2 4.1 7.7 4.9 2.7 9.3 5.4 2.8 1.3 2.2 5.4 5.6 4.4 6.0 11.4 6.3 1.1 1.3 6.5 12.2 4.9 6.6 1.2 0.8 6.7 3.1 6.7 7.0 1.5 2.3 7.5 1.4 1.3 7.7 1.4 0.9 8.1 8.0 4.5 5.1 8.8 8.6 9.7 2.1 3.1 3.4 3.0 11.2 1.3 2.1 11.4 1.3 2.4 11.7 1.4 2.5 12.6 4.5 12.6 3.7 3.5 14.5 1.6 Al
Fe
39.0 41.5 43.0 43.5 47.0 47.0 47.0 47.0 30.0 32.0 42.0 42.0 42.0 44.5 47.5 50.0
19.0 P(bcc) 1277 20.5 48.5 32.0 8.0 26.0 26.5 35.0 61.5 40.0 4.0 18.5 19.0 12.5 21.5 0.5
Land&B8mstein New Series III/26
Remarks
9,-1
K
387
coefficients (Tables)
1.6 1.6 16.4 3.6 1.2 2.7 3.3 4.4 1.3 7.7
1.2 -1.2 -5.9 1.7 0.3 0.7 0.2 -0.2 -28.6 -4.6 21.9 -1.0 -1.2 0.5 -
-0.4 0.4 0.3 0.5 -1.3 0.5 0.7 0.3 -0.5 -10.9
85T
1 = Al; 2 = Ni; 3 = Fe
In units of IO-l5 m’s1l
Ni
I= Zn; 2 = Al; 3 = Cu 11 Solid-solid couples with intersecting diffusion paths; appreciable repulsive interaction between Al and Zn identified by positive cross coefficients; limited studies carried over T- range of 1043.0. 1203K. At Cu-5.3 at.% Al-5.7 at.% Zn, the Q [kJmol- I] values for the coefficients, o”:, , o”:, , o”&, and & are, respectively, 196, 196, 198, and 200, with corresponding Do [10-4m2s-1] values of 1.28, 0.57, 0.42 and 2.07. At Cu-8.2 at.% Al-8.0 at.% Zn, the reported Q [kJmol-‘1 values for the four coefficients are, respectively, 189, 194, 202 and 199, with the corresponding Do [10e4 m2 s-l] values of 1.14, 1.08, 1.58 and 3.74.
0.8 0.6 2.5 1.2 0.5 1.1 0.8 1.6 3.4 1.3 16.2 0.9 0.7 0.6 -
Dayananda
Solid-solid diffusion 12 couples with intersecting diffusion paths; significant interaction among the components, as Al and Ni interdiffuse up each other’s concentration gradient. The crosscoefficients change signs across the p phase field; the main coefficients appear to be functions of the parameter Fe/(Fe + Ni).
76M
(continued)
6.8.1 Ternary interdiffusion
388 Composition at.%
Remarks
T
0”:2
a1
Ni (continued) Fe 17.5 P(bcc) 1273 42.1 86.2 24.5 88.4 26.0 43.2 16.7 9.94 14.5 4.07 15.5 4.45 10.0
-36.7 -22.0 -17.9 -11.6 - 9.2 - 5.54 - 1.24
- 47.6 -105.8 -122.7 - 27.5 - 15.0 - 1.79 - 1.66
71.8 38.8 29.1 14.9 13.3 11.4 3.78
7.0 8.0 8.0 8.6 9.0 9.2 12.2 12.5
57.5 y(fcc) 48.5 50.0 45.7 49.5 43.8 31.8 29.0
2.07 2.33 1.86 2.43 1.78 2.40 2.57 1.93
-1.09 -0.92 -0.88 -0.88 -1.45 - 1.07 -1.02 -1.06
-0.68 -0.99 -0.97 -1.36 -1.12 -1.72 -3.23 -2.10
1.25 1.64 1.59 2.02 1.75 2.09 2.21 2.25
C
Co
R2lR
0.85 1.16 1.85 2.43 2.62 3.08
4.78 (fee) 1323 0.01 4.77 0.01 4.75 0.03 4.69 0.04 4.73 0.05 4.68 0.07
Layered finite couple; quasi-steady state method; C interdiffusion slightly enhanced down a Co gradient.
C
Cr
1 = C; 2 = Cr; 3 = Fe
1.05 1.11 2.24 2.91
1.33 (fee) 1323 -0.08 2.13 -0.09 1.32 -0.18 1.31 -0.21
Fe
Fe
Solid-solid y/p multiphase 12 79c couples with intersetting diffusion paths; significant cross-interactions between Al and Ni; for alloys with >5 at. %Fe variations of the main coefficients expressedby log,,,@, [cm’s-‘1 = - 2.80XNi - 10.32X,, - 5.08 log,,@,[cm2s-‘1 = - 1.25X,, - 10.45X,, - 5.95. o”:, > B:, for most compositions; variations of the coefficients with composition in y not as significant as in 8 phase.
l=C;2=Co;3=Fe
R2lR
@2/R, 2.59 (fee) 1.58 1068 -0.10 2.85 0.91 1.59 2.66 2.02 2.84 2.98
Ref.
B:2
Al 27.0 27.0 27.3 31.5 32.5 33.5 35.5
Fe
Fig.
K a:,
C
[Ref. p. 435
coefticients (Tables)
Mn
13
64B
Layered finite couple; 13 quasi-steady state method for the determination of the ratio of cross to main coefficients; the negative ratios indicate that C interdiffusion is reduced appreciably down a Cr gradient.
64B
l=C;2=Mn;3=Fe
62K
13
Quasi-steady state method with layered finite couple; C diffusion slightly reduced down a Mn gradient.
1.57 1126 -0.08 1.6 1188 -0.03 -0.04 1.59 1.57 -0.08 1.58 1261 -0.05 1.57 -0.08 1.57 -0.10
Dayananda
Land&-Btimstein Ne\r Series 111’26
Ref. p. 4351
6.81 Ternary interdiffusion
coefficients (Tables)
Composition at.% C
Fe
2.22 (fee) 2.68 3.02 1.05 1.25 1.83 1.84 2.10 2.23 2.33 2.55 2.73 2.77 C
Cr
(fee) 9.0 9.0 9.0 9.2
Landolt-Bihstein New Series III/26
R/~:l
Ni 0.94 1083 1.87 1175 1.87 1.89 1323 0.95 1.88 0.94 1.88 0.94 1.88 0.94 1.87 0.94
Fe Si (fee)
2.73 (fee) 1.78 1.39 2.83 1.86 2.54 3.08 I.97
Co
Remarks
1.82 1.85 1.84 1.82 1.84 1.83 1.82 1.83
1323
1126 1188 1261 1331
@,/l?~, ratios determined 13 by quasi-steady state method with layered finite couples; the ratios appear to be independent of temperature over the range 1083... 1323 K; interdiffusion of C enhanced down a Ni gradient.
0.12 0.05 0.05 0.07 0.09 0.08 0.10 0.09 0.10 0.09 0.09 In units of 10-l’ m’s1i 0.34 0.023
0”:2/0”:1 0.24 0.08 0.15 0.26 0.17 0.24 0.28 0.18
Ni 21.4 1573 6.0 11.0 39.5 14.0 59.0 13.0 78.0
Fig.
Ref.
1 = C; 2 = Ni; 3 = Fe
0.10 0.10
4.8
389
13 Layered finite couples; quasi-steady state method; carbon interdiffusion in Fe-C - Si austenites appreciably enhanced down a Si concentration gradient; the ratio of the coefficients independent over the temperature range investigated.
In units of lo-l4 m’s11 -0.01 -0.06 -0.26 -0.25
1 = C; 2 = Si; 3 = Fe Darken type couple: Fe-3.89 wt.%Si-0.478 wt.%C vs. Fe-O.05 wt.% Si-0.441 wt.% C; 13 day anneal; up-hill diffusion of carbon against its own concentration gradient; fii3j calculated from a fit to the experimental profiles by Kirkaldy ignoring the term involving & ; a large interaction between C and Si gradient.
-0.1 -2.6 -4.5 -5.1
64B
49D, 57K
62K
1 = Cr; 2 = Ni; 3 = Co 2.0 5.0 5.0 7.0
Dayananda
Solid-solid diffusion couples with intersecting diffusion paths; Ni interdiffusion is reduced down a Cr gradient, as indicated by a large negative @, .
66L
6.8.1 Ternary interdiffusion
390
T
Zomposition It.%
Remarks
Fe
Ni
4.9 (fee) 72.5 1409 5.3 0.9 56.4 4.8 ,I.1 57.2 4.9 :3.0 18.2 2.4 13.8 55.0 4.8 16.5 3.5 1.8 !0.4 10.3 2.2 !4.9 6.0 1.95 !5.1 34.9 4.5 !5.4 66.1 5.35 !6.0 32.7 4.55 !6.8 32.4 4.8 !8.7 40.4 5.0 10.3 31.3 5.0 54.0 15.7 4.4 16.0 8.5 3.5 39.6 28.5 4.7 39.7 51.0 4.9 10.0 51.o 4.9 51.5 26.0 4.65 55.0 15.8 4.6 57.0 14.0 4.55 52.2 25.6 4.65 56.5 16.3 4.6 7.0 36.7 3.0 34.6 6.3 37.2 51.6 5.0 56.5 25.4 4.7 1.6 a(fcc) 2.2 9.2 10.3 11.4 11.5 15.2 23.7 25.0 25.5 29.2 29.2 30.1 30.3 30.6”) 30.6”) 31.1 33.3 35.5 36.5 38.5 44.8 48.0
[Ref. p. 435 Fig.
Ref.
K a:,
Zo
coefficients (Tables)
72.3 1588 8.5 68.3 6.7 4.8 35.6 31.4 4.0 19.7 3.4 70.2 6.8 15.5 3.8 25.3 4.7 49.0 6.5 66.5 6.7 31.2 6.4 67.3 6.4 41.9 6.6 61.5 6.6 40.7 6.4 40.7 6.8 65.6 6.1 30.2 6.1 35.4 6.5 19.9 5.4 6.25 29.0 27.8 6.4 13.5 5.3
o”:,
@*
a2
In units of lo-l5 m2s-’ 0.3 1.1 1.1 0.8 1.25 0.6 0.95 1.0 2.2 0.9 2.0 3.4 2.0 1.7 1.9 1.45 2.5 1.4 1.5 3.0 2.7 2.75 3.0 3.3 1.5 -
5.9 6.9 6.9 1.05 7.0 0.15 0.45 0.3 2.8 4.7 2.8 2.8 4.2 2.8 0.8 0.3 2.1 2.2 3.9 2.1 0.7 0.65 2.15 1.0 3.0 4.2 1.9
1 = Co; 2 = Ni; 3 = Fe 13.0 10.8 11.5 2.1 11.0 1.0 1.4 1.1 6.1 10.2 6.1 6.15 6.7 6.1 2.75 2.1 4.7 6.6 7.7 4.5 2.8 2.5 4.8 2.65 1.75 -
In units of 10-14mZs-’ 21.0 12.0 0.25 11.5 19.0 1.0 4.1 8.0 0.9 3.0 7.1 0.5 1.5 3.9 15.0 0.9 7.3 1.4 1.3 3.5 2.3 2.1 5.7 2.2 9.3 5.1 1.6 4.8 10.0 2.8 2.9 6.8 4.2 8.8 0.2 2.8 3.4 8.0 1.9 4.2 9.3 2.6 3.9 8.1 2.9 4.0 7.6 0.2 4.0 8.8 2.7 2.7 6.7 2.7 7.3 3.2 3.1 2.1 5.7 2.9 2.6 6.6 2.4 2.1 6.0 4.9 3.6 1.6
Dayananda
Solid-solid diffusion couples with intersecting diffusion paths; the interdiffusion fluxes of Co and Ni are enhanced down each other’s gradient; the large positive crosscoefficients as’s indicate that Co and Ni repel each other in Fe.
67s
Solid-solid couples with 14,15 69V intersecting diffusion paths; up-hill diffusion of Co down a Ni concentration gradient and vice versa. o”:, increases from the Fe corner to the Ni-rich part of the ternary isotherm; @, increases towards the Co-rich corner; @, and i?:, both indicate a maximum on the Fe-Ni side at 75 at.% Ni; data are consistent if DC,> D& w D& for ternary alloys. “) Two measurements withdifferent couples. (continued) Landoh-BBmstein New Series W/26
6.8.1 Ternary interdiffusion
Ref. p. 4351 Composition at. % Co Fe 48.0 48.3 51.5 54.5 60.5 65.7 67.9 68.0 74.0 2.1 3.8 6.6 28.8 40.5 47.0 56.5 56.5 74.2 Co
2.15y(fcc) 3.20 3.35 3.00 3.70 4.2 5.10 6.00 6.00 6.30 6.40 6.70 7.50 8.95 9.00 9.20 9.25 9.35 10.00 10.00 10.00
Land&Biimstein New Series III/26
391 Fig.
Ref.
m*s-’ Ni (continued) 46.5 6.7 46.5 6.6 21.0 6.8 9.8 5.3 27.0 6.9 27.8 6.3 25.7 6.5 4.9 5.3 2.9 5.2 33.1 3.5 55.0 6.5 72.2 7.2 50.1 5.5 38.0 3.6 26.8 6.5 3.7 -
V Fe [wt.%]
Fe
Remarks
s;
48.8 (fee) 1.2 1273 1.77 47.2 . . 4.5 2.98 46.1 6.6 2.69 45.1 6.7 8.0 11.5 42.85 3.56 13.8 42.1 1.08 Cr
coefficients (Tables)
Ni 81.10 1373 6.2 73.70 6.8 36.65 4.9 38.00 5.8 68.70 7.0 65.15 7.3 56.85 8.1 48.50 5.1 24.30 3.7 22.80 3.9 43.60 6.8 39.80 5.5 68.30 4.4 82.10 5.1 24.00 4.7 36.00 3.6 17.45 3.7 28.55 5.1 42.40 5.6 49.00 4.7 55.90 7.5
2.0 2.0 3.6 4.1 4.1 2.5 2.8 4.1 4.2 2.1 4.0 2.8 4.4 4.2
2.6 2.3 1.8 1.0 1.5 1.3 1.1 0.6 0.3 3.1 10.0 7.8 1.9 -
7.4 7.2 4.5 3.6 5.1 5.2 5.0 3.4 2.7 9.8 3.2 7.7 3.0 3.0
0.72 1.6 1.6 7.3 1.8 3.6
0.05 4.3 5.5 5.01 4.3 0.66
-3.3 -0.3 0.5 -1.1 -1.6 -0.3 -0.3 -1.1 -0.1 -2.1 -0.7 0.2 0.1 -0.2 -0.2 0.5 -1.1 -1.8 -0.5 -0.8
Solid-solid diffusion couples with intersecting diffusion paths; the interdiffusion of V is enhanced down a Co gradient and vice versa.
82A
1 = Cr; 2 = Ni; 3 = Fe
In units of IO-l5 m2se1 -0.4 -0.4 -0.1 0.2 -0.3 -0.2 -0.2 -0.4 -0.3 -0.1 -1.9 -1.1 0.5 -0.2 -0.1 0.3 0.3 -0.6
At extrema in Ni or Co profiles.
1 = V; 2 = Co; 3 = Fe
In units of IO-l5 m2sA1 0.77 3.03 3.8 5.0 3.46 3.85
69V
10.3 10.8 3.6 4.1 10.0 9.2 7.6 5.9 2.6 2.9 5.2 4.9 9.3 7.7 1.8 2.7 0.9 2.7 3.5 3.9 7.3
Dayananda
Solid-solid diffusion 16,17 85Dl couples with intersecting diffusion paths as shown in Fig. 16. @, has its highest values around 8. lo-l5 m2s-’ for alloys with about 60 at.% Ni and decreases in value as the composition changes towards either the Ni or Fe corner of the ternary isotherm; the cross coefficients S:, and o”& are mostly negative and an order of magnitude smaller than the main coefticients, o”:, and a;,, which vary more with Ni concentration than with Cr concentration. (continued)
6.8.1 Ternary interdiffusion
392 /Composition at.%
T K
Cr
Ni (continued) 5.2 59.35 4.6 63.80 4.2 67.80 4.3 82.50 4.5 34.15 4.9 50.00 4.0 73.55 4.2 67.35 40.20 5.7 4.3 77.05 5.9 47.00 51.oo 5.3 5.7 32.10 4.6 34.80 7.3 53.50 48.65 8.2 5.0 56.50 4.7 71.55 5.9 38.80 53.80 8.0 4.1 67.00 7.8 50.00 5.9 46.10 42.15 6.0 4.9 58.05 43.85 7.3 5.4 70.40 52.25 6.1 5.5 48.00 6.3 46.10 4.2 66.60 4.9 60.70
Ni [wt. %1”
2.10 (fee) 2.76 3.1 6.7 7.8 8.5 8.8 8.9 10.0 10.5 11.4 11.5 12.1 12.1 12.1 12.4 12.7 13.5
Remarks
$,-, a:,
Cr Fe 10.15 11.10 12.40 12.40 12.65 13.33 14.65 15.80 16.20 16.25 16.80 17.50 18.00 18.80 18.60 19.20 19.60 19.90 20.20 20.40 20.50 21.50 21.60 21.80 22.00 22.55 22.80 22.95 23.80 24.2 24.50 26.80
coefficients (Tables)
4.04 1523 11.3 10.8 3.75 7.1 0.90 9.55 1.98 1.40 8.8 8.1 0.98 8.4 0.79 9.3 1.99 1.65 9.2 2.00 9.6 1.81 9.4 2.02 9.6 8.9 1.00 1.01 8.6 1.92 9.5 1.05 8.7 9.7 2.05 8.8 1.20
a:2
a:,
-1.0 -1.1 -1.1 -3.3 0.9 0.1 -2.0 -1.6 0.2 -3.4 0.7 -0.8 0.6 0.8 -0.7 -1.0 -1.8 -2.0 0.6 -1.0 -2.0 -1.2 -1.6 0.3 -1.5 -0.5 -0.7 -0.8 -0.6 -0.3 -1.1 -2.1
2.3 2.1 0.2 0.5 -0.3 -0.7 0.7 -0.5 -1.1 -0.1 -0.5 -1.0 -1.6 -0.6 -0.1 -1.5 -2.2 -0.5 -1.1 -0.7 -0.4 -0.7 -1.2 -0.8 -2.2 -1.5 -1.7 -0.9 -0.2 0.1 -0.7 -1.4
2.0 1.9 1.3 0.6 1.4 1.5 1.0 1.7 1.1
Fig.
Ref.
a:2 85Dl
9.1 9.7 9.6 9.8 2.8 3.9 8.9 6.9 4.1 9.5 4.6 5.5 3.6 3.2 7.5 6.9 6.4 6.9 3.8 6.6 7.5 6.6 5.6 4.2 6.2 4.8 4.1 4.5 4.3 4.1 4.7 6.1
In units of lo-l4 m2sV1 2.7 2.3 1.9 3.0 2.8 2.4 2.8 6.9 8.0 7.0 7.7 6.4 8.9 8.1 7.3 11.5 6.1 7.9
[Ref. p. 435
18.7 18.4 13.1 11.4 14.5 16.3 12.0 16.7 13.4
Dayananda
1 = Cr; 2 = Si; 3 = Ni Solid-solid diffusion 18 couples with intersecting diffusion paths; o”:, and a:, are similar at high Cr concentrations; the positive cross-coefficients indicate that Cr and Si interdiffusion fluxes are enhanced down each other’s gradient; o”:, increases with Cr concentration.
82J
Landolt-Bcknstein New Series Ill,26
Ref. p. 4351
6.8.1 Ternary interdiffusion
T
Composition at.%
q
K Ql
CU
Mn
coefficients (Tables) Remarks
m2sW1 o”:, El
Mn
Ni
Zn
a(fcc) 1.2 6.9 1123 8.7 1.8 10.3 18.2 2.4 8.1 11.4
cqfcc) 1.3 1.6 1.8 3.1 3.1 3.3 3.9 4.0 4.3 4.5 4.5 4.9 5.4 5.7 6.3 6.8 7.2 7.8 8.1 8.4 8.9 9.9 10.2 10.3 10.3 12.0 12.5 12.9 13.7 14.2 14.5 15.1 15.1
4.1 1073 2.0 5.9 2.5 6.7 2.6 3.1 2.4 10.5 6.3 11.0 6.9 4.0 3.0 12.4 8.8 9.5 5.4 2.3 2.4 13.3 9.1 5.1 3.8 2.8 3.2 1.7 2.6 6.4 5.0 2.0 3.6 7.2 6.3 3.8 4.2 3.9 3.8 8.3 8.9 2.5 3.3 9.4 10.5 2.8 4.6 4.8 5.7 9.7 11.1 5.3 6.8 10.9 16.9 3.3 6.0 5.9 8.3 3.5 6.3 12.1 19.9 6.3 8.2 12.6 19.8
Fig.
1 = Cu; 2 = Ni; 3 = Mn Solid-solid diffusion 19 couples with intersecting diffusion paths; the composition points of intersection where the 0”; were calculated are not available; data shown on the Ni - Mn - Cu isotherm (seeFig. 19).
0.4 -0.4 0.5 0.4 2.6 3.4 0.4 2.3 1.4 0.4 3.0 0.5 0.2 0.3 1.5 0.1 1.9 0.4 0.7 2.1 0.5 3.0 0.3 0.7 3.0 0.9 3.6 0.4 1.2 0.5 6.2 1.7 3.9
80Y
1 = Zn; 2 = Mn; 3 = Cu
In units of IO-l4 m’s1l 0.68 1.1 2.6
Ref.
&
1173
cu
393
-0.02 -0.17 - 0.08
9.0 14.6 12.2
Vapor-solid diffusion couples with intersecting diffusion paths; errors in S;, values can be as much as 100%.
65D
0.3 0.1 0.2 0.4 0.7 1.0 0.4 1.0 1.4 0.9 2.0 0.6 0.7 0.8 1.8 0.6 2.2 1.5 1.5 3.0 1.0 5.2 0.6 1.8 2.9 1.9 2.5 0.8 2.7 1.2 5.5 6.7 6.6
2.5 3.6 3.4 2.7 5.4 5.6 3.4 7.4 5.7 3.1 7.1 4.2 3.6 3.3 5.3 3.7 6.5 4.7 5.0 8.3 4.4 8.2 4.8 6.2 10.1 7.5 12.7 5.9 9.5 6.4 15.2 9.6 15.8
Solid-solid diffusion 20 couples with intersecting diffusion paths; positive cross coefficients indicate that interdiffusion fluxes of Zn and Mn are enhanced down each other’s gradient.
86T
(continued)
Landolt-Biirnstein New Series III/26
Dayananda
6.8.1 Ternary interdiffusion
394 Composition at.%
Remarks
T
Mn Zn (continued) 15.6 3.8 7.0 17.9 7.1 13.8 18.6 4.3 7.9 19.8 7.6 12.5 31.0 4.6 10.8 21.9 8.0 15.0 22.5 4.8 10.4 24.1 8.6 15.3 26.7 5.4 13.7 28.5 5.6 13.9
Cu
Ni Sn [wt. %]
(fee)
4.7 13.7
Zn 24 20 19 14 23
10 18 40 40
15 22 24 26
48 48
23 24
0”:2
a:1
0”:2
0.6 0.9 0.9 1.4 0.9 1.1 1.2 1.0 1.4 1.6
1.5 4.8 3.6 4.8 2.6 3.4 4.2 4.6 10.1 7.9
7.1 12.1 8.3 11.9 9.7 12.9 10.6 13.3 11.8 12.3
Ref.
1048
1.3 0.18
2.9 8.1 5.1 6.6 6.0
2.1 3.3
15.3 1048 27 43 19.5 15.8 35.5 23.0 47.7 26.9 30.1 8.9 9.0 12.4 8.6 16.0 8.9 12.4 4.0 10.8 3.9 10.8 3.9
-
4.96 1.23
5.0 -
In units of 10-l’ m2sW1 -1.8 -0.5 3.0 -0.4 -2.8 0.8 -0.8 1.2 -1.7 -0.5 -6.9 0.6 -0.6 -9.6 5.2 -2.8 -1.9 -1.3 -2.7 -18.8 -14.5 -16.9 -12.8 - 5.3 - 1.4 - 1.2 - 0.9 - 2.0 - 0.3 - 0.3
-
86T
1 =Ni;2=Sn;3=Cu
In units of lo-l4 m2sT1
8.0 1063 5.0
Cu Ni a(fcc) 37 42 43 46 47
a(fcc) 3.7 3.9 4.9 15.9 18.1 19.0 21.8 30.1 31.9 32.1 34.1
Fig.
K R
cu
[Ref. p. 435
coefficients (Tables)
-3.8 -1.9
3.1 2.1 4.4 2.3 -
- 2.6 -13 -11.4 -19.4 -10.2 - 6.7 - 8.8 - 7.7 - 5.9 - 5.8 - 4.8
8.9 13 9.5 11.1 7.4 0.6 3.5 2.3 2.4 0.7 0.6
Darken-type couples with an initial 6 wt.% step in Sn or Ni at x = 0; Kirkaldy analysis with o”f2 = 0; strong interaction between Sn and Ni indicated by up-hill diffusion of Sn against a Ni cont. gradient. The data are considered approximate. l=Zn;2=Ni;3=Cu 21 Solid-solid diffusion couples at composition points of intersecting diffusion paths. The cross coefficients are essentially negative.
72B
77s
At maxima and minima in Zn concentration profiles. At maxima and minima in Ni concentration profiles. Solid-solid diffusion 21 couples; intersecting diffusion paths; the negative a:, becomes negligibly small for Ni-rich alloys with low Zn; &,/@, ranges over 0 to O-0.5, while @,/fi:, varies over -l.Oto -8.0.
82K
(continued)
Dayananda
Land&-BBmstein New Series III!26
6.8.1 Ternary interdiffusion
Ref. p. 4351
-3
Dll Cu
Ni 38.7 44.8 51.3 61.6 63.6 70.0 80.6 81.8
Zn (continued) 2.3 5.0 21.3 9.5 4.8 21.2 2.4 13.7 12.0 2.3 1.5 6.0 1.3 9.8 1.5 12.0
18.1 31.0 64.4 14.8
28.8 2.7
n(fcc) 1.3 5.1 1048 19.0 23.1 1.3 11.1 4.4 6.4 19.9 5.2 6.7 17.0 9.5 9.6 8.2 6.8 9.9 6.2 5.7 10.0 4.8 10.1 3.6 5.2 10.3 1.8 4.3 6.2 10.5 3.6 5.0 10.8 1.9 11.4 24.2 42.0 12.5 12.5 9.7 14.4 4.6 4.9 5.0 15.3 4.8 17.2 2.8 3.7 17.5 5.6 8.4 18.0 2.9 6.4 3.0 19.0 3.1 24.5 4.1 0.9 a(fcc) 12.9 35.6 56.0 78.1
26.0 1048 17.0 15.0 10.5
@2
&l
-0.1 -0.9 -2.0 -0.1 -
-
-1.2 -5.2 -2.7 -1.8 -0.8 -1.3 -1.0 -0.2 -0.3 -0.5 -0.4 -4.6 -4.5 -0.6 -0.7 -0.4 -2.4 -0.9 -0.3 -
Fig.
Remarks
0”; rn’s-l
T K
Composition st. %
395
coefficients (Tables) Ref.
o”L
5.1 6.4 6.9 2.5 1.1 1.4 1.1 1.1
-10.2 - 1.9 - 1.2 - 1.7 - 0.9 - 1.1 - 1.1 - 1.1 - 1.2 - 1.2 - 1.3 - 3.2 - 0.9 - 0.7 - 2.6 - 0.7 - 0.3 - 0.8 - 0.3
0.3 4.6 2.3 0.7 1.8 0.4 0.4 0.5
The large negative ratio 21 of o”~,/& reflects the fact that along lines of constant Ni concentration, the thermodynamic activity of Ni is decreasedby increase in Zn but increased by increase in Cu concentration.
-
At maxima in Ni concentration profiles.
1.0 1.9 1.7 1.9 1.4 1.8 1.0 0.9 0.7 1.0 0.7 2.8 1.5 0.9 1.5 0.9 1.0 0.4 0.4 0.2
21 Solid-solid diffusion couples with intersecting diffusion paths; diffusion temperatures ranged over 1023... 1133 K; the variation of the coefficients [m’ s- ‘1 at 9.9 Ni-4.9 Zn [at.%] are expressedby:
o”X% -2.4 -4.2 -4.8 -3.7
82K
83T
194RT kJmol-’
o”:, = 1.75 * lo-’ exp -
190RT kJmol-’
L?:, = 2.96. 10e6 exp [ -
191RT kJmol-’
o”,“, = 3.48. 10e6 exp [ o”:, = 2.3. lo-’ exp
208RT kJmol-’
Ratios of cross/main interdiffusion coefficients determined at zero-flux planes (ZFP) for Ni, developed in Ni-isoactivity couples.
1 1 1 1
84K
0”:,/0”:3
16.1 12.9 23.7 22.9 31.0 20.8
0.8 0.9 1.2 1.0 1.0 1.0
Determined at ZFP’s for Cu observed in Cu-isoactivity couples.
10.5 21.5 33.9 32.7
1.2 1.2
Determined at ZFP’s for Zn.
6.6 16.5 23.8 25.2 30.0 53.4
(continued)
Land&-Biirnstein New Series III/26
Dayananda
396
6.8.1 Ternary interdiffusion
Composition at.%
Remarks
T
Ni
Zn
o”:,
(continued)
o”:,
1.0 5.3 1133 101.6 2.0 6.0 123.8 2.9 6.4 110.3 5.9 16.7 294.1 9.0 8.8 74.2 9.8 6.2 45.7 9.9 5.3 40.9 10.0 3.9 35.9 10.1 4.0 41.3 10.4 2.3 30.3 10.7 2.3 34.6 14.4 11.1 51.7 15.6 5.2 27.6 16.5 5.5 36.8 17.6 5.9 26.0 18.2 4.8 23.9 18.3 3.2 18.4 24.1 18.6 3.3 20.2 3.4 17.7 24.5 3.9 15.3 1.7 11.8 2.3 6.4 3.1 5.2 4.5 6.5 5.6 16.7 7.7 12.1 11.0 5.3 16.2 17.8 25.1 9.8 11.3 22.5 30.5 5.5
u(fcc)
Fig.
Ref.
o”:,
m% -4.0
Determined at ZFP’s for Ni.
-2.6 u(fcc)
[Ref. p. 435
K Gl
Cu
coefficients (Tables)
0.25 8.10 1173 0.60 7.68 4.32 7.51 7.82 7.49 9.12 7.44 9.92 7.38 0.50 9.15 4.25 10.22 9.52 11.51 10.72 11.78 22.00 14.29 22.33 14.33 16.40 15.48
349.2 9.3
19.5 21.4 14.5 15.2 10.8 14.1 20.3 51.2 28.7 17.2 9.7 12.1 34.6
-12.0 -22.4 -20.2 -65.8 - 8.8 - 5.6 - 6.1 - 3.2 - 4.4 - 1.6 - 2.1 - 2.0 - 2.6 - 5.9 - 2.6 - 2.2 - 1.1 - 1.7 - 1.1 - 1.2 -63.7 -22.8 -12.0 -17.2 -65.5 - 20.4 - 5.4 -43.0 - 3.2 -
1.4 0.7 2.4 -13.8 -10.0 - 7.6 - 6.8 - 6.2 - 1.6 - 3.8 - 1.1 - 4.2 0.7 - 0.1 - 3.8 - 1.2 - 1.0 2.0 - 4.1 - 3.0 -21.4 - 2.0
In units of lo-l4 m’s-’ - 8.0 0.7 - 6.3 -0.5 1.4 - 3.2 -1.0 - 1.9 -0.9 - 1.4 -1.0 - 1.2 - 7.2 1.9 -12.3 -6.7 -3.1 - 6.1 -1.8 - 3.4 -8.5 - 1.4 - 1.8 -4.7 - 5.1 -9.3
7.1 7.1 8.0 16.6 7.8 4.6 5.0 5.5 4.5 3.2 2.9 5.1 3.7 4.1 5.5 3.6 1.6 1.2 1.7 1.3
Solid-solid diffusion couples with intersecting diffusion paths.
10.6 7.8 6.5 8.7 16.6 7.4 4.7 14.0 2.4
At maxima and minima in concentration profiles of Zn.
-
2.2 2.1 1.7 1.2 1.1 1.0 3.8 2.4 1.8 2.3 1.7 3.3
84K 22
84T
At maxima in concentration profiles of Ni. 4.7 Solid-solid diffusion couples with intersecting diffusion paths.
73w
(continued)
Dayananda
Land&BCmstein New Series 111’26
Ref. p. 4351 Composition at. %
T
0”;
K
m2s-l 0”:1
Cu
Cu
Ni 18.20 25.00 9.11 9.92 21.80 9.00 9.95 35.32 10.25 11.42
Zn (continued) 15.40‘ 19.0 12.52 10.1 7.75 11.7 7.94 14.1 12.10 11.5 9.10 13.1 9.33 15.4 16.68 7.3 12.45 27.2 12.82 20.6
Sn
Zn
(fee) 1.7 2.8 3.7 4.2
o”:, -
3.4 1.2 0.8 1.1 1.5 2.0 2.6 1.4 3.7 2.1
Remarks 0”:1
o”,“,
-8.6 -2.6 -0.8 -1.0 -4.7 -1.9 -2.6 -2.8 -2.4 -1.8
3.0 1.2 1.3 1.3 1.7 2.6 2.4 1.4 1.9 1.3
In units of lo-r4 m2 s 1
15.0 1023 3.8 10.5 3.1 8.4 3.4 3.6 2.7
4.1 4.5 4.6
9.4 1.7 3.4
2.1 2.6 3.1 3.2 3.5
11.2 11.9 14.3 8.7 9.5
4
5
1094 2.6
6
5
771 2.4
Fe Ni a(bcc) 0.0 0.0 0.0 0.69
coefficients (Tables)
6.8.1 Ternary interdiffusion
5.4 2.3 2.6
397 Fig.
Ref.
73w
1 = Zn; 2 = Sn; 3 = Cu
2.1 0.76 0.35 0.19
0.03 0.3 1.1 0.9
0.68 1.4 3.5 2.1
Vapor-solid couples with 23 intersecting diffusion paths; Cu- Sn and Cu - Sn - Zn alloys with a nominal Cu/Sn ratio of 97/3 employed as diffusion disks and vapor sources; up-hill diffusion of Sn.
-
3.5 1.3 2.3
-
At maxima in Sn profiles.
0”:2/0”:1
9.0 9.7 5.0 4.8 4.6
Determined at ZFP compositions
In units of lo-l3 m2s-l 24 5 0.78 0.97 1.5+ Darken-type couples; O.l6C& cross coefficients assumed constant; &, In units of lo-l6 m2s-l essentially independent of C,,; B,“, strongly IO.9 4.3 0.77+ 0.24 C& dependent on C,,; Sn flows down a Zn gradient ; multilayered finite couples also employed to increase the sensitivity for the cross coefficients and data shown as plots.
P In units of IO-l4 m2sv1 1.95 1173 4.20 2.0 5.0 2.2 6.10 2.34 4.79 1.26
68Dl
65K
1 = P; 2 = Ni; 3 = Fe 73H
(continued) Land&-Biimstein New Series III/26
Dayananda
6.8.1 Ternary interdiffusion
398 Composition at.%
Remarks
T K a:,
Fe
Ni
x(bcc) 0.0 0.0 0.0 0.41
x&c) 0.0 0.0 0.0 0.10 0.10 0.28 0.30 0.30 0.36 0.37 0.44 0.47 0.58 0.60 0.70 0.71 0.74 0.79 0.80 0.81 0.90 0.91 0.91 0.91 1.13 1.41 1.58
o”:,
a:,
[Ref. p. 435
coefficients (Tables) Fig.
Ref.
a:*
P (continued) 1.95 1273 2.0 2.2 2.30
2.15 2.55 2.80 3.27
In units of IO-l3 m2sW1 -0.15 0.775
1.95 1373 8.0 2.0 9.6 2.2 11.5 1.86 3.70 2.39 12.8 1.86 3.70 2.36 13.1 2.93 14.6 2.32 13.1 2.95 14.9 2.73 13.9 3.70 1.86 2.88 15.8 2.57 13.0 2.50 12.3 3.70 3.03 17.5 1.86 2.65 13.6 2.84 14.3 3.03 15.0 2.76 15.0 3.12 17.0 3.01 16.3
In units of IO-l3 rn’s-l 2.50 5.70 -0.61 3.98 3.10 6.90 -0.40 4.18 -0.62 4.76 -0.44 4.30 5.20 -0.67 4.55 7.20 3.30 5.45 4.80 4.53 8.00 5.85 -0.76 3.50 -0.42 -0.47 5.55 6.50 6.30
y(fcc) 11.8 0.44 1173 6.0 0.48
2.65 4.65
In units of IO-l5 m*s-l 0.018 0.047 0.011
y(fcc) 12.4 0.43 1273 5.64 0.49
2.21 1.45
In units of IO-l4 m*s-’ 0.014 0.026 -0.002 0.015
y(fcc) 4.7 4.7 6.7 7.8 7.8 8.0 8.4 9.0
5.9 7.5 7.10 7.4 7.5 -
In units of IO-l4 m*s-’ 0.012 0.082 0.031 0.308 0.051
0.51 1373 0.68 0.44 0.29 0.47 0.0 1.70 0.0
Dayananda
73H
Solid-solid diffusion 25 couples with intersecting diffusion paths and Darken-type couples; experimental error too large to evaluate the cross coefficients o”:, ; the addition of P increases the main coefficients; temperature dependence expressedby: for ct (2.3 at.% P, 0.05 at.% Ni) &,[mzs-‘] = 2.72.10e4 -218.6kJmo!-’ *exp RT ( > @,[m*s-‘1 = 0.62.10T4 -215.6 kJmol-’ *exp RT >
73H
Solid-solid couples; 25 73H intersecting diffusion paths; o”:2 measured by Darken-type couples, o”:, not measured due to large errors; P additions increase the main coefficients; temperature dependence of coefficients given by: . (continued) Landok-B6mstein New Series III/26
Ref. p. 4351
6.81 Ternary interdiffusion
,Composition at. %
T K
0”; rn’s-’ 0”:1
Fe
Ni 9.0 9.5 9.60 10.0 10.7 10.7 11.0 11.5 12.0 12.0 12.2 12.2 12.2 12.2 12.2 13.0 13.6 14.25 14.25 14.25
coefficients (Tables)
P (continued) 1.03 10.0 1.05 10.1 1.70 0.96 10.2 1.70 0.0 0.90 9.87 0.0 0.91 9.74 0.43 9.4 0.51 9.5 0.62 9.6 0.36 9.3 1.70 1.70 0.47 9.1 0.38 6.15 0.89 8.82 1.26 9.18 3.28
Remarks
@2
0”:1
a;2
0.020 0.10 0.02 -
-
0.225 0.261 0.404 0.057 0.225 0.448 0.061 0.216 0.063 0.202 0.482 0.487 0.140 -
399 Fig.
Ref.
For y (0.45 at.% P, 73H 12.5 at.% Ni): D:, [m2s-‘1 = 0.51 . 10e4 - 230.3kJmol-’ +exp RT ( > Dz,[m2s-1] = 1.13. 10T4 - 287.2kJmol-’ . exp RT ( > For y (0.45 at.% P, 6 at.% Ni): &[m2s-‘1 = 0.53. 10m4 - 284.7kJmol-’ . exp RT >
In units of lo-l3 mzsW1 0.002 0.075
y(fcc) 11.l
0.45 1473
Ti
V
Zr
17.5 21.0 37.0 37.0 37.0 37.0 39.0 41.0 44.0 48.5 49.5 54.0 54.0 54.0 55.0 55.0 55.0 55.5 56.0 56.5 57.5 57.5 57.5 58.0 58.0 58.0
5.0 (bee) 1073 12.4 2.6 5.0 11.7 1.8 3.0 7.3 0.3 4.0 8.1 0.6 5.5 9.0 1.6 7.5 9.2 2.0 5.5 8.7 1.5 57.0 0.03 -0.16 55.0 0.03 0.03 50.5 0.04 0.17 49.5 0.04 0.02 9.0 5.7 1.0 2.5 9.5 5.5 16.0 6.8 3.3 37.5 0.16 0.18 42.0a) 0.10 0.07 42.0a) 0.07 0.07 6.0 5.3 0.9 4.5 5.2 0.4 2.1 27.0 1.9 6.21 0.25 36.5 39.08) 0.13 0.2 39.0y 0.13 0.18 17.0 3.6 2.1 33.5 0.54 0.7 0.12 - 0.004 40.5
1 = V; 2 = Zr; 3 = Ti
In units of IO-i4 m2 s-i -0.8 -0.6 -0.2 -0.2 -0.1 -0.01 -0.2 0.005 0.004 0.004 0.007 -0.6 -0.4 -0.2 0.1 0.05 0.03 -0.7 -1.1 0.6 0.2 0.01 0.02 1.0 0.33 0.02
2.8 2.8 3.9 3.9 2.8 2.1 2.2 0.09 0.12 0.15 0.24 2.4 2.0 1.0 0.23 0.44 0.43 2.8 3.5 1.0 0.47 0.23 0.25 1.4 0.63 0.36
Solid-solid diffusion 26 couples with intersecting diffusion paths; o”:, increases with Zr content at a constant V level; the cross-coefficients are quite sensitive to V and Zr levels for Ti-rich alloys; at about 30 at.% V and 15 at.% Zr the crosscoefficients become comparable to the main coefficients. “) Two runs.
74B
(continued)
Landolt-BBmstein New Series III/26
Dayananda
6.8.1 Ternary Composition at.%
coefficients
Ti
V
59.5 60.0 60.0 60.5 63.0
65.0 66.0 66.0 66.5 67.0 67.5 67.5 67.5 67.5 68.0 69.5 70.0 71.5 73.0 74.0 74.5 77.0 77.5 78.0 78.5 80.5 81.0 82.0 82.0 84.5 85.0 86.0
27.5 35.0 38.5 22.0 17.5 13.5 14.0 27.5 32.0 24.5 8.0 20.0 6.5 16.5 6.5 6.5 8.5 13.0 29.5 18.0 12.0 19.0 19.0 13.0 19.0 19.0 15.0 14.0 14.0 9.0 14.5 9.0 9.0 9.0 8.5 8.5
Zr
54.0 58.2 63.3 63.6 63.9 66.7 67.2 70.35 76.4
38.0 28.2 21.1 6.1 18.1 (bee) 13.3 13.0 28.64 19.4
(Tables)
Remarks
T K a:,
64.0 64.0 64.0 64.0
interdiffusion
(continued) 1.2 0.17 0.14 1.9 2.0 3.8 3.8 0.82 0.2 1.1 2.7 2.0 2.5 2.0 2.7 2.2 2.5 3.4 0.4 1.7 3.1 1.4
1.1 1.8 0.7 0.7 1.4 1.7 1.5 2.2 0.94 2.3 1.5 1.7 2.2 2.0
-
a:2 1.7 0.14 -0.007 1.8 1.5 2.1 1.9 0.6 -0.07 0.8 0.3 0.7 0.3 0.8 0.6 0.01 0.3 2.4 -0.55 0.54 2.2 0.18 0.18 0.32 0.1 -0.01 0.8 0.26 0.16 0.08 -0.47
o”:, 0.6 0.12 0.02 1.2 0.7 0.9 1.3 0.4 0.08 0.54 2.0 0.6 1.5 0.9 1.4 1.8 2.0 1.5 0.03 0.6 1.4 0.54 0.50 0.7 0.3 0.33 0.7 0.65 0.68 0.4 0.5
[Ref. p. 435 Fig.
Ref.
&
1.0
0.1
1.0
0.02 -0.55 -0.53 -0.54
1.3 0.5 0.7 0.4
0.56 0.46 1.5 1.8 2.5 2.5 1.2 0.7 1.4 4.4 1.7 3.5 2.1 3.3 3.8 3.5 3.3 0.9 2.0 3.6 2.0 1.9 3.2 1.9 2.0 2.3 2.7 2.7 4.1 2.7 4.4 4.4 4.2 4.2 4.6
0.09 1.2 1.8 0.7 1.5 2.0 2.2 -0.83 -0.08
-
0.11 0.9 1.6 3.1 1.8 2.9 3.1 1.3 1.8
Dayananda
74B
At extrema in V concentration profiles.
6.8.2 Ternary intrinsic diffusion coefficients (Tables)
Ref. p. 4351
401
6.8.2 Ternary intrinsic diffusion coefficients Composition at.%
T
0;
K
m2s-i 0231 @2
D:l Cd Zn 42 ;“fcc) 5.0 24.6 17.5 873 5.7 8.4 9.2 9.4 13.0 13.5 18.4 21.6
11.0 24.4 11.1 18.0 18.1 11.2 11.1 11.2
D:,
Remarks D:l
7.1 1.9
0.46 5.7 0.69 1.0 2.8 0.76 1.3 2.7
0.48 12.7 0.68 1.9 3.0 0.76 1.4 2.8
1 =Zn; 2=Cd; 3=Ag
0.39 2.4 0.18 1.0
-1.1 -0.55
--3.8 1.2 Pairs diffusion of vapor-solid couples
0.02 2.2 0.09 0.25 2.0 0.35 1.1 2.7
-0.22 -2.3 -0.14 -0.72 -1.3 -0.23 -0.60 -1.8
-0.43 -4.1 -0.43 -1.1 -2.2 -0.28 -1.0 -2.5
0.59 6.5 0.72 1.5 3.7 0.94 2.9 7.2
Ref.
&
In units of lo-l3 m2 s-l 0.90 1.7
Fig.
27,28 72C
exposed to the same alloy vapor source. The marker planes of complementary couples agreed within + 0.25 at.% Zn or Cd and the average composition reported; parabolic motion of markers observed with time; Di's increase in magnitude with Cd concentration at constant Zn levels and with Zn concentration at constant Cd levels. Zn diffused up its own concentration gradients in several couples; Cd increasesthe chemical acitivity of Zn in Ag.
In units of IO-i0 m2 s-l ;bcc) 1::; :;:: 21.7 23.6
1.2 3.1 1.3 1.4 0.46 0.85
Co
Cr
Ni
(fee)
9.0 9.0 9.0 9.2 17.2 24.9
21.0 1573 7.0 39.5 12.0 59.0 15.0 78.5 15.0 58.3 21.0 58.4 44.0
Land&-Biirnstein New Series III/26
0.21 2.0 0.08 1.1 0.11 0.99
-0.47 --1.7 -0.19 1.8 Intrinsic coefficients diffusion in j3 are -0.15 -0.66 2...3 orders of magnitude larger than those in c1 alloys. l=Cr;
In units of lo-r4 m2se1 0.24 0.37 0.4 0.02 1.1 1.3
2.0 3.0 3.0 6.0 6.0 7.0 14.0 10.0 6.0 13.0 21.0 15.0
- 0.01 - 0.22 - 3.2 - 4.4 - 5.1 -24.0
Dayananda
-0.9 -2.0 -3.9 -6.8 -7.0 -8.0
2=Ni; 3=Co
Solid-solid couple 29 pairs with similar marker compositions; marker motion normally towards the Cr and/or Ni-rich side of couples.
66L
zomposition It.%
Remarks
T K D:,
Cu
[Ref. p. 435
6.8.3 Atomic mobilities and vacancy wind parameters (Tables)
402
Mn
13.5 1123 10.1 19.2 14.2
cu
Zn
[fee) 1.7 2.1
D:t
D:2
D:t
1.5 1.5
0.04 3.5 0.2 4.8
-1.0 -0.6
l=Zn; -0.3 -1.5
9.7 4.3
3.1
0.5 0.2
-4.7 -2.0
2=Mn; 3=Cu
Pairs of vapor-solid couples with similar composition at inert alumina marker planes; oxygen free high conductivity Cu and Cu5.5 at.% Zn binary alloy exposed to selected ternary alloys used as vapor sources.
65D
1 =Zn; 2=Sn; 3=Cu
In units of lo-l4 m2 s-i
18.3 1023 14.7
Ref.
0:~
In units of IO-l3 m2s-’
Zn
Ifcc) 4.1 4.1
Su
0:~
Fig.
-4.6 -2.8
Cu-Sn and Cu - Sn - Zn alloys with a nominal Cu/Sn ratio of 9713 employed as diffusion disks and vapor sources.
68Dl
6.8.3 Atomic mobilities and vacancy wind parameters Composition at.%
T K B,
Ag ;fcc)
Cd
Zn
5.0 24.6 17.5 873 5.7 8.4 9.2 9.4 13.0 13.5 18.4 21.6
11.0 24.4 11.1 18.0 18.1 11.2 11.1 11.2
a sNm-’
Bi
ms-‘N-’ B2 B3
Remarks
In units of IO’ ms-‘NW’
l=Zn; In units of lop2 sNm-’
0.62 0.77
0.41 0.37
0.65 5.02
2.012 2.936
0.69 5.02 0.75 1.55 1.9 0.58 0.99 2.3
0.35 3.66 0.36 0.68 0.7 0.27 0.63 1.4
0.36 2.83 0.18 0.93 0.37 0.15 0.32 9.6
1.31 0.129 0.542 0.898 0.197 1.231 0.817 0.807
Dayananda
Fig.
Ref.
30
75c
2=Cd; 3=Ag
Pairs diffusion of vapor-solid couples with similar marker composition; parabolic motion of markers with I observed; up-hill diffusion of Zn against its own concentration gradient in several couples; Cd increasesactivity of Zn and vice versa; vacancy wind effect contributes significantly to increase J,, and JCdand to decreaseJAg.
Land&BGmWin New Series 111126
Ref. p. 4351
6.8.3 Atomic mobilities and vacancy wind parameters (Tables)
Composition at. %
T K
Remarks o”:,
CU
Mn
Ni
5.3 20.5 (fee) 1173 12.8 14.9 20.3 4.9
cu (fee)
Mn
Zn
(fee) 15.2 9.2 17.4 23.2 22.2
Land&-Biirnstein New Series III/26
El
Fig.
In units of IO4 ms-‘N-’
1 =Cu; 2=Mn; 3=Ni
2.92 16.7 7.26 3.19 23.1 3.56 2.47 7.19 2.51
Solid-solid diffusion couples with Al,O, and W wire markers: Dayananda analysis; Henry’s law assumedto be valid; simple atomic mobility model.
7.6 9.8
2.4 3.4
0.4 0.7
1123
17.5 1073 1.2 28.1 14.0 6.8 2.2 5.1 2.4 21.3 20.0
0.46 5.6 1.0 1.1 6.4
Ref.
R2
In units of IO7 ms-‘N-l
4.1 13.5 1123 4.1 19.2
(A range of compositions)
82
403
0.61 0.41 1.8 0.88 0.73 1.4
Dayananda
l=Zn;
2=Mn;
80Y
3=Cu
Vapor-solid diffusion couples with alumina inert markers; Dayananda analysis; Henry’s law assumed to be valid; vacancy wind effect ignored.
68132
Isomobility contours 31 determined from steady-state profiles set up in a Cu membrane exposed to vapors of Zn and Mn for 4...6 days.
7ow
Solid-solid diffusion couples; Dayananda analysis at marker planes; validity of Henry’s law assumed; simple atomic mobility model.
86T
6.8.4 Tracer diffusion coefficients for ternary alloys Composition at.%
Tracer
Do*
.10-4mZs-’ Al
Fe
Zn
0 0.005 0.02 0.1 0 0.005 0.02
I.4 I.47 I.47 I.48 2.13 2.13 2.13
Al
Mg
Zn
(fee)
1.11 1.12 1.13 1.14 2.77 2.80 2.83 2.86 4.43 6.63
0.71 I .49 2.11 0.71 I.48 2.11 -
Al
Ni
Ti
19.92 (fee) 20.83 21.84
5.13 5.01 5.13
Q* kJmol-’
Temperature D* (T [K]) Remarks range K m2s-* (measured) .1(-j-
Zn65
0.58 0.59 0.62 0.61 1.39 0.35 0.32
124.5 124.3 125.0 126.0 129.6 120.7 119.9
733.s.883
Zn65
0.34 0.25 0.23 0.31 0.24 0.27 0.21 0.17 0.28 0.50
121.5 119.2 118.0 119.5 119.5 119.0 116.8 115.1 118.6 121.1
693.e.883
Ref.
14
30.0 (783.7) Tracer electroplated on polycrystalline samples; sectioned by lapping; activ30.8 ity analysis; 02” essentially indepen28.9 dent of Fe over the concentration 31.2 31.2 range investigated. 33.8 35.0 . I()-
Fig.
77B
14
52 (808) 55.9 (808) 58.3 (809) 62.6 (808) 51.6 (809) 56 (808) 63.7 (808) 64.9 (808) 61.5 (809) 68.3 (808)
Polycrystalline samples with grain size > 1 mm; tracer electroplated; sectioning by lapping and activity analysis; log Dzn varies linearly with Zn and Mg concentrations.
77B
Tracer electroplated on polycrystalline sample (I .. .2 mm grain size); serial sectioning and analysis. D& in Ni,(AlTi) insensitive to Ti additions and deviations from stoichiometry.
71H
. lo- 16
Ni63
0.055 0.039 0.085
262.9 259.7 266.9
1173...1573 2 (1322)
C
Cr
Fe
Ni
0.02 0.74 0.52 (fee) 0.02 4.65 0.36 C
Co
Fe
Cl4
Fe
Fe
Ti
15
4
Co
MYn [wt.%]
Ni
19.5
20.3 60.0 20.45 38.8 20.6 19.5
40.6 59.7
873 ... 1173 773 ... 1173
Tracer applied by carbonizing; sectioning and residual activity method.
57G
0.4
154.9
873.e.1173
Tracer applied by carbonizing; sectioning and residual activity method.
57G
.10-l*
MO Ni
0.015 0.41 2.94 (fee)
Co
142.4 154.9
Ni
0.015 5.25 0.36 (fee)
C
0.1 0.5
Cr
Fe [wt.%]
Ni
17
(fee)
12
Co60 C
Si
0.02 0.03 0.03
0.19 0.14 0.17
1.0
159.1
0.008
214.4
8
57G
55Gl
1373 ... 1473 .1()-14
co60
0.86 0.22 0.05
253.3 240.7 228.2
1293 ... 1413 2.2 (1373) Solid-solid couples formed with alloys containing tracer bonded to alloys 1293 ... 1453 0.15 (1373) with no tracer; sectioning and activ1353 ... 1433 0.86 (1353) ity analysis.
5562
.1()-M
NCs3
0.13 0.36 0.0088
264.2 279.7 251.2
Fe5’
0.58
280.9
CP Fe5g
[wt.%] 18
873 ... 1173 2.14 (1073) Tracer applied by carbonizing; sectioning and residual activity method.
8.72 (1377) Polycrystalline sample; 8 grains/mm*; 15.6 (1393) tracers deposited dropwise or by 4.7 (1372) evaporation; serial sectioning by lathe machining, hand grinding or rf sputtering and activity analysis. . 10-16 1081... 1473 1.9 (1267) Tracer electroplated on 347 stainless steel; residual activity method. 873 . ..I573
73Pl 73P2
55L (continued)
Composition at.%
Cr 20
Tracer Do* .10-4~2~-’ Ni
Et.%] (fee)
19 19 19 19 19 19 19 19 19 19 19 19
10 30 45 55 65 75
[wt.%] (fee) 20 15 45 15 22 45 15+1.4Si 20 15 20 15 45 22 45 15+1.4Si 20 15 20
kJmol-’
(continued)
25Ni/ Nb
[wt.%] (fee) 10 30 45 55 65 75
e*
Cr” Fes9 Ni63
0.19 1.74 4.06
Fes9
2.5. 1O-3 1 1.2 4.5 1.0 4.102
217.7 278.4 255.4 255.4 272.1 343.3
Ni63
1.4 1.4 2.6 7.2. 1O-2
301.5 301.5 401.9 297.3 297.3 253.3
5.3 2.1 1.5 5.1 8.3 4.0 4.1 7.1 1.5
308 288 286 303 309 293 295 303 300
246.2 284.3 282.6
Temperature D* (T [K]) Remarks range K m2s-’ (measured)
Fig.
. lo-16 1113...1563 24.4 (1367) Polycrystalline ; 2 . . *4 mm grain size; tracers deposited by electroplating; layers removed 1173***1573 by grinding; residual activity method for 1113...1563 Ni.
Ref.
6982 68s 6932
.10-‘5
2.104 2.8
1173*** 1473 1.7 (1373) 2.0 3.0 6.0 4.5 4.6 .I()-‘5 12730.. 1473 0.7 (1373) 0.55 1.6 1.8 1.6 1.8
Polycrystalline samples; residual activity method.
73G
73G
.10-‘5
Fes9
Crsl
Ni”
1233.e.1673
1.21 (1381) Polycrystalline samples with grain diameter ~0.6 mm or 3 mm; Fes9 and NiS7 deposited 2.63 2.12 by electroplating and Cr” by drying CrCI, solution; annealed in Ar, He or vacuum; sec1.88 1233 ... 1673 1.99 tioning by grinding; D& > D& > D;l;, at all T with D&/D& g 2.5 and D&/D& z 1.8. 3.28 2.77 2.5 1233 ... 1673 0.58
32
80R2
15 22 15+1.4Si Cu
Ni
1.8 1.1 4.8
45 45 20
293 291 310
0.96 0.92 0.62 .1(-j-14
Zu
99.999 90.25 80.08 70.94 90.08 82.72 72.04 65.06 80.28 69.68 63.95 55.17 71.73 60.97 47.12 40.30
9.92 12.55. 11.21 10.82 19.72 19.42 20.80 20.59 28.27 29.49 33.08 30.70
9.75 19.92 29.06 4.73 16.75 24.12 10.90 15.25 24.24 9.54 19.80 29.00
Cd7 -
0.30 0.55 0.63 0.16 0.27 0.36 0.33 0.21 0.15 0.18 0.00 0.11 0.34 0.55 0.58 0.72
202.2 200.1 192.2 169.6 209.3 206.0 195.9 184.2 205.2 200.6 190.1 183.8 218.6 218.6 212.7 210.6
1013...I318 1059...1283 1018~~~1210 993*.*1177 1177...I323 1058.e.1276 1013...1276 1056...1216 1105...1361 1073.e.1323 1025...1276 1021...1222 1181... 1386 1177...1323 1139...1338 1080..- 1239
99.999 90.25 80.08 70.94 90.08 82.72 72.04 65.06 80.28 69.68 63.95 55.17 71.73 60.97 47.12 40.30
9.92 12.55 11.21 10.82 19.72 19.42 20.80 20.59 28.27 29.49 33.08 30.70
9.75 19.92 29.06 4.73 16.75 24.12 10.90 15.25 24.24 9.54 19.80 29.00
Ni6’j
i.94 1.06 0.22 0.12 0.31 0.13 0.16 0.08 0.06 0.12 0.09 0.1 0.29 0.42 0.33 0.31
232.8 219.0 195.1 180.9 218.6 207.7 200.1 189.2 206.0 208.1 201.8 196.4 226.9 227.8 221.1 216.0
1128 ... 1328 1064... 1268 1050~~~1219 1012~~~1168 1202... 1379 1052...I300 1057...1272 1067.s.1232 1128..-I370 1110~~~1314 1110~~~1286 1064... 1256 1174...1407 1177..*1347 1143..:I323 1158++.1268
3.55 (1185) Tracer electroplated on large grained (1 ... 3 7.20 (1177) mm), polycrystalline homogeneous alloys; 17.9 (1177) lathe sectioning and activity analysis; empiri49.3 (1177) cal relation for D& [cm' s- '1 at 1173 K: 2.02(1177) log IOD& = - 3.53X;,116 +3.6X;;p2 -9.46; 2.50(1177) variation of Q& with composition: 7.03 (1177) Q&=2014.7 (1+2.37x4,;=) $1 -O.O7X;;2g) 14.0 (1177) -1809.9 kJmol-l. 1.14(1177) 2.10 (1177) 3.54(1177) 8.56(1185) 0.74 (1181) 1.03 (1177) 1.84 (1175) 3.22 (1177)
33(a), 34
72A
33(b), 35
72A
.10-‘4
0.82 1.86 4.6 9.88 1.02 0.79 2.02 3.21 0.53 0.76 0.89 1.89 0.29 0.34 0.43 0.78
(I 176) Tracer electroplated on polycrystalline homoge(1173) neous alloys; lathe sectioning and activity (1179) analysis; empirical relation for D& [cm2 s - '1 (1168) at 1173 K: log,,D&= -4.05$i3 +3.28Xi;07 (1202) -9.96. (1174) (1174) (1176) (1177) (1179) (1169) (1174) (1174). (1177) (1169) (1174)
(continued)
Composition at.%
Tracer Do* .10-4~2~-1
Cu
Ni
99.999 89.9 79.5 69.8 90.7 80.4 70.2 60.1 81.8 70.8 60.6 50.3 71.4 61.2 50.8 40.7
9.3 9.3 9.3 9.1 18.2 18.8 18.6 18.7 28.6 28.2 28.2 27.9
Zn
Q’ kJmol-’
Temperature D* (T [K]) range m2s-r K (measured)
(continued) Zn6’
10.1 20.5 30.2 10.3 20.5 30.8 10.4 20.8 31.0 10.6 21.0 31.4
0.24 0.64 0.35 0.32 0.36 0.49 1.41 0.39 0.89 0.36 1.09 0.73 1.37 1.44 1.17 1.13
188.8 190.9 176.7 164.5 200.1 195.9 196.4 173.3 214.8 199.7 201.4 187.2 226.5 220.2 208.9 198.5
1073 **. 1313 1021 -.- 1252 1021 .a. 1213 973...1175 1068.e. 1313 1023... 1278 1023 a.. 1249 973 .** 1174 1068... 1278 1073*** 1313 1073... 1284 1021 ... 1213 1143*** 1353 1128...1314 1073... 1278 1033...1249
Remarks
Fig.
. I()- 14 3.86 (1119) Tracer electroplated on polycrystalline homogeneous alloys; lathe sectioning and activity 23.3 (1174) analysis; empirical relation for 49.3 (1173) D&[cm2s-‘1 at 1173 K: 158.0 (1175) log,&” = -3.20X,, +5.21 Xi:‘-9.0; 3.85 (1270) variation of Q& with composition: 9.55 (1270) QL=122.3X~i03-2211.0X~b8 +190.5 kJmol-‘. 10.5 (1121) With few exceptions Q$, > Q& > Qz”. 61.6 (1174) 2.51 (1173) 5.34 (1173) 12.8 (1175) 33.5 (1174) 1.24 (1173) 2.30(1173) 9.72 (1207) 15.1 (1172)
33(c), 36
Ref.
72A, 66D
409
6 Diffusion in ternary alloys (Figures)
Ref. p. 4351 0.87
Al-Ag-Zn ,
Figures for 6
"AI D
.,o-z7
AgAg
6
fiA’Al Agln
/
-0.6
a-0.81
Al
12
3
4
5
6
8a-*9
7
Al b
a
12
3
4
5
6
7
5
6
7
8-W
9
“Al
0 ZnAg
Al
12
3
4
5
C
/
,
6
7
/
do-*'J 4.2
I
8 -10-29
Al
A Fig. 4. Al- Ag-Zn. Ternary interdiffusion coeffkients (0” in IO-r3 m’s-‘) and iso-interdiffusion coefficient lines at 785K; (a) o”&,, (h) a&,, (c) &A,,, and (d) I?&,. Binary B values are also included on the Al - Ag and Al - Zn sides in (a) and (d) [84Ml].
AL-Ag-Zn
.,oe27 1
12
3
4
d
xz,-
X1,-
Fig. 5. Al - Ag -Zn. Ternary interdiffusion coefficients (D in 10-l” m’s-‘) and iso-interdiffusion coeffkient lines at 832 K; (a) at:,,, (h) &, (c) @A,,, and (d) &, . Binary d data also included on the Al - Ag and Al - Zn sidesin (a) and (d) [84M2]. ‘I
o"Al AgAg
*.O
3
Al-
a
1
2
3
4
5
6
fJ.10-* 9
7
Al
12
l
-1.1
l
3
4
- 1.5
l -0.87
-1.5
5
6
7
b
xzno"Al ZnAg
.4 /
Al
c
12
Land&-Bhnstein New Series III/26
3
4
5
xz,-
6
7
1
8.10.* 9
AL
d Dayananda
12
3
4
5
xz,-
6
7
8 .lO-* 9
Ag-Au-Cu
“AU
0CUCU
20
Fig. 6. Ag- Au-Cu. Ternary interdiffusion coefficients (d in lo- I6 ma s- ‘) and iso-interdiffusion coefficient lines at 998 K; (a) @&, and (d) (b) @&p (c) &&/&?&, The open circles in (c) &JD&. correspond to the estimated ratio of a Cu the coefficients on the basis that fi”, varies little with Ag content; and the dashed contours in (d) represent the ratio of the thermodynamic derivatives,
c cu
20
b Cu
4 All
4
d cu
4
Ref. p. 4351
6 Diffusion in ternary alloys (Figures)
a
b
Fig. 7. Ag - Cd - Zn. Diffusion paths for vapor-solid couples at 873 K; fip coefficients were determined at several intersec. tion points such as those made by the paths in (a) with those in (b) [72CJ. For Fig. 8 seenext page
12
I 9
9
IL LY
L l.Y 6
6
3
3
0
0 IE
.15 wt%
Wi%
12
12
I
9
6
CA1 -
lAl
-
Fig. 9. Co- Al-Cr. Approximate contour maps for interdiffusion coefficients (0” in lo-l5 m* s-r) for Co-rich Co-Al-Cr dloys at 1373K; (a) B&,, (b) @c,, (c) fi&,,. and (d) @& [80Rl]. I
Landolt-Bornstem New Series III/26
Dayananda
412
I
6 Diffusion in ternary alloys (Figures)
I
4
ii’Ag ’ II
II
II
I
II
I
09 -:= Ia * 0
76
78
80
82
81
[Ref. p. 435
86 a-2 88
4 Fig.8. Ag-Zn-Cd. Interdiffusion Ag-Zn-Cd alloys with a C&cT=873 K.
ratio of 3.8 I726
X-Ag
ZSI-
Al-Cr-Ni
$jp7 -\45.0*10-*
a
22.5
0
b
-204\ .*
22.5
c-x
45.0 *lo-2
22.5 cr ?g. 10. AI-Cr-Ni. Variation of ternary interdiffusion coeflicients with composition for Ni-base Al-Cr-Ni 1473K; (a) El ,,,, (b) @‘,$,, (c) &,, and (d) 6&, [87Nl]. d
Dayananda
-x
0
Cr
0 alloys at
Land&-BBmstein New Series III,l26
Ref. p. 4351
6 Diffusion in ternary alloys (Figures)
Al-Cu-Zn
1.3 .I.4 \\ %.2 $4
. 1.0 09
CU
p
25 -10-Z /
5
2.4 .2is\,
\2.l
\
2.0
10
a
.3.5
l *
'.
/
-CU 0 ZnAl
2nln
, -3.2
15 10-2
XAI-
5
cu b
10
15 w2
xAl-
-cu 0Al ln
- cu 'ALAI
1.0
E /i;
/
I
$0.07 0.3I-0.3
cu n
Fig. 11. Al-Cu-Zn. Cu-rich Al-Cu-Zn
Land&BBmstein New Series III/26
. 0.3
0.8 *I
I
$01 1 l O.4 .p5 zo.7 /
0.5 0.6
5
!;.2.7
-1.3
.2.'
.-0.03 /
,
10 “-
“Al -
J.3
15 *lo-* _
d
xAl-
Ternary interdiffusion coefficients and iso-interdiffusion coefficient lines (8 in lo- ‘s mz s-l) for alloys at 1173 K; (a) &‘,, (b) &, (c) 6&, and (d) fi$, [85T].
Dayananda
6 Diffusion in ternary alloys (Figures)
414
[Ref. p. 435
Ni
10
20
30
40
50
60
70
80 40-290
Fe
Ni b
10
20
30
40
50 XF.-
60
70
80 -10-290
Fe
/
Ni
”
”
”
20
30
40
C
/
”
”
10
”
50 k---L
”
”
\,
60
70
80 alO” 90
Fe
”
Fe 50 60 70 80 10-290 20 30 40 Ni 10 d 1, Fig. 12. Al-Fe-Ni. Ternary interdiffusion coefficients (din 10-15m2s-1) for p @cc)and y (fee) Al- Fe-Ni alloys; (a) a&,,(b) a:;,,,(c) fi&,, and (d) B&i; data identified by l and o correspond to 1277 [76M] and 1273K [79C], respectively. Dayananda
Land&-BCmstein New Series III!26
6 Diffusion in ternary alloys (Figures)
Ref. p. 4351 0.4
415
Co-Fe-Ni
0.3
0.2
I
0.1
r< r,
0 Ni Fe Fig. 14. Co -Fe-Ni. Experimental diffusion paths for solid-solid diffusion couples at 1588K with several composition points of intersection [69v].
-0.1
-0.2
-0.3 0
1
2
xc-
3
.10-*
4
Fig. 13. C-Co-Fe, C-Cr-Fe, C-Mn-Fe, C-Ni-Fe, C - Si - Fe. Variation of @,/@, with carbon concentration for austenites in the ternary systems; 1 = C; 2 = Co, Cr, Mn, Ni or Si; and 3 = Fe. The solid lines represent the estimation based on Eq. (6.16) [62K], [64B].
Fe
IO
20
30
40
For Fig. 15 see next page.
50
60
70
80 -1o‘2 90
Ni
Fig. 16. Fe -Ni - Cr. Experimental diffusion paths for diffusion couples in the y (fee) region annealed at 1373K for 7 days [85Dl]. Letters A ... T indicate alloy compositions used for the assembly of couples.
Land&BBmstein New Series III/26
Dayananda
416
6 Diffusion in ternary alloys (Figures)
Fe
a
10
Fe 0-COCO
co
Co-Fe-Ni
20
30
40
50
60
70
80 -lo-* 90
Ni
INi -
D”Fe CoNi
co
10 b
[Ref. p. 435
20
30
40
50
60
70
80.10m290
Ni
xNi -
Fig. 15. a-Co-Fe-Ni (fee). Ternary interdiffusion coefficients (d in IO-l4 m2 s-l) and iso-interdiffusion coefficient lines on the ternary isotherm at 1588K; (a) a&,,, (b) DTzN,,(c) a:&, and (d) @&, [69v]. The data on the Fe -Co and Fe -Ni sides in (a) and (d), respectively, correspond to binary d values [69v].
Dayananda
Landolt-BBmstein New Series III!26
Ref. p. 4351
6 Diffusion in ternary alloys (Figures)
417 “Fe 0 NiCo
in 4.i Fe
d
3.1 .
"
"
10
20
30
40
50
"
60
70
80
10
20
30
40
50
60
70
80 w
Fig. 15c, d.
Land&-Bihstein New Series III/26
Dayananda
90 010~~Ni
90
.Ni
6 Diffusion in ternary alloys (Figures)
a
XNi
[Ref. p. 435
-
.~/ ,$&/;:l5.q,/;7.3 ,$I”!;;~-;;o.&,o c/ ‘Y, / ” ” ” ” ” ” Fe m.
10
b
20
30
40
50
INi
60
70
80 40“ 90
Ni
-
Fig. 17. Cr-Fe-Ni. Variation with composition of the main ternary interdiffusion coefficients (d in lo-” m* s-l), (a) I?,$, and (b) 6:&j at 1373 K [85Dl]. Iso-interdiffusion coefficient lines are also shown.
Dayananda
Ref. p. 4351
6 Diffusion in ternary alloys (Figures)
.,$ m2/s IO
.,$ _
ov 0
m2/s 20
C
4
8
12
16 wt%
Ccr Ccr Fig. 18. Cr -Ni - Si. Variation of the ternary interdiffusion coefficients with Cr and Si concentrations for Ni-rich Cr -Ni-Si alloys at 1523 K. (a) @c, and binary 0” for Ni-Cr as functions of Cr concentration; (b) @c, as a function of Si concentration; (c) D& as a function of Cr concentration; (d) @& as a function of Si concentration, and (e) Bgsi and binary 0” for Ni - Si as functions of Si concentration [82J].
Land&-Bhstein New Series III/26
Dayananda
e 3 cSi -
4 wt%
5
[Ref. p. 435
6 Diffusion in ternary alloys (Figures)
Ni
a
c Fig. 19. Cu-Mn-Ni. Ni-rich Cu-Mn-Ni
b
A” -
d
Xc,-
Ternary interdiffusion coefficients (6 in 10-l’ m* s-l) and iso-interdiffusion coefficient lines for alloys at 1173K; (a) @&, (b) @!&, (c) D2zu, and (d) @hi [8Oyl.
Dayananda
LandolbB6mstein New Series Ill!26
Ref. p. 4351
6 Diffusion in ternary alloys (Figures)
CU
cu b
a
421
IO
20
-cu DMnZll
cu
c
io
20 'M"-
-10"
40-*
30
xMn -CU
0MnMn
30
d
XM"----
Fig. 20. Cu-Mn-Zn. Ternary interdiffusion coefficients and iso-interdiffusion coefficient lines (0” in lo-l4 m’s-‘) for Cu-rich CL(fee) Cu -Mn - Zn alloys at 1073K ; (a) i&, , (b) &$,,, , (c) fizz”, and (d) @&,“. The binary 0” values for Cu - Zn and Cu-Mn alloys are included in (a) and (d), respectively [86T].
Land&Biirnstein New Series III/26
Dayananda
6 Diffusion in ternary alloys (Figures)
-Ni-Zn
0-CU lnln
/
0.40 .-‘, 0.39
Ni
a
[Ref. p. 435
10
20
30
40
50
--
l
60
70
80 -10-2 -90
”
”
”
‘(i”
50
60
70
80 *lo-2 90
cu
XC”-
”
”
”
”
10
20
30
40
1 01 “3’ U.UP’I/0.03
a?2
cu
XC”-
Fig. 21. cc-Cu-Ni -Zn (fee). Ternary $erdifTusion coefficients and iso-interdiffusion coefficient contours (6 in !:31;;1m’s-‘) at 1048K;(a) a$,, (b) - D,,,i, (c) - @&, and (d) &a,. Open circles: [77S],full circles: [82K] and triangles:
Dayananda
Landolt-BBmstein New Series III!26
6 Diffusion in ternary alloys (Figures)
Ref. p. 4351
/
/
*VP ,///
0.70-_
/ 80
0.20 -+
0.14 go
0.69.
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011 ---.,
/ ‘Ni
169
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&OS
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o~a28-0.17
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V
IO
20
+. -1
-\ 0.51
l
1.33 4;\ 1.1I
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\
A
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V
V
40
50
60
70
l
O.iZ-. Of7 $7
l
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20 0.26
.
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0
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.
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.--\ 30
.
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0.32
0.88
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/
l 0.25-
0.19
-
423
0
80 *IO-’
XC”-
-cu 0NiNi
‘-L,o3 0% 0.07- -__-_
0.360 .0.46 0.12O Q.rJ8
. 0.07 -----
i.“.“r. .0.06 --OS,2 .----, 0.04
l ois
-
0.06
ct(1m,
. 0.23 *..
----&'A, Y.“”
-
---l
0.04
--2.
-1
-0.07
-c-
a02n
0.03
Ni u
V
V
IO
20
”
”
30
40
”
50 AC”-
Fig. 21 c, d.
Land&Bhnstein New Series III/26
Dayananda
”
60
”
70
“.‘“;
O.OP
81
424
6 Diffusion in ternary alloys (Figures)
[Ref. p. 435
cu
a
INi
10
cu
b
-
20
C
XNi
-10-2 30
10
cu
d
-
2-i xNi
.lU2
30
-
Fig. 22. Cu-Ni-Zn. Ternary interdiffusion coeffkients and iso-interdiffusion coefficient tines (d in to-r5 mss-1) at 1133K ; (a) a&. , @) - &,r, (c) &$,, and (d) @&. The binary d for Cu - Zn and Cu - Ni alloys are also included in (a) and (d), respectively [84T]. 16 .10-2
I
1
I
Cu-Sn-Zn
14 12
t
10
I 458 9, 4
-1
0
I
I
I XI
1
2
3 x/fi
4 -
5
I
d--
I
6
7 .10-7m/s”2 9
Dayananda
Fig. 23. Cu-Sn-Zn. Experimental and calculated concentration profiles for a vapor-solid couple diffused at 1023 K for 4days; the ternary coefficients (in IO-l4 m*s-‘) used for the calculation are: fi&. = 3.5, Bh& = 0.7, a&, = 0 75, &” = 2.0 [68Dl].
Land&-B?msfein New Series 111126
Ref. p. 4351
0
12
6 Diffusion in ternary alloys (Figures)
3
4
5X-* 6 .1_0-'
425
p
-CU Dsnsn
Sn1n
IO
40
5
30 20
2
0 0
12
/
/
3
4
a
/
I
5W26 0
1
2
I 4
3
I 5 do-* 6
Xl, -
0
12
3
4
5.10-* 6 0
b
1
2
3
4
5.W* 6
Fig. 24. Cu-Sn-Zn. Isodiffusion coefficient contours for ternary interdiffusion coefficients. (a) T=1094 K, 0” in IO-l4 m2 s-l, (b) T= 771 K, d in 10-l’ m’s-’ [65K].
Land&Biirnstein New Series III/26
Dayananda
[Ref. p. 435
6 Diffusion in ternary alloys (Figures)
5? -
a+ liq. I
2-
i& 49 -
.1.1 .RO
atbcc)
37
2-
l-
b "d
I a5
I 1.0
I 1.5
I 2.0
I 2.5
I 10
I
I
15 .10-* 4.0
*Hi -
Fig. 25. Fe-Ni -P. Isodiffusion coefficient contours for (a) @i, (b) &TNi for c( @cc) Fe-Ni-P alloys (b in 10-‘3m2s-1) and for (c) fi& (in alloys IO-l4 m2s-‘) and (d) bFr NlNl(in lo- l6 m*s-‘) for y (fee) Fe-Ni-P at 1373K (73HJ.
Dayananda
Land&-BBmsIein New Series III/26
427
6 Diffusion in ternary alloys (Figures)
Ref. p. 4351
I
oIC
I
I
I
I
I
I
51-2-
y +liq.
17 / 0-i 0
1
3.1 ,
2
4
6
5.1
8
Fig. 25c, d.
Landolt-Biimstein New
Series III/26
Dayananda
5.7_,
10
6.1s L3J
12
14 -1O-2 16
[Ref. p. 435
6 Diffusion in ternary alloys (Figures)
428
a -1i
/
60/ ,'
Dv2r
/ ,4y2.0 l 0.6
IO-*
ao;
Ti
b
20
40 xv -
t.17
0.y
3.'
"
60
-10-2
80
Fig. 26. Ti-V-Zr. Isodiffusioncoellicient contours(b in 1O-‘4 m* s-‘)at 1073K;(a) DT,,. (b) DTz,, (c)@v, and (d) D&. The binary d values for Ti -V and Ti -Zr alloys arc included in (a) and (d), respectively [74B].
Dayananda
Land&BBmstein New Series III~26
Ref. p. 4351
429
6 Diffusion in ternary alloys (Figures)
-Ii D zrv
Ti
L
13 “‘“”
0.02.
20 ”
u
.0.02 -
40
A” -
Ti
d Fig. 26 c, d.
Land&-BBmstein New
SeriesIII/26
Dayananda
0.007. fOO4
0.004 . .o.oos "
60
-IO-*
80
6 Diffusion in ternary alloys (Figures) 25 .,a-~
I I
I
Ag-Cd-Zn
!
Surface movement Zn .
l-l!
II
Cd o (3d)
A (5d)
i
0
[Ref. p. 435
:
II
I
I
I
I
I
0.5
1.0
1.5
2.0
2.5
3.0
q
(8d)
W7 m/s1’2 4
0
250
b
a x/p---Fig. 27. For figure caption seenext page.
500
750 s”‘10
-c-
.,o-‘3 mVs 6
I
2
%=
: xi-‘” mVs 3
0 0
5
10
a
15
20
0 0
25 -lo-* 30
.,&!
20
25 010.~ 30
20
25 *lo-* 30
8
02
I
4
r&T ; .;O-I-;
CT-: d 4 .,I)-13 m*h 3
6
2
4
1
2
0
c
15 ‘Cd-
m*/s 12
4
0
10
.,o!
m*/s 6
I
5
b
xCd-
5
10
15
X*n----
20
0 0
25 *lo-* 30
d
Fin. 28. For fkure caption seenext Dage. Dayananda
5
10
15
X2,Land&-B6mstein New Series III/26
Ref. p. 4351
6 Diffusion in ternary alloys (Figures)
4 Fig. 27. Ag - Cd - Zn. (a) Concentration profiles of Zn and Cd for the vapor-solid couple with Ag disk exposed to an alloy (70.0 Ag- 11.OZn- 19.0 Cd). Circles, triangles and squares correspond to 3, 5 and 8 days of diffusion time, respectively. The refiles satisfy the requirement that Ci is a function of x/ 9 t. (b) Marker burial and surface movement for the couple are functions of ,/i [72C].
431
10-'2 m2/s
~ 2 1P3 8 6 4 2
I g.1~ 4 Fig. 28. a-Ag - Cd - Zn. Variation of intrinsic diffusion coef- s.-, ficients at 873 K as functions of Cd concentration at (a) ~j- s s 11 at.% Zn, and(b) 18 at.% Zn; and as functions of Zn con4 centration at (c) 5 at.% Cd and (d) 9 at.% Cd. 1 = Zn, 2 = Cd, 3 = Ag [72C]. 2
1P 8 6 4
Fig. 29. Co - Cr - Ni. Variation of intrinsic diffusion coeffi- b cients at 1573K as functions of Cr concentration at a Ni concentration of 59 at.% [66L].
2 1P
0
5
10
15 xc, -
20
25 -10-2 30
3.0 .107 m/sN
0
a
5
10
15
20
25 ~10-~ 30
0
5
10
0
5
IO
15
20
25 -1O-230
15
20
25 .1O-2 30
“”
3.0 401 m/sN
d
X1,-
Fig. 30. u-Ag - Zn - Cd. Atomic mobilities of Zn and Cd at 873 K as functions of Cd concentration with (a) 11 at.% Zn, (b) 18 at.% Zn, and as functions of Zn concentration for alloys with (c) 5 at.% Cd and (d) 9 at.% Cd [75C]. Land&-Biirnstein New Series III/26
Dayananda
432
6 Diffusion in ternary alloys (Figures)
[Ref. p. 435 iu 2
pnn 2
0.4 4A
a
0.5
-4
b
Fig. 31.Cu-Mn-Zn. Isomobilitylines (/?,in lO’ms-‘N-l) for (a) Zn and (b) Mn at 1123K [7Ow]. For Fig. 32 see next page.
a
cu
b
10
20
30
x,i-
4 Fig. 33. Cu-Ni -Zn. Isotracer diffusion coeffkient contours (D* in 10-13 mz s-l) for (a) D&,(b) D&and (c) 02, for Cu-rich Cu -Ni - Zn alloys at 1173K [72A].
Dayananda
Ref. p. 4351
10-l m*/I
6 Diffusion in ternary alloys (Figures)
1400 "C 1300 I
-T 1200
-T
1000
1100
1400 "C 1300 10-'* I I m*/s
I’
Cr-Fe-Ni l-l--
IO-'
12013
I
\ \\
-14
10
I *&-
\
*c;-
\ t\
10-l
,o-l5
10-16
10-l
.58
0.68
0.63
b -1 2ocI
, o-l:
IO
1101 3
10-l"
m*A
. K 1s .
\
-Ii-.-l
10-l
0.58 0.63
1' 1
lo-l3
10-l
a
433
0.68
0.73
-1c
l/T-
1400 "C 1300 I I
1200
1000
m*/s
, o-l:
c \ IO" \
t vv 5
I *<
\
,o-l'
t * ?\ ,-
0 %. \
v
\ \ .
10-16
1O-16
,o-li
10-17 0.
.,o” K-1 0. 0.63 0.68 d l/TFig. 32. Cr - Fe -Ni. Plots of logD* vs. l/T for tracer diffusion of Ni, Fe and Cr in (a) 15 Cr-65 Fe-20 Ni, (b) I5 Cr-40 Fe-45 Ni; (c) 22 Cr-33 Fe-45Ni (open symbols are for 20 Cr-35 Fe-45 Ni from [73G]) and (d) 15Cr-63.6 Fe-20Ni- 1.4Si alloys, respectively [80R2]. All concentrations in at.%. 0.
c
Landolt-Bornstem New Series III/26
0.63
0.68 l/T-
0.73
.l
t-1
[3.83
Dayananda
6 Diffusion in ternary alloys (Figures)
434
[Ref. p. 435 -1
-1 10-“2 mvs 6 b
2
Fig. 34. Cu-Ni -Zn. Temperature dependence of D& for alloys with approximately 20 at.% Ni; (I): 80.28Cu-19.72Ni; (2): 69.68Cu- 19.42Ni-10.90Zn; (3): 63.95Cu-20.80Ni - 15.25Zn and (4): 55.17Cu-20.59Ni-24.24Zn [72A].
-1
0.95 .W3K-’ 1.05 0.85 l/TFig. 36. Cu-Ni-Zn. Temperature dependence of 0;. for alloys with approximately 20 at.% Ni; (I): 81.8Cu-18.2Ni; (2): 70.8Cu-18.8Ni-10.4Zn; (3): 60.6Cu-18.6Ni-20.8Zn and (4): 50.3Cu - 18.7Ni -31 .OZn [72A]. 0.65
0.75
lo-l2 m2/s 6 4
2
10-15 6.1 i-16
0.65
0.85 l/l -
4 Fig. 35. Cu -Ni -Zn. Temperature dependence of D& for alloys with approximately 20 at.% Ni; (I): 80.28Cu-19.72Ni; (2): 69.68Cu-19.42Ni-10.90Zn; (3): 63.95Cu-20.80Ni- 15.25Zn and (4): 55.17Cu-20.59Ni-24.24Zn [72A]. 0.95 .lO-)K’ 1.05
Dayananda
Land&-BBmstein New Series III/26
6.9 References for 6
435
6.9 References for 6 310 450 49D 52H 52W 55B 55Gl 5562 55L 56F 57G 57K 58K 61K 62G 62K 63Kl 63K2 63P 63s 64B 65D 65K 652 66D 66L 67s 672 68Dl 68D2 68M 68s 69Sl 6982 69V 70K 70M 7ow 71D 71H 72A 72B 72C 73G 73H 73Pl 73P2 73w 74B 75c 76M 77B
Onsager, L.: Phys. Rev. 37 (1931) 405. Onsager, L.: Ann. N.Y. Acad. Sci. 46 (1945-46) 241. Darken, L.S.: Trans. AIME 180 (1949) 430. Heumann, T.: Z. Phys. Chem. 201 (1952) 168. Wagner, C.: Thermodynamics of Alloys, Reading, MA, U.S.A.: Addison Wesley Publishing Company, Inc. 1952. Baldwin, R.L., Dunlop, P.J., Gosting, L.J.: J. Am. Chem. Sot. 77 (1955) 5235. Gruzin, P.L., Noskov, B.M.: Probl. Metallogr. Phys. Met. 4 (1955) and AEC.Tr.2924, p. 355. Gertsricken, S.D., Dekhtyar, 1.Y: Proc. 1955 Geneva Conference 15 (1955) 99. Linnenbom, V., Tetanbaum, M., Cheek, C.: J. Appl. Phys. 26 (1955) 932. Fujita, H., Gosting, L.J.: J. Am. Chem. Sot. 78 (1956) 1099. Gruzin, P.L., Polikarpov, I.A., Federov, G.B.: Fiz. Metal. Metalloved. 4 (1957) 94. Kirkaldy, J.S.: Can. J. Phys. 35 (1957) 435. Kirkaldy, J.S.: Can. J. Phys. 36 (1958) 899. Kirkaldy, J.S., Mason, G.R., Slater, W.J.:Trans. Can. Inst. Min. Metall. 64 (1961) 53. Guy, A.G., Smith, C.B.: Trans. Am. Sot. Met. 55 (1962) 1. Kirkaldy, J.S., Purdy, G.R.: Can. J. Phys. 40 (1962) 208. Kirkaldy, J.S., Weichert, D., Zia-Ul-Haq: Can J. Phys. 41 (1963) 2166. Kirkaldy, J. S., Zia-Ul-Haq, Brown, L.C.: Trans. Am. Sot. Met. 56 (1963) 834. Philibert, J., Guy, A.G.: C.R. Acad. Sci. 259 (1963) 2281. Shuck, F.O., Toor, H.L.: J. Phys. Chem. 67 (1963) 540. Brown, L.C., Kirkaldy, J.S.: Trans. TMS-AIME 230 (1964) 223. Dayananda, M.A., Grace, R.E.: Trans. TMS-AIME 233 (1965) 1287. Kirkaldy, J.S., Brigham, R.J., Weichert, D.H.: Acta Metall. 13 (1965) 907. Ziebold, TO., Cooper, A.R.: Acta Metall. 13 (1965) 465. DeHoff, R.T., Guy, A.G., Anusavice, K.J., Lindemer, T.B.: Trans. TMS-AIME 236 (1966) 881. Leroy, V.: La diffusion a l’etat solide -Application au systemeternaire Ni -Co - Cr, Centre National de Recherches Metallurgiques, 1966. Sabatier, J.P.,Vignes, A.: Mem. Sci. Rev. Metall. 64 (1967) 225. Ziebold, TO., Ogilvie, R.E.: Trans. TMS-AIME 239 (1967) 942. Dayananda, M.A., Kirsch, P.F., Grace, R.E.: Trans. TMS-AIME 242 (1968) 885. Dayananda, M.A.: Trans. TMS-AIME 242 (1968) 1369. Manning, J.R.: Diffusion Kinetics for Atoms in Crystals, Princeton: D. Van Nostrand Co., Inc., 1968. Smith, A.F., Gibbs, G.B.: Met. Sci. J. 2 (1968) 47. Strostriim, C., Hillert, M.: J. Iron & Steel Eng. 207 (1969) 77. Smith, A.F., Gibbs, G.B.: Met. Sci. J. 3 (1969) 93. Vignes, A., Sabatier, J.P.: Trans. TMS-AIME 245 (1969) 1795. Kirkaldy, J.S.: In: Adv. in Mater. Res., Vol. 4, Herman, H. (ed.) New York: Interscience Publishers, 1970, p. 55. Manning, J.R.: Metall. Trans. 1 (1970) 499. Whittenberger, J.D., Dayananda, M.A.: Metall. Trans. 1 (1970) 3301. Dayananda, M.A.: Metall. Trans. 2 (1971) 334. Hancock, G.F.: Phys. Status Solidi 7 (1971) 535. Anusavice, K.J., DeHoff, R.T.: Metall. Trans. 3 (1972) 1279. Bastow, B.D., Kirkwood, D.H.: J. Inst. Met. 100 (1972) 24. Carlson, P.T., Dayananda, M.A., Grace, R.E.: Metall. Trans. 3 (1972) 819. Guiraldenq, P., Poyet, P.: Mem. Sci. Rev. Metall. 70 (1973) 715. Heyward, T.R., Goldstein, J.I.: Metall. Trans. 4 (1973) 2335. Perkins, R.A., Padgett, Jr., R.A., Tunali, N.K.: Metall. Trans. 4 (1973) 2535. Perkins, R.A.: Metall. Trans. 4 (1973) 1665. Wan, Chung-Chu: Ph.D. Thesis, 1973, University of Florida, Gainesville, FL, U.S.A. Brunch, A., Steeb, S.: Z. Metallkd. 65 (1974) 765. Carlson, P.T., Dayananda, M.A., Grace, R.E.: Metall. Trans. A 6A (1975) 1245. Moyer, T.D., Dayananda, M.A.: Metall. Trans. A 7A (1976) 1035. Beke, D., Godeny, I., Kedves, F.J.: Acta Metall. 25 (1977) 539.
Land&-BBmstein New Series III/26
Dayananda
436 17s 79c 79D 80Rl 80R2 80Y 82A 82J 82K 83D 83K 83T 84K 84M1 84M2 84T 85Dl 85D2 85K 85T 86T 87Nl 87N2
6.9 References for 6 Sisson, Jr., R.D., Dayananda, M.A.: Metall. Trans. A 8 A (1977) 1849. Cheng, G.H., Dayananda, M.A.: Metall. Trans. A 10A (1979) 1415. Dayananda, M.A., Kim, C.W.: Metall. Trans. A 10A (1979) 1333. Roper, G.W, Whittle, D.P.: Met. Sci. 14 (1980) 21. Rothman, S.J.,Nowicki, L.J., Murch, G.E.: J. Phys. F 10 (1980) 383. Yokota, M., Harada, R., Mitani, H.: Trans. Jpn. Inst. Met. 21 (1980) 573. Angelo, P.C.: Ph.D. Thesis, 1982, Dept. of Metallurgy, Indian Institute of Science,Bangalore, India. Johnston, G.R.: High Temp. - High Pressures14 (1982) 695. Kim, C.W.: Ph. D. Thesis, 1982, School of Materials Engineering, Purdue University, W. Lafayette, Indiana, U.S.A. Dayananda, M.A.: Metall. Trans. A 14A (1983) 1851. Kim, C.W., Dayananda, M.A.: Metall. Trans. A 14A (1983) 857. Takahashi, T., Kato, M., Minamino, Y., Yamane, T.: Z. Metallkd. 74 (1983) 727. Kim, C.W., Dayananda, M.A.: Metall. Trans. A 15A (1984) 649. Minamino, Y., Yamane, T., Tsukamoto, K., Takahashi, J., Kimura, H.: Z. Metallkd. 75 (1984) 943. Minamino, Y., Yamane, T., Tsukamoto, K., Takahashi, J., Kimura, H.: Trans. Jpn. Inst. Met. 25 (1984) 142. Takahashi, T., Kato, M., Minamino, Y., Yamane, T: Met. Sci. 18 (1984) 580. Duh, J.G., Dayananda, M.A.: Diffusion and Defect Data 39 (1985) 1. Dayananda, M.A.: Proc. Symp. entitled “Diffusion in Solids - Recent Developments,” held in Detroit, U.S.A. 1984.Dayananda, M.A., Murch, G.E. (eds.),The Metallurgical Society AIME, 1985. Kansky, K.E., Dayananda, M.A.: Metall. Trans. A 16A (1985) 1123. Takahashi, ‘I, Kato, M., Minamino, Y, Yamane, T.: Trans. Jpn. Inst. Met. 36 (1985) 462. Takahashi, T., Kato, M., Minamino, Y, Yamane, T.: J. Jpn. Inst. Met. 50 (1986) 243. Nesbitt, J.A., Heckel, R.W.: Metall. Trans. A 18A (1987) 2075. Nesbitt, J.A., Heckel, R.W.: Metall. Trans. A 18A (1987) 2061.
Dayananda
Land&-BBmstein New S-criesIII!26
Ref. p. 4681
7.1 General remarks
437
7 Diffusion in amorphous alloys 7.1 General remarks The amorphous alloys in this chapter are more precisely denoted as amorphous metallic alloys. They are also called metallic glassesif they have been produced by rapid quenching from the melt. Amorphous alloys are thermodynamically not stable and may undergo structural transitions such as relaxation and crystallization during thermal annealing treatments. In the course of these transitions, usually controlled by diffusion processes,the extraordinary properties of the amorphous alloys are significantly changed or even destroyed by the process of thermal annealing. Diffusion studies on amorphous alloys can also be accompanied by structural transitions. Therefore, diffusion experiments in these materials are difficult to perform. The experiments are limited to very short diffusion lengths, often not more than about 10 nm, becausethe diffusion time at high temperatures is limited by the onset of crystallization, whereas at low temperatures the penetration is limited by the low diffusivity. An additional difficulty in the diffusion measurements arises from the change of the diffusivity in the amorphous state as a function of the annealing time if structural relaxation takes place. In amorphous alloys, the structural change is explained mainly by rearrangements of the short-range order in the course of annealing treatments. Fig. 1 [88H5] shows that the diffusivity change can be significant in materials which have been produced by melt spinning. t-
,p”
0.5 I
1.0 I
1.5 I
2.0 I
2.5405s : I
“Fe in Feg’Zrg I
lo-‘* \.
I
T= 673 K I
I
) 5gFe in Fe91Zrg
I
I 5gFe in FeTaSiqB12
I
’
633
_I lo-l9 LQ 1o-2o
59r- 1:- r^
1o-2’ 59r,.:,
1o-22
7-ILL
C^
Fig. 1. Instantaneousself-diffusion coefficients, or(t), vs. the diffusion annealing time measured in different amorphous alloys at various diffusion temperatures [88H5]. All amorphous alloys have been produced by melt spinning. The materials show relaxation effects which have significant influence on the self-diffusivities. Upper abscissa scale is for dashed lines, lower scale is for solid lines.
cm
----l--&i
563 --- 4s--- ;;;K Zr in FeTRZrlz
5gFe’in‘Fe7gW,B;, I 1o-23l 0 0.5 1.0
1.5
2.0
2.5-10”s
Becauseof the time dependenceof the diffusion coefficients the values deduced from the penetration profiles are time-averaged values, (D). If (0) (t) is known as a function of the annealing time t, the instantaneous tracer diffusion coefficient o(t) follows from D(t)=(D)+t
Land&-Biirnstein New Series III/26
HorvPth
a@‘> 7.
(7.1)
438
7.2 The effect of different production methods
[Ref. p. 468
Only in experiments with adequate preannealings or in materials with negligible relaxations, (D) is close to D(f). Since a!! measureddiffusion coefficients are more or less time-averaged values, for simplification in the following, (D) is replaced by D. The method by which an amorphous alloy has been produced seemsto play an important role in the diffusion measurements.This is true also for the side of the specimen on which the experiment is carried out. Numerous unconventional diffusion investigations, mostly by indirect methods, have been applied to evaluate the diffusion coefficients. Such items aggravated of course the valuation of the data. The reliability of individual sets of diffusion data depends here very much on the method of investigation. Today it is clear that meaningful! diffusion results are achieved mostly in relaxed or isoconfigurationa! amorphous states. These states can be established in most amorphous materials by carefully studied annealing treatments, denoted as preannealing treatments. This procedure for obtaining reliable diffusion measurements was not recognized sufficiently until rather late [85Hl, 85Pj. Unfortunately, in most of the diffusion investigations on amorphous alloys, the problems of structural transitions have not been noticed, or have been ignored. The latter obviously arises from an underestimation of its consequencesfor the diffusion results. In spite of the lower reliability of a number of studies, it is helpful to consider as much as possible useful information about diffusion. This gives in many casesat least an idea about the numbers for the diffusion quantities and if necessarya platform for more accurate studies in this difficult diffusion field. Under these circumstances, the comparison and examination of the diffusion data had to been done with an appropriate generosity. Diffusion studies of gasesin amorphous alloys have not been considered. For instance, the we!! investigated diffusivity of hydrogen depends strongly on its concentration in the host system.The dependenceof diffusion coefficients even on rather low concentrations of the diffusing specieswould not tit into the presentation of the tables. For diffusion of hydrogen in amorphous alloys the reader is referred to the reviews in [82K2,82K3,87Kl, 87K2]. Reviews of diffusion in amorphous alloys are given in [83Ll, 83C1, 85C, 88Ml].
7.2 The effect of different production methods A wide composition range of amorphous alloys has been produced owing to the rapid developments of the production techniques. Most of the amorphous alloys contain transition metals as components, either in combination with each other or with metalloids, rare-earth elements,actinides or non-transition metals. There is also a group of amorphous alloys consisting of non-transition metals only, but their diffusion properties have not been investigated so far. Amorphous alloys are often produced by rapid quenching from the melt, mostly by melt spinning on a metal wheel. The so-called splat quenching of melt drops is less important for production of larger amounts. A significant feature of the amorphous materials produced by rapid quenching is that they may have different properties on the two sides of the foil due to the different quenching rates. The side which had direct contact to the wheel or cooling substrate during quenching may have experienced a higher cooling rate than the opposite side. Contradictory results of different studies in someinvestigations have been attributed to this effect. Compositions of amorphous alloys which cannot be produced or only with great difficulty by rapid quenching can be produced in many casesby co-sputtering or co-evaporation. Moreover, the production of amorphous alloys atom by atom may be an explanation of the obviously more relaxed structure of the co-sputtered or co-evaporated materials in comparison to the rapidly quenched alloys. This follows from the significant relaxation effects on the diffusion coefficients often found in rapidly quenched alloys. Therefore, those diffusion investigations which have been performed in preannealed (relaxed) rapidly quenched alloys or in co-sputtered or co-evaporated alloys have to be regarded as more meaningful. Other lesscommon methods to produce amorphous alloys are electrolytic deposition, irradiation damaging, and ion-beam mixing. The local composition and the structure of amorphous alloys produced in theseways are usually poorly defined. The alloys are not favourable for sound diffusion investigations becausethe experimental results may suffer from the inhomogenities of the structure. The most recent method to produce amorphous alloys is the solid-state reaction of mixtures of appropriate metals. The solid-state reaction starts either from multilayer thin crystalline metal films or from mechanically alloyed mixtures of crystalline powders. In some cases,diffusion coeffkients have been deduced for amorphous regions which have been produced by solid-state reactions. Reviews of this researchfield are given in [86J,88B1, SSJ.889, 88821.
Hodth
Landolt-BBmstcin New Series 111126
Ref. p. 4681
7.3 Methods of diffusion investigations on amorphous alloys
439
7.3 Methods of diffusion investigations on amorphous alloys Since the reliability of the results listed in the tables depends on the experimental method even more than in other diffusion fields, the most frequently applied methods on amorphous alloys are briefly mentioned. From this, the strengths of the individual investigation methods may become more evident. More details about the various experimental methods are given in chapter 1 of this volume. Conventional methods like mechanical sectioning are not adequate to measure steep diffusion profiles. The sectioning is too coarse for profiles measurable in amorphous alloys. In many cases,atoms can be detected most sensitively if they are radioactive. The most sensitive method for micro-sectioning of a diffusion profile is the ion-beam-sputtering technique. A combination of both, the radiotracer technique with ion-beam-sputtering, has been successfully applied in many experiments to measure the diffusion coefficients in amorphous alloys directly. Fig. 2 shows how unambigously the diffusion coefficient can be determined from a Gaussian profile. In a plot of the logarithm of the concentration versus the depth squared the slope is proportional to l/D (seealso Eq. 1.11 of chapter 1). A technique similar to the above is the radiotracer technique in combination with high-frequency sputtering @f-plasmasputtering). In a number of experiments secondary-ion-mass spectroscopy (SIMS) has been used for the direct measurement of the diffusion profiles. Fig. 3 shows a typical diffusion profile. Although this method is well established and has been improved in the recent years for measuring steepdiffusion profiles, the sensitivity of the radiotracer methods usually cannot be reached. Since in self-diffusion experiments the concentration of enriched stable isotopes can be measured with great background problems only, SIMS is mainly used for investigation of foreign-atom diffusion.
104
I h 103 Z ?z 50 uC ti F 102
g=12ih k
1
\
; 15 10
h
1
J
0
150
300
450
0
60 nmL 750
X2Fig. 2. “Fe tracer diffusion profiles in amorphous Fe,,W,B,, (0) and Fe,,B,, (0) at 593 K for non-preannealed specimens. The parameters shown on the profiles are the diffusion times [88H5]. The diffusion coefficients may be evaluated directly from the slope of the diffusion profiles. X: penetration depth. Land&-Bhstein New Series III/26
30
60
90
x-
120
150nm 1SO
Fig. 3. Typical SIMS profiles for the spreading of a Cu tracer impurity layer in amorphous Ni,,Zr,, after annealing at 573 K [86Hl]. The diffusion coefficient of Cu is evaluated from the broadening of the concentration profile (dashed line). The full line representsthe concentration profile before diffusion. X: depth.
Horvith
[Ref. p. 468
7.3 Methods of diffusion investigations on amorphous alloys
440
This is also true for Auger-electron spectroscopy (AES) studies, which are usually applied in combination with ion-beam sputtering. The results suffer from concentration gradients which are present during the measurements. Fig. 4 shows profiles in an amorphous alloy measured by the AES method. Rutherford backscattering (RBS) of He+ has been used in caseswhere the diffusion of heavy atoms in amorphous alloys of lighter atoms was investigated. In this method, the energy spectrum of the backscattered ions is measured, and has to be transformed to a diffusion profile (Fig. 5). The results which may be achieved by RBS are not regarded as sensitive as the radiotracer method. Nuclear reaction methods have been used to measurethe boron diffusion for instance, which is very difticult to measure with the direct methods mentioned above.
* -+ T
*a orb. units 4.0
iron
.
4 Fig. 4. Typical AES profiles obtained on sputter etching through a 390 nm layer of Si deposited on amorphous Fe,,B,, after annealing for 2 h at 623 K [83L2]. (The sputter time I is proportional to the depth of the profiles.) The peak to peak signals have to be standardized for the evaluation of the concentration profiles which the diffusion coefftcients are determined from.
150r
is8
392
396
400
404 408 Chonnels -
412
416
420
424
Fig. 5. RBS spectra taken with perpendicularly incident 2MeV He+ ions: Hg in amorphous Pd,sCu,Si,, before (0) and after (0) diffusion at 681 K for 48 h. Depth scale: one channel corresponds to 2.1 keV, equivalent to 1.9 nm [88B4]. The diffusion coefficients are evaluated from the concentration profiles obtained from the difference of the RBS spectra.
Hodth
Landolf-B6mstein New Series III/26
Ref. p. 4681
7.4 Use of the tables and figures
441
X-ray scattering methods have been applied in several studies to measure the interdiffusion coefficient of compositionally modulated multilayer thin films of amorphous or crystalline materials. This is a powerful technique to measure very small interdiffusion coefficients. Crystallization investigations, in particular primary crystallization applying transmission-electron microscopy (TEM), have been used to measure diffusion coefficients as well. Diffusion data deduced from indirect experiments should be considered with some caution. However, since in many casesgood agreement with directly measured values could be achieved such data appear valuable. From indirect techniques only interdiffusion coefficients can be determined.
7.4 Use of the tables and figures The diffusion data on amorphous alloys have been classified in tables starting in alphabetical order with the data on cobalt-base alloys followed by the tables of copper-, iron-, nickel-, palladium-, silicon-, and zirconiumbase alloys. The first column of the tables contains the host amorphous alloy and the production method if this has been given in the paper. The second column shows the diffusing element. In many cases,e.g., for interdiffusion measurements,this element cannot be stated. For rapidly quenched amorphous alloys, a preannealing treatment (column 3) must be regarded asnecessary for a reliable and well defined diffusion measurement. Exceptions are those investigations in which the dependence of the diffusion coefficients on the diffusion time was measured (e.g.,Fig. 1). In the next columns (4 and 5), the temperature range of the diffusion experiment and the diffusion coefficient at 573 K, if possible, are given. In most cases,the latter was extrapolated from the Arrhenius function for D(T) (Eq. 1.50 of chapter 1) for the sake of comparison. If 573 K is far away from the investigated temperature range, D at 573 K has to be regarded with care. In cases,when D at 573 K was taken as a data point from the paper, it may deviate slightly from a value obtainable from the Arrhenius parameters Do and Q of the tables (columns 6 and 7). These data points were taken in caseswhere the reliability for D seemedto be increased through that. Very often the Do (preexponential factor) and Q (activation enthalpy) values had to be taken from the figures becausethey were not given explicitly. Therefore, small deviations from the values which the authors may have obtained are possible. Uncertainties in the data given in the papers have not been taken into account. The remarks column (8) will help to estimate the reliability of the diffusion results. In most of the experiments, chemical-diffusion coefficients (D) have been obtained from interdiffusion experiments or steep penetration profiles. The penetration depth, 2(0”t)“‘, is typically in the order of several tens of nm. In many cases,the diffusing element was deposited on the specimen surface in thicknesses of the same order of magnitude as the penetration depth. These experiments have remarks like “concentration gradient” or “interdiffusion”. Diffusion of isolated atoms is found by tracer investigations (diffusion coefficient D*). In some of the papers, the term “marker” has been used instead of tracer. Markers conventionally designate the “inert particles” which are incorporated at the interface of two materials to measurethe Kirkendall shift (seechapter 1.4 of this volume in the general introduction). Only results which seemvery reliable have been given in the Arrhenius plots in the figures (column 9). The referencesare given in column 10.
Land&BBmstein New Series III/26
Horviith
7.5 Diffusion Host system (produced by)
Diffusant
Preannealing temperature p]/ time [s]
Diffusion temperature K
tables for amorphous D [m2/sl/
at temperature p]
DO m2/s
alloys Q
Remarks
Fig.
Ref.
kJ/mol
7.5.1 Diffusion in cobalt-base amorphous alloys Co90Zrlo
-
-
*I
6.6. lo-241573
1.8. lo+3
290
Concentration gradient; 0” indi- rectly from rates of primary crystallization; *): the temperature regime has not been given
88K2
Cc&, 1 (melt spinning)
To
633/*)
633
1.10-m...
_
_
Radiotracer; sectioning by ionbeam sputtering; in unrelaxed material, D* is a function of diffusion time; *): preannealing at different periods of time
88Ml
(production method not mentioned)
‘+3&d,, (co-sputtering) Co,oJ320
5.4 * 10-19
5’Co
63313600
515.e.695
3.6. 10-20/573
8.03.10-'
147
Radiotracer; sectioning by ionbeam sputtering
6
88Ml
i9=Au
63313600
632.0.684
1.67. 1O-25/573
4.15.10-2
256
Radiotracer; sectioning by ionbeam sputtering
-
90D
To
6231345600
498.e.602
3.3. lo-=/573
1 . IO-”
115
Implanted radiotracer; sectioning by &plasma sputtering
6
82Gl
-
-
573.e.693
1.2. lo-201573
7.2. 1O-3
195
Concentration gradient; d indi- rectly from rates of primary crystallization; B diffusion is assumed for d; Do from Fig. 9 of [81K2]
81K2
-
-
*I
8.4. 1O-2'/573
4 * 10-s
193
Concentration gradient; 0” indi- rectly from rates of primary crystallization; *): the temperature regime has not been given
88Kl
(melt spinning)
Co,,Bz,
B
573 ... 6331 3600 . . .7200
568 ... 623
8.3 . 10-20/573
1.3 * 10-14
57
Concentration gradient; AES; Do from Fig. 3 of [88M2]
-
85M, 88M2
Si
573 .-. 6331 3600.. .7200
573 ... 623
1.2. lo-2o/573
4.1. lo-l2
93
Concentration gradient; AES; Do from Fig. 3 of [88M2]
-
85M. 88Mi
-
-
523
3.10-21... 1 .10-21
_
_
Interditfusion of thin crystalline films of Co and Zr through amorphous Co,,Zr,,; d indirectly from X-ray scattering; *): the composition of the alloy may vary
86K2
(melt spinning)
Co60Zr40 *) (solid state reaction)
7.5.2 Diffusion in copper-base amorphous alloys Cu,oAg,o/
-
308
5.7. lo-=... 1.4.10-2s
_
-
Interdiffusion of thin amorphous films; d indirectly from resistivity measurements; in unrelaxed material, d is a function of diffusion time
-
84R
317
1.2. lo-=... 5.2. 1O-25
_
-
Interdiffusion of thin amorphous films; d indirectly from resistivity measurements; in unrelaxed material, B is a function of diffusion time
-
84R
321
1.4. lo-24... 8.3. 1O-25
_
-
Interdiffusion of thin amorphous films; d indirectly from resistivity measurements; in unrelaxed material, d is a function of diffusion time
-
84R
308...321
3.6. IO-“/573
7.3 * 10-7
113
Interdiffusion of thin amorphous films; d indirectly from resistivity measurements; *): diffusion data from the isoconfigurational (relaxed) state
-
84R
Cu,oAg,o
(co-evaporation)
-
-
-
*)
DO
Host system (produced by)
Diffusant
Preannealing temperature [K]/ time [s]
Diffusion temperature K
D[m*/sll at temperature [K]
Q
Remarks
m2/s
kJ/mol
CuGL
-
-
713
5.3. lo-‘91713
-
-
Concentration gradient; d indirectly from crystal-growth rates; Zr diffusion is assumed for b
80F
Cu50Zr50 (melt spinning)
Ag
-
590... 658.5
6.7. 10-22/573
1.3 . lo- l5
69
Concentration gradient; AES; b on the “wheel side” of the material
87S5
Ag
-
590.m-658.5 7.5. 10-22/573
1.2.10-‘4
79
Concentration gradient; AES; d on the “non-wheel side” of the material
8785
Au
-
59O.a.658.5 4.4. 10-21/573
1.7. 10-7
149
Concentration gradient; RBS; d on the “non-wheel side” of the material
8735
(splat quenching)
Fig.
Ref.
7.5.3 Diffusion in iron-base amorphous alloys Fe,,%
*9Fe
-
633
2.9. lo-=... 4.1 . 10-19
_
_
Radiotracer; sectioning by ionbeam sputtering; in unrelaxed material, D* is a function of diffusion time
-
88P
59Fe
-
673
3.6. IO-rs... 2.4. IO-l8
_
_
Radiotracer; sectioning by ionbeam sputtering; in unrelaxed material, D* is a function of diffusion time
-
88P
5gFe
673/9000 or 633164800
473.e.773
3.5 * lo-201573
3.1 * 10-7
142
Radiotracer; sectioning by ionbeam sputtering
7
87H3, 88P
g5Zr
673/9000
593.a.743
1.8. 10-2’/573
2.1 . 10-3
242
Radiotracer; sectioning by ionbeam sputtering
7
88H5, 88P
(melt spinning)
Fe90Zrlo
-
-
*I
3.1 . lo-271573
20
305
Concentration gradient; 0” indirectly from rates of primary crystallization; *): the temperature regime has not been given
-
88K2
%JL
Si
-
571,646
4.5. lo-231573
1.4. 10-7
170
Concentration gradient; AES
-
83L2
%A3
Si
-
571, 646
9 * lo-231571
-
-
Concentration gradient; AES; no diffusion detected at 646 K
-
83L2
WA4 (melt spinning)
Si
63217200
571,646
4.5.10-231573
1.4. 10-7
170
Concentration gradient; AES; d independent of preannealing
83L2
-
-
483 ... 650
7.8 ’ 10-21/573
2.10-4
180
Concentration gradient; d indirectly from rates of primary crystallization; B diffusion is assumed for d
-
8OK2
-
-
639.e.659
5.2. 1O-23/573
8.5 * lo+20
474
Concentration gradient; 4 indirectly from crystal growth rates; B diffusion is assumed for D; Do and Q from Fig. 7 of [82N)
-
82N
-
-
523
1 .;p1,‘-;,
-
-
Interdiffusion of thin amorphous films; d indirectly from X-ray scattering; in unrelaxed material, d is a function of diffusion time
-
8262
-
-
573
8. 10-23 . . . 3.10-24
-
-
Interdiffusion of thin amorphous films; d indirectly from X-ray scattering; in unrelaxed material, d is a function of diffusion time
-
82G2
(melt spinning)
(melt spinning) (melt spinning)
Fe85B15ho/ Pds5%)50
(co-sputtering)
(continued)
Host system (produced by)
Diffusant
Preannealing temperature [K]/ time [s]
Diffusion temperature K
D [m%l/ at temperature [K]
Q
Remarks
Fig.
Ref.
m2/s
kJ/mol
DO
(Fe,5B15)50/(Pd,5Si15)50 (continued) (co-sputtering)
-
523/*)
483.e. 543
4.5 . 10-241573
2.7. lo+
195
Interdiffusion of thin amorphous films; d indirectly from X-ray scattering; Do from Fig. 5 of [8262]; *): preannealing for different periods of time
-
8202
Fe85B15
P
-
488.e. 543
2.7 - 10-2’/573
4.5 * 10-s
178
Tracer: SIMS
-
81E
Feloo-Al Feloo-yB, x, y = 15...62; (co-sputtering)
-
-
573
2.9. I()-20... 5.10-21
-
Interdiffusion; AES; in unrelaxed material, b is a function of diffusion time; (a at a B concentration of 30%)
86s
-
-
525.a. 624
1.2. IO-=/573
7.3. 10-6
173
Interdiffusion; AES; Do and Q at a B concentration of 30%; Do from Fig. 6 of [86S]
-
86s
525.~. 624
1 . IO-2’/573
3.7 - 10-i’
72
Interdiffusion; AES; Do and Q at a B concentration of 45 %; Do from Fig. 6 of [86S]
-
86s
(melt spinning)
Fe85P15
-
-
573,603
I.6 . IO- 19/573
I -10-2
184
Concentration gradient; b indirectly from rates of primary crystallization; P diffusion is assumed for 6; Do and Q from Fig. 6 of [82K4]
-
82K4
Fe8,B16
Si
63217200
571,646
4.5 . lo-231573
I.4 * 10-7
170
83L2
-
-
483... 660
7.8. IO-211573
2.10-4
180
Concentration gradient; AES; d independent of preannealing Concentration gradient; ij indirectly from rates of primary crystallization; B diffusion is assumed for d
(melt spinning)
(melt spinning)
80K2
-
-
483.s.663
I. lO-22/483 4. lo-‘91573 2 . IO- “1663
-
180
-
-
523...663
1.8. 1O-21/523 2.2. lo-291573 3.8 . IO- “1663
-
-
Fe84BC 6 10 (melt spinning)
-
-
483.e.613
2. 1O-22/483 1 . lo-‘91573 5. 10-18/613
-
190
Concentration gradient; d indirectly from rates of primary crystallization; B diffusion is assumed for b; curved Arrhenius plot for B;(T)
80K2
Fe84P 10C 6 (melt spinning)
-
-
633...703
1.3. lo-231573
23
266
Concentration gradient; ij indirectly from rates of primary crystalliztion; B diffusion is assumed for 6; Do and Q from Fig. 6 of [82K4]
80K2, 82K4
Fes2B18
Au
-
575e.e645
1.5. lo-211573
8.9. IO-”
129
Concentration gradient; AES
-
8732
Au
-
575... 645
1.4. lo-211573
2.3. IO-”
112
Concentration gradient; RBS and AES
-
8784
Au
6531600
576... 645
9.2. lo-=/573
1.5. 10-I’
123
Concentration gradient; RBS; d independent of preannealing; Do from Fig. 2 of [8833]
8883
Au
-
575... 645
1.3. lo+/573
4.7.10-l’
116
Concentration gradient; RBS
-
8884
Au
6531600
575e.e645
1.3 . lo-211573
8.9. IO-”
119
Concentration gradient; RBS
7
8884
cu
6531600
576... 638
9.8. 10-21/573
2.10-7
Concentration gradient; AES; fi independent of preannealing; Do from Fig. 2 of [8833]
7
8833
kJ%C8
(melt spinning)
Concentration gradient; d indirectly from rates of primary crystallization; B diffusion is assumed for d; curved Arrhenius plot for D”(T) Concentration gradient; B indirectly from rates of primary crystallization; metalloid diffusion is assumed for d; curved Arrhenius plot for D:(T)
80K2
82K4
(melt spinning)
146
(continued)
DO
Remarks
Fig.
Ref.
(5.9 * lo- 14) (74)
Concentration gradient; RBS; no clear Arrhenius behavior for d(T)
-
8884
8.0 . lo- 2’/573
2.5. lo+
159
Concentration gradient; RBS
-
88S5
600 . . .640
2.2. lo-2’/573
0.31
221
Concentration gradient; RBS
7
8835
-
559...6448
2.7. lO-21/573
5.7 * 10-4
190
Concentration gradient; AES
-
83L2
Si
57317200
598...696
1.4. lo-211573
2.9 - 1O-2
212
Concentration gradient; AES; b independent of preannealing
82L
-
-
613-e-678
6. 10-20/613 3.10-‘91643 2 - lo- ‘a/678
-
-
Concentration gradient; d indirectly from rates of primary crystallization; B diffusion is assumed for 6; curved Arrhenius plot for 6(T)
80K2
Fe81B,3.5Si3.5C2 Si
-
623.a.723
4.6. 1O-22/573
1.7 - 10-l’
72
Concentration gradient; AES; d indirectly from Si segregation to a free surface
86V
Fe80.5B19.5 (melt spinning)
Si
-
571,646
4.5 . lo-231573
1.4 * 10-7
170
Concentration gradient; AES
-
83L2
Fe80B20 (melt spinning)
198A~
-
554, 594
1 .,10102~;3.
-
-
Radiotracer; sectioning by ionbeam sputtering
-
8lVl
Au
-
546 . . .643
4.4 * lo-2’1573
2.1 . lo-’
150
Concentration gradient; AES
-
8732
Au
-
546.e-643
3.4 * lo-211573
1.3. lo-’
149
Concentration gradient; RBS
-
8733
Au
6231900
546-e. 643
3.1 * lo-=/573
2.2 * 10-7
152
Concentration gradient; RBS
7
8733
Host system (produced by)
Diffusant
Preannealing temperature [K]/ time Is1
Diffusion temperature K
at temperature [K]
m2/s
Fe,,B,, (continued) (melt spinning)
Pb
-
601... 636
1.1 * lo-201573
Sb
-
575.**640
Sb
6231600
Si
Fe82B12Si6
Fe82M02B16 (melt spinning)
D[m’/sl/
Q
kJ/mol
(melt spinning)
(melt spinning)
Au
6231900
546.e.643
3.1 . lo-=/573
1.2. 10-7
149
“Fe
-
543, 562
-
-
“Fe
-
593
3 . 10-221543 2. 1O-21/562 2.4. lo-21 . . . 2.4. 1O-22
-
-
“Fe
593121600
543...655
3 . lo-=/573
7.9. 10-2
235
Pb Si
63217200
546...582 571, 646
1.3. lo-201573 4.5. lo-=/573
4.3 1.4. 10-7
225 170
-
-
623...673
7.8. 1O-21/573
2 * 10-4
180
Fe80B 12Si8 (melt spinning)
-
-
633 ... 693
1 . lo-‘*/573
1.1 . 10-4
154
Fe7gB21 (melt spinning)
Si
-
571,646
4.5 . lo-231573
1.4. 10-7
Fe7gWlB20 (melt spinning)
“Fe
-
593
1.5. 1()-21... 7.1 * 10-23
-
Fe78Bi3Sig (melt spinning)
5gFe
673/*)
673
6.3. IO-20... 9.10-21
Concentration gradient; RBS; d independent of preannealing; Do from Fig. 2 of [8883] Implanted radiotracer; sectioning by ion-beam sputtering Radiotracer; sectioning by ionbeam sputtering; in unrelaxed material, D* is a function of diffusion time Radiotracer; sectioning by ionbeam sputtering Concentration gradient; RBS Concentration gradient; AES; d independent of preannealing Concentration gradient; B indirectly from rates of primary crystallization; B diffusion is assumed for ij
-
8833
-
81V3
-
88H5, 880
7 -
88H5, 880 8783 83L2
-
80K2
Concentration gradient; 0” indirectly from rates of primary crystallization; B diffusion is assumed for 0”
-
83C2
170
Concentration gradient; AES
-
83L2
-
Radiotracer; sectioning by ionbeam sputtering; in unrelaxed material, D* is a function of diffusion time
-
880
Radiotracter; sectioning by ion- 89U beam sputtering; in unrelaxed material, D* is a function of diffusion time; *): preannealing (continued) for different periods of time
Host system (produced by)
Preannealing temperature [K]/ time [s]
Diffusion temperature
67417200
B
Diffusant
Fig.
Ref.
m2/s
Q
Remarks
at temperature [K]
kJ/mol
551.+. 783
1.8. IO-“/573
4.6. lo-’
202
Radiotracer; sectioning by ionbeam sputtering
8
87H3, 89U
-
573.s.633
6.8 . lo- ‘91573
5.9. 10-s
109
Concentration gradient; SIMS
-
84D
B
6331600
573...633
1.1 . IO--201573
4.3 * 1o+a
259
Concentration gradient; SIMS
8
84D
Fe77.5B22.5 (melt spinning)
Si
63217200
571, 646
4.5. lo-231573
1.4. IO-’
170
Concentration gradient; AES; 6 independent of preannealing
83L2
Fe7,B2, (melt spinning)
Si
-
571, 646
4.5 . lo-231573
1.4 * 10-7
170
Concentration gradient; AES; partial crystallization occurred at646K
83L2
Fe,$,,
Si
573 ... 6331 3600*..7200
583.a.613
7.10-201573
2.5. 10-l’
28
Concentration gradient; AES; Do from Fig. 3 of [88M2]
-
85M, 88M2
Fe74B26 (melt spinning)
Si
571,646
4.5 * lo-231573
1.4 * lo-’
170
Concentration gradient; AES; partial crystallization occurred at646K
83L2
Fe s5.sNi18.5B 26 (melt spinning)
B
473.0.593
4.3 . lo-=/573
3 * lo-‘3
97
Concentration gradient; d indirectly from deboriding by oxidation of the surface in combination with photometric analysis
88B5
Feb2Nih2B 16
-
592***707
7.2. 10-21/573
0.1
210
Concentration gradient; d indi- rectly from rates of primary crystallization; B diffusion is assumed for 6; Do from Fig. 2 of [80Kl]
Fe,,Bi,Si, (continued) (melt spinning) “Fe
Fe7,P1,C7
Db2/sl/
DO
K
(melt spinning)
(melt spinning)
(melt spinning)
-
80Kl
Fe41Ni41B18
-
-
650, 678
3. lo-“/650 2. lo-‘*/678
-
-
Concentration gradient; 0” indirectly from rates of primary crystallization; B diffusion is assumed for 0”
-
80K2
-
6331240
573...673
2.2. 10-2l/573
1.1 . lo+3
260
Concentration gradient; 0” indirectly from rates of primary crystallization; B diffusion is assumed for 0”
-
82K4
“Fe
613/*)
613
6.4. IO-21 . . . 1 .10-21
-
-
Radiotracer; sectioning by ionbeam sputtering; in unrelaxed material, D* is a function of diffusion time; *): preannealing for different periods of time
87P
5gFe
573 ... 633/*)
552... 643
7.9 ’ lo-231573
1.1 . 10-2
221
Radiotracer; sectioning by ion- 8 beam sputtering; *): preannealing for different periods of time
85P, 87P
-
-
592... 707
7.2. 1O-21/573
0.1
210
Concentration gradient; d indi- rectly from rates of primary crystallization; B diffusion is assumed for fl; Do from Fig. 2 of [80Kl]
80Kl
-
6331240
593.a.713
2.2. lo-211573
1.1 . 1o+s
260
Concentration gradient; 0” indirectly from rates of primary crystallization; B diffusion is assumed for d
-
82K4
Au
-
573...685
1.3. lo-221573
9.4. 10-5
196
Concentration gradient; RBS
-
82A1
Au
6581300
573..*685
9. lo-231573
1.9 * 10-4
201
Concentration gradient; RBS
8
82Al
Au
6581300
573...685
1.2. lo-221573
1.6. 1O-4
199
Concentration gradient; RBS; B independent of preannealing; d, Do, and Q include the data of non preannealed states
82Al
(melt spinning)
Fe4,Ni4,B2,
(melt spinning)
(continued)
Host system (produced by)
DO
Fig.
Ref.
m2/s
Q
Remarks
at temperature [K]
kJ/mol
613...643
1.5. 10-‘9/613 7.5. lo-I91633 8 ’ lo-I81643
-
-
Concentration gradient of B isotopes; SIMS; curved Arrhenius plot for B(T)
-
80C
-
478...553
9.9.10-2r/573
3.1 . 10-6
159
Concentration gradient; 6 indi- rectly from boriding and deboriding by oxidation of the surface in combination with photometric analysis
84B
59Fe
573/*)
573
7.5. IO-=... 4.5.10-23
-
-
Radiotracer; sectioning by ionbeam sputtering; in unrelaxed material, D* is a function of diffusion time; *): preannealing for different periods of time
85H2, 89U
“Fe
593/*)
593
2.0. I(-)-=... 3.3.10-22
_
-
Radiotracer; sectioning by ionbeam sputtering; in unrelaxed material, D* is a function of diffusion time; *): preannealing for different periods of time
86H2
59Fe
613/*)
613
4.3.1()-21... 1.4. 10-t’
_
-
Radiotracer; sectioning by ionbeam sputtering; in unrelaxed material, D* is a function of diffusion time; *): preannealing for different periods of time
86H2
59Fe
573 - -. 633/*)
571 . . * 643
5.5. IO--231573
2.7. lO-2
227
Radiotracer; sectioning by ion- 8 beam sputtering; *): preannealing for different periods of time
85H1, 86H2
“Ge
-
570, 591
< 1 . lo-22/570
-
-
Radiotracer; sectioning by ionbeam sputtering
81Vl
Diffusant
Preannealing temperature [K]/ time Is1
Diffusion temperature K
658/300
B
Fe,,Ni,,B,, (continued) 1°B (melt spinning)
D[m2/sl/
-
Fe40Ni40P14B6
s2P
573 . . .633/*)
573.e.644
1.3 * lo-231573
1 . lo+4
295
Implanted radiotracer; sectioning by ion-beam sputtering; *): preannealing for different periods of time; D* is roughly independent of preannealing
-
-
592...707
7.2. 10-21/573
0.1
210
Concentration gradient; d indi- rectly from rates of primary crystallization_; B diffusion is assumed for D; Do from Fig. 2 of [80Kl]
80Kl
5gFe
-
541-e. 617
2.5. 10-21/573
1.10-3
193
Implanted radiotracer; sectioning by ion-beam sputtering
81V3
“Fe
-
423...573
1.7. lo-211573
2.6 . IO- l6
57
Radiotracer; “Kriukov-Joukhovitsky- and Gruzin method”
83s
P
-
623
5.10-20... 1 .10-2l
-
-
Concentration gradient; AES; d indirectly from P segregation to a free surface
76W
P
523/*)
45Oe.3800
5.1 ’ 10-231573
7.10-6
188
Concentration gradient; AES; 4 indirectly from P segregation to a free surface; d independent of preannealing; *): preannealing for different periods of time
81B
=P
-
553 ... 573 I) 5.5 * lo-=/573 573 ... 583 II) 2.4. 10-22/573 583 1.. 613 III) 4.3 . 10-22/586
1 . lo+6 -
299 -
Implanted radiotracer; sectioning by ion-beam sputtering; D* has been observed in three amorphous stages: I) - III)
81V2
=P
-
443...529
1.8. 1O-22/573
2.4. IO-l3
100
Radiotracer; “Kriukov-Joukhovitsky- and Gruzin method”
-
83s
-
-
633 ... 833
7.7 * lo-=/573
4.1 . 1o+‘O 370
Concentration gradient; 0” indirectly from crystal-growth rates; Do from Fig. 8 of [81M]
-
81M
(melt spinning)
8
-
86H3
(continued)
Host system (produced by)
Preannealing temperature [K]/ time Is]
Diffusion temperature K
‘Dh2/sl/
m2/s
Q
Remarks
at temperature [K]
kJ/mol
-
623..+653
6.6 * lo-2’/573
2.7. 1O+4
270
Concentration gradient; fi indi- rectly from crystal-growth rates; metalloid diffusion is assumed for d; Do and Q from Fig. 12 of [8IT]
-
-
650...675
3.9 * IO-241573
2.5. IO+6
327
Concentration gradient; d indirectly from crystal-growth rates; P diffusion is assumed for d
P
523/*)
450-.. 800
I.5 * IO-22/573
7.4. 10-6
183
Concentration gradient; AES; d indirectly from P segregation to a free surface; d independent of preannealing; *): preannealing for different periods of time
Diffusant
Fe,,Ni,,P,,B, (continued) (melt spinning) -
Fe31%oCr16
DO
V2PJ3,
(melt spinning)
Fig.
-
Ref.
82F
7.5.4 Diffusion in nickel-base amorphous alloys B
5231600
413 .a.473
2.1 * IO-2o/413 3.4 * IO-201453 3 ’ IO-‘91473
-
-
Concentration gradient; SIMS; no Arrhenius behavior for @T)
-
84D
Ni,,P,,Si, (melt spinning by single roller technique) (melt spinning by twin roller technique)
B
6131600
503.*.533
3.3 . IO-‘91573
1.5.10-9
106
Concentration gradient; SIMS
9
84D
B
6131600
503...533
3. IO-‘91573
2.6. IO-’
109
Concentration gradient; SIMS
-
84D
NW& (melt spinning)
B
5231600
413.a.473
4.5 * lo-is/573
2.10-12
62
Concentration gradient; SIMS
9
84D
Ni80P20 (melt spinning)
Au
-
442 . . .506
1.4. lo-2o/573
1.5. 10-S
132
Concentration gradient; AES and RBS
-
88B2
Ti
-
473... 527
1.2. lo-“/573
8.6. 10-s
163
Concentration gradient; AES
-
88B3
-
-
463 .-..660
8.8 * lo-‘91573
5.10-g
107
Interdiffusion of thin crystalline films of Ni and Zr through amorphous Ni,,Zr,,; d indirectly from DSC measurements; *): the composition of the alloy may vary
-
87H2
Au
-
633...733
4.6. 10-23/573
3.3. 10-S
163
Implanted tracer; RBS; Do from Fig. 3 of [86Bl]
-
86Bl
Bi
-
673 ... 763
1.2. lo-231573
1.3. lo-lo
143
Implanted tracer; RBS; Do from Fig. 3 of [86Bl]
-
86Bl
(co-evaporation)
cu
-
573
1.5 ’ lo-2i/573
-
-
Tracer co-evaporated; SIMS
-
88H1, 88H2
(melt spinning)
Hg
-
663...748
1.4. 10-241573
1.9. 10-4
221
Implanted tracer; RBS; Do from Fig. 3 of [86Bl]
-
86Bl
Pb
-
648...773
2.10-231573
7.7 * lo-lo
149
Implanted tracer; RBS; Do from Fig. 3 of [86Bl]
-
86Bl
Au
-
613.v.773
2 ’ lo-231573
4.2. 1O-6
190
Concentration gradient; RBS
-
82A1, 82Kl
Au
7731600
613...773
3.6. 10-23/573
4.9. 10-7
177
Concentration gradient; RBS
9
82A1, 82Kl
Au
7731600
613...773
2 * lo-231573
1.5. 10-6
185
Concentration gradient; RBS; d independent of preannealing; b, Do, and Q include the data of non preannealed states
82A1, 82Kl
Ni,,B,,Si, (melt spinning)
NW&
*I
(solid state reaction)
Ni.dh
(melt spinning)
W4W6
(melt spinning)
Host system (produced by)
Diffusant
Preannealing temperature [KJ/ time [s]
Diffusion temperature K
Fig.
Ref.
m2/s
Q
Remarks
at temperature [K]
kJ/mol
Nib4Zrj4Pd, *) (ion-beam mixing)
Au
-
723-a. 780
3.5 * lo-241573
8.9 . IO- *
180
Implanted tracer; RBS; Do and Q from Fig. 3 of [86B2]; *): the composition of the alloy may vary
-
86B2
Ni62.gZr37.1
cu
-
573
1.1 . lo-=/573
-
Tracer co-evaporated; SIMS
-
88H1, 88H2
Ni62Zr38 *I (ion-beam mixing)
Au
-
623,673
2.5. lo-=/573
1.5 * 10-6
184
Implanted tracer; RBS; Do and Q from Fig. 3 of [86B2]; *): the composition of the alloy may vary
-
86B2
Ni,,Zr,,Pd, *) (ion-beam mixing)
Au
-
653.e. 783
3.5 . lo-241573
8.9. IO-*
180
Implanted tracer; RBS; Do and Q from Fig. 3 of [86B2]; *): the composition of the alloy may vary
-
86B2
Ni61Zr3g/‘%Zr6,
Ni
-
528e.a573
5.9 * lo-211573
-
105
Interdiffusion; RBS; Q from Table 1 of [86Hl] if an Arrhenius law is assumed for d
-
86Hl
Zr -
-
528s..573
< 5.9 * lo-=/573
-
Interdiffusion; RBS
-
86Hl
528...573
9.1 * lo-2o/573
-
(99)
Interdiffusion; RBS; Q from Table 1 of [86Hl] if an Arrhenius law is assumed for d
-
86Hl
Ag
-
723 ..a 873
4.7. 10-21/723 1.9. IO-“/783 2.3 . lo- ‘s/873
-
212
Concentration gradient; AES; curved Arrhenius plot for &T)
-
85A
D W/U
DO
(co-evaporation)
(co-evaporation)
Ni60m40
(melt spinning)
(splat quenching)
(melt spinning)
Ni5g.5m40.5
Ag
-
723...873
1.2 * lo-‘31573
6.9 +IO-’
184
Concentration gradient; AES; no clear Arrhenius behavior for D(T); Do and Q from Fig. 3 of [86A]
-
86A
Ag
8731300
723...873
2.2 . 10-241573
1.3. 10-7
184
Concentration gradient; AES; no clear Arrhenius behavior for d(T); Do and Q from Fig. 3 of [86A]
9
86A
Al
-
723.s.873
1.2. lo-231573
2.5. IO-l1
135
Concentration gradient; AES; Do and Q from Fig. 4 of [85A]
-
85A
Pb
-
723...873
4.6 . lo- ‘O/723 1.5. lo-‘*/773 4.3. 10-18/873
-
-
-
85A
-
871
4.2. 10-20/871
Concentration gradient; AES; curved Arrhenius plot for D;(T) Concentration gradient; 0” indirectly from crystal-growth rates
-
83C3
-
903.e.943
5.3. lo-381573
5.9. lO+l’
538
Concentration gradient; 6 indirectly from crystal-growth rates; Do from Fig. 3 of [87L]
-
87L
Au
-
670+.. 873
8.7. 10-22/573
1.4.10-‘3
90
Concentration gradient; RBS
-
82Kl
Au
8731300
675...877
2.W22/573
9.1. IO-l3
106
Concentration gradient; RBS
82Kl
Au
8731300
670... 877
6.2 . lo- “/573
3.5 . lo-l3
96
Concentration gradient; RBS; d independent of preannealing; b, Do, and Q include the data of non preannealed states
9 -
-
723 ... 873
3 . IO-“/723 7. IO-“/823 5. IO-17/873
81Kl
723136000
823
4. lo-“/823
Implanted tracer; nuclear reaction “B(p, @Be; no clear Arrhenius behavior for D*(T) Implanted tracer; nuclear reaction ’ ‘B(p, ar)‘Be
(melt spinning) 82Kl
81Kl (continued)
Host system (produced by)
Diffusant
Ni,,,,Nb,o., (continued) i*B (melt spinning)
Fig.
Ref.
m2/s
Q
Remarks
at temperature [K]
kJ/mol
573.e.873
2 * lo-=/573 3 * lo-‘91773 2. IO-“/873
-
-
-
86Kl
8781420
623.e.853
5.2 * lo-=/573
3.9. 10-J
240
Implanted tracer; nuclear reaction “B(p, @Be; no clear Arrhenius behavior for D*(T) Imuianted tracer: nuclear reaction ’ ‘B(p; a)*Be
9
86Kl
Preannealing temperature [K]/ time [s]
Diffusion temperature K
-
D[m2/sl/
DO
Ni58.5Zr41.5 *)
Ni
-
498 ... 598
3.5 * lo-‘91573
7 * 10-7
135
Interdiffusion of thin crystalline tilms of Ni and Zr through amorphous Ni,,.,Zr,,.,; d indirectly from X-ray scattering; *): the composition of the alloy may vary
-
87Sl
NLPb
Au
-
723
2. 10-23/723
-
-
Implanted tracer; RBS
-
81P
W5~45 (co-sputtering)
Au
-
763.e.873
1.8. 1O-3o/573
5.1. lo+2
356
Concentration gradient; RBS; Au diffusion is obtained by assuming 6,, : d,, = 100; Do from Fig. 7 of [82D]
Ni54.9Zr45.1
cu
-
573
2.9. lo-‘l/573
-
-
Tracer co-evaporated; SIMS
Ni50Zr50 (co-evaporation)
Au
-
573
4.3 * lo-241573
-
-
Tracer co-evaporated; RBS
86Hl
Au
-
573...653
1.7 * lo-231573
1.5. 10-a
164
Tracer co-evapoorated; RBS; D* from Fig. 1 of [87Hl]
87Hl
Au
-
573.e.649
4.8 - 10-24/573
1.5 * 10-s
170
Tracer co-evaporated; RBS
10
88H1, 88H2
Bi
-
573
5 ’ 10-24/573
-
-
Tracer co-evaporated; RBS
-
88H3
(solid-state reaction)
(co-sputtering) 82D, 83D
-
(co-evaporation)
88H1, 88H2
6OCo
568/l 73 000
486.a.643
1.8. IO-“/573
3.6. 1O-7
135
Tracer; ion-beam sputtering; D* independent of preannealing
10
88H1, 88H2, 88H6, 88H7
Cr
-
573
2.1 . lo-221573
-
-
Tracer co-evaporated; SIMS
-
87Hl
Cr
-
573
1.6. lo-**/573
-
-
Tracer co-evaporated; SIMS
-
88H3
cu
-
573
2.6. IO-*‘/573
-
-
Tracer co-evaporated; SIMS
-
86Hl
cu
-
473...653
2.5. lo-*l/573
1.8. IO-’
145
Tracer co-evaporated; SIMS; D* from Fig. 1 of [87Hl]
-
87Hl
cu
-
473 ... 653
3.1 . lo-*i/573
1.8. 1O-7
151
Tracer co-evaporated; SIMS
10
88H1, 88H2
Fe
-
573
8.4 . IO- **I573
-
-
Tracer co-evaporated; SIMS
-
87Hl 88H1, 88H2
Fe
-
*)
3 * lo-=/573
7.5. 10-7
158
Tracer co-evaporated; SIMS; *): the temperature regime has not been given
-
(solid state reaction) *)
Ni
-
573
5.6. IO-*l/573
-
-
Interdiffusion of thin crystalline films of Ni and Zr through amorphous Ni,,Zr,,; d indirectly from RBS; *): the composition of the alloy may vary
-
87Hl
(co-evaporation)
63Ni
-
526.e.638
3.6. IO-*‘/573
1.7. 10-7
139
Tracer; ion-beam sputtering
10
88H1, 88H2, 88H6, 88H7
Ti
-
573
1.6. 1O-23/573
-
-
Tracer co-evaporated; SIMS
-
88H1, 88H2
523/*)
45Oe.e800
1.4. lo-**/573
2.9 * 10-7
168
Concentration gradient; AES; d indirectly from P segregation to a free surface; d independent of preannealing; *): preannealing for different periods of time
-
81B
Ni36Fe32Cr14P12B6P (melt spinning)
(continued)
Host system (produced by) Ni,,Fe,,Cr,,P,,B, (melt spinning)
Diffusant
Preannealing temperature w]/ time [s]
(continued) -
-
-
Diffusion temperature K
D [m2/sl/
DO m2/s
Q
Remarks
Fig.
Ref.
at temperature [K]
kJ/mol
623.e.648
1.8 - 10-22/573
17
252
Concentration gradient; fi indirectly from crystalgrowth rates; Do from Fig. 6 of [81H]
-
81H
573..:653
4.1 . lo-2973
5.8
243
Concentration gradient; fi indirectly from crystalgrowth rates; metalloid diffusion is assumed for d; Do and Q from Fig. 4 of [82K4]
-
82K4
7.5.5 Diffusion in palladium-base amorphous alloys Pd85Si15h1/
-
-
523
3.8. lo-25 . . . 4.10-26
-
-
Interdiffusion of thin amorphous films; B indirectly from X-ray scattering; in unrelaxed material, d is a function of diffusion time
80R
ll”Ag
-
460... 552
8.1 . 1O-22/573
2*10-‘0
125
Implanted radiotracer; sectioning by &plasma sputtering
75G
-
484
4.8. IO-25 . . . 1.10-26
-
-
Interdiffusion of thin films; d indirectly from X-ray scattering; in unrelaxed material, d is a function of diffusion time
80R
484/*)
484, 511
7.8. 1O-24/573
1.3. 10-s
167
Interdiffusion of thin films; d indirectly from X-ray scattering; *): preannealing for different periods of time
80R
(Fe85B15h9 (co-sputtering)
Pd81Si19
(splat quenching)
Pd80Au7%3)70/Fe30 (co-sputtering)
-
-
Pd80Si20
195A~
573/90000
498...543
6. 10-24/498 6.7. 1O-23/531 2.4. 1O-22/543
-
183
6Li
-
513 ... 563
2. lo-2o/513 2.4. lo-“/543 6. 10-18/563
1.1o+l*
385
500
2.3 . lo- 26/500
-
-
(co-evaporation)
(splat quenching)
(not mentioned) Pd,,Cu,Si,, (melt spinning)
P48Si22*I
(ion-beam mixing at 73 K)
Implanted radiotracer; sectioning by if-plasma sputtering; no clear Arrhenius behavior for D*(T) Implanted tracer; nuclear reac- tion 6Li(n, ol)T; no clear Arrhenius behavior for D*(T) d indirectly from steady-state creep measurements
82Gl
76B
72M
Au
-
533 ... 588
1.4. lo-211573
1.3. 10-S
175
Implanted tracer; RBS; Do from Fig. 3 of [87B]
-
87B
Au
-
533 ... 598
9.4. lo-221573
3.10-3
203
Implanted tracer; RBS; Do from Fig. 3 of [88B4]
-
88B4
Bi
-
553 ... 598
1.4. lo-221573
3.9 . IO+ lo
356
Implanted tracer; RBS; Do from Fig. 4 of [88B4]
-
88B4
Hg
-
553...598
1 . lo-221573
3.4 * lo+2
269
Implanted tracer; RBS; Do from Fig. 4 of [88B4]
-
88B4
Ir
-
558.~. 598
8.8. lo-23/573
1.1 . 10+13 385
Implanted tracer; RBS; Do from Fig. 3 of [88B4]
-
88B4
Pb
-
553 ... 598
2.3. lO-22/573
4.1 . lo+4
288
Implanted tracer; RBS; Do from Fig. 4 of [88B4]
-
88B4
Pt
-
533 ... 598
2.1 . lo-=/573
3.5. 10-9
134
Implanted tracer; RBS; Do from Fig. 3 of [88B4]
-
88B4
Tl
-
553...598
1.8. 1O-22/573
1.1 . lo+2
261
Implanted tracer; RBS; Do from Fig. 4 of [88B4]
-
88B4
w
-
558.~. 598
4.1 . lo-231573
4.9. lo+5
308
Implanted tracer; RBS; Do from Fig. 3 of [88B4]
-
88B4
Au
-
573.m.633
6. 1O-22/573 1.6. 10-20/613 1.5. 10-20/633
-
-
Implanted tracer; RBS; no Arrhenius behavior for D*(T); *): the composition of the alloy may vary
-
86B2 (continued)
Host system (produced by)
Diffusant
Preannealing temperature [K]/ time [s]
Diffusion temperature K
D [m”/sl/ at temperature [K]
Pd,,Si,, (continued) (ion-beam mixing at 295 K *)
Au
-
573.e.633
Au
613/5400
Au
Pd,,.5Cu6%6.5
DO
Q
Remarks
m2/s
kJ/mol
4.3 . IO-=/573 9.5. 10-21/613 3. 1O-2o/633
-
-
573.a.633
2.6 - I0-22/573 1 . 10-20/613 3.2. IO-2a/633
-
-
Implanted tracer; RBS; no clear Arrhenius behavior for D*(T); *): the composition of the alloy may vary Implanted tracer; RBS; no clear Arrhenius behavior for D*(T)
-
533.a.613
3.8 . IO-2’1573
1.4. 10-14
72
Implanted tracer; RBS; Do from Fig. 2 of [78c]
-
78C,
Au
6231300
533.a.653
1.4. IO-221573
6.8. 10-E
161
Implanted tracer; RBS; Do from Fig. 2 of [78c]
-
78C
Au
-
533.e.653
3.3 . IO-=/573
3 * 10-S
175
Concentration gradient; RBS
-
82Al
Au
6231300
533.a.653
3.1 . IO-=/573
1.2. 10-5
171
Concentration gradient; RBS
6
82Al
Au
6231300
533-a-653
3.2. IO-21/573
1.9. 10-5
173
Concentration gradient; RBS; b independent of preannealing; d, Do and Q include the data of non preannealed states
82AI
Au
-
553.e.653
3.2. 10-2’/573
6.7 - 1O-4
190
Implanted tracer; RBS; Do from Fig. 4 of [86B2]; *): the composition of the alloy may vary
-
86B2
Au
583/I 800
553-e-653
1.9. IO-=/573
4 * 10-4
190
Implanted tracer; RBS; Do from Fig. 4 of [86B2]
-
86B2
Au
-
553,588
8.1 . 10-21/553 4.7. IO-2a/588
-
-
Implanted tracer; RBS; *): the composition, of the alloy may vary
-
86B2
(splat quenching or melt spinning)
(melt spinning)
Pd,,Si,, *I
(ion-beam mixing at 303 K)
P44Si26l )
(ion-beam mixing at 73 K)
Fig.
Ref.
86B2
86B2
7.5.6 Diffusion in silicon-base amorphous alloys Si,,Ti,, *) (solid-state reaction)
-
-
623...673
6.1 . 1O-22/573
2.4. 10-4
193
Interdiffusion of thin crystalline films of Si and Ti through amorphous S&T&; d indirectly from TEM; *): the composition of the alloy may vary
-
88H4
7.5.7 Diffusion in zirconium-base amorphous alloys Zr80C020 (melt spinning)
-
-
*I
2.9. 10-‘8/573
0.6
190
Concentration gradient; d indirectly from rates of primary crystallization; *): the temperature regime has not been given
-
88K2
Zr80Fe20
-
-
*)
1.2. lo-‘S/573
2
200
Concentration gradient; d indirectly from rates of primary crystallization; *): the temperature regime has not been given
-
88K2
Zr,6Fe24
59Fe
-
563
7.6. IO-21 . . .
-
-
Radiotracer; sectioning by ionbeam sputtering; in unrelaxed material, D* is a function of diffusion time
-
88P
-
-
Radiotracer; sectioning by ionbeam sputtering; in unrelaxed material, D* is a function of diffusion time
-
88P
(melt spinning)
(melt spinning)
6.6.10-22
59Fe
-
573
1.1()-19...
2.5. 1O-21
59Fe
563/10 800
493.. 613
2.8. 1O-21/573
0.6
223
Radiotracer; sectioning by ionbeam sputtering
11
87H3, 88P
95Zr
563110800
533 . . 613
3.9. lo-221573
7.10+6
310
Radiotracer; sectioning by ionbeam sputtering
11
87H3, 88P
Host system (produced by)
Diffusant
Preannealing temperature [K]/ time Is1
Diffusion temperature K
Db2/sl/
DO
at temperature [K]
m2/s
Zr,,Fe,,
‘9Fe
-
563
1.2. lo-21... 1.6. 1O-22
59Fe
563/8100
533***593
9sZr
-
Au
Q
Remarks
Fig.
Ref.
-
-
Radiotracer; sectioning by ionbeam sputtering; in unrelaxed material, D* is a function of diffusion time
-
88P
2.8 . lo- 22/573
26
252
Radiotracer; sectioning by ionbeam sputtering
11
88P
563
9.1 . 10-22 . . . 1.5 * 10-22
-
-
Radiotracer; sectioning by ionbeam sputtering; in unrelaxed material, D* is a function of diffusion time
-
88P
-
553.e.613
1.3 * lo-2r/573
3.3 * 10-s
180
Concentration gradient; RBS
-
82A1, 82A2, 82Kl
Au
6131600
553.e.613
5.9 * lo-=/573
0.44
229
Concentration gradient; RBS
11
82A1, 82A2, 82Kl
Au
6131600
553-s-613
1.3 * lo-=/573
2.2 * 10-4
189
Concentration gradient; RBS; 6, Do, and Q include the data of non preannealed states
-
82A1, 82A2, 82Kl
(co-evaporation)
63Ni
-
493.a.573
3.3 . lo-201573
1 .10-s
115
Radiotracer; sectioning by ionbeam sputtering
-
88C
(melt spinning)
Pb
-
553.e.613
1.7. lo-‘91573
5.8 . lo+’
269
Concentration gradient; RBS
-
82A2
Pb
6131600
553.e.613
8.4 . lo- 20/573
1.2 * lo+4
254
Concentration gradient; RBS
11
82A2
Pb
6131600
553.e.613
1.1 . lo-‘9/573
8.3. 1O+4
262
Concentration gradient; RBS; d independent of preannealing; 6, Do, and Q include the data of non preannealed states
-
82A2
Pt
-
552.9.612
6.8 * lo+/573
34
238
Concentration gradient; RBS
-
82A2
(melt spinning)
Zr66.J% 3 (melt spinning)
kJ/mol
H
Pt
6131600
552...612
2.9. lo-‘l/573
2.2
229
Concentration gradient; RBS
Pt
6131600
552...612
4. lo-211573
8.6
234
Concentration gradient; RBS; d independent of preannealing; d, Do, and Q include the data of non preannealed states
Zr6J%
Au
-
564...608
2.7. lo-“/573
1.1 . lo+2
259
Zr&L (co-evaporation)
cu
-
573
1.8. 10-20/573
-
WA%.5 (melt spinning)
-
-
635
4. IO-la/635
Zr61.7Ni3s.3
cu
-
573
ZMQ (melt spinning)
Au
-
550...619
Au
-
600
Au
-
cu
-
11 -
82A2
Implanted tracer; RBS; Do and Q from Fig. 4 of [86Bl]
-
86Bl
-
Tracer co-evaporated; SIMS
-
88H1, 88H2
-
-
Concentration gradient; d indirectly from rates of primary crystallization
-
82s
-
-
Tracer co-evaporated; SIMS
-
88H1, 88H2
8. IO-‘l/573
8.7. 1O-7
154
Concentration gradient; AES
-
8782
1.4. 10-20/600
-
-
Concentration gradient; AES
-
8734
600
1.6. 10-20/600
-
-
Concentration gradient; RBS
-
87S4
573
2.7. IO-‘l/573
-
-
Tracer co-evaporated; SIMS
-
88H1, 88H2
(melt spinning)
(co-evaporation)
Zr55.6NL4.4
(co-evaporation)
82A2
[Ref. p. 468
7 Diffusion in amorphous alloys (Figures)
466
Figures for 7 -T
700 K 650
600
500
550
4 Fig. 6. Diffusion coeflicients in cobalt- and palladium-base amorphous alloys. The Arrhenius lines have been evaluated from the data given in the Tables 7.5.1 and 7.5.5 for Do and
Q.
Curve I: “Co in Co,,Zr,,
(produced by melt spinning)
[88Ml];
Curve 2: Au in Pd,,,,Cu,Si,,,, (produced by melt spinning) [82Al]; Curve3: “Co in Co,,Gd,, (produced by co-sputtering)
::-:::I 1.5
1.5
[82Gl];
1.6
1.7 . ._
1.8
1.9
.10-3K-' 21
l/1 -
Curve 4: lg5Au in Co,,Zr,, [90D].
(produced by melt-spinning)
-1 104"6
750 K 700
650
600
550
500
mVs 10“'
lO“5. 1.2
1.3
1.6
1.5
1.6
1.7
1.8
1.9
2.0
.lO+K“
2.2
Fig. 7. Diffusion coefficients in melt spun iron-base amorphous alloys, The Arrhenius lines have been evaluated from the data given in Table 7.5.3 for Do and Q. Curve 1: “Fe in Fe,,Zr, [8783, 88P]; Curve 2: Cu in Fe,,B,, [88S3]; Curve 3: Sb in Fe,,B,, [8835]; Curve 4: Au in Fe,,B,, [8783]; Curve 5: Au in Fe,,B,, [88S4]; Curve 6: 5gFein Fe,,B,, (8885,880]; Curve 7: “Zr in Fe,,Zr, [88H5, 88P].
HorvPth
Landoh-Bhmstein New Series III/26
7 Diffusion in amorphous alloys (Figures)
Ref. p. 4681
,o-,7
800 K 750 I I II
-T 700 II
650
600
550
467
1
IO-251 1.2
1.3
1.4
1.5 1.6 l/T -
1.7
W3K4
1.9
Fig. 8. Diffusion coefficients in melt spun iron-base amorphous alloys. The Arrhenius lines have been evaluated from the data given in Table 7.5.3 for Do and Q. Curve I: B in Fe,,P,,C, [84D]; Curve 2: “Fe in Fe,,Ni,,B,, [85P, 87P]; Curve 3: 5gFe in Fe,,Ni,,B,, [85Hl, 86H2]; Curve 4: Au in Fe,,Ni,,B,, [82Ai]; Curve 5: a2P in Fe,,Ni,,B,, [86H3]; Curve 6: sgFe in Fe,,B,,Si, [87H3, 89U].
1.1
1.5
1.3
1.7 l/T-
1.9
2.1
-lOJK-'
Fig. 9. Diffusion coefficients in melt spun nickel-base amorphous alloys. The Arrhenius lines have been evaluated from the data given in Table 7.5.4 for Do and Q. Curve f: B in N&P&, [84D]; Curve 2: B in Ni,,P,,Si, [84D]; Curve 3: Au in Ni,,Zr,, [82Al, 82Kl]; Curve 4: rrB in Ni 59.Wzto.sWW; Curve 5: Ag in Ni,,Nb,, [86A]; Curve 6: Au in Ni,,,,Nb,,,, [82Kl].
-T 650 K
,o-~7
m*/s
600 ,
550 ,
\
lo-l9 -y
'
' \
I ~ 10-2' IO.22
Horvi%th
\
\ \
17
\
1.5
Land&-Biirnstein New Series III/26
500
\
10-1'8
10-20
b Fig. 10. Diffusion coefficients in the co-evaporated amorphous alloy Ni,,Zr,, . The Arrhenius lines have been evaluated from the data given in Table 7.5.4 for Do and Q. Curve f: “Co in Ni,,Zr,, [88Hl, 88H2, 88H6, 88H7]; Curve 2: 63Ni in Ni,,Zr,, [88Hl, 88H6, 88H7]; Curve 3: Cu in Ni,,Zr,, [88Hl, 88H2]; Curve 4: Au in Ni,,Zr,, [88Hl, 88H2].
2.5
1.6
1.7
1.8 l/T-
1.9
2.0 .W3K-'
468
7.6 References for 7 4 Fig. 11. Diffusion coefficients in melt swn zirconium-base amorphous alloys. The Arrhenius lines have been evaluated from the data given in Table 7.5.7 for Do and Q. Curve 1: Pb in Zr,,,,Ni,,,, [82A2]; Curve 2: “Fe in Zr,,Fe,, [87H3, SSP]; Curve 3: Pt in Zr,,,,Ni,,,, [82A2]; Curve 4: “Zr in Zr,,Fe,, 18783, SSP]; Curve 5: Au in Zr,,,,Ni,,, [82Al, 82A2, 82KlJ; Curve 6: “Fe in Zr,,Fe,, [SSP].
K'
7.6
72M 75G 76B 76W 78C 80C 80F 80Kl 80K2 80R 8lB 81E 81H 81Kl 81K2 81M 81P 81T 81Vl 81V2 81V3 82Al 82A2 82D 82F
2.2
References for 7
Maddin, R., Masumoto, T.: Mater. Sci. Eng. 9 (1972) 153. Gupta, D., Tu, K.N., Asai, K.W.: Phys. Rev. Lett. 35 (1975) 796. Birac, C., Lesueur, D.: Phys. Status Solidi (a) 36 (1976) 247. Walter, J.L., Bacon, F., Luborsky, F.E.: Mater. Sci. Eng. 24 (1976) 239. Chen, H.S., Kimerling, L.C., Poate, J.M., Brown, W.L.: Appl. Phys. Lett. 32 (1978) 461. Cahn, R.W., Evetts, J.E., Patterson, J., Somekh, R.E., Kenway Jackson, C.: J. Mater. Sci. 15 (1980) 702. Freed, R.L., Vander Sande, J.B.: Acta Metall. 28 (1980) 103. Kiister, U., Herold, U.: J. Phys. (Paris) 41 (1980) C8-352. KBster, U., Herold, U., Hillenbrand, H.-G., Denis, J.: J. Mater. Sci. 15 (1980) 2125. Rosenblum, M.P., Spaepen,F., Turnbull, D.: Appl. Phys. Lett. 37 (1980) 184. Baer, D.R., Pederson, L.R., Thomas, M.T.: Mater. Sci. Eng. 48 (1981) 283. Edelin, G., Tete, C.: Ser. Metall. 15 (1981) 739. von Heimendahl, M., Kuglstatter, G.: J. Mater. Sci. 16 (1981) 2405. Kijek, M., Ahmadzadeh, M., Cantor, B., in: Proc. Int. Conf. Metallic Glasses: Scienceand Technology, Vol. 2, Hargitai, C., Bakonyi, I., Kemtny, T. (eds.), Central Research Institute of Physics, Budapest, 1981, p. 397. Kiister, U., Herold, U., Nolte, F., Weissenberg,H., in: Proc. Int. Conf. Metallic Glasses: Scienceand Technology, Vol. 2, Hargitai, C., Bakonyi, I., Kern&y, T. (eds.), Central Research Institute of Physics, Budapest, 1981, p. 253. Morris, D.G.: Acta Metall. 29 (1981) 1213. Peercy, P.S., Doyle, B.L.: Bull. Am. Phys. Sot. 26 (1981) 389. Tiwari, R.S., Ranganathan, S., von Heimendahl, M. : Z. Metallkde. 72 (1981) 563. Valenta, P.: Thesis, UniversitHt Stuttgart, 1981. Valenta, P., Maier, K., Kronmiiller, H., Freitag, K.: Phys. Status Solidi (b) 105 (1981) 537. Valenta, P., Maier, K., Kronmiiller, H., Freitag, K.: Phys. Status Solidi (b) 106 (1981) 129. Akhtar, D., Cantor, B., Cahn, R.W.: Acta Metall. 30 (1982) 1571. Akhtar, D., Cantor, B., Cahn, R.W.: Ser. Metall. 16 (1982) 417. Doyle, B.L., Pecrcy, P.S., Wiley, J.D., Perepezko, J.H., Nordman, J.E.: J. Appl. Phys. 53 (1982) 6186. Fernengel, W., Kronmiiller, H., Rapp, M., He, Y.: Appl. Phys. A 28 (1982) 137. HorvAth
Land&-BErnskin New Series III,/26
7.6 References for 7 82Gl 8202 82Kl 82K2 82K3 82K4 82L 82N 82s 83Cl 83C2 83C3 83D 83Ll 83L2 83s 84B 84D 84R 85A 8X 85Hl 85H2 85M 85P 86A 86Bl 86B2 86Hl 86H2 86H3 86J 86Kl 86K2 86s 86V 87B 87Hl 87H2 87H3 87Kl 87K2 Landolt-BBmstein New Series III/26
469
Gupta, D., Tu, K.N., Asai, K.W.: Thin Solid Films 90 (1982) 131. Greer, A.L., Lin, C.-J., Spaepen,F., in: Proc. 4th Int. Conf. on Rapidly Quenched Metals, Masumoto, T., Suzuki, K. (eds.), Japan Inst. of Metals, Sendai, 1982, p. 567. Kijek, M., Akhtar, D., Cantor, B., Cahn, R.W., in: Proc. 4th Int. Conf. on Rapidly Quenched Metals, Masumoto, T., Suzuki, K. (eds.), Japan Inst. of Metals, Sendai, 1982, p. 573. Kirchheim, R., Sommer, F., Schluckebier, G.: Acta Metall. 30 (1982) 1059. Kirchheim, R.: Acta Metall. 30 (1982) 1069. Kiister, U., Herold, U., Becker, A., in: Proc. 4th Int. Conf. on Rapidly Quenched Metals, Masumoto, T., Suzuki, K. (eds.), Japan Inst. of Metals, Sendai, 1982, p. 587. Luborsky, F.E., Bacon, F., in: Proc. 4th Int. Conf. on Rapidly Quenched Metals, Masumoto, T., Suzuki, K. (eds.), Japan Inst. of Metals, Sendai, 1982, p. 561. Nunogaki, K., Katao, Y, Kiritani, M., in: Proc. 4th Int. Conf. on Rapidly Quenched Metals, Masumoto, T., Suzuki K. (eds.), Japan Inst. of Metals, Sendai, 1982, p. 509. Scott, M.G., Gregan, G., Dong, YD., in: Proc. 4th Int. Conf. on Rapidly Quenched Metals, Masumoto, T., Suzuki, K. (eds.), Japan Inst. of Metals, Sendai, 1982, p. 571. Cantor, B., Cahn, R.W., in: Amorphous Metallic Alloys, Luborsky, F.E., (ed.), London: Butterworth, 1983, p. 487. Chang, C.F., Marti, J.: J. Mater. Sci. 18 (1983) 2297. Collins, L.E., Grant, N.J., Vander Sande, J-B.: J. Mater. Sci. 18 (1983) 804. Doyle, B.L., Peercy, P.S., Thomas, R.E., Perepezko, J.H., Wiley, J.D. : Thin Solid Films 104 (1983) 69. Limoge, Y, Brebec, G., Adda, Y, in: DIMETA 82 - Diffusion in Metals and Alloys, Kedves, F.J., Beke, D.L., (eds.), (Diffusion and Defect Monograph SeriesNo. 7), Switzerland: Trans. Tech. Publications, 1983, p. 285. Luborsky, F.E.: J. Appl. Phys. 54 (1983) 5732. Schuehmacher, J.J.,Guiraldenq, P.: Acta Metall. 31 (1983) 2043. Brodowsky, H., Sagunski, H.: Z. Phys. Chem. N. F. 139 (1984) 149. Doi, M., Itoh, Y, Chang, D.-Y, Imura, T.: Phys. Status Solidi (a) 83 (1984) 529. Reda, I.M., Wagendristel, A., Bangert, H.: J. Non-Cryst. Solids 61/62 (1984) 985. Akhtar, D., Misra, R.D.K.: Ser. Metall. 19 (1985) 603. Cantor, B., in: Rapidly Quenched Metals, Steeb, S., Warlimont, H. (eds.), Amsterdam: Elsevier, 1985, p. 595. Horvath, J., Freitag, K., Mehrer, H., in: Rapidly Quenched Metals, Steeb, S., Warlimont, H. (eds.), Amsterdam: Elsevier, 1985, p. 751. Horvath, J., Pfahler, K., Ulfert, W., Frank, W: J. Phys. (Paris) 12 (1985) C8-645. MiDe, U., Methfessel, S., in: Rapidly Quenched Metals, Steeb, S., Warlimont, H. (eds.), Amsterdam: Elsevier, 1985, p. 775. Pfahler, K., Horvath, J., Frank, W., Mehrer, H., in: Rapidly Quenched Metals, Steeb, S., Warlimont, H. (eds.), Amsterdam: Elsevier, 1985, p. 755. Akhtar, D., Misra, R.D.K. : Ser. Metall. 20 (1986) 627. B&tiger, J., Dyrbye, K., Pampus, K., Torp, B.: Int. J. Rapid Solid. 2 (1986) 191. Bettiger, J., Mikkelsen, N.J., Nielsen, S.K., Pampus, K.: J. Non-Cryst. Solids 83 (1986) 35. Hahn, H., Averback, R.S., Rothman, S.J.: Phys. Rev. B 33 (1986) 8825. Horvath, J., Mehrer, H.: Cryst. Lattice Defects Amorph. Mater. 13 (1986) 1. HorvLth, J., Freitag, K., Mehrer, H.: Cryst. Lattice Defects Amorph. Mater. 13 (1986) 15. Johnson, WL.: Prog. Mater. Sci. 30 (1986) 81. Kijek, M.M., Palmer, D.W., Cantor, B.: Acta Metall. 34 (1986) 1455. Krebs, H.U., Samwer, K.: Europhys. Lett. 2 (1986) 141. Stobiecki, F., Palmer, W, Reill, W., Roll, K., Hoffmann, H.: J. Non-Cryst. Solids 88 (1986) 209. Van Wyk, G.N., Roos, WD.: Appl. Surf. Sci. 26 (1986) 317. Bettiger, J., Pampus, K., Torp, B.: Europhys. Lett. 4 (1987) 915. Hahn, H., Averback, R.S., Fu-Rong Ding, Loxton, C., Baker, J.: Mater. Sci. Forum 15-18 (1987) 511. Highmore, R.J., Evetts, J.E., Greer, A.L., Somekh, R.E.: Appl. Phys. Lett. 50 (1987) 566. Horvath, J., Pfahler, K., Ulfert, W., Frank, W., Kronmiiller, H.: Mater. Sci. Forum 15-18 (1987) 523. Kirchheim, R.: Acta Metall. 35 (1987) 281. Kirchheim, R., Stolz, U.: Acta Metall. 35 (1987) 281. Horviith
470 87L 87P 87Sl 8782 8783 8784 8785 88Bl 88B2 88B3 88B4 88B5 88C 88F 88Hl 88H2 88H3 88H4 88H5 88H6 88H7 88J 88Kl 88K2 88Ml 88M2 880
88P 88Sl 88S2 8833 88S4 88% 89U 90D
7.6 References for 7 Limoge, Y.: Mater. Sci. Forum 15-18 (1987) 517. Pfahler, K., Horvlth, J., Frank, W.: Cryst. Lattice Defects Amorph. Mater. 17 (1987) 249. Schultz, L., in: Science and Technology of Rapidly Quenched Alloys, Tenhover, M., Tanner, L.E., Johnson, W.L. (eds.), Materials Research Society, 1987. Sharma, S.K., Mukhopadhyay, P., Kuldeep, Amimesh, K. Jain: J. Non-Cryst. Solids 94 (1987) 294. Sharma, S.K., Kuldeep, Amimesh K. Jain: Thin Solid Films 152 (1987) 511. Sharma, S.K., Banerjee, S., Kuldeep, Amimesh K. Jain, in: Proc. Int. Conf. on Thin Films, New Delhi, 1987. Stelter, E.C., Lazarus, D.: Phys. Rev. B 36 (1987) 9545. Bakker, H., Loeff, PI., Weeber,A.W., in: Proc. Int. Conf. on Diffusion in Metalis and Alloys (DIMETA 88) Balatonfiired, Hungary, 1988; Defect and Diffusion Forum 66-69 (1989) 1169. BohiE, V., Majkovl, E., Luby, S., Sandrik, R., Veseljr,M., in: Proc. Int. Conf. on Diffusion in Metalls and Alloys (DIMETA 88) Balatonfiired, Hungary, 1988; Defect and Diffusion Forum 66-69 (1989) 567. BohaE, V., Luby, S., Majkovi, E., Veseljr,M., in: Proc. Int. Conf. on Diffusion in Metalls and Alloys (DIMETA 88) Balatonfiired, Hungary, 1988; Defect and Diffusion Forum 66-69 (1989) 561. Bottiger, J., Dyrbye, K., Pampus, K., Tot-p, B., Wiene, P.H.: Phys. Rev. B 37 (1988) 9951. Brodowsky, H., Fieischhauer, J., Maaz, J., in: Glasiger Zustand metallischer Systeme, Deutsche Forschungsgemeinschaft, 1988, p. 120. Chandrashekhar, G.V., Gupta, D., Newcomb, S., Spit, F.M.H., Tu, K.N.: Defect and Diffusion Forum 59 (1988) 261. Frank, W., Horvith, J., Kronmiiller, H.: Mater. Sci. Eng. 97 (1988) 415. Hahn, H., Averback, R.S., Hoshino, K., Rothman, S.J.: unpublished. Hahn, H., Averback, R.S., Shyu, H.-M.: J. Less-Common Metals 140 (1988) 345. Hahn, H., Averback, R.S.: Phys. Rev. B 37 (1988) 6533. Holloway, K., Sinclair, R.: J. Less-Common Metals 140 (1988) 139. Horvith, J., Ott, J., Pfahler, K., Ulfert, W.: Mater. Sci. Eng. 97 (1988) 409. Hoshino, K., Averback, R.S., Hahn, H., Rothman, S.J.: Defect and Diffusion Forum 59 (1988) 225. Hoshino, K., Averback, R.S., Hahn, H., Rothman, S.J.: J. Mater. Res. 3 (1988) 55. Johnson, W.L.: Mater. Sci. Eng. 97 (1988) 1. Ktister, U., in: Glasiger Zustand metallischer Systeme, Deutsche Forschungsgemeinschaft, 1988, p. 140. Kiister, U., Blank-Bewersdorff, M.: J. Less-Common Metals 140 (1988) 7. Mehrer, H., Dbrner, W, in: Proc. Int. Conf. on Diffusion in Metalls and Alloys (DIMETA 88) Balatonfiired, Hungary, 1988; Defect and Diffusion Forum 66-69 (1989) 189 and private communication. MiBe, U., Methfessel, S., in: Glasiger Zustand metallischer Systeme, Deutsche Forschungsgemeinschaft, 1988, p. 160. Ott, J., Horvath, J., Frank, W: to be published. Pfahler, K., Horvlth, J., Frank, W.: to be published. Schultz, L.: Mater. Sci. Eng. 97 (1988) 15. Schwarz, R.B., Johnson, W.L.: J. Less-Common Metals 140 (1988) 1. Sharma, S.K., Banerjee, S., Kuldeep, Amimesh K. Jain: Appl. Phys. A 45 (1988) 217. Sharma, S.K., Banerjee, S., Kuldeep, Amimesh K. Jain: Acta Metall. 36 (1988) 1683. Sharma, S.K., Kuldeep, Amimesh K. Jain: Mater. Sci. Eng. 100 (1988) 145. Ulfert, W., Horvath, J., Frank, W: Cryst. Lattice Defects Amorph. Mater. 18 (1989) 519. Diirner, W., Mehrer, H.: private communication.
Horvith
Land&Bhstein New Series III/26
Ref. p. 5001
8.1 Introduction
471
8 Diffusion of C, N, and 0 in metals 8.1 Introduction Becausethey usually dissolve interstitially in metals, C, N and 0 have diffusion coefficients that are mostly much larger, at similar temperatures, than the coefficients for self and substitutional solute diffusion. This, and the fact that these diffusants are gases,or readily available in gas or vapour form (e.g.CO,, CH, etc.), have an impact on the choice and availability of methods used to measure their diffusion coefficients. We consider here, briefly, the methods discussedgenerally in chapter 1 and comment on their use and applicability for C, N and 0 diffusion.
8.1.1 Direct methods 8.1.1.1 Steady-state methods These are particularly appropriate for C, N and 0. The steady-state concentration gradient may be measured directly or calculated from equilibrium solubility data. The flux may be measured by standard gas flow methods or, with suitable electrodes supplying and removing diffusant in an electrochemical cell that can sometimes be devised, by measurement of electrical current. The time delay method is also often used, entailing measurement of the time to reach the steady state.
8.1.1.2 Non-steady-state methods 8.1.1.2.1 Thin layer methods Of the three diffusants, only for C is there a suitable isotope for the usual application of this method using radiotracers viz. 14C. Because of its weak S emission the residual activity method (Gruzin-Seibel) is often adequate and therefore frequently employed, although the 14Cactivity profile is sometimesdirectly determined. 8.1.1.2.2 Diffusion couple methods These are sometimes used, although not so commonly as with substitutional alloys. Both the simple erfc solution (Grube) and the Matano-Boltzmann method of analysis have been employed. Although the initial concentration distribution is not the step function of conventional diffusion couples, we include here “couples” prepared by ion implantation for there is the same principle employed of comparing concentration distributions before and after diffusion. The Nuclear Reaction Analysis (NRA) method, so useful for the determination of C, N and 0, is also experimentally a natural complement to the ion implantation method of sample preparation. The two techniques are frequently employed together. 8.1.1.2.3 In-diffusion and out-diffusion methods Under the heading of in-diffusion are to be included those caseswhere reaction of the sample with the source of diffusant occurs leading, in addition to the inner primary solid solution layer that is always present, to the growth of one or more outer layers of other phases, corresponding to the intermediate phases existing in the system at the diffusion temperature. For example, carbide, oxide or nitride phase layers may occur on samples into which C, 0 or N is being diffused. If c (x) has been determined, d(c) can be calculated for each of the phases by the Matano-Boltzman method (Eq. 1.43of the General introduction). However, such complete concentration data may not be available and approximations are then made to achieve an analysis of the experiment. Thus it is assumed,at least, that the phase boundary concentrations are those appropriate to phase equilibrium. With the positions of the phase boundaries known and some assumedform for c(x), perhaps linear in x, Eq. 1.43can be used to obtain d(c). Otherwise, an average diffusion coefficient for each phase can sometimes be deduced from measurements of the rate of migration of each phase boundary and knowledge of the boundary concentrations. Also included here are measurementsof D by observation of internal oxidation (or nitridation) whereby the rate of in-diffusion of 0 (or N) is monitored by observing, as a function of time, the depth to which a third relatively immobile element, dissolved in very dilute substitutional solution, becomesoxidised. Occasionally, the rate of de-oxidation of an oxidised third element is studied. Land&BBmstein New Series III/26
Le Claire
412
8.1 Introduction
[Ref. p. 500
By out-diffusion in the present context is simply meant outgassing for N and 0, decarburising for C, processesthat usually entail samples containing diffusant in primary solid solution so that the simple erf solutions apply for the analysis of the results. When a suitable electrochemical cell can be contrived wherein diffusion in the sample determines the overall cell transport, the progress of in- or out-diffusion may be monitored through measurementsof the cell current. Alternatively, a surface concentration change can be followed by measurement of the cell EMF or a surface potential.
8.1.2 Indirect methods For the diffusion of C, N and 0 in beemetals by far the most commonly employed indirect methods are those basedon the Snoek effect -internal friction methods and, at the lower temperatures, measurementsof anelastic stressor strain relaxation. The latter technique provides values of D at temperatures that may extend down to ambient, and even below. Thus, with mass flow (direct) measurementsmade up to the highest temperatures, the diffusion coefficients of C, N and 0 in many bee metals are known over temperature ranges much more extensive than for most other metal systems.C, N and 0 diffusion data can therefore provide material for very searching tests of the linearity of the Arrhenius relation for interstitial diffusion. As with all the indirect methods, the deduced values of D are model sensitive. For the interpretation of Snoek effect based measurements on bee metals it is usually assumed that the solute atoms occupy octahedral interstitial sites. Apart from occasional measurementsby magnetic relaxation methods, little use is made in the study of C, N and 0 diffusion of the other indirect methods referred to in chapter 1.
8.1.3 Summary of methods I Ia Ib
Steady-state methods: Gradient determined directly. Gradient via equilibrium (solubility) data. Time to steady-state method. Flux measured electrochemically.
t; II IIa IIb
Thin layer methods: c vs. x determined by sectioning. Residual activity method (Gruzin-Seibel) Diffusion couple methods: With determination of c vs. x curve and Matano-Boltzmann analysis, or D, assumedconstant, from an analytical solution. In multiphase samples, D calculated from phase boundary displacement rates and boundary concentrations.
III IIIa (i) III a (ii)
In-diffusion and out-diffusion methods. In (i), out (ii): D calculated from c vs. x curves. D calculated from total gain or loss, or rate thereof. With multiphase layers, D calculated from phase boundary widths and displacement rates. D calculated from internal oxidation (i), or de-oxidation (ii), rates. Diffusion monitored electrochemically.
IV IVa IVb IVc IVd IVe
Indirect methods: Snoek effect. Internal friction or elastic after-effects. Magnetic after-effects
V Va Vb
IIIb
The code (numbers and letters) assigned to each method is employed in the Tables to indicate the method used in determining the results quoted. Where appropriate, additional information on the method may be added . in the “Method/Remarks” column. All measurementsmay be assumedto have been made on polycrystalline material (“pc”), unless otherwise indicated by the abbreviation “SC”(single crystal). The temperature range quoted is the range over which measurementswere made and used by the author to calculate the quoted values of Do and Q. Extrapolation too far outside this range may not in some casesgive reliable values for D, as will be evident from some of the graphical presentations. Le Claire
Iandolt-BBmstein New Series III/26
473
8.2.1,2, 3.1 Alkali, alkaline earth, scandium group metals
Ref. p. 5001
8.2 Diffusion tables for C, N, and 0 in metals Q
Solute Do 10m4rn’s-l
Temperature range K
kJ mol-’
Method/Remarks
Ref.
8.2.1 Alkali metals - Group IA Li, Na, K, Rb, Cs, Fr There are no reported measurements of the diffusion rates of C, N or 0 in the alkali metals.
8.2.2 Alkaline earth metals - Group IIA Be, Mg, Ca, Sr, Ba, Ra Diffusion in Be C
3.2. lO-5
158.6
D = 2.0. IO-l4&se1 = 2.2. IO-l3mzsml = 1.3 * 1O-‘3 m2se1 D N 5. lo-14 mzs-1
N 0
“Highly pure Be.” D sensitive to purity. See[79Z]
1273 1373 1473I 1298
IVa (i),
14C
70G 7262
III a (ii)
62P 57M
-
< 573
“No measurable diffusion”
52.3
773 .+.873
IIb,
14C
762
773 ... 1023
IIb,
14C,99.95%
68P
Diffusion in Mg C
2.1 . 10-7
N 01
No data available.
Diffusion in Ca C
2.7. lO-3
N 01
97.5
No data available.
Diffusion in Sr - No data available. Diffusion in Ba - No data available. Diffusion in Ra - No data available.
8.2.3 Scandium group and rare earth metals 8.2.3.1 Scandium group metals - Group IIIA SC,Y, La, AC Diffusion in SC C
4.5 D= = = =
205 5.0. lo-” m2sm1 1.6. 1O-1o m2s-’ 1.5. 10eg m2s-’ 2.9. IO-’ m2se1
1273... 1573(a) 1488(cc) 1568(a) 1648(P) 1713(P)
IIb,
14C
742
IIIa (ii),
14C,very low C concentration
76Sl
(continued) Land&-BBmstein New Series III/26
Le Claire
8.2.3.2 Rare earth metals
474 Solute Do
Q
10m4m2s-’
kJ mol-’
[Ref. p. 500
Method/Remarks
Ref.
IIIa (ii), very low N concentration
76Sl
IIIa (ii), very low 0 concentration
76Sl
Combined data of [66C] and [76D], recalculated. SeeFig. 1
76D
III a (ii),
14C
66C
IIb,
14C
76D
IIIa(ii),
very low N concentration
66C
Temperature range K
Diffusion in SC,continued N
D
Diffusion c
D= = = =
6.2.10-" m2sm1 2.5 . lo-10 m2sm1 1.4 * 10eg m2s-’ 1.5. 10eg m2s-’
1488(u) 1568(u) 1633(P) 1698(8)
D= = = =
2.8 . IO-‘0 m2s-’ 1.3. 10mgm2s-’ 6.6. 10mg m2s-’ 1.7 +lOm8m2s-’
1498(u) 1573(or) 164303 1693(P)
in Y
1.7. 104
272
D=1.4.10eg m2s-’ = 5.0. lo-’ m2s-’ = 1.32.10-** m2s-’ -= 9.71 .10-*’ m2s-’ N
3
D = 3.1.10-10 m’s1’ = 5.3. 1O-‘o m2s-’ = 3.8. low9 m2s-* 9.4. 10-j D= = = = =
Diffusion
86.7
1.3 . 1()-‘0 m2s-1 2.0. 10mgm2sW1 9.7.1O-‘O m2sb1 1.1 . lop9 m2s-’ 2.6. lob9 m2s-’
0
Diffusion
1508(u) 1733(or)I 1273(u) 1388(ci)I 1508(or) 1623(a) 1733(a)I ll73.*.1733(or) 1173(u) 1673(u)I 1508(u) 1623(u) 1733(CL) I
Combined data of [64Bl] and [66C]. SeeFig. 1
-
IVb(i)
64Bl
IIIa (ii), very low 0 concentration
66C
IIb,
14C
82D
IIIa (ii),
14C,very low C concentration
78s
in La
83.7 4.1 . 10-3 D = 4.7. lo-” m2s-’ = 7.4. lo-” m2s-* = 7.6. lO-‘O m2s-* v
1273... 1733(or)
723...1128(8) 1083(l-9 11230) 1148(y)I
D = 4.6. IO-” m2sw1 = 5.2.10-” m2se1 = 4.6.1O-‘O m2s-*
1083(8) 1123(p) 1148(y)I
IIIa (ii), very low N concentration
78s
D = 6.6. I()-” m2s-’ = 1.7. 10m10m2se1 = 1.3. low9 m2s-’
1083(PI 1123(p) 1168(Y)
IIIa (ii), very low 0 concentration
78s
in AC
- No data available.
8.2.3.2 Rare earth metals Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu - No data available.
Diffusion
in Ce
Diffusion
in
Pr - No data available.
Diffusion
in
Nd - No data available.
Diffusion
in Pm
- No data available. Le Claire
Landok-BBmsfein New Series III/26
Ref. p. 5001
8.2.3.2 Rare earth metals
Solute Do
Q
low4 rn’s-’
kJ mol-’
Temperature range K
475
Method/Remarks
Ref.
IIb,
14C
83D2
III a (ii),
14C,very low C concentration
72P
Diffusion in Sm C N 0I
3.6
146.4
773...1173(01)
No data available.
Diffusion in Eu - No data available. Diffusion in Gd C
N
D= = = = =
5.8. lOA” m2se1 1.6. lO-‘O m2se1 2.3 . lo-10 m2sv1 1.2. 10Mgrn2se1 1.2. 10eg m2s-’
D= = = =
9.0. 1.9. 2.7. 8.3.
10pl’ m2sM1 lO-‘O m2se1 10-IOm2s-1 1O-1o m2se1
D = 3.8. 1O-1o rn2s-’
0
= 6.7 * 10-10 m2s-’ = 8.7. lO-‘O m2sT1 = 6.9. IO-’ m2sm1
1323(cc) 1398(ct) 1473(ol) 151803) 1538(P) 1323(a) 1398(a) 1473(a) 1538(P) 1323(a) 1398(a) 1473(a) 15% (l-9
IIIa (ii), very low N concentration
72P
IIIa (ii), very low 0 concentration
72P
873 .*+1430
IIb,
14C
83Dl
953 ... 1473
IIb,
14C
85D
14C,very low C concentration
69P3
Diffusion in Tb - No data available. Diffusion in Dy - No data available. Diffusion in Ho C N 0>
2.8. 1O-2
125.6
No data available.
Diffusion in Er C N 0>
1.14.10-2
117.2
No data available.
Diffusion in Tm - No data available. Diffusion in Yb - No data available. Diffusion in Lu
C
N 0
Land&-Biimstein New Series III/26
= 1.6. j()-1o m2sm1 = 1.7. fOelo m2s-’ D= 1.2. lO-‘O m2se1
1723 1873 1603i
IIIa (ii),
= 5.9. 1O-1o m2s-’ D= = 6.3. 3.0. 10-‘Om2s-’ lO-‘O m2se1 D = 1.3. 10eg rn’s-’ = 2.0. 10mgm2sm1 = 5.1 . 10e8 m2se1
1723 1873 1573I 1603 1723 1873
IIIa (ii), very low N concentration
69P3
IIIa (ii), very low 0 concentration
69P3
Le Claire
476
8.2.4 Titanium group metals
Solute Do 10m4rn*s-l
Q kJ mol-’
Temperature range K
Method/Remarks
[Ref. p. 500 Ref.
8.2.4 Titanium group metals - Group IVA Ti, Zr, Hf Diffusion in Ti 5.06 7.9. 10-4 6.0. 10-j 3.2. 10-j 3.02. 1O-3
182.1 127.7
1013...1113($ 873 ... 1073 (u)
94.6 79.1 83.7
1603...1873@) 1223 .+. 1923(p) 1373...1673@)
0.21 0.21 1.2. 10-2
224.0 221.8 189.5 184.2 238.6 141.5 101.3 154.1 148.2
723 . +.973 (u) 1573...1813(u) 1173...1843(0() 1573...1943(0() 1623...1973(0() 1173...1843@) l603...1853(g) 1773...1943@)
1.47.10-2 0.2 3.5. 10-2 2.0. 10-3
0.155 2.04.10-2 0.45 0.408 0.778 0.14 0.45 8.3. 1O-2
0.15
201.0 196.9 203.5 138.2 150.7 130.6 138.2
2.0. 10-2
115.0
1573...1873@) 573...1223(@ 923...1148@)
l203...1418(a) 1023...1423@) 1223...1423(@ 1403...1623@) 1223...1623@) l608...1848(p)
III b, av. D over a-camp. range IIb, 14C IIIa (ii), very low C concentration IIb, 14C IIb, 14C SeeFig. 2 III a (ii), IVc (i) IVc (i), IIIb IVc (i), IVa (i), III a (ii) IIIb IVc (i) SeeFig.
ion implanted couples av. D over ar-camp.range av. D over u-camp. range av. D over solubility range
56W 72N 75c 65K 66N2 83A 79v 54w 71R 69EI 54w 75c 71R 79v
3
IVa (i), av. D over solubility range III a(i), av. D over solubility range III b, av. D over solubility range D indep. of concentration IVa (i) III a (ii) Combined data [56C, 69S] IIIa (ii), very low 0 concentration SeeFig. 4
83D3 77D 70R 731 69s 56C 69s 75c
II b, II b, IIIa (ii) IIb, IIa,
75A 72N 65P 75A 65A
Diffusion in Zr 2.0. 10-3 151.59 128.5 3.5. 10-S 111.8 4.8 . 1O-3 133.1 8.9. 1O-2 3.6. IO-2 143.2 D = 3.9 . lo-10 m2sm1 = 5.0. lO-1o m2sm1 = 8.7.10-10 m2sm1 0.56 241.4 0.15 226.5 4.6. IO-4 166.2 8.0. 1O-2 222.3 0.3 238.6 5.7. 10-3 135.6 1.5.10-2 128.5 D = 3.3. lo-lo m2sw1 = 5.4. lO-1o m2sv1 = 1.2 310mgm2s-’
873...1123(~) 873...1138(~)
1173...1523@) 1143...1523@) 1373.*.1873(g) 1898 (P) 1973
(PI (l-9
14C 14C 14C 98.6% Zr
IIIa (ii), very low C concentration
7OSI
2073
.’* (u)
773 973 923...1123(@
l173...1373(or) 1373...1773@) 1623...1973@)
1173...1373@) 1193...1913@)
(PI (P) 2073(P) 1898 1973
SeeFig. 5 IIIa (ii), IVa (ii), IVa (i) IVc (i), IVa (i) IVa (i),
ion implanted couples av. D over u-camp. range av. D over u-camp. range av. D over p solubility range
IIIa (ii), very low N concentration
84A 66R 71P 711 69El 71P 54M 7OSl
SeeFig. 6
Le Claire
Land&BBmstein New Series Ill.l26
Ref. p. 5001
82.5 Vanadium group metals
Solute Do
Q
lop4 m2sT1 kJ mol-’ 0
1.32
201.8
6.61 . 1O-2 184.2 16.5 229.0 3.92 213.4 2.63. 1O-2 118.1 0.98 171.7 D = 1.4 * IO-’ rn’8-l = 3.0. 10eg m2sm1 = 3.8. 10-gm2s-1
Temperature range K 563 ... 1773(ct) 563 . . - 923 (a) 923 ... 1773(a)I 1273... 1689(a) 1273... 1773(p) 1323... 1473(p) 1898(P) 1973(P) 2073(P)
477
Method/Remarks
Ref.
Various. Best single representation of data. 23 Refs. More precise bimodal representation of the same data. IVc (i) IIa, IIIa (ii) and IIIb D indep. of cont. IVb (i) IIIa (ii), very low 0 concentration
77R 81P 77P2 67Dl 7OSl
SeeFig. 7
Diffusion in Hf C
N
0
74 312.3 D = 2.5. lo-l1 m2s-’ = 3 2. lo-” m2se1 0.8 ’ 211.4 4.2. 1O-2 167.5 2.4. 1O-2
242.3
1393... 2033 (a) 1923(a) 1983(a) 2073 ... 2373 (p) 2093 . . .2403 (p) 823.+.1173(x)
IIb, Hf + 1.5 wt% Zr
68M
III a (ii), Hf + 3 wt % Zr, very low C concentration
73c
IIb, 14C,Hf + 1.5 wt % Zr SeeFig. 8a
68M
IIIa (ii), Hf + 3 wt % Zr, ion implanted couples
84A
IIIa (ii), Hf + 3 wt % Zr, very low N cont.
73c
D = 1.3. lo-” m2s-’ = 2.0. lo-l1 m2se1 = 2 8. lo-l1 m2sp1 8.0. 1013 124.3
2103 ... 2383 (p)
IIIa (ii), Hf + 3 wt % Zr, very low N cont. SeeFig. 8b
73c
0.66 -
773...1323(@ 1973, 1673(a)
IVb (i) and c, purity not specified IVb (i), measurementsconfirm [64P]. Numerical values not quoted. IVa and b(i)
64P 67K2
IVa (i), Hf + 5 wt % Zr
63W
2.1”) D= = = = 0.32
212.8 3.8. 7.6. 1.6. 17. ’
221.9 lo-l5 m2se1 IO-l4 m2s-’ lo-lo m2s-’ lo-lo m2s-’ 171.2
1923 (cl) 1958 (a) 1983 (a) 1
1023 ... 1223(ct) 1073(a) 1223(cc)I 1943(a) 1983(cc)1 2088 . ..2403@)
73P
III a (ii), Hf + 3 wt % Zr, very low 0 concentration III a (ii), Hf + 3 wt % Zr, very low 0 cont. SeeFig. 9
73c 73c
3 Corrected.
8.2.5 Vanadium group metals - Group VA V, Nb, Ta Diffusion in V C
8.8 . 10-3
116.364
333 ... 2098
Combined data [59P] (Va), [67Sl] (IIIa(ii)), [6882] (IVa (i)) SeeFig. 10
7282
N
4.17. 1O-2 5.02. 1O-2
148.46 151.05
333 .**2098 440... 1923
7282 77B1, 80Bl
1.1 * 10-2 7.6. 1O-2
145.1 158
Combined data Combined data [67Sl] (IIIa (ii)) Combined data Combined data SeeFig. 10
“)440...630 630...2098
[59P] (Va), [67Sl] (IIIa(ii)) [54P, 69M, 77Bl] (Va), [54P, 69M, 77Bl] (Va) [67Sl, 84Kl] (IIIa(ii))
84Kl (continued)
Land&-Biirnstein New Series III/26
Le Claire
[Ref. p. 500
8.25 Vanadium group metals
478 Solute Do 10v4 rn’s-l
Q kJmol-’
Temperature range K
Method/Remarks
Ref.
Combined data [59P] (Va), [67SI] (JIIa(ii)) Combined data [54P, 69M, 77Bl] (Va), [67Sl] (JHa(ii)) Combined data [77Bl] (Va), [79L] (JVe) 30 data points SeeFig. 10
7282 77B1, 80BI 79L
Diffusion in V, continued 0
2.46.10-* 2.66.10-*
123.490 124.717
333 ... 2098 358 .+.2098
1.56.10-*
123.0
358 ... 2098
‘) The collected results are best represented by two Arrhenius lines, one above, one below about 630 K. For discussion of deviations from simple Arrhenius behaviour in the diffusion of C, N and 0 in V, Nb and Ta, see [78F, 79F, 80M, 80B2]. Diffusion in Nb 1.0. 10-2
141.92
403...2613
1.8. lo-* 9.32 . lo- 3
159.1 146.53
1873...2393 1373... 1673
2.56 10-2
543...1873
6.3 . I 0-2
161.5
623...1873
5.86. 1O-3
109.65
296.~. 1823
6.95. 1O-3
110
296... 1823
4.2. 1O-3
107.2
303 ... 1773
1.7. 10-2
108
873... 1373
6.7. 1O-3
161.6
463 ... 2953
2.57. IO-*
180
3.7. 10-J 8.5. lo-’
156.8 164.5
5.21 . 1O-3
158.48
483...1673
8.7. IO-3
170.8
2473 ... 3243
Combined data [59P] (Va), [6732] (JVa (i)), [72Sl] (IIIa(ii)) IVb (ii), av. D, 0 concentration x I % IIb 14C See’Fig. 1I
72SI 72H 66Nl
Combined data [53A, 53M, 59P, 66H2, 66V, 70A, 70M, 73A, 77B2] (Va), [59A] (JVa (i)). I9 data points Combined data [53M, 66H2, 70M] (Va), [59A] (JVa (i)), [84Kl] (HIa (ii)) SeeFig. 12
77B2, 80BI
Combined data [53A 53M, 59P, 66H2, 66V, 70A, 70M, 73A, 77B2,3] (Va), [59K, 61K, 73M] (IVa (i)), [65L] (IV b (ii)), [77Kl] (JVe) 40 data points Data of [79L] (IVe) with data used in [77B3]. 123 data points Combined data [66H2,70M, 77B3,81 W, 8301 (Va), [77Pl] (IVa (i)) IVd and e(ii) SeeFig. 12
77B3, 80Bl
Combined data [59P, 6IFj (Va), [6682] (IVa (i)), [72Sl] (HIa (ii)) IIb 14C See’Fig. 13
72Sl
84KI
79L 830 79K
Diffusion in Ta C
N
1473...1873 ‘)483 ... 630 630...1573
Combined data [53A, 56P, 78B] (Va) Combined data [53A, 53M] (Va), [61Al] (JVa (i)), [77H2] (HIa (ii)) Combined data [53A, 53M, 56P, 78B] cc)iiyl Al] (IVa (i)). 21 data points
66Nl
84Kl 78B, 80Bl 8OV
See Fig. 14
‘) Seefootnote, Sect.8.2.6, Diffusion in V. Le Claire
Landok-BSmsfein New Series III/26
8.2.6 Chromium group metals
Ref. p. 5001 Solute Do
0
10-4m2s-1
kJ mol-’
Temperature range K
1.05.10-2
110.43
298 ... 1673
3.5. 10-3
99.3
873 ... 1873
1.1 . 1or2
115.5
873 ‘.. 1373
Q
479
Method/Remarks
Ref.
Combined data [42K, 53A, 53M, 56P, 69C, 78B] (Va), [57Gl] (IIIa(ii)), [61Al] (IVa(i)) 26 data points Combined data [77K2] (IVe (i)), [79K] (IVa (ii)) IVe (ii) SeeFig. 14
78B, 80Bl 79K 86L
8.2.6 Chromium group metals - Group VIA Cr, MO, W Diffusion in Cr C
8.3. 1O-3 8.74. 1O-3 4.0. 10-l 9.0. 10-3
N
3.0. 1.6. 9.6. 7.0.
117.2 110.9 163.3 110.9
63G 662 672 68B2
328 . ..445 338...463 1273... 1673 573...823 1329 1413 1506I
Va Va IVd, internal nitridation III a (ii), ion implanted couples
62M 67Kl 72A 84K2
IVa (i)
64B2
m2se1 w 155 155
1623
IVb (ii) Theoretical estimate Deduced from [55C] and [63S]
55c 63s
171.7 171.7 164.5 115.85
1473 ... 1873 1783 . ..2243 1618..+2033 493...543
IIb, 14C IVb (i), pc and SC IV b (ii) Via rate of C precipitation. Results suggest non-linear Arrhenius for C in MO See[76K] III a (ii), 14C,very low C concentration IV b (ii) SeeFig. 17
66N2 67R 70K
author’s solubility data
68F 69El 705 72W
D w 5. lo-l3
5.10-4
1773 1873 1773 1773
IVa (i), (ii) Va (423 ... 435 K), IVa(ii) (1423 ... 1873 K.) IVa (ii), samples saturated with H IIb 14C See’Fig. 15
10-4 101.7 1O-2 115.1 1O-3 119.3 10-4 134.2 D = 2.6. lo-11 m2s-1 = 4.1 . lo-l1 m2sm1 = 7.9. lo-” m2sm1
0
1073... 423 ... 1473 ... 1473 ...
SeeFig. 16
Diffusion in MO C
2.04. 1O-2 3.4. 10-2 4.0. 10-2 2.10-3 3.3 . 10-2 1.04.10-2
N
0
153.0 139.00
2.3. 1O-2 3.0. 10-3 4.3. 10-3 2.98 . lo- 3
2163...2593 1533...2283
138.2 115.9 108.9 102.6 D = 1.8. lo-l5 m2s-’ = 2.8. lo-l2 m2sm1 2.11.10-2 120.4
1100...2500 1773...2273 1573...2273 1323...2198 873 9731 1373...2273
3.0. 10-2 2.8. 1O-2
~400~~~500 -
Land&-Biirnstein New Series III/26
130 105.2
Ib, IVb (ii) IVb (ii) IVb(ii),
av. D over sol. soln. range
75Y 7632 78L
IVb (ii)
78A
IVb (ii) SeeFig. 18
82K
Va Va
68Bl 64Ml
Le Claire
8.2.7 Manganese group metals, 8.2.8 Iron group metals
480
[Ref. p. 500
Method/Remarks
Ref.
kJmol-’
Temperature range K
0.3 9.22.10-3 8.91 . IO-’ 3.15.10-3 3.45.10-j
207.7 169.1 224.0 172 158.3
1523...1723 2073 ... 3073 1473...1873 373...673 1773... 2073
IVa (i), see[7233] for criticism IIIa (ii), 14C IIb 14C Va’ IVa(i), sc SeeFig. 19
64A 65K 66N2 68SI 72S3
7.0 10-3 5.4 1.1 . 10-J 1.2. 10-z 2.4. 10-j 2.37. 1O-3 4.3
138.2 259.6 97.6 134.2 118.9 149.9 224.0
2073 ... 2873 1073... 2473 1073s.. 2473 1773...2273 1673...2473 1273.‘. 2073 873... 1073
Ib, solubility from [44N] Ib, author’s solubility data Data of [68F2], solubility from [69FI] IVd, internal nitridation IVb (ii) IV b (ii) IIIa (ii) SeeFig. 20
68C 68F2 705 691 70J 7ow 84K2
IVb(i)
61A2, 64L 635 64L
Solute Do 10-4m2s-1
Q
Diffusion in W
D x 1 . 10‘-11 1.3. 10-4
m2s-1
1973
x 100.5 100.5
Va Deduced from [61A2] and [63Jl
x 1973
8.2.7 Manganese group metals - Group VII A Mn, Tc, Re Diffusion in Mn - No data available. Diffusion in Tc - No data available. Diffusion in Re C
0.1
221.9
1570...2050
IVb(ii)
68D
N
0.14
153.7
1673.s.2073
IVb (ii)
72J
0 - no data available.
8.2.8 Iron group metals - Group VIII Fe, Ru, OS Diffusion in Fe C
3.94 10-3
80.22
233 ... 623 (a)
1.67. IO-3
78.08
233 ... 347(a)
Combined data [58R, 64M23 (Vb), [5OW3, 54H, 54T, 56G, 66L2] (Va). 29 points Combined data [58R, 64M2] (Vb), [5OW3, 54Tj (Va). 23 points
66L2 7633
SeeFig.21
Ik Claire
Land&-BBmsfein Ne\v Series III,/26
Solute Do 10m4rn’s-l
481
8.2.8 Iron group metals
Ref. p. 5001
Temperature range K
Q kJ mol-’
Method/Remarks
Ref.
The Arrhenius plot for C in a-Fe is linear only at the lower temperatures; there is distinct positive curvature at higher temperatures, evident from the data of [69L] (Va, SC.),[49H, 49S,64H] (IIIa(ii)), [62S] (IVc(ii)) over the range 680 ... 1140 K. SeeFig. 21. [7633] considers the linear region more limited than does [66L2] and presents a relation for D valid over the whole a-range, namely log D [m2s-‘1 = - 4.9064 - 0.5199X + 1.61 1O-3X2 with X = 104/T(Tin K) 0.45 0.668 0.234
154.1 156.84 147.81
a-range 1123...1578(~) 1198...1673&) y-range
All data referred to above. 83 points.
7633
III a(i), limiting values, cont. + 0 IVb(ii), 0.47 at % C Reassessmentof [5OWl], cont. --) 0
5OWl 64s 86A
Diffusion in the y-range is strongly concentration dependent. [5OWl] and [64S] measure and report D(c). [86A] has reassessed[5OWl] and reports the following relation for D as a function of T and concentration over the whole y-range. D = 4.53. 10m7 (1 + y,(l - y,)8339.9/T}exp{-
with N
(T-’
- 2.221 . 10m4)(17767 - 26436~~))
y, = x,/(1 - x,), x, = mol fraction of C, Tin K
7.8. 1O-3
79.1
4.88. 1O-3
76.83
773 . .. 1183(o$ 1663... 1743(s) 226...1183(01)
1.26. 1O-3
73.44
223 ... 323 (a)
Combined data [54F] (IVb (ii)), [56B] 6462 (IVb(i)), [6462] (IVb(i), (ii)) I Combined data [61M, 66B] (Vb), [5OW2, 66L2 54F, 54H, 54T, 56G, 57G3, 63W2,66L2] (Va), [54F, 66P] (IVb (ii)), [6462] (IVb (i, ii)) I 45 points 7633 Combined data [61M, 66B] (Vb), [5OW2, 54F, 54H, 54T, 63W2] (Va). 24 points SeeFig. 22
[66L2] considers the Arrhenius plot linear over the whole a-range. /76S3]claims to identify a small curvature above x 323 K and presents a relation valid over the whole c1-and &range. log D [m2s-‘1 = - 5.948 -0.4334X + 6.08 1O-4X2 with X = 104/T(Tin K) 168.56 0.91 167.1 111.12 92.1
All data referred to above. 52 points
76S3
1173...1623(7)
Combined data [54F] (IVb (ii)), [51D, 64Gl] (IVa (i))
64Gl
IVd, Fe + 0.072 wt % Si IVd, Fe + 0.9 % P (P-stabilised cl-Fe) IVd, Fe + 0.43 and 0.90 wt % Ti. Data extrapolated to zero sol. cont. 5.75 168.94 1173...1573($ IVd, Fe + 0.1% Al Fe + 0.069. . .0.274 wt % Al. 1223...1373($ IVd, Fe + 0.07.. .0.92 wt % Si [84T]. 1.3 166 i Data extrap. to zero sol. cont. 3.72. 1O-2 97.68 1623...1773(6) IVd, Fe + 0.1% Al Note: Data for the a-range are probably valid too for the &range. SeeFig. 23 0
0.4 0.1 3.78. 1O-3
c1... &range
973...1123(@ 1173...1563(~) 1023...1123@)
Diffusion in Ru - No data available. Diffusion in OS - No data available.
Land&-Biirnstein New Series III/26
Le Claire
69B 6833 86T2 6783 86Tl 6783
8.2.9 Cobalt group metals, 8.2.10 Nickel group metals
482 Solute Do 10e4 m2s-’
Q kJ mol-’
Temperature range K
[Ref. p. 500
Method/Remarks
Ref.
8.2.9 Cobalt group metals - Group VIII Co, Rh, Ir Diffusion in Co C
0.21 1.765 0.31 0.53 0.63 0.0589
144.9 173.8 153.7 161.2 161.5 167*)
873..+1673 1123...1373 1073... 1673 1223...1323 1210...1320 976... 1673
IIIa(ii), 0.12 wt% C IVb(ii), 0.1% C IVa (i), 0.1 wt% c IVb(i) “Vacuum metallurgical technique” II b, 14C,*) forced Arrhenius fit to experimental data; better description: (140 kJ mol-‘) (1 + 0.109 s2) D=7.6.10m6exp RT -I s = magnetic long range order parameter
63K 64s 66H2 68L 77L 891 m2s-1
1
0.0872 N-No
data available.
0
67.8 10.0
149.3
241.2 221.1
723 ..- 1073
1323...1573 1323...1573
IVa (i), 14C SeeFig. 24
9oc
IVd, Co + 0.08 wt % Si Co + 0.55 wt % Si IVd, SeeFig. 24
72G2 7262
Diffusion in Rh - No data available. Diffusion in Ir - No data available.
8.2.10 Nickel group metals - Group VIII Ni, Pd, Pt Diffusion in Ni 2.48 0.08 0.12 0.13 0.98 0.366
168.3 138.2 137.3 144.4 161.2 149.36
1003... 1293 873...1173 873... 1673
0.048
145.7
373...803
2.05
169.1
1210...1320
1153...1403 1123*..1373
IV b (ii) II b, 14C III a (ii), 14C,0.1 wt% c II b, 14C IVb(i) IVb(ii), 0.1 wt % C. Data also for NiFe alloys 0.5 wt % C. Diffusion of C in Va, b, C-C pairs “Vacuum metallurgical technique”
52L 5762 63K 65s 66Ll 66Sl 67D2 77L
See Fig. 25 3.10-6 1.82. IO4
95.6
423...773
301.4
D=4.0.10-13m2s-’ = 1.8. lO-12 m2se1 = 5.6. lO-12 m2s-’
III a (ii), ion implanted samples
87L
1173.**1573
IVd(i),
67G
1323 1373 1423
IVb(i)
Ni + 0.7 to 4.49 at% Cr Extrap. to zero Cr cont.
69A
(continued) Le Claire
Land&BCmstein New Series III,/26
Ref. p. 5001
483
Temperature range K
Method/Remarks
Ref.
D = I ’32. lO-‘O rnzsml 2.06 182 2.68 . IO5 297.4
1073... 1473 623 .++1273 1666 1273... 1573 1273... 1623
69B 712 72Rl 72K 73Ll
6.2. IO4 4.9 . 10-2
1273... 1623 1123...1673
IVd (ii), SC,Ni + 0.058 wt % Si IV b (ii) IVe (ii) IVe (ii) IVd (i), Ni + 0.02.. .2 at % Be. Extrap. to zero Be cont. Alternate talc. of data of [73LI] IVe (i) SeeFig. 26
Solute Do 10e4 rn’s-l 0
8.2.11 Noble metals - Group IB
7.9 . 104
12.1
Q kJmol-l 309.4
241
292.6 164
73L2 87P
Diffusion in Pd C N-No
Some qualitative observations
7OS2
data available. IVe
98
0
85P
Diffusion in Pt c N-No 0
Some qualitative observations
7OS2
data available. 9.3 326.6 D= 18...44.10-15m2s-1 . .
1708... 1777 297
IC
IVe (i)
72V 69H
82.11 Noble metals - Group IB Cu, Ag, Au Diffusion in Cu C-No
data available.
N-No
data available.
0
1.7. 10-2 2.4 +IO-2 8.6. 10-2
67.0 77.9 85.4
1073... 1300 1073... 1273
5.8. 1O-3 9.68 . 1O-3 1.16. 1O-2
57.4 61.23 67.3
873 ... 1273 830... 1280 973 ... 1300
IVe (i) Ib (e), solubility data from [69Pl] Data of [74R] recalculated, solubility data from [77HI] IVd (ii), solubility data from [77Hl] IVe (ii) IVe (ii) SeeFig. 27
69P3 74R -
IV b (ii)
62E
Ib(e) IVe (ii) Ic SeeFig. 28
68B3
79K 81A 83N
Diffusion in Ag C-No
data available.
N-No
data available.
0
3.66. 1O-3 46.1 D = 2.7. 10-gm2s-1 = 2.9. 10mgm2s-l 4.9 . 10-3 48.6 4.67. 1O-4 33.88
680... 1140 1083 1093 1036... 1J210 523 ... 675
Diffusion in Au - No data available.
Land&-Biirnstein New Series III/26
Le Claire
72R2 73G
8.2.12, 13,14,15 Group II B, group III B, group IVB, actinide group metals
484 solute Do
10m4m2sm1 kJ mol-’
Ref.
Method/Remarks
Temperature range K
Q
[Ref. p. 500
8.2.12 Zinc group metals - Group IIB Zn, Cd, Hg Diffusion in Zn C
1.0. 10-s 1.6. IO-*
N-No
data available.
76D 762
IIb 14C IIb’ 14C See’Fig. 29
439...656 589...663
50.2 30.6
0 -No data available. Diffusion in Cd - No data available.
8.2.13 Aluminum group metals - Group IIIB Al, Ga, In, TI There are no reported measurements of the diffusion rates of C, N or 0 in any of the group IIIB metals.
8.2.14 Group IVB metals Sn, Pb There are no reported measurementsof the diffusion rates of C, N or 0 in any of the group IVB metals.
8.2.15 Actinide group metals AC, Th, Pa, U, Np, Pu Difiusion in AC - No data available. Diffusion in Th 6lP2
l713..*1953(g)
IVa (i), 0.4 wt % C. D decreasesslightly with increase in C cont. IIIa(ii)
94.2 71.2
1173...1673(@ 1723...1988@)
IVb(i) IIIa(ii)
54G 69P2
1.3. 102
205.2
1273... 1473(u)
61Pl
1.3. 10-3
46.05
1713... 1973(g)
IVd (ii), deoxid. with Ca of Th containing ThO, particles IIIa(ii)
2.7. 10-2”)
159.1
1273... 1473(or)
2.2 * 10-2
113.0
N
2.1 . 10-s 3.2 . IO- 3
0
C
69P2
69P2
‘) Estimated from reported D values. Do not quoted in [6lP2]. Diffusion in Pa - No data available.
Le Claire
LandolbB6mstein New Series III/26
Ref. p. 5001
8.2 Diffusion of C, N, and 0 in metals (Figures)
Solute Do
Methods/Remarks
Ref.
kJ mole1
Temperature range K
123.0
l130...127O(y)
IIIa (ii),
76S2
Q
10-4m2s-’
485
Diffusion in U C
0.218
N-No
data available.
14C
0 -No data available. Diffusion in Np - No data available. Diffusion in Pu - No data available.
Figures for 8
-T
-1
,o-B 1500"C 1300 1200 1100 1000
900
m2/s
10-n m2/s
10-12 IO-"0 0.55 0.60 0.65 0.70 0.75 0.80 .10-3K’ 0.90 l/TFig. 1. Y. Diffusion coefficients for C and 0 diffusion in u-Y vs. (reciprocal) temperature.
Land&-Biimstein New Series III/26
0.8 0.9 1.0 40-3K-’ 1.2 l/TFig. 2. Ti. Diffusion coefficient for C diffusion in CL-and P-phaseTi vs. (reciprocal) temperature.
Le Claire
0.5
0.6
0.7
8.2 Diffusion of C, N, and 0 in metals (Figures)
486
0.5
0.6
0.7
0.8
0.9 l/l-
1.0
1.1
1.2
.@K-'
[Ref. p. 500
1.4
Fig. 3. Ti. Diffusion coefficient for N diffusion in CL-and P-phaseTi vs. (reciprocal) temperature.
Le Claire
Land&-BBmslein New series III,/26
Ref. p. 5001
8.2 Diffusion of C, N, and 0 in metals (Figures) ,o-B 1600 1400“C1200 I I I
487
I’
1000 I
801 I
‘500 I
600 I
m2’s [75Cl 169Sl J
10-q
I
I
Ti
\
I
I
I
I
I
Fig. 4. Ti. Diffusion coefficient for 0 dif- b fusion in CL-and P-phaseTi vs. (reciprocal) .remperarure. ~. ~-I--
67 1o-‘gl 0.5
0.6
0.7
0.8
0.9 1.0 ,I,,IT ---
1.1
I
I
1.2 W3;-’
I
600 I I
1.4
I
10-16 Fig. 5. Zr. Diffusion coefficient for C dif- b fusion in CL-and P-phase Zr vs. (reciprocal) temperature. Land&-BBmstein New Series III/26
IO-17 0.4
0.5
0.6
Le Claire
0.7
0.8 0.9 l/T -
1.0
1.1 .10-3K-’ 1.3
488
8.2 Diffusion of C, N, and 0 in metals (Figures)
0.4
0.5
a6
0.7
0.8 l/T-
0.9
1.0
[Ref. p. 500
1.1
Fig. 6. Zr. Diffusion coefficient for N diffusion in a- and p-phase Zr vs. (reciprocal) temperature.
Le Claire
Land&-B6mstein New Series III/26
Ref. p. 5001
8.2 Diffusion of C, N, and 0 in metals (Figures)
489
4 Fig. 7. Zr. Diffusion coefficient for 0 diffusion in w and P-phase Zr vs. (reciprocal) temperature.
0.4
0.5
0.6
2000"c1600 IO-8 ,(I mV: 10-g
0.7 1200 I
0.8 l/l
1000 I
0.9
1.0
Fig. 8. Hf. Diffusion coefficients for C diffusion (a) and N diffusion (b) in c(-and .10-3K-' 1.3 P-phase Hf vs. (reciprocal) temperature.
1.1
v
-T
2000"C1600 I ,I
1200 I
1000 I
-T
473Cl
lO"O 10-l' 10-1'2 10-1'3
I
10-14 10-1'5 10-16 10-17 10-18 10-19 10-20 10-n ttit, 0.4
0.5
0.6
0.7
0.8
0.9
1.0 40%'
;I 1.2 4
l/T Land&-Biimstein New Series III/26
Le Claire
0.5
0.6
0.7
0.8 l/T-
0.9
1.0 40-3K-'
1.2
8.2 Diffusion of C, N, and 0 in metals (Figures)
490 0
1000
800
[Ref. p. 500
600
Fig. 9. Hf. Diffusion coefficient for 0 dif0.1
a5
0.6
0.7
0.8 l/l
0.9
1.0
1.1
.lO-"K'
1.3 fusion in u- and p-phase Hf vs. (recipro-
cal) temperature.
-
-1 1800 "C 1100 1200 1000
0.4
0.5
0.6
II.7
0.8 0.9 l/T -
I
I
1.0
1.1
I
40-3K4 1.3
4 Fig. 10. V. Diffusion coefficient for C, N, 0 diffusion vs. (reciprocal) temperature.
Ref. p. 5001
8.2 Diffusion of C, N, and 0 in metals (Figures)
lo-* ,
-7 2400 2000°C1600 1400 1200 III I, I, I I
101 I
800 I
600 I
10-g
Nb -
1o-l0
--tt
10-l' I
a
lo-'*
0.3
0.4
0.5
0.6
0.7
I
I
0.9
1.0
.I o-2K-1
l/T-
Fig. 11. Nb. Diffusion coefficient for C diffusion vs. (reciprocal) temperature.
-T
,o-g 1600 1400°C1200
1000
E100
600
’
t
0.8
1.0
1.1
1.2
.10-3K-1
l/7-
Fig. 12. Nb. Diffusion coefficient for N and 0 diffusion vs. (reciprocal) temperature.
Landolt-B6mstein New Series III/26
Le Claire
[Ref. p. 500
8.2 Diffusion of C, N, and 0 in metals (Figures)
492
-1 10-q
1600
2600 "C 2000
1200
600
800
1000
m2/s
10-l'
lo-" t Q
I I6i~ii I
I-----, I
lo-'3
I
I I
\I I \
lo-"
10“"
10-16 0.3
0.4
0.5 l/T-
Fig. 13. Ta. DiffusioD
coefficient
for C diffusion
vs. (reciprocal)
temperature.
-1 10-8, 2800 ,
(1600 I 1400 ,
,"C , 2000 ,
1200 , ,
1000 I,
m’kl8OYl’ lo-'
"\
1o-'7 0.3
Fig.14. ature.
j
800 I'
I
0.9
1.0
I
600 '
I
.
I 0.4
0.5
Ta.Diffusioncoenicicnts
0.6
0.7 l/l-
0.8
.10-3K'
1.2
forNandOdiffusionvs.(reciprocal)temper-
Le Claire
Landolf-BBmstein New Series III/26
8.2 Diffusion of C, N, and 0 in metals (Figures)
Ref. p. 5001
800
10-14 0.5
0.6
0.7
0.8
0.9 l/T-
493
600
1.0
1.1
.l O-3K-'
1.3
Fig. 15. Cr. Diffusion coeffkient for C diffusion vs. (reciprocal) temperature.
-1 ,o.B
1400"C 1000 800
600
400
300
1.50
1.75
200
100
m2/s 10-1'0 1o-12 - [iA
0.50
'
0.75
'
1.00
1.25
2.00 l/T -
2.25
2.50
2.75
3.00
Fig. 16. Cr. Diffusion coeffkient for N diffusion vs. (reciprocal) temperature.
Landok-Biimstein New Series III126
Le Claire
.10-JK-'
3.50
494
8.2 Diffusion of C, N, and 0 in metals (Figures)
[Ref. p. 500
Fig. 17. MO. Diffusion coefficient for C diffusion vs. (reciprocal) temperature, T = 220 .. .270 “C is experimental range in [75yl.
10-n )
2000“C 1600
1200 I,
lOhO I,
800
600
1
10-1’0 I 10”’ Q 10-12 10-l’) [78Al \,
lo-” 10-15 0.3
0.8 0.9 1.0 40-jK-’ 1.2 0.7 l/l Fig. 18. MO. Diffusion coefficient for N diffusion vs. (reciprocal) temperature. 0.4
0.5
a6
Le Claire
Landolt-BCmstein New Series HI/26
Ref. p. 5001
8.2 Diffusion of C, N, and 0 in metals (Figures)
495
-1 “C 2400 2000 1rP 2800 I I I I
1600 I
I
1200 I
I
m2/s 10-g
W
. \/[65K
1
I
IO-‘0
I
\
cl
i >\I
10-l' -
I [72s'31
\.
rr, .I
;l;3;p; 0.35
0.40
I
I
I
yJA’ 0.45
0.50
0.55
0.65 40”K4
0.60
0.75
l/T Fig. 19. W Diffusion coefficient for C diffusion vs. (reciprocal) temperature. T = 100 ... 400 “C is experimental range in [68Sl].
c-T
,om8 2600 IllI 22OO”C1800 11 1 1400 1 m% jpc1 ,>
600 I
800 I
1000 I
I
W
(f68Fl recolculoted)
I" 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
.W3K-’
l/TFig. 20. W. Diffusion coefficient for N diffusion vs. (reciprocal) temperature.
Land&-BBmstein New Series III/26
IA?Claire
1.2
8.2 Diffusion of C, N, and 0 in metals (Figures)
496
104
[Ref. p. 500
800 II 600°C I , 41
m7/s_
lf~-~~,o-2b-*
10-26 0.5
- I64Hl + I49Sl 16251 . I69LI 1.0
1.5
2.0
2.5 l/l
3.0
3.5
.lO-jK-’
4.5
-
Fig. 21. Fe. Diffusion coefticicnt for C diffusion in a-Fe vs. (reciprocal) temperature.
-1 1400 1000°C 600 I,, I
.
200
100
0
-50 n
Fe
~1 lo-l6 10-16 10-m lo-?‘22 10-Z’ 0
0.5
1.0
1.5
2.0 2.5 l/T -
3.0
15
40-3K-’ 4.5
Fig. 22. Fe. Diffusion coefficient for N diffusion in a, y and &phase Fe vs. (reciprocal) temperature. Circles: calculated from equation quoted from [76S3].
Le Claire
Ref. p. 5001
8.2 Diffusion of C, N, and 0 in metals (Figures)
I
IO‘"
497
I
a
II-
0.5
0.6
0.7
0.8
0.9
.I()-aK-'
'
l/l-
Fig. 23. Fe. Diffusion coefficient for 0 diffusion in CL,y and &phase Fe vs. (reciprocal) temperature.
-1 10-q m2/s,
1400 "C 1200 1000 IIII I I \
I
800 I
600 I
I
500 I
1
104'0
[89il\\\ lo-"L
lo-'5 ,n-16
0.5
0.6
0.7
0.8
0.9 l/l
1.0
1.1
1.2
.1O-3K-'
1.4
-
Fig. 24. Co. Diffusion coefficient for C and 0 diffusion vs. (reciprocal) temperature. Two curves for 0 diffusion from [7262] are from samples with different Si content.
Land&-B6mstein New Series III/26
Le Claire
8.2 Diffusion of C, N, and 0 in metals (Figures)
498
[Ref. p. 500
-1 1~00"c1200
1P
1000
500
600
800
m21s lo-'0
10‘"
lo+ a5
0.6
0.7
0.8
0.9
1.0
1.1
40JK-'
1.2
600 I
4 Fig. 25. Ni. Diffusion coefikient for C diffusion vs. (reciprocal) temperature. Line from [6X5] is shown dashed because temperature range is not re1.4 ported.
500 I
1
Ni
5 10‘"
1o-'5
lo-20 0.5
0.6
0.7
0.8
0.9 l/l-
1.0
1.1
1.2
Le Claire
.lo-$(-'
,
4 Fig. 26. Ni. Diffusion coefficient for 0 diffusion vs. (reciprocal) temperature. Land&-BBmstein New Series III/26
Ref. p. 5001
8.2 Diffusion of C, N, and 0 in metals (Figures)
IP
1000“C
-T 800
900
700
600
m2/s 6 4 I 2 a y-9 6 L
/z[74Rl
1
Fig. 27. Cu. Diffusion coefficient for b 0 diffusion vs. (reciprocal) temperature.
lo-“0 0.75
0.80
0.85
0.90
,8b'7gKh,
0.95 1.00 l/T-
[8,A]
1.05
1.10
@K'
1.20
52El \ [73Gl \
Fig. 28. Ag. Diffusion coefficient for b 3 diffusion vs. (reciprocal) tempera:ure.
10-l' 0.8
0.9
1.0
.5
.10-3Kq
1
l/T -
400 "C I,
, o-1:
-T 300 I
200 I
m2/:
Zn -601
I
10“' \
I76Zl
a
IO-"
jig. 29. Zn. Diffusion coeffkient for C diffusion vs. b reciprocal) temperature. Landolt-Biimstem New Series III/26
1.4
Le Claire
1.6
1.8 l/T-
2.0
2.2 .lO-'K“ 2.4
500
8.3 References for 8
8.3 Referencesfor 8 12K MN 49H 49s SOW1 5OW2 5OW3 51D 52L 53A 53M 54F 54G 54H 54M 54P 54T 54W 55C 56B 56C 56G 56P 56W 57Gl 5762 5763 57M 58R 59A 59K 59P 61Al 61A2 61F 61K 61M 61Pl 61P2 62E 62M 62P 62s 63G 63J 63K 63s 63Wl 63W2 64A 64Bl 64B2 64H 64Gl 64G2
Kt, T.S.: Phys. Rev. 74 (1942) 9. Norton, ES., Marshall, A.L.: Trans. Metall. Sot. AIME 154 (1944) 351. Ham, J.L.: Unpublished. Cited in [49S]. Stanley, J.K.: Trans. Metall. Sot. AIME 185 (1949) 752. Wells, C., Batz, W., Mehl, R.F.: Trans. Metall. Sot. AIME 188 (1950) 1174. Wet-t, CA.: J. Appl. Phys. 21 (1950) 1196. Wert, CA.: Phys. Rev. 79 (1950) 601. Darken, LX, Smith, R.P., Filer, E.W.: Trans. Metall. Sot. AIME 191 (1951) 1174. Lander, J.J.,Kern, H.E., Beach, A.L.: J. Appl. Phys. 23 (1952) 1305. Ang. C.Y: Acta Metall. 1 (1953) 123. Marx, J.W.,Baker, J.M., Siversten, J.M.: Acta Metall. 1 (1953) 193. Fast, J.D., Verrijp, M.B.: J. Iron Steel Inst. London 176 (1954) 24. Gerds, A.F., Mallet, M.W.: J. Electrochem. Sot. 101 (1954) 175. Hasiguti, P.R., Kamoshita, G.: J. Phys. Sot. Jpn. 9 (1954) 646. Mallett, M.W., Belle, J., Cleland, B.B.: J. Electrochem. Sot. 101 (1954) 1. Powers, R.W., Doyle, M.V.: Acta Metall. 2 (1954) 605. Thomas, W.R., Leak, G.M.: Philos. Mag. 15 (1954) 986. Wasilewski, R.S., Kehl, G.L.: J. Inst. Met. 83 (1954) 94. Caplan, C., Burr, A.A.: Trans. Metall. Sot. AIME 203 (1955) 1052. Busby, P.E., Hart, D.P., Wells, C.: Trans. Metall. Sot. AIME 206 (1956) 686. Claisse, F., Koenig, H.P.: Acta Metall. 4 (1956) 650. Guillet, L., Hocheid, B.: Rev. Metall. 53 (1956) 122. Powers, R.W., Doyle, M.V.: Acta Metall. 4 (1956) 233. Wagner, EC., Bucur, E.I., Steinberg, M.A.: Trans. Am. Sot. Met. 48 (1956) 742. Gebhardt, E., Seghezzi, H.D., Stegher, A.: Z. Metallkd. 48 (1957) 624. Gruzin, P.L., Polikarpov, YuA., Federov, G.B.: Phys. Met. Metallogr. 4 (1) (1957) 74. Guillet, L., Gence, G.: J. Iron Steel Inst. London 186 (1957) 223. Moore, A., Cher, D.A.: U.K. Rept. A.W.R.E-O-51/57 (1957). Rathenau, G.: J. Appl. Phys. 29 (1958) 239. Albrecht, W.M., Goode, WD. Jr.: U.S.A. Rept. B.M.I. 1360 (1959). Klopp, W.D., Sims, C.T., Jaffee, R.I.: Trans. Am. Sot. Met. 51 (1959) 282. Powers, R.W., Doyle, M.V.: J. Appl. Phys. 30 (1959) 514. Albrecht, W.M., Klopp, W.D., Koehl, B.G., Jaffee, R.I.: Trans. Metall. Sot. AIME 221 (1961) 110. Allen, B.C., Maykuth, D.J., Jaffee, R.I.: J. Inst. Met. 90 (1961) 120. Frantsevich, I.N., Koven’skiy, 1.1.:Dopov. Akad. Nauk. Ukr. SSSR 11 (1961). Kofstad, P., Kjollesdal, H.: Trans. Metall. Sot. AIME 221 (1961) 285. Maringer, R.E.: J. Appl. Phys. 32 (1961) 3665. Peterson, D.T.: Trans. Metall. Sot. AIME 221 (1961) 924. Peterson, D.T.: Trans. Am. Sot. Met. 53 (1961) 765. Eichenauer, W., Muller, G.: Z. f. Metallkd. 53 (1962) 321, 700 (Corrigendum). de Morton, M.E.: J. Appl. Phys. 33 (1962) 2768. Pemsler, J.P., Anderson, R.W., Rapperport, E.J.: U.S. Rept. A.S.D./T.D.R./62-1018 (1962). Smith, R.P.: Trans. Metall. Sot. AIME 224 (1962) 105. Gruzin, P.L., Zemskiy, S.V., Rodina, I.B.: Met. Metallogr. of Pure Metals IV (1963) 243. Jacobs, A.J.: Nature 200 (1963) 1310. Kovenskiy, 1.1.:Fiz. Met. Metalloved. 16 (1963) 613. Stringer, J., Rosenfield, A.: Nature 199 (1963) 337. Wallwork, G.R., Smeltzcr, W.W.:J. Electrochem. Sot. 110 (1963) 943. Wert, C.A., Keefer, D.: Acta Metall. 11 (1963) 489. Aleksandrov, L.N., Shchelkonogov, V.Ya.: Sov. Powder Metall. Met. Ceram. 4 (1964) 288. Borchardt, H.J.: J. Inorg. Nucl. Chem. 26 (1964) 711. Buck, R.H., Waterhouse, R.B.: J. Less Common Met. 6 (1964) 36. Homan, C.G.: Acta Metall. 12 (1964) 1071. Grieveson, P., Turkdogan, E.T.: Trans. Metall. Sot. AIME 230 (1964) 407. Grieveson, P., Turkdogan, E.T.: Trans. Metall. Sot. AIME 230 (1964) 1604. JA Claire
Landolt-BC5msfein Ne\v Series 111126
8.3 References for 8 64L 64Ml 64M2 64P 64s 65A 65K 65L 65P 65s 66B 66C 66Hl 66H2 66Ll 66L2 66Nl 66N2 66P 66R 66Sl 6682 66V 662 67Dl 67D2 67G 67Kl 67K2 67R 67Sl 6782 6783 672 68Bl 68B2 68B3 68C 68D 68Fl 68F2 68L 68M 68P 68Sl 6882 6883 69A 69B 69C 69El 69E2 69H 691 69L Land&-Biirnstein New Series III/Z
Lee, C.H.: Nature 203 (1964) 1163. Ma, Y, Son, J.: Acta Metall. Sinica 7 (1964) 68. Maringer, R.E.: J. Appl. Phys. 35 (1964) 2375, 31 (1960) 2295. Pemsler, J.P.: J. Electrochem. Sot. 106 (1959) 1067, 111 (1964) 1185. Smith, R.P.: Trans. Metall. Sot. AIME 230 (1964) 476. Andrievski, R.A., Zagryazkin, V.N., Meshcheryakov, G.Ya.: Symposium on Thermodynamics and Atomic Transport in Solids, Vienna (1965); Fiz. Met. Metalloved. 21 (1966) 140. Kovenski, 1.1.: Diffusion in BCC Metals (ASM 1965) p. 283. Litman, A.P.: Phys.’ Status Solidi 11 (1965) K47. Pavlinov, L.V., Bykov, B.N.: Fiz. Met. Metalloved. 19 (1965) 397. Shovensin, A.B., Minkevitch, A.H., Scherbinski, G.B.: Izv. Vyssh. Uchebn. Zaved. Chern. Metall. 1 (1965) 95. Bosman, A.J.: Thesis Amsterdam (1960); Acta Metall. 14 (1966) 1659. Carlson, O.N., Schmidt, EA., Peterson, D.T.: J. Less Common Met. 10 (1966) 1. Hoffman, R.A., Wert, CA.: J. Appl. Phys. 37 (1966) 237. Hehenkamp, Th.: Acta Metall. 14 (1966) 887. Lafitau, H., Gendrel, G., Jacque, L.: C. R. Acad. Sci. (Paris) C263 (1966) 1033. Lord, A.E., Beshers, D.N.: Acta Metall. 14 (1966) 1659. Nakanechnikov, AI., Pavlinov, L.V., Bykov, V.N.: Phys. Met. Metallogr. 22 (1966) (2) 73. Nakanechnikov, A.I., Pavlinov, L.V., Bykov, V.N.: Fiz. Met. Metalloved. 22 (1966) 234. Podgurski, H.H., Gonzalez, D.: Unpublished, cited in [66L2]. Rosa, C.J., Smeltzer, WV,!: Electrochem. Technol. 4 (1966) 149. Smith, R.P.: Trans. Metall. Sot. AIME 236 (1966) 1224. Son, P., Ihara, S., Miyake, M., Sano, T.: J. Jpn. Inst. Met. 30 (1966) 1137. Van Ooijen, D.J., Vandergroot, AS.: Acta Metall. 14 (1966) 1008. Zemskiy, S.V., Spasskiy, M.N.: Fiz. Met. Metalloved. 21 (1966) 129. Debuigne, J.: Met. Corros. Ind. 42 (1967) 186. Diamond, S., Wert, C.: Trans. Metall. Sot. AIME 239 (1967) 705. Goto, S., Nomaki, K., Skoda, S.: J. Jpn. Inst. Met. 31 (1967) 600. Klein, M.J.: J. Appl. Phys. 38 (1967) 167. Kofstad, P., Espevic, S.: J. Less Common Met. 12 (1967) 382. Rudman, P.S.: Trans. Metall. Sot. AIME 239 (1967) 1949. Schmidt, EA., Warner, J.C.: J. Less. Common Met. 13 (1967) 493. Son, P., Ihara, S., Miyake, M., Sano, T.: J. Jpn. Inst. Met. 31 (1967) 998. Swisher, J.H., Turkdogan, E.T.: Trans. Metall. Sot. AIME 239 (1967) 426. Zemskiy, S.V., Lyakhin, B.P.: Fiz. Met. Metalloved. 23 (1967) 913. Baranova, VI., Golovin, S.A., Krishtal, M.A., Lerner, M.I.: Fiz. Khim. Obrab. Mater. (1968) (2) 61. Borisov, E.V., Gruzin, P.L., Zemskiy, S.V.: Zashch. Pokrytiya Met. 2 (1968) 104. Bazan, J.C.: Electrochim. Acta 13 (1968) 1883. Conn, P.K., Duderstadt, E.C., Fryxell, R.E.: Trans. Metall. Sot. AIME 242 (1968) 626. Ducros, D., Le Goff, P.: C. R. Acad. Sci. (Paris) C267 (1968) (12) 704. Fromm, E., Jehn, H.: J. Less Common Met. 14 (1968) 474. Frauenfelder, R.: J. Chem. Phys. 48 (1968) 3966. Lafitau, H.: C. R. Acad. Sci. (Paris) C267 (1968) 132. Meshcheryakov, G.Ya., Andriyevskiy, R.A., Zagryazkin, V.N.: Fiz. Met. Metalloved. 25 (1968) 189. Pavlinov, L.V., Gladyshev, A.M., Bykov, YN.: Fiz. Met. Metalloved. 26 (1968) 823. Shchelkonogov, V.Ya., Aleksandrov, L.N., Piterimov, V.A., Mordyuk, V.S.: Phys. Met. Metallogr. 25 (1968) (1) 68. Son, P., Miyake, M., Sano, T.: Tech. Rep. Osaka Univ. 18 (1968) 317. Stewart, A.K., Hepworth, M.T.: Trans. Metall. Sot. AIME 242 (1968) 698. Alcock, C.B., Brown, P. B.: Met. Sci. J. 3 (1969) 116. Barlow, R., Grundy, P.J.: J. Mater. Sci. 4 (1969) 797. Canelli, G., Verdini, L.: Nuovo Cimento B59 (1969) 19. Eremeyev, VS., Ivanov, YuM., Panov, A.S.: Izv. Akad. Nauk SSSR, Met. 4 (1969) 262. Evans, J.H., Eyre, B.L.: Acta Metall. 17 (1969) 1109. Hoare, J.P.: J. Electrochem. Sot. 116 (1969) 1390. Iden, D.I., Himmel, L.: Acta Metall. 17 (1969) 1483. Lord, A.E.: J. Acoust. Sot. Am. 45 (1969) 1382. Le Claire
502
59M 59Pl 59P2 59P3 59s 70A 70G 70J 70K 70M 70R 7OSl 7OS2 7ow 711 71P 71R 712 12A 72Gl 7262 72H 72J 72K 72N 72P 72RI 72R2 72SI 7282 7283 72V 12W 73A 73c 73G 731 73Ll 73L2 73M 13P
74R 742 75A 75c 75Y 76D 76K 76Sl 76S2 7633 762 77Bl
8.3 References for 8 Mondino, M.A., Vassalo, D., de Achterberg, M.C.: J. Mater. Sci. 4 (1969) 1117. Pastoreck, R.L., Rapp, R.A.: Trans. Metall. Sot. AIME 245 (1969) 1711. Peterson, D.T., Carnahan, T.: Trans. Metall. Sot. AIME 245 (1969) 213. Peterson, D.T., Schmidt, EA.: J. Less Common Met. 18 (1969) 111. Sokirianskii, L.F., Ignatov, D.V., Shinyaev, A.Ga.: Fiz. Met. Metalloved. 28 (1969) 287. Ahmad. M.S., Szkopiak, Z.C.: J. Phys. Chem. Solids 31 (1970) 1799. Gladkov, V.P., Zotov, V.S., Papirov, I.I., Skorov, D.M., Tikhinski, G.F.: Poluchenie i Issledovanie Svoistv Chistykh Metallov (Kharkov) F.T.I. Akad. Nauk. Ukr. SSR 2 (1970) 56. Jehn, H., Fromm, E.: J. Less Common Met. 21 (1970) 333. Kunz, J., Reichett, W.: J. Less Common Met. 20 (1970) 327. Miner, R.E., Gibbons, D.E., Gibala, R.: Acta Metall. 18 (1970) 419. Rosa, C.J.: Metall. Trans. 1 (1970) 2517. Schmidt, EA., Carlson, O.N., Swanson, C.E.: Metall. Trans. 1 (1970) 1371. Selman, G.L., Ellison, P.J., Darling, A.S.: Platinum Met. Rev. 14 (1970) 14. Wagner, R.L.: Metall. Trans. 1 (1970) 3365. Iyer, S.K.: Thesis (1971). Univ. of Pennsylvania, USA. Paid&, J., Le Delliou, R.: C. R. Acad. Sci. (Paris) C272 (1971) 249. Repkin, V.D., Kurtukov, G.V., Kornilov, A.A., Bespalov, V.V.: Metalloterm. Protsessy Khim. Met. (1971) 320. Zholobov, S.P., Malev, M.D.: Zh. Tekh. Fiz. 41 (1971) 677. Arnold, J.L., Hagel, W.C.: Metall. Trans. 3 (1972) 1471. Gladkov, V.P., Zolkov, V.S., Skorov, D.M.: Sov. J. At. Energy 32 (1972) 179. Grundy, P.J., Nolan, P.J.: J. Mater. Sci. 7 (1972) 1086. Hoerz, G., Lindenmaier, K.: Z. Metallkd. 63 (1972) 240. Jehn, H., Hohlock, K., Fromm, E.: J. Less Common Met. 27 (1972) 98. Kerr, R.A.: M. SC.Thesis (1972), Ohio State University, USA. Nakanechnikov, A.I., Pavlinov, L.V.: Izv. Akad. Nauk SSSR, Met. 2 (1972) 213. Peterson, D.T., Schmidt, EA.: J. Less Common Met. 29 (1972) 321. Ramanarayanan, T.A., Altstetter, C.J.: Metall. Trans. 3 (1972) 3239. Ramanarayanan, T.A., Rapp, R.A.: Metall. Trans. 3 (1972) 3239. Schmidt, EA., Carlson, O.N.: J. Less Common Met. 26 (1972) 247. Schmidt, EA., Warner, J.C.: J. Less Common Met. 26 (1972) 325. Shepela. A.: J. Less Common Met. 26 (1972) 33. Velho, L.R., Bartlett, R.W.: Metall. Trans. 3 (1972) 65. Weaver, D.E.: USA Rept. UCRL-51182 (1972). Arakelov, A.G., Blanter, M.S., Kissil’, A.Ye., Kovaleva, L.A., Stekachev, I.T.: Fiz. Met. Metalloved. 35 (1973) 826. Carlson, O.N., Schmidt, EA., Sever, J.C.: Metall. Trans. 4 (1973) 2407. Gryaznov, V.M., Gul’yanova, S.G., Kanizius, S.: Russ. J. Phys. Chem. 47 (1973) 1517. Ignatov, D.V., Model, M.S., Sokirianskii, L.F., Shinyaev, A.Y.: Titanium Sci. Techn. IV (1973) 2535. Lloyd? G.J., Martin, J.W.:Met. Sci. J. 6 (1972) 7, 7 (1973) 75. Louthan, M.R., Dexter, A.H.: Met. Sci. J. 7 (1973) 76. McKee, I., Wallwork, G.R.: J. Less Common Met. 30 (1973) 249. Pieraggi, B., Dabosi, F.: J. Nucl. Mater. 46 (1973) 183. Ramanarayanan, T.A., Worrell, W.L.: Metall. Trans. 5 (1974) 1773. Zotov, V.S., Miroshnichenko, T.I., Protasova, A.M.: Diffusion Processesin Metals (Tul’skiy Politkh. Inst.) 2 (1974) 73. Agarwala, R.P., Paul, A.R.: J. Nucl. Mater. 58 (1975) 25. Carlson, O.N., Schmidt, EA., Lichtenberg, R.R.: Metall. Trans. 6A (1975) 725. Yoshioka. K., Kimura, H.: Acta Metall. 23 (1975) 1009. Dubovtsev, R.M., Zotov, V.S., Miroshnichenko, T.I., Nikolayev, N.A.: Fiz. Met. Metalloved. 42 (6) (1976) 1314. Kimura, H., Yoshioka, K.: Mater. Sci. Eng. 24 (1976) 171. Schmidt, EA., Carlson, O.N.: J. Less Common Met. 50 (1976) 237. Schmidt, EA., Carlson, O.N.: Metall. Trans. 7A (1976) 127. da Silva, J.R.G., McLellan, R.B.: Mater. Sci. Eng. 26 (1976) 83. Zotov, V.S., Tseldkin, A.P.: Sov. Phys. J. 19 (1976) 1652. Boratto, F.J.M., Reed-Hill, R.E.: Ser. Metall. 11 (1977) 1107. Le Claire
Land&BBmsfein Ne\v Series III!26
8.3 References for 8 77B2 77B3 77D 77Hl 77H2 77Kl 77K2 77L 77Pl 77P2 77R 78A 78B 78F 78L 78s 79F 79K 79L 79v 792 8OBl 8OB2 8OM 80V 81A 81P 81W 82D 82K 83A 83Dl 83D2 83D3 83N 830 84A 84Kl 84K2 84T 85D 85P 86A 86L 86Tl 86T2 87L 87P 891 9oc
503
Boratto, F.J.M., Reed-Hill, R.E.: Metall. Trans. SA (1977) 1233. Boratto, F.J.M., Reed-Hill, R.E.: Ser. Metall. 11 (1977) 709. Dechamp, M., Lehr, P.: J. Less Common Met. 56 (1977) 193. Horrigan, V.M.: Metall. Trans. 8A (1977) 785. Hirvonen, J., Anttila, A.: Ser. Metall. 11 (1977) 1139. Kirchheim, R., Mathuni, J., Fromm, E.: Z. Metallkd. 68 (1977) 97. Kirchheim, R., Albert, E., Fromm, E.: Ser. Metall. 11 (1977) 651. L’nyanoi, V.N.: Fiz. Khim. Obrab. Mater. 3 (1977) 104. Perkins, R.A., Padgett, R.A.: Acta Metall. 25 (1977) 1221. Perkins, R.A.: J. Nucl. Mater. 68 (1977) 148. Ritchie, I.G., Atrens, A.: J. Nucl. Mater. 67 (1977) 254. Anttila, A., Hirvonen, J.: Appl. Phys. Lett. 33 (1978) 394. Boratto, F.J.M., Reed-Hill, R.E.: Ser. Metall. 12 (1978) 313. Ferraro, R., McLellan, R.B.: Mater. Sci. Eng. 33 (1978) 113. Lorang, G., Langeron, J.P.: High Temp. High Pressures 10 (1978) 165. Schmidt, EA., Martsching, G.A., Carlson, O.N.: J. Less Common Met. 68 (1978) 75. Ferraro, R., McLellan, R.B.: Mater. Sci. Eng. 39 (1979) 47. Kirchheim, R.: Acta Metall. 27 (1979) 869. Lauf, R.J., Altstetter, C.J.: Acta Metall. 27 (1979) 1157. Vadchenko, S.G., Grigor’yev, Yu.M., Merzhanov, A.G.: Russ. Metall. 2 (1979) 150. Zotov, VS.: Fiz. Khim. Obrab. Mater. 4 (1979) 125. Boratto, F.J.M., Reed-Hill, R.E.: Mater. Sci. Eng. 43 (1980) 97. Boratto, F.J.M., Reed-Hill, R.E.: Mater. Sci. Eng. 45 (1980) 290. McLellan, R.B.: Mater. Sci. Eng. 45 (1980) 289. Vadchenko, S.G., Grigor’yev, Yu.M., Merzhanov, A.G.: Izv. Akad. Nauk SSSR, Met. 5 (1980) 223. Albert, E., Kirchheim, R., Dietz, H.: Ser. Metall. 15 (1981) 673. Pawel, R.E., Campbell, J.S.: J. Electrochem. Sot. 128 (1981) 1999. Weller, M., Zhang, J.X., Li, G.Y., K&, T.S., Diehl, J.: Acta Metall. 29 (1981) 1047, 1055. Dubovtsev, R.M., Zotov, V.S., Miroshnichenko, T.I.: Fiz. Met. Metalloved. 54 (1982) 1128. Katlinskii, V.I.: Fiz. Khim. Obrab. Mater. 6 (1982) 134. Anttila, A., R&&en, J., Keinonen, J.: Appl. Phys. Lett. 42 (1983) 498. Deshkevich, Ye.V., Dubovtsev, R.M., Zotov, V.S.: Fiz. Met. Metalloved. 55 (1983) 186. Deshkevich, Ye.V., Dubovtsev, R.M., Zotov, V.S.: Metallofizika 5 (1983) 90. David, D., B&anger, G., Garcia, E.A.: J. Electrochem. Sot. 130 (1983) 1423. Narula, M.L., Tare. V.B., Worrell, W.L.: Metall. Trans. 14B (1983) 673. Okamoto, M.: Acta Metall. 31 (1983) 1169. Anttila, A., RHisanen, J., Keinonen, J.: J. Less Common Met. 96 (1984) 257. Keinonen, J., RHisanen, J., Anttila, A.: Appl. Phys. A34 (1984) 49. Keinonen, J., R&&en, J., Anttila, A.: Appl. Phys. A35 (1984) 227. Takadi, J., Kashiwagi, K., Adachi, M.: J. Mater. Sci. 19 (1984) 3451. Deshkevich, Ye.V., Dubovtsev, R.M., Zotov, VS.: Fiz. Met. Metalloved. 60 (1985) 1206. Park, J.W.,Altstetter, C.J.: Ser. Metall. 14 (1985) 1481. Agren, J.: Ser. Metall. 20 (1986) 1507. Lee, L.J., Altstetter, C.J.: Acta Metall. 34 (1986) 131. Takadi, J., Yamamoto, S., Kikuchi, S., Adachi, M.: Metall. Trans. 17A (1986) 221. Takadi, J., Yamamoto, S., Adachi, M.: Z. Metallkd. 77 (1986) 6. Lappalainen, R., Anttila, A.: Appl. Phys. A 42 (1987) 263. Park, J. W!, Altstetter, C.J.: Metall. Trans. 18A (1987) 43. Iijama, Y, Makuta, F., Agarwala, R.P., Herano, K.: Mater. Trans., JIM 30 (1989) 984. Cermak, J., Mehrer, H.: Z. Metallkde., in press.
Land&-BCmstein New Series III/26
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9.1 Introduction;
9.2 Methods of measurements (direct methods)
[Ref. p. 510,556
9 The diffusion of H, D and T in solid metals 9.1 Introduction The tables and figures in this chapter present information concerning the diffusion of hydrogen and/or its isotopes deuterium and tritium, in solid metals. Some results of measurementsin the presenceof varying levels of hydrogen concentration are included; however, apart from a few exceptions, those pertaining to the diffusion of hydrogen in alloys and compounds have been excluded. In spite of this restriction, the volume of data compiled is quite large; for example, 150 referencesare cited for iron alone. For convenience, the referencesto each solvent are listed separately. Many of the methods described in chapter 1 of this volume have been applied to the study of hydrogen diffusion. In the following resume some of the advantages or limitations of the methods, as they apply to that solute, are noted. Where possible, referencesare given to reviews or original papers that introduce or typify the use of a measuring technique. An excellent general review is given in [75v]. For a number of solvents, large discrepancies occur among both the observed diffusivities and the related parametersD” and Q. This is particularly true when the results have been obtained from permeation, absorption or desorption measurementsthat are sensitive to the presenceof oxide layers on the specimen surfaces.Recent improvements in these techniques have led to better agreement with data obtained by methods that are inherently free from surface effects. Discrepancies can also arise if the hydrogen is trapped by impurities or lattice defectsin the solvent metal. An excellent review and critique of this and other problems specifically found in the important Fe-H system has been given by Kiuchi and McLellan [83K(Fe)]. In assessingthe results presented in the tables, consideration has been given to the method of measurement, the temperature range covered and the level of agreementamong separatestudies. Those parametersjudged best to represent the intrinsic diffusion of hydrogen in a solvent are indicated by an asterisk (*) in the reference column of the tables. In a few cases,no “best values” are identified. Arrhenius plots of the diffusion coefficients of hydrogen in most of the solvents are given, either for the recommended results, or as a compilation of several results. In the following, the format adopted closely parallels that of the genera! introduction; where appropriate, referenceis made to the relevant sections of chapter 1.
9.2 Methods of measurementsof diffusion coefficients of hydrogen in metals 9.2.1 Direct methods (Seesubsection 1.6.1)
9.2.1.1 Steady-state permeation (Seesubsection 1.2.3,equation (1.20) and subsection 1.6.1.1,equations (1.40, 1.42)) If, in equation (1.20),the steady-state concentrations c,, c2 on the entry and exit surfaces of a permeation membrane are maintained by fixed partial pressuresp, 1, pm2of molecular hydrogen gas, H,, the flux J across the membrane may be written as J=W,,W
(Pi, -PkJ
(9.1) where K,, is Sievert’s constant and d the membrane thickness. Experimental conditions are usually chosen such that dissociation in the gas phase is negligible and p, Jp,,, , ~0. Equation (9.1) then reduces to
J=P/4 ,h
(9.2)
where P=(K,,D) is the permeation constant and p the total pressure on the entry side. Provided the surface processesof adsorption and dissociation are rapid and the flux is not impeded by oxide surface layers, diffusion through the membrane is rate-controlling. The diffusivity, D may then be determined from the measured flux provided K,, is known from solubility measurements. If oxide surface layers impede the flux, erroneously low diffusivities and large activation energies may be deduced. Surface cleaning in UHV, followed by deposition of a thin protective layer of palladium may reduce or eliminate this problem. (See[76Bl (Ta), 76B2 (Ta), 84Z(Pd)J). Landok-BBmstein New Series III/26
Ref. p. 5561
9.2 Methods of measurements (direct methods)
505
9.2.1.1.1 ‘Ikansient permeation methods (Seesubsection 1.6.1.1) Rapid establishment of a fixed hydrogen concentration c1 on the entry side of the membrane by contact with the H, gas induces a transient, time dependent flux J, prior to the final steady-state flux J,. Several methods are used to determine the diffusivity from the characteristics of this time-lag. It may be shown, for example, that J,/J,z(2d/m)
exp(- d2/4Dt)
(9.3)
and for (J,/J,)=OS, D =0.138 d2/t. A UHV, gas-permeation system is shown in Fig. 1.
01
* B 2
-
IO
;T 4
3 4,
b Fig. 1. Schematic diagram of: (a) a UHV, gas-phase permeation system and (b), the permeation specimen [83H (Al)]. f : balloon; 2: H, gas reservoir; 3: quadrupole mass separator; 4: vacuum gauge; 5: ion pump; 6: titanium gettering pump; 7: sorption pump; 8: thermocouple; 9: heater; 10: specimen; 11: aluminum gasket; 12: aluminum disc.
9.2.1.1.2 Electrochemical permeation method In one example of this method the metal to the studied functions as a bipolar membrane electrode in an electrolytic permeation cell. (SeeFig. 2). Hydrogen is generated on the cathode side and the entry concentration c1 is controlled by an applied voltage. On the exit side the potential is maintained positive so that the arriving H atoms are oxidized. The equivalent electrical current generated by the oxidizing processis a sensitive measure of the flux through the membrane. The electro-chemical permeation cell may be operated in several modes including (i) the step method, (ii) the pulse method, and (iii) the oscillation method. These are discussedin [72Z (Pd)], in which analysesare given for the associatedtime-lag relations. Two examples of the latter are indicated in Fig. 3. Electrochemical methods are useful over a relatively limited temperature range and may be subject to surface effects.(But see [82N (Fe)] in which such effects are avoided).
Land&-B6mstein New Series III/26
Kidson
[Ref. p. 510,556
9.2 Methods of measurements (direct methods)
506
4 Fig. 2. Schematic diagram of an electrolytic permeation cell [81S, see 9.3.1.11. M: specimen membrane; G: ground; R, , R,: reference electrodes. Dashed lines represent porous partitions in the cell.
r I valve’ 6 voltmeter
E2
=
G
I
I
1
I 4
Fig. 3(a). Schematic plot of time dependenceof pressure in b an initially evacuated, closed chamber on the exit side of a permeation membrane; the gas pressureon the entry side was established at I = 0. The time-lag. T, defined as the intercept, extrapolated from the steady-state linear rise in pressure is related to the diffusivity D and membrane thickness, d, by T = d*/6 D [73R (Ni)]. (b) Recorded time dependence of the Hi ion current (proportional to the permeation rate) in a continuously pumped chamber on the exit side of a permeation membrane. The ion current was detected by a quadrupole mass spcctrometer (see Fig. 1(a)). The arrow indicates the time at which the hydrogen was evacuated from the entry side of the membrane. The diffusivity D can be evaluated by fitting the transient, build-up of ion current I(/) to (i) A exp(- 1/4r), for small r, (ii) A(1 - 2 exp(- x2 7)) for large T, where T = Df/d*, dbcing the membrane thickness and A a constant P3K WI
a
0
0
f-
5
10
9.2.1.2 Absorption/Desorption
15
20
25 s
30
t-
b
methods
(Seesubsection 1.2.3,equations (1.22a), (1.22b); subsection 1.2.4,equation (1.24) and subsection 1.2.5, equation (1.26)) Cylindrical or spherical specimens are generally used. These methods are applicable at relatively high temperatures; again, care must be used to avoid problems related to surface layers.
9.2.1.3 Concentration profile methods (Seesubsection 1.6.1.2.1) Several methods are available for the determination of the concentration profile C(x, t) of the diffusing hydrogen isotope. They include: (a) secrioning the dirfirsion zone and determining the hydrogen concentration by vacuum-extraction [72K (Zr)]. (b) using tritiwn as the diffusant, (i) sectioning and counting the P-activity in each section [86Q(Ti)] or (ii) preparing a surfaceparallel to the diffusion axis and measuring the P-activity by auto-radiography [62C(Zr)].
Kidson
507
9.2 Methods of measurements (direct methods)
Ref. p. 5561
(c) nuclear reaction analysis (See 1.6.1.2.2(d)) The 15N resonant reaction ‘H(15N, ay)“C has been used to determine hydrogen concentration profiles. The principles of the method are shown schematically in Fig. 4 [80B (Ti)]. (d) neutron radiography The large neutron scattering cross section of hydrogen permits the use of neutron radiography as a means of determining the concentration profile as described in [77Z (Nb)]. (e) X-ray measurements of the lattice expansion associated with increases in hydrogen concentration may be used to measure the concentration profile [72Zl (Ta)]. The method is shown schematically in Fig. 5.
I I -+s 0
X-
0.094
60.3"
0.074
60.4"
0.054
60.5",
0.034
60.6"
a
EN= &es
.: , . .' . . _. ,;:
..,.. ..'." . . ,'. . '
.,
,'..
.,'. _
..: .._
,'
;
,.' _.
:
:
I c
.
I
.
','.
0.014
..
:,
0
_ EN,
> 4,s
.,
:,
_'
*, ,.. . ..
.. :
: .-. :.
‘...
‘.
.. _
25
60.8" mm 50
X-
Fig. 5(a). Schematic diagram showing the principle of the gravimetric method for the measurement of the diffusion of H in a tantalum tube. As diffusion progressesfrom right to left, the associated lattice expansion causes a shift of the lattice planes relative to the balance fulcrum. (b) n: concentration of H along the specimen length; 0: angle of reflection of the (321) Ta lattice planes [72W (Ta)].
,_ :
-‘,_ ,.‘.,‘_,
Eres
Landolt-BBmstein New Series III/26
‘.
,’
0
b
_’ .’
._’
I c3 8 P
c
",
,. .,. ‘. -. -. . ,_ .
i/
b
,.
60.7"
EN- E,,,ocS -
..‘.., .
.._ 4 Fig. 4(a). Schematic diagram of experimental arrangement for determination of concentration profile by use of the resonant nuclear reaction. rH(15N, ay)“C. TC: target chamber; S: specimen; D: y detector; C: collimator; I&: energy of “N beam; E,,,: resonanceenergy of nuclear reaction; S: depth at which EN is reduced to E,,, to produce the reaction. (b) Schematiddiagram showing the principle of measuring the H profile; as the incoming “N beam energy EN is increased, the depth at which the resonant energy E,,, interacts with the H, increases. (c) Example of concentration profile obtained. Fig. 4a, b, c taken from [80B (Ti)].
Kidson
508
9.2 Methods of measurements (indirect methods)
[Ref. p. 556
9.2.1.4 Diffusion couple methods without profile measurements (See subsection 1.6.1.2.3) (a) Grovimetric nre~ho~;a tubular specimen is initially charged with hydrogen over a portion of its length and attached to a highly sensitive balance. As diffusion of hydrogen progressesalong the tube, the associated lattice expansion (see9.2.1.3(e) above) produces a continuously measurable shift in the center of gravity of the specimen, from which the diffusion coefficient is determined [72W (T’a)]. (b) The resistomefric method; (see 1.6.1.2.3) has been applied to hydrogen diffusion. (See, for example, P3S WI).
9.2.2 Indirect methods (See subsection 1.6.2)
9.2.2.1 Relaxation methods (See subsection 1.6.2.1) (a) Go&y-eJ%ct (See 1.6.2.1(b)) Two methods of measuring the Gorsky-effect have been reported: (i) the quasi-static method [6882 (Nb)] and (ii) the dynamic, or internal friction method [69C(Nb)J. These techniques are insensitive to surface problems associated with permeation studies, they have been used over a wide range of temperature and have played a major role in revealing quantum-mechanical aspectsas diffusion. (b) The dif/lrsion-elastic phenomenon is the inverse of the Gorsky-effect. As hydrogen diffuses from one side of thin strip due to a concentration gradient, it produces a macroscopic strain gradient, which can be monitored to determine the diffusivity [76C (Ni)]. The close relationship between the two methods is shown in Figs. 6(a), (b). (c) Moperic ufler eSfect (See 1.6.2.1(a)) The jump frequencies and the associated activation energies of H, D and T have been determined from measurements of the magnetic after effect. (See [82H (Nil]). (d) Resisfivity recovery method The isochronal recovery of electrical resistivity of hydrogen-charged and quenched metal solvent wires, has been used to measure hydrogen diffusion coefficients and to detect hydrogen mobility at temperatures of a few Kelvin [76Yl @Ii)]. (e) Resistivity relaxation
A known concentration gradient may be established by, for example, imposing a temperature-gradient on an initially uniform distribution of hydrogen in a solvent. On removal of the temperature gradient, the kinetics of the return of the hydrogen to a uniform distribution are followed by resistivity changes. The method is independent of surface effects [76H (V)].
4 Fig. 6(a). Schematicdiagramshowingthe principle of the quasi-staticGorsky-effectmethod.E,: instantaneouselastic strain on application hydrogen diffusion
of the load; E.: anelastic, time-depen-
dent strain associatedwith the induceddiffusion of the hydrogenatoms[7OS(V)]. T: relaxationtime,relatedto the diffusion coefficient D and specimenthicknessd through T = d2/(13.55 0).
a Kidson
landok-B6mstein New Series III/26
509
9.3 Further readings
Ref. p. 5561
Original stote of the lattice Direction of diffusion
Absorption
Oesorption
T 8 z f
1
Primary couse
Diffusion flux
Consequence
Inhomogeneous distribution of interstitiols lnhomogeneous elastic deformotion
Acting forces
Only inner stresses
Final stote of the lattice. direction of flux 0
f-
0
--
f-
Fig. 6(b). Principle of the diffusion-elastic effect. The non-uniform lattice expansion associatedwith the diffusion of H from left to right causesa curvature of the specimenat a rate proportional to the diffusion flux [76C (Ni)]. M: moment, y: deflection.
9.2.2.2 Nuclear methods (a) Nuclear magnetic resonance (NMR) (See 1.6.2.2(a)) The extensive use of NMR for the study of hydrogen diffusion in metal-H solid solutions and in metal hydrides is favoured by two properties of the proton; (i) its spin of l/2 produces only dipolar interactions with its surroundings; the lack of quadrupole coupling greatly simplifies the interpretation of the NMR spectra (ii) the strength of the NMR signal is proportional to the gyromagnetic ratio, y. The proton has the largest y of all known, stable nuclei [72C (Nb)]. (b) Quasielastic neutron scattering (QENS) (See 1.6.2.2(b)) This method is also especially suited to the study of hydrogen diffusion. The neutron scattering cross-section of the proton is an order of magnitude larger than that of the deuteron and all other nuclei. Like other nuclear methods, it is independent of surface related problems.
9.2.2.3 Other methods Other indirect methods that have been used to a limited extent include (i) Mhsbauer spectroscopy (see subsection 1.6.3.2(b) and [76H2 (Ta)]). (ii) Perturbed angular correlation (see [85P (Ta)]). (iii) Field emission current fluctuations This method has been used for detailed studies of surface diffusion (see [80D (W)]). (iv) Atom-probe field-ion microscopy (FIM) This method has been used to study the diffusion of implanted hydrogen atoms in tungsten at 29K (see [84M
(w>l>.
9.3 Further readings A number of excellent reviews of both experimental and theoretical studies of the diffusion of hydrogen in metals have appeared in recent years. The experimental work has been greatly stimulated by the development of the Gorsky-effect techniques complemented by nuclear methods. The theoretical studies are motivated by the availability of detailed experimental data, by readily observable quantum-mechanical effects at low temperatures and by the relative simplicity of the proton. The references below cover both areas, as well as the proceedings of conferences and data compilations specific to hydrogen and not listed in chapter 1. Land&-Biimstein New Series 111126
510
9.3 Further readings
9.3.1 Reviews and collected papers Reviews 72B 72C 72G 72V 722 75v 78K 78V 79s 81s 83K 84H 85F 86P
Birnbaum, H.K., Wert, CA.: DfJirsion of Hydrogen in Metals, in: Ber. Bunsenges.Phys. Chem. 76 (1972) 806. Cotts, R.M.: Hydrogen Diffirsion Studies using Nuclear Magnetic Resonance, in: Ber. Bunsenges. Phys. Chem. 76 (1972) 760. Gissler, W.: Quasielastic Neutron Scattering bJ1Hydrogen in Transition Metals, in: Ber. Bunsenges. Phys. Chem. 76 (1972) 770. Vblkl, J.: The Gorsky Eflect, in: Ber. Bunsenges. Phys. Chem. 76 (1972) 797. Zuchner, H., Boes, N.: Elcctro-chemical Methods for Diffusion Measurements, in: Ber. Bunsenges. Phys. Chem. 76 (1972) 783. V61k1,J., Alefeld, G.: Hydrogen DifJlrsion in Metals, in: Diffusion in Solids: Recent Developments. Nowick, A.S., Burton, J.J.(eds.), New York: Academic Press, 1975. Kehr, K.W.: Theory of the Difftrsion of Hydrogen in Metals, in: Hydrogen in Metals I, Alefeld, G., Viilkl, J. (eds.), Topics in Applied Physics 28 (1978) 197. Valkl, J., Alefeld, G.: DiJirsion of Hydrogen in Metals, in: Hydrogen in Metals I, Alefeld, G., V61k1,J. (eds.), Topics in Applied Physics 28 (1978) 321. Springer, T.: Investigations of Metal-Hydrogen System by Means of Neutron-Scattering, in: Z. Phys. Chem. NF 115 (1979) 317. Subramanyan, P.K.: Electrochemical Aspects of Hydrogen in Metals, in: Comprehensive Treatises of Electrochemistry, 4., Bockris, J.O’M., Conway, B.E., Yeager, E., White, R.E. (eds.), New York: Plenum Press, 1981. Kiuchi, K., McLellan, R.B.: The Sohrhiiity and Dif/lrshity of Hydrogen in Well Annealed and Deformed Iron, in: Acta Metall. 34 (1983) 961. Hempelmann, R.: DiJjtsian of Hydrogen in Metals, in: J. Less Common Met. 101 (1984) 69. Fukai, Y, Sugimoto, H.: Dijjjrsion of Hydrogen in Metals, in: Adv. Phys. 34 (1985) 263. Petty, W., Vogl, G.: Potential and Limits of Nuclear Methods in Diffusion Studies, in: Vacancies and Interstitials in Metals and Alloys (Int. Conf., Berlin 1986), Material Science Forum 15-18, 1986.
Collected papers 86A
Ashby, M.F., Hirth, J.P. (eds.): Perspectives in Hydrogen in Mefals, Pergamon Press, 1986.
9.3.2 Diffusion data An on-going compilation of diffusion and thermodynamic data appears in: Physics Data: Gases and Carbon in Metals. E. Fromm (ed.), Berlin: Springer.
9.3.3 Proceedings Some recent proceedings of international conferencesconcerning the diffusion of hydrogen in metals and related topics are listed below: Hydrogen in Metals (Int. Mtg., Jiilich 1972) JUL-conf-6, 1972. L’Hydroghne dons les Metaus (Congr. Int. Paris 1972), Paris: fiditions Science et Industrie, 1973. Effect of Hydrogen on the Behavior of Materials (Proc. Int. Conf., Jackson Lake Lodge 1975),Thompson, A.W, Bernstein, I.M. (eds.), New York: AIME, 1976. Reactirity of Solids (8th Int. Symp., Gothenburg, Sweden 1976), Gothenburg: Chalmers Univ. of Tech., 1976. Hydrogen in Metal.7 (2nd Int. Congr., Paris 1977), Oxford: Pergamon Press, 1977. Internal Friction and Ultrasonic Attenuation in Solid7 (Proc. 6th Int. Conf., Tokyo 1977), Tokyo: Univ. Tokyo Press, 1977. Hydrogen in Metals, I, II, Topics in Applied Physics Vol. 28, 29, Alefeld, G., Valkl, J. (eds.), Berlin: Springer 1978. Hydrogen in Metals (Int. Conf. Wroclaw, Poland) 1983. Properties and Applications of Metal Hydrides (Int. Symp. IV, Eilat, Israel) 1984.
Kidson
Land&-BBmstein New Series III/26
9.4 Diffusion Solvent element
D&rsant
H cont.
DO
Q
10m4rn2se1 kJ mole1
tables for H, D, and T in solid metals Fig.
Temperature range Remarks K
Ref.
9.4.1 Alkali metals Li, Na, K, Rb, Cs, Fr No data available.
9.4.2 Alkaline earth metals Be, Mg, Ca, Sr, Ba, Ra
Data available only for Be and Ba. Be Ba
H
1073...1173
T
2.3. 1O-3
18.42
H
4.0.10-3
19.01
473 ... 1273 473*..893
D (1073...1173 K)x10-13
63P, 64P
m’s11
Tracer
7
67i
99.98% Ba, Cont. profile determined by sectioning and vacuum fusion analysis.
8
68P *
9.4.3 Scandium group and rare earth metals SC,Y, La, Ce, Pr, etc. Data available only for Y and Lu. Y
Lucl
H
3.0. IO2
153.24
1048 -.+ 1223
99.8 % Y, purified by electron-beam melting, cylindrical specimens. Diffusivity determined from electrotransport data.
66C
H
1.03.10-l
64.35
673...773
Cont. profiles determined from epithermal and subthermal neutron beam.
76F
40.52
160...400
99.98% Y. NMR method.
79A
51.14
673,873
99.9995% Y, polycrystalline specimens. Quasielastic neutron-scattering method. D(873K)=7.10-10m2s-1.
84A
H
30.5 at.%
H
21.50 at.%
H
20.0 at.%
49.21
500
NMR.
87L
H
x 17 at.%
27.02
170...420
Polycrystalline specimens. Second-moment NMR measurements.
71B
(7.8 . 10V3)
(continued)
Solvent element Lu
Diffusant
H cont.
DO 10-4m2s-1
Q
Temperature range Remarks K
kJmol-’
Fig.
Ref.
(continued) CY.
H D
z5***20 at.%
54.03 61.75
200...230
Polycrystalline specimens.Internal friction attributed to Snoek effect (but see discussion in [86V)).
u
H D
z 15 at.%
24.12 24.12
I*.*300
Single-crystals, orientations along both a and c axes of the hcp structure. Resistivity and heat capacity were measured.
a
H
x 5 at.%
2.5. IO-’ 2.2. 10-Z
55.48 (a) 55.48 (b)
38O.e.540
1.7. 10-Z 4.7. 10-Z
55.38 60.79
99.999% Lu single-crystals. Gorsky-effect (quasi-static); (a) along a axis. (b) along c axis. 99.9% Lu polycrystalhne specimen.
H D
83V 86D 86V
9 (4, (b)
87V *
10(a) w
54w
9.4.4 Titanium group metals Ti, Zr, Hf Ti u
P u
H
1.8. 10-2
51.83
H
1.95.10-J
27.8
923 -.. 1273
Polycrystalline, cylinder. Concentration profiles determined by sectioning and vacuum extraction for a-Ti. Absorption measurements for p-phase.
H
2.7. 1O-3
59.36
973 *** 1173
Gas volumetric permeation method.
IO(a) (2)
56K
H H
1.45 * 10-Z 3.75.10-a
53.38 35.34
923...1123 1173..+1293
Iodide Ti cylinders. Desorption method.
Na) (3)
58A
H
5.7 * 10-J
36.4
773.e.973
60s
H
1.8. IO-2 1.95 * 10-4
51.81 27.79
> 773
65L
H
3.0 * 10-z
61.54
880... 1100
99.9% Ti, polycrystalline cylinders. Absorption method. D (1173 K) = 1.8. IO-* m’s-‘.
W4 (4)
1.15.10-2
46.02
773.a.973
Permeation.
IO(a) (3
773 ... 1097
H H
68P
I
9.4.4 Titanium group metals
Ref. p. 5571
m 4
hl oi
Land&Bhstein New Series III/26
Kidson
Solvent element Ti
Diffusant
H cont.
DO
10-4mZs-1
Q
kJmol-’
Fig.
Ref.
Temperature range K
Remarks
673
The T tracer was diffused in from the gas phase. Cont. profiles determined by sectioning and monitoring P-activity. D(673K)x2~10-10m2s-1.
864
(continued) CL
T
CL
T
s.05.10-4
30.68
293.a.803
T tracer implanted as a thin layer below an anodically grown oxide film. Cont. profiles determined by serial sectioning and monitoring S-activity.
87s
H
1.09.10-3
47.73
333-e-548
54G
D
7.3. 10-4
47.73
99.8 wt.% Zr (excluding 2.4% Hf) foil 0.127... 0.50 mm thick. Absorption method.
CL
H
4.2. lO-4
23.86
673 ~1.873
Absorption method.
54s
a
H
7.14.10-4
29.56
578 ... 883
Arc-melted iodide Zr cylinders. Cont. profiles determined by radial sectioning, vacuum-fusion method.
57M
u-Zirc.-2
H
2.17. IO-’
35.08
533-s. 833
Zircaloy-2 rod. H cont. profiles determined by sectioning and vacuum-extraction.
60Sl
u P u
H H
4.6. IO-’ 7.0. 10-3
39.65 35.75
473...973 1073...1373
T
1.53.10-J
37.97
422-e. 513
Reactor grade Zr. Cont. profile of tritium determined by autoradiographic method.
62C
B
H
5.32. lo-’
34.83
1033 ... 1283
Arc-melted iodide Zr rods (0.624 cm radius) and spheres (0.764. . .1.029 cm radius). Absorption method.
63G
H
7.0. 10-3
44.59
548...973
Iodide Zr, sponge Zr, Zircaloy 2, 4. Cont. profiles determined from serial sectioning, vacuum extraction. No differences in diffusivity for the 3 materials.
72K
Zru
ZirE-2 Zirc.4
0.1 wt.%
6OS2
*
2.1 . 10-4
58.86
195s..477
Zircaloy-2 foils. Tritium recoil injected from surface, using the 6Li(n, u)‘H reaction. Cont. profiles determined by etch-sectioning and B-counting.
74E
2.8 at.%
4.0*10-2
56.93
500..-823
99.99% Zr foil, electrolytically charged with H. Dynamic Gorsky-effect (internal friction) method.
76M
cl-Zirc.-2 T
0.1 wt.%
1.04.10-a
42.1
473*..1073
Zircaloy-2 foils, 0.25 mm thick. Tritium implanted in collimated zone. Cont. profiles determined by sectioning, vacuum extraction and S-counting.
8OG
a-Zirc.-2
1.6. 1O-3 .. .
Diffusivities measured as in [8OG] as a function of hydrogen content. Effective diffusion coefficient given by D,, = 0.f.; f= = fraction of H in the a-phase.
82K
a-Zirc.-2
T
CL
H
T
0.14wt.% Hf
6.0. 1O-4
T
41.8
473.e.633
97 % Hf, 2.8 % Zr foils, tritium implanted at 90 MeV. Cont. profiles determined from B-activity. Influence of hydrides noted.
12
83K *
9.4.5 Vanadium group metals V, Nb, Ta V
4.4. 10-4
5.69
D
61 rwm by wt. 880 ppm by wt.
3.1 . 10-4
7.04
H
0.2... 4.3
3.5. 10-4
4.82
2.4. 1O-3 2.3. 1O-3
7.52
H
IlO***
99.99% V foils, 20 urn thick. Dynamic (internal friction) Gorsky-effect method. Noted that DJDD increased with decreasing temperature.
69C,7OC
273.0.600
99.987% V, 1.26 mm diameter wire with bamboo structure. Quasi-static Gorsky-effect. Isotope effect not consistent with classical theory of diffusion.
7os,7ov
Data reported by [69C, 7OC] are re-analysed without the assumption of a single-relaxation time.
71D
298
Pd coated V foils. Electrochemical pulse method. D (298K) = 1.96 . IO-’ m2 s-l.
73B
4.a.60
99.98% V wire. Resistivity ratio
[email protected] 20 1.* 70. The resistivity recovery, following quenching and annealing showed Q(D)/Q(H) x 1.2e.e1.3, consistent with [7OC,7OS].
74A
at. % H D H H
9.64 10.47
0.6.e.l.O at.%
(continued)
Solvent element
Diffusant
H cont.
DO
Fig.
Ref.
Q
kJ mol-’
Temperature range K
Remarks
tom4 rn’s-i
4.3 * 10-4 4.8. lO-4
6.07 7.95
273 ..a 373
V foils, cleaned in ultra-high vacuum, Pd coated. Electrochemical time-lag method.
768
1.94.10-4
3.86
175 **a300
MRC V foil, 50 urn thick. Resistivity relaxation method. Diffusivity is concentration dependent (MRC: Materials Research Corporation).
76H
8.8 * 10-4
10.59
813.e.1373
Absorption method. A sharp break in the Arrhenius plot at x 870 K was attributed to surface effects.
77E
323.a.383
99.7 % V polycrystalline foil, I mm thick. Neutron radiographic method. Diffusivities more than an order of magnitude below [7OC], [7OS],[76B].
772
= 18 *. . 1000. Quasi-static Gorsky-effect method. No change in D" or Q for this level of impurities. * e300Kle42r = 2.5; marked lowering of diffusity observed.
78F
78V
V (continued) H D H
0.044 *** 1.29 at.%
H H
11.0 at.%
H D
3.1 . 10-4 3.8. lO-4
4.34 7.04
148.e.573
H*
2.2.10-a *
6.27*
236.0.373
2.9 3IO-4
4.15
173.a.666
Best tit of selected literature data obtained from surface-independent methods.
3.1 * 10-4 3.8. lO-4 5.6. IO-4
4.34 7.04 9.07
143-e-573 173.e.573 133.e.373
99.99% V wire; RRR x 20. Quasi-static Gorskyeffect method.
3.1 * 10-4 * 1.63. IO-3
4.63 *0.58
200...340
V single- crystal. Time dependent resistivity method. External stress along (1 I I) axis produces 60-fold* increase in diffusivity at 222 K. Attributed to delocalization of H over 4 neighboring tetrahedral sites.
H
< 0.065 at.%
H D T
< I.4 at.%
H
1.4 at.%
&OOKh?4.2K
78F
13
834
83s
*
Nbcl
H
H D
1.2 at.%
H
H
H
2.15 * 10-2
39.23
573 es-973
99.998% Nb rods and sheet, 0.3 mm thick. Absorption method. Desorption rates indicated surface effects.
59A
5.4. 10-4 5.6. 1O-4
10.61 13.03
270... 560
Nb wire; grain-size x wire diameter. Quasi-static Gorsky-effect method.
6832
5.4. 10-4
10.52
235...830
99.9% Nb sheet, 0.021 mm thick. Dynamic Gorsky-effect (internal friction) method. Deviation from linear Arrhenius plot for Ts 225 K.
69C, 70C
MRC, Zone-refined Nb rods, 12 mm diameter, RRR > 1000. Quasi-elastic neutron-scattering method. Diffusivities for H cont. = 3.2 at.% agree well with [7W [7wl, [7OCl.
70G
3.2 at.% 33 at.%
3.3 . 10-4
11.58
393 ... 583
0.2 . . .4.3 at.%
0.9 . 10-4 5.0. 10-4
6.56 10.23
120... 300 300...600
5.4. 10-4
12.45
240...600
D
99.983% Nb wire, 0.76 ... 1.26 mm diameter, bamboo structure, RRR > 1000. Quasi-static Gorsky-effect. Nonclassical isotope effects observed.
14
7os, 7ov, 75V, 78V *
H
20...400
Single crystal, (100) orientation, RRR x 400, and polycrystalline Nb rods, 6 mm diameter. Internal friction peaks studied. Found Q (Snoek peak) > Q (Gorsky-effect [7OS]).
7ow
H
1173
D (1173 K) = [1.6..-2.7). 10-8m2s-1.
71c, 74c
235...830
Data of [69C], [7OC] re-analysed, without assuming a single-relaxation time. Apparent deviation from linear Arrhenius plot for Tc 225 K is removed (but see discussion in [7OVJ).
71D
510
Nb single-crystals, 2 x 1.2 x 0.4 cm3. Quasi-elastic neutron-scattering method; [loo], [I IO], [ll I] directions. The observed anisotropy of the width functions is not consistent with H atoms occupying tetrahedral nor octahedral sites.
71K
473...973
MRC Nb rods, 4.7 mm diameter. Absorption method. H cont. profiles determined from microhardness measurements.
710
H
H
I-i
1.2. 10-3
11.29
9 at.%
1.77.10-2
41.85
(continued)
Solvent element Nb
Diffusant
H cont.
DO 10-4mZs-1
kJmol-’
Q
Temperature range Remarks K
Fig.
12.3 at.%
6.5 - lO-4
10.61
403 . . a673
Quasi-elastic neutron-scattering method.
72Bl
5.77 * 10-4
12.55
303***1173
Desorption and permeation methods.
72H, 74P, 76C2
Ref.
(continued) H T H
2.9-e-44 at.%
10.61
3460.0475
99.98 % Nb single-crystals and foils, 25 pm thick. NMR, proton spin-lattice relaxation method.
72Ll,72L2
H
0.01 -0-0.15 5.6. IO-’ at.% 2.9 * 10-4 4.1 * 10-4
5.89 8.97 11.87
150.0.225 225 so.320 150.0.320
Resistivity-relaxation method. Break in Arrhenius plot at x 225 K for H confirmed (see [7OS],[7Oq).
72W1, 72W2
W-W
20..-300
Nb, zone-relined; doped with N (0.e. 1.2 at.%) and 0 (0 a.. 0.16 at.%). Internal friction measurements. Q values are for (H-H) pairs, (H-O) pairs. Quantum effects observed at low temperatures.
73Bl
298
Nb foils, 50 *. .350 pm thick; heated in UHV to x 2000 K, Pd-coated. Electrochemical, pulse permeation method. D (298 K) = 2.1 . IO-” m2 s-r.
73B2
313
See [73B2]: Electrochemical, oscillating method. D (313 K) = 2.7 .10-i’ m2 s-l.
73B3
165.e.400
“High purity” Nb foils, 7 pm thick, for dynamic, (d), Gorsky-effect method. Nb sheet, 1 mm thick used for quasi-static (s) Gorsky-effect method. In the absence of hydrides, the deviation from a linear Arrhenius plot at low temperatures [69C], [7OS],[7Ov] was not observed (see [74M2]).
74Ml
180...473
Nb wire, 0.76 mm diameter, RRR: 1500 ... 2000, doped with N. Quasi-static Gorsky-effect method. Find N suppressesthe break in Arrhenius plot reported in [69C], [7OS]and [7Ov]. For N < 0.01 at.%, full curve given by sum of exponentials, having Do and Q values shown.
74M2
D H
(HYG) 16.3 13.40
H
X0
H
X0
H
1.6 at.% 2.2 at.%
2.8. lO-4 2.8. lO-4
8.59 (d) 8.59 (d)
0.095 at.% 0.11 at.% 0.28 at.%
1.7. 10m4 1.6. lO-4 2.4. lO-4
7.82 (s) 7.72 (s) 9.26 (s)
5.0. 10-5 5.2. lO-4
5.98 12.06
H
H
0.01 *.-0.19 at. %
5.89 8.97 11.87
D
150...225 225...320 15O.e.320
99.985% Nb foils, 12.5... 50 pm thick. Resistivity method used to measure heat of transport Q* and H, D diffusivities. Break in Arrhenius plot at Tx 225 K confirms results of [69C], [7OS],[7Ov].
74w
Absence of break in Arrhenius plot reported in [74Ml] attributed to (i) smaller temperature range of study and (ii) impurities.
75A
273... 373
Nb foils, 0.05 ... 0.7 mm thick, Pd-coated in UHV. Electrochemical permeation time-lag method.
76B
180...373
Nb wires, 1.5 mm diameter, RRR: 1500.. .2000, * 0.4 at.% H and 0.7 at.% N added. Quasi-elastic neutron-scattering method. H was trapped by N, diffusivity decreased.Results of [74M2] confirmed.
76R
200...350
Resistometric method for determining diffusivity. Precision and temperature range inadequate to confirm or deny break in Arrhenius plot.
76W
H
H D H
< 0.05 at. % < 0.06 at. %
3.6. 1O-4
10.46
5.0. 10-4
11.72
0.4 at.%
H
H
0.2 at.%
H H D T H
0.11 at.% 0.9 at.% 0.93 at.%
3.6. 1O-4
9.94
14o.e. 300
1.1 . 10-3
14.06
723a.a1100
Absorption method. For Ts 873 K, surface effects were observed.
1.63. 1O-4 5.94.10-4 4.45.10-4
7.72 12.83 13.02
19o.e. 310 233.~~310 233...310
Polycrystalline Nb wire, 1 mm diameter or sheet, 1 mm thick. Quasi-static Gorsky-effect. Lack of break in Arrhenius plot for hydrogen attributed to limited temperature range.
1.2.10-4
6.67
165.e.250
Polycrystalline Nb wire, 1.5 mm diameter. Quasi-elastic neutron-scattering method. Adding about 0.04 at.% N or 0 reduced D below 250 K, confirming [74M2].
77c 77E 14
77Ml
77R
(continued)
Solvent element Nb
Diffusant
H cont.
DO 10-4m2s-t
Q
Temperature range K
Remarks
kJmol-’
6.5 at.% 20.26 at.% 20.89 at.% 25.60 at.% 27.06 at.% 28.17 at.% 4.58 at.% 12.74 at.% 18.63 at.% 24.98 at.% 27.80 at.% 33.02 at.%
4.9. 10-4 8.1 . 1O-4 8.6.10-4 7.2 * 10-4 7.6 - 1O-4 9.8. 1O-4 6.0. 1O-4 7.1 * 10-4 9.0. 10-4 9.6. 1O-4 10.1 .10-4 6.5. 1O-4
11.00 14.76 15.63 16.02 16.50 18.04 13.51 15.15 16.79 18.14 18.24 17.75
435-s. 573 435a.a573 435a.a573 435... 573 435-a. 573 435-e. 573 31o.e. 573 400 . . * 573 45o.e. 573 450-a. 573 450-a. 573 450.*. 573
Quasi-static Gorsky-effect method.
78B1,79V
5.79 9.65
120...260 290...480
79D
21.23 42.5 . . . 48.2
120...305 305...480
99.99% Nb foils, 20 ... 25 urn thick. (Stack of 90 layers of foil used.) NMR, spin-lattice relaxation method. Contributions due to diffusion in both u- and B- phases in 2-phase regions observed.
6.65 8.30
lo*.- 100
Nb foils, 15 urn thick. Quenching and recovery of resistivity method. D (hydrogen, 34 K) = 1 * 10e2’ m2 s-l. D (deuterium, 50 K) = 2 * 10e2’ m2 s-l.
79E
365.e.500
99.99% Nb foil, 50 urn thick. Pulsed-field-gradient spin-echo NMR method. Q increased with decreasing proton cont. for each total (H + D) cont. Conclude diffusion of H is a cooperative process between diffusing atoms.
79F
293..a581
Nb single-crystal rod, 12 mm diameter, [1lo] orientation. Quasi-elastic neutron-scattering method. Interpretation of data requires complex jump-model. D (581 K) = 5. lo-’ m2 s-r.
79Ll
Fig.
Ref.
(continued) H
D
H E 83 H D
H
(H + W Nb 0.20 . . .0.75
H
2.0 at.%
x (2.7) * 10-4
H
H
21.42
1.5 at.%
H, D
T
39 -.. 58
Nb, polycrystalline sheet, cathodically charged with H, and doped with N. Internal friction method. Q values refer to (H-N) pair reorientation.
80Z
0.09 . . .5
99.99% Nb polycrystalline rods, 6 mm diam., doped with 1.26 at.% 0. Neutron scattering measurements used to obtain tunneling matrix element of 18.33 kJ mol-l.
81W
12O.e.450
MRC MARZ grade Nb foils, 0.1 mm thick. RRR > 1000; specimens doped with N from 0.01 . . .0.8 at. %. Quasi-static Gorsky-effect method. H and D diffusivities decreasedwith increasing N; Oriano trapping model inadequate.
82Q
4.4. 10-4
12.83
153...373
MRC MARZ grade Nb foils, 0.1 ... 0.25 mm thick; RRR > 1000, tritium cont. 0.4 at.%. Quasi-static Gorsky-effect method. No break in Arrhenius plot observed for T.
4.4. 10-4 3.1 . 10-4
12.8 14.0
7oo.e. 1400
99.998% Nb, polycrystalline tube, grain size about 1 cm diameter. UHV permeation time-lag method. For 1100 5 Ts 1400 K, @g/D:) z ,/!?. Measured diffusivities affected by surface effects for T< 1100 K.
83Sl
H
SIK
84W2
H, -I-
130...450
99.99% Nb single-crystal rods, [I IO] orientation along rod axis. Specimens doped with N and 0 to act as traps for H. Low temperature specific heat and neutron spectroscopy used to measure tunneling matrix element, giving 18.3 and 20.26 kJ mol- ‘, respectively. NMR; spin-spin and spin-lattice relaxation rates measured to determine diffusivity of H and T Trapping at impurities, dislocations and hydride precipitates observed.
X0
H D
3.3 . . .4.25 at. %
455
99.9 % Nb polycrystalline bar, 0.75 mm thick. Quasi-static Gorsky-effect method, with and without applied magnetic field of 10 T. No effect observed on’ D. D (455 K, 3.3 at.% H) = 2.47. 10m9rn’s-l.
14
834
85M
85V
(continued)
Solvent element Nb
Diffusant
H cont.
DO 10-4mZs-1
Q
kJmol-’
Temperature range Remarks K
Fig.
Ref.
(continued) 285
a
H
Tao!
H
a
H
4.76 at.% x 9.0 at.%
a
H
a
H
z 7 at.% x9-*.40 at.%
3.39.10-4 1.56. IO3 1.396. IO4
58.62 134.8 140.7
773 e-0973 723-a-873
7.5.10-Z
60.29
673...873
5 6.7
200~~~400
5 15.5 26.37
i12
< 1 at.% < 1 at.%
a
H D
a
H
a
H
x 6 at.%
a
KD
x 5 at.%
a
H
0.05 *-- 0.1 at.%
Natl. Res. Corp. Ta powder, x 37 urn diameter. NMR spin-lattice relaxation method. Q values decreasedwith H cont. in a and 8i phases.
65M 65P
66Cl,66C2
673.a.873
Ta membranes, Pd-coated. Permeation method.
675
298
99.9% Ta sheet strip, 0.05 mm thick; one half charged with H. Cont. changes due to diffusion monitored with lattice parameter X-ray method. D (hydrogen, 298 K) = 1.3.10-lo m2s-‘; D (deuterium, 298 K) = 1.4.10-lo m2 s-l.
692
54O.a.870
High purity Ta sheet, 2.3 mm thick, bonded to PdAg duplex membranes on each side. Permeation time-lag method.
70H
11.72 11.72
6.1 . 1O-4
14.65
273-e. 433
7.5. 10-Z
60.29
‘43.46
Electron-beam melted Ta cylinders, 6 *.a7 mm diameter, mechanically polished. Desorption method. Ta foils, Pd-coated. Permeation method.
60K 62M
Internal friction (Snoek effect). D (hydrogen, 298 K) = 1.7 * 10-l’ m’s-i. D (deuterium, 298 K) = 2.2. lo-l3 m2 s-l. Polycrystalline Ta wire, 0.3 mm diameter. Resistivity changes associated with H migration used to determine diffusivities.
1.92 * 10-s 2.5. lo-’
7.5 * 10-s
MARZ grade Nb polycrystalline foils, 50 urn thick, and single crystals. Electrotransport, combined with resistivity measurements used to measure D under hydrostatic pressures from 0 to 3.5 GPa. Diffusivity increased x 10% at. 1 GPa. Both classical and quantum theory predict decreased diffusivity. Desorption method.
66M
CL
H
0.2 ***4.3 at. %
D u
H
u
H
0.12...0.25 at. %
253...573
99.996% Ta polycrystalline wire, RRR > 1000. Quasi-static Gorsky-effect method.
14.47
210...525
99.9 % Ta sheet, 6.. .I1 pro thick; electrolytically loaded with H. Dynamic Gorsky-effect method (internal friction).
71c
20.10
273 ~~~423
Ta wire, 0.3 mm diameter. Improved version of monitoring H cont. changes by resistivity (see
71M
4.4. 10-4
13.51
4.9 * 10-4
15.73
3.0. 10-4
1.7. 10-a
15
70s *
WMI). u
D
3.3 . 10-4
16.98
170*** 390
See [71C]. Linear Arrhenius plot over the range 210 .. .390 K; deviation observed at 170 K.
72Cl
CL
H
13 at.%
1.9. 10-4
10.40
421*..613
Powdered Ta specimens. Quasi-elastic neutronscattering method.
7263
CL
H
5 12 at.%
6.5. 1O-4
15.07
270...330
Ta tube; one end loaded with H, placed on sensitive beam balance. Diffusion determined from shift in center of gravity associated with H migration along the tube. D (298 K) = (I... 2.5) . 10-l’ m2 s-l, decreasing with increasing H content.
u
H
6.64. 1O-4
14.65
300 . . a360
Ta sheet, 0.1 mm thick; one half charged with H. Diffusion monitored by lattice parameter changes with H cont., determined by X-ray method.
7221
P
H
1.4. 10-s 9.2. lo+ 9.7 * 10-4 1.1 . 10-7 2.8 +1O-4
8.1 14.1 20.3 12.7 20.2
87e.e110 110~.~160 160*.*230 78*.*118 118...210
99.95% Ta wire, 0.3 mm diameter. UHV; absorption method. Assumed diffusion in S-phase surface region dominates.
7362
4...60
Ta wire, RRR 3000 a**5000. H or D loaded in UHV system. Mobilities determined from resistivity recovery, following quench. H, D mobility at 10 K best accounted for by polaron model.
73Hl
D
L
U
K D
U
H
2.0. 10-2
20.70
773.e.1173
15
72W
73K (continued)
Solvent element
Diffusant
H cont.
DO 10-4m2s-*
Q
kJmol-1
Temperature range K
Remarks
Fig.
Ref.
Ta (continued) 13 at.% 33 at.%
10.4 15.0
5.0. 10-4 6.4. 1O-4
Powdered Ta, reacted with H, gas. Quasi- and inelastic neutron-scattering methods. Conclude jumps occur from tetrahedral to tetrahedral sites in both phases. Diffusivity in u-phase decreases with increasing H concentration.
73R
273.e. 673
Ta wire, 0.3 mm diameter. See [66M], [71M].
74Ml
584
99.996% Ta single-crystal, [l lo] axis along cylinder axis. Quasi-elastic neutron-scattering method. D (584 K) = 2.8 * 10T9 m2 s-l, in good agreement with [7OS].Results cannot be fitted by any simple jump model.
74R
14.48
273a.a373
Ta membrane, Pd-coated in UHV. Electrochemical pulse permeation method.
76B2
13.50
230.-0400
99.996% Ta foils, electrolytically loaded with H. Q determined from motional narrowing of Miissbauer line.
76H2
15.61
773 ... 1373
Absorption method. Sharp break in Arrhenius plot at z 973 K suggestssurface effects.
77E
4.2 ... 100
MRC MARZ grade Ta wire, 0.125 mm diameter. See [73Hl]. Specimen doped with D quenched and annealed simultaneously with T-doped specimen. Annealing kinetics of D, T similar at each substage; QT > Qb.
77H
323-a-383
“Commercial purity” Ta. Neutron-radiographic method used to measure H cont. profile for diffusivity determination.
772
15.34 17.95
-e 2 at.%
< 0.05 at.%
7.0. 10-4
5 14.5 at.%
1.0. 10-3 D,T
1.7.10-J
18.12
H
5 at.% 10.23 12.04 14.30 19.0 21.5 at.% 3.5 at.% 5.57 7.40 10.95 13.04 15.68 19.0 22.36 at.%
4.1 . 10-4 4.3. 10-4 4.0.10-4 4.0. 10-4 3.0. 10-4 4.0. 10-4 6.6. 10-4 6.2. 1O-4 6.2. 1O-4 5.3. 10-4 5.7. 10-4 5.3. 10-4 5.5. 10-4 4.1 . 10-4
13.32 13.99 14.18 14.47 14.67 16.50 16.31 16.50 16.50 16.50 16.89 17.08 18.43 18.91
270 . . ~440 3oo.e.430 300...470 3OO.e.425 32O.e.415 320... 573 295 ... 573 295.e.573 295...573 330..* 573 295...573 3oo.e. 573 31o.e. 573 33o.s. 573
H
5... 7 at.%
3.47.10-4
14.76
299...873
See [66M], [71M], [74Ml].
78M
H
13.42 24.36 32.71 37.38 39.76 40.37
12.93 12.83 13.12 13.89 13.70 13.78
77...470
Ames Laboratory pure Ta. NMR proton spin-lattice relaxation time method. Phase boundaries in Ta - H system located.
79H
H
ZO
3.86 13.51 3.76 15.44
< > < >
250 250 250 250
Resume of results obtained by several methods, mainly quasi-static Gorsky-effect. Sharp break in Arrhenius curve at x 250 K is confirmed; the effect is reduced by additions of nitrogen.
103 . ..473
Quasi-static Gorsky-effect method. Additions of N (0.02 ... 0.9 at.%) reduce break in Arrhenius plot for H and D diffusion at x 250 K. (See [79v]).
133.e.250 25O.e.373 133 ... 373 133 ... 373
MRC MARZ grade Ta foils, 0.1 ... 0.25 mm thick, RRR > 1000. Quasi-static Gorsky-effect method. No break observed at 250 K for T (nor for D, contrary to [79Vj).
15...30
High purity Ta doped with x 300 ppm 181Hf. Perturbed angular correlation method used to study H trapping at “‘Hf, and H diffusion.
D
D
H, D
ZO
H
X0
D T
w 1 at.%
H
2.0.10-6 4.4.10-4 1.2 * 10-6 4.6. 1O-4
2.8. 4.2. 3.8. 3.7.
1O-6 1O-4 1O-4 10-4
4.05 13.12 14.76 15.63
78Bl
15
79v *
824 15
83Q *
85P (continued)
Solvent element
Diffusant
H cont.
DO
10-4mzs-1
Q
kJmol-’
Fig.
Ref.
Temperature range K
Remarks
20 -. .290 180...290
99.99% Ta polycrystalline foils and single crystals, (11I)-orientation. ‘H implanted at 4 or 7 keV near surface, and detected following anneals by ‘H(“N, cry)‘% resonance reaction. D(20K)=4.10-20m2s-1; D (150 K) = lo-‘* m2 s-l.
85W
4.2 . . .30
Perturbed angular correlation method (see [85P]), used to identify configurations of trapped H atoms. Also, conclude deuterium is immobile below 30 K.
87P
Ta (continued) a
H 26
a
H
9.4.6 Chromium group metals Cr, MO, W Data available only for MO and W. MO
H
5.9. 10-Z
61.55
848 ... 1253
Desorption method.
60H
MO wire, saturated with H. Q deduced from yield point behavior.
6lL
H
37.90
H H
2.0
34.60 74.53
673 ... 1473
99.9 % MO single- and polycrystalline specimens. Permeation method using mass spectroscopy.
H
4.8.10-s
37.68
1123...2023
Do and Q values deduced by [73P] from permeability
[68F] and solubility [720] data. T
1.0. 10-s
64.48
423.e. 823
D
(1.04 . lo-Z)*
(58.0)*
523...730
MO single crystals. Tritium used as tracer to study effects of oxide layer on diffusivity. Found D ([ilo]) < D ([loo]), due to differences in oxide surface layers. 99.8 % MO membrane, 0.127 mm thick. Permeation time-lag and desorption methods. Markedly different diffusivities obtained from “rise” to steady-state and decline * from steady-state permeation measurements; attributed to surface effects.
665 712,732 68F, 720, 73P 74M1, 74M2
75c
H
3.51 .10-Z
58.6
H
523 . . .2023
Desorption method, using mass spectroscopy. Do and Q values averaged from those of present study and selected literature data.
78K1, 78K2
573 ... 1073
Permeation time-lag method; entry of H from ionized gas-phase.Arrhenius curve shows sharp break at x 773 K.
792
H
2.4. 1O-4
10.6
770... 1170
99.95 .. .99.99 % MO membranes, 0.18 mm thick; cleaned by argon etching and/or Pd-coated. Permeation time-lag method. Concludes large Q values reported in literature due to surface effects.
H
7.25.10-4
173.8
1783 ee.2175
W wire filaments. Desorption rate in UHV used to determine difhtsivity.
H
8.1 . IO-’
82.90
H
4.1 . 10-s
37.68
H D
(5. 10-S)
D H
I9= 0.1 0.3 0.6 0.9 I9= 0.3 0.6 0.9
1.55~10-’
2.so.10-5 5.0 . 10-5 1.48. 1O-4 1.16. IO+ 5.8 . IO-’ 5.85. IO-’
82K
*
64M
Commercial W wire, 1 mm diameter. Desorption method [69F] suggestswires were not initially equilibrated.
17(a) (4
64R
1100...2400
99.95% W rod, 3.17 diameter; produced by sintering and rolling. Nominal density > 99.9%. Desorption method.
17(a) U)
69F *
(20.1) (20.3)
143.e.200
Surface diffusivities of H and D on (110) plane of W
17.04 19.55 20.10 21.35 19.93 20.30 22.40
138 ... 160
80D
single-crystal. Field-emission current-fluctuation method. For T< 140 K, H diffuses via pure tunneling.
e* H
16
29
Surface diffusivities (see [SOD]). 0* is a measure of fractional (110) surface coverage by the diffusant. Thermally activated diffusion found for T> 13Oe.e160 K, depending on the isotope and 8. Below these temperatures, tunnelling occurs.
W single-crystal; H implanted normal to (110) planes at 29 K. Field-ion microscopy used to monitor H movements during controlled pulse field evaporation. Volume diffusivity determined as D (29 K) 2 IO-” m2 s-l. Suggests non-classical diffusion.
17(b)
82D
84M
(continued)
Solvent element W
Diffusant
H cont.
DO
Q
kJmol-’
Temperature range K
Remarks
10-4m2s-1
(1.3 * lo-s) (1.3 * 10-q
(19.68) (19.68)
83 a-. 173
W single-crystal. Surface diffusion of H and D on (110) planes measured by field-emission fluctuation method [80D]. Find little anisotropy on (110) planes.
Fig.
Ref.
(continued) H D
85T
9.4.7 Manganese group metals Mn, Tc, Re No data available.
9.4.8 Iron group metals Fe, Ru, OS
Data available only for Fe. Fear
H
2.71 . 1O-4
Do and Q obtained by applying the time-lag analysis
38.52
24E
[40B] to data. See [56S]. u.
H
1.1 * 10-z
36.59
296.e.353
Fe membranes. Analysis for the permeation time-lag method given and used for first time.
18(b) Gv
40B
CL
H
7.6 - 1O-4
9.55
293 ... 1073
Permeation method.
WW (14
47s
u
H
2.17. lo-’
12.10
673.e.1173
“Pure” Fe. Permeation method.
W-4 (3)
50G
u
H
8.85.10-4
12.77
423.e.1173
99.96% Fe rods, vacuum cast; surfaces machined, but not polished. Desorption method.
18(b) (24
56s
u
H
9.3.10-4
11.30
473 **a1047
Armco Fe. Desorption method.
18(b) m
58E
U
H
5.0 * 10-a
14.30
298.e.363
Mild steel (0.09% C, 0.35% Cr); discs; 0.5 **a1 mm thick. Monitored diffusion on exit side with mass spectrometer.
58F
U
H
1.8. lo*
50.24
195 se-473
Cylindrical specimen cut from forgings. Desorption method.
58H
U
H
4.95 * 10-4
6.53
571... 1151
Desorption method.
18(b) (9)
58M
H H H
H
H
1.20.10-3
16.10
1.02.10-3
10.80
6.7. 1O-4
9.17
298...1173 823... 1173 703...998
Desorption method. 99.9 + % Fe. Permeation method.
18(b)
58Z
(24 59s
99.9 + % Ferrovac Fe discs, 6.8 mm thick. Absorption and desorption methods. Surface impurities can influence results. No significant change with cold-work.
18(b)
60C
(23)
1.2. 10-l 1.4. 10-3
32.74 13.40
298..-473 473 ... 1053
99.9 + % Ferrovac Fe; cylindrical specimen, hot-rolled or swaged, then machined. Desorption method. Low temperature behavior attributed to H trapping.
18(b)
3.65. 1O-3
22.40
298..-923
Desorption method.
1809
55J, 605
(2.5)
61L
WI H
2.2. 10-3
13.8
303...363
Permeation time-lag method.
18(b)
61R
WI H
3.9. 10-4
4.52
H
399..-966
99.9% Fe. Permeation time-lag method. Annealed and cold-worked specimen gave same results.
298
Armco Fe membranes, 0.77 mm thick. Electrochemical permeation method. D (298 K) = 8.3. IO-’ m2 s-l.
63D
64W
H
1.42. 1O-3
13.69
523...873
99.8 % Fe foils, 0.214.. .0.568 mm thick. Permeation transient method.
H
6.0. 1O-4
5.57
283 . ..348
Armco Fe, single- and polycrystalline and zone-refined Fe membranes. D (298 K, single-crystal) x 1.3 . D (298 K, polycrystal).
H D H D
6.42. 1O-4 5.55.10-4 6.63. 1O-3 4.85. 1O-3
8.04 8.04 44.80 44.80
573...1183
99.98% Fe spherical specimen. Gas-volumetric desorption method.
i3 H
2.88 . lo- 1 1.1 . 10-z
93.60 15.11
1723 ... 1788
180-4 0
180-4 (13)
63B
65M, 66B
66H
1183 ... 1373
353 *.*453
99.8 % Fe membranes; 1, 0.5 and 0.25 mm thick; specimen surfaces mechanically polished, Pd coated on entry side. Permeation time-lag method.
18(b) (6)
66s 66W (continued)
Solvent element
Diffusant
H cont.
DO 10-4mZs-’
kJmol-’
Q
Temperature range Remarks K
Fig.
Ref.
(8. 10-3)
8.37
4-a. 300
“High-purity” Fe sheet, 1 mm thick, cathodically charged with hydrogen. Internal friction (Snoek peak) method.
67Gl
Fe (continued) a
H
a
H,D
633...833
99.95% Fe tube; 1.87 mm wall. Steady state permeation method. Using solubility data of Sievert for H, D, they find (DJD,) = 1.20.
6762
a
H
298
Johnson-Mathey Co. “pure” Fe discs, mechanically polished; 1 mm thick; surface not Pd coated (see [66Wj). Permeation time-lag method. D (298 K) z 1.5 . 10m9m2 s-l.
68W
a
H
1.14 * 10-3 5.1 * 10-l 1.7 * 10-l
35.60 40.79 36.18
283... 343 296.e.357 296.e.357
99.996% Fe Desorption method. 99.67 % Fe Concludes low diffusivities due to 98.60 % Fe trapping in voids associated with non-metallic inclusions.
a
H
3.24 - 1O-2
18.83
296-a-348
Fe membranes. Electrochemical permeation method.
70B
a
H
2.2 - 10-3
12.97
283...373
99.5% Fe discs, 0.8 mm thick. Permeation time-lag method. Diffusivities not affected by surface conditions.
7oc
H
7.8. lO-4
7.95
Do, Q in the absence of traps; deduced from literature data and trap model.
700
H
6.1 . IO-’
24.8
288...333
Permeation transient method.
H
9.4 * 10-4
11.30
573 --. 1023
“Pure” Fe. Permeation time-lag method.
H
4.74 * 10-4
5.86
599 ... 1089
Desorption method.
H
2.5.10-J
9.21
283-e. 343
Armco, 99.99% Fe. Electrochemical permeation method.
18(b) (26, 26’, 26”)
18(b) W)
69E2
70R2 70s
18(b) (4
71D 71s
Y 6
H H
1.01 .10-z l.09.10-3
47.25 12.54
1184... 1667 1667... 1811
CL
H
9.21 .10-4
11.30
573 ... 1073
72G
u
H
4.15.10-4 4.74.10-4
4.27 5.90
297.a. 973 585 ... 1092
72H, 79D
u
H
8.2
140... 153
Internal friction method.
73c
298
99.9965% Fe. Permeation method. D (298 K) = 7.4. IO-’ m2 s-l.
73D2
313.e.363
Electrochemical permeation method.
73M
295
Armco Fe. Electrochemical permeation method. Diffusivity at 295 K varied with H cont. C as: D (295 K, C)=(4.05~10-g+4.687~10-3 C)m’s-‘. (C in mole fractions)
73Nl
u
72Bl
Average from literature data.
u.
H
u
H
u
H
2.3. IO-’
6.70
32O.e.833
Triply zone-refined Fe, Pd coated. UHV permeation method.
18(b) (4
73N2
CL
H
1.05.10-3
7.49
278...353
Pd-coated Fe. Electrochemical permeation method.
W4 u.3
74A3
u.
H
1.4. 10-Z
17.57
278...333
Armco 99.8% Fe, annealed and plastically deformed specimen. Electrochemical permeation method; exit side Pd-coated.
18(b) WI
74K2
U
H
1.97. IO5 3.71 .10-3
69.50 17.45
298.s.353 353...573
Armco 99.7% Fe. Permeation time-lag method.
74s1, 77s
U
H
5.5. 10-4
5.19
315.a.343
Cold-worked Fe specimen. Permeation method.
74Y
U
H
2.14. 1O-4
6.2
298 ... 573
Desorption method.
18(b) (20)
75Kl
U
H
1.01 .10-3
6.67
342..-619
99.9 + % Fe; Pd-coated. Permeation method.
W-4
75M
U
H
8.3. 1O-4
10.96
643 ... 1023
7582
U
H D
2.29.10-3 1.62. 1O-3
10.46 10.46
297...623
76L
18.4
(8)
(continued)
Solvent element
Diffusant
H cont.
DO
Q
Fig.
Ref.
kJmol-’
Temperature range K
Remarks
10-4mZs-1
1.7 * IO5 3.8. 1O-3
69.04
298.e.353
Ammo Fe. Permeation time-lag method.
353 a**573
18(b)
17.57
77Cl,77C2, 77c3
1.03 * 10-3 3.74.10-J
11.3 34.0
298-e. 1184 1184.e.1667
Do and Q values averaged from selected literature
Fe (continued) CL
ci.
H
H
(19, 193
78K
data.
cc
H D
1.61 . 1O-3 1.52~io-3
7.07 8.08
322..a779
Cpass, zone-refined Ferrovac E Fe, discs, 1.33 mm thick, Pd-coated. UHV permeation time-lag method.
a
H D
1.21 * 10-J 1.15~10-J
7.05 8.60
283...333
99.996% Fe, zone-refined membranes, 0.6.. .1.5 mm thick, Pd-coated. Diffusivities determined from absorption and desorption transients. Linear Arrhenius plots.
78Rl
H
7.5. 10-4
10.13
230-m.1100
Best iit of selected literature data, large deviations for Ts 298 K
78V
H
1.1. 10-3
6.7
230...300
Single- and polycrystalline Fe, Pd-coated. Electrochemical permeation method.
H
3.1 * 10-4
4.6
343.e. 675
“Very pure” Fe membrane. Permeation time-lag method.
79w
2.23. 1O-3
6.7
Cpass, zone-refined Fe; Pd-coated. Electrochemical permeation time-lag method. Comparison of results from annealed and deformed specimen indicate trapping binding energy x 60 kJ mol-‘.
80K
H
x 2. lo-’ at.%
W-4 (4
18(b) WI
784
79H
CL
H
6.2. 1O-4
4.86
283...343
99.9% Fe single-crystal; Ni-coated. Electrochemical permeation method.
18(b) (7)
8lY
a
H
4.2. 1O-4
3.85
2530.. 1040
Anion-exchange and vacuum-floating zone-refined Fe; RRR 5000~~~6000.For T= 253.e.322 K, the alternating current electrochemical permeation method; for T= 673 ... 1040 K, the permeation time-lag method. Trapping seen for T< 290 K.
1864
82N
*
H
1.23. 1O-4 (1 ... 2.52) * 10-3
H D
5.69 (6.7 ... 7.12)
233..-353 323..+823
Best representation of data from statistical analysis of selected literature data. Concludes electrochemical methods, with Pd-coated membranes and desorption methods are reliable.
83K
31.4 (7.1) 31.4 (8.6)
283.a. 333
99.997 % Fe, Zone-refined membranes, cold-rolled to
83R
273...333
H
7.69. 1O-4
5.8
H D
4.43 .10-4 4.28. 1O-4
5.31 6.47
H
6.04. 1O-4
6.99
H
0.6 mm thick, Pd-coated on entry side. Electrochemical permeation time-lag method. (Q) values refer to annealed specimen, see [78Rl]. Trap binding energy z 25 kJ mol- ‘. Annealed Fe specimen contained 30 *.. 110 ppm C; diffusivity independent of C cont. Large decrease in diffusivity on cold-worked specimen. Trap binding energy z 23 *. *27 kJ mol- ‘.
85H
Found D (hydrogen)/D (deuterium) ratio depended on temperature and + 1 with increasing temperature.
85T
500... 1000
Duplex-membranes of Cu/Fe. Permeation time-lag method. Some effects of surface oxide and/or bulk trapping noted.
86T
284,286
Fe membrane. Electrochemical permeation time-lag method. For annealed Fe: D (T, 286 K) = 9. IO-lo m2 s-l. D (H, 286 K) = 4.10-l’ m2 s-l. For 9 % cold-worked Fe: D (T, 284 K) = 3 . IO-” m2 s-l. D(H,284K)=4.10-‘0m2s-1.
87H
9.4.9 Cobalt group metals Co, Rh, Ir Data available only for Co. co a
H
2.49. 1O-3
26.08
1363 ... 1689
Permeation method, using a Sievert’s cell.
H
2.45. 1O-3
25.74
z 1250..a 1820
Permeation; Do and Q values are best lit for combined data of [66S] and [85S].
66s 19 (4
(continued)
Solvent element
Diffusant
H cont.
DO 10s4 m*s-’
Q
kJ mol-’
Temperature range Remarks K
Fig.
Ref.
Co (continued) ci
H
B
H
3.4 - 10-Z 8.3. lO-3
(:i -Fe)
H D T
B
H
0.02 at.%
9.27. lO-4
148...203
H-loaded Co. Magnetic after-effect method. Relaxation processesobserved suggest H atoms are at the orthorhombic sites between near-neighbor solvent atoms.
72D
29.30
303e.0323
Electra-deposited Co layer, 1 urn thick. Electrochemical permeation method. D (303 K) = 1.22. 10-‘4m2s-1 D (323 K) = 2.41 . IO-l4 m2 s-l.
72 K
57.78 49.40
473.e.673 673 ... 823
99.9 % Co foils, 0.4 mm thick; room-temperature P-phase (hcp) contained small amount of high temperature u-phase (fee) and had a strong texture (103) planes parallel to foil. Permeation method.
43.76 50.17 50.13
120~~~220
fee Co-Fe (16 at.%) alloy. Magnetic after-effect method. The relaxation peaks of D, T occur at same temperature, jump frequencies v are v,.,+ vD x vT. 140 < T< 200 K.
23.28
278.a.332
MARZ grade Co foils, 0.109 mm thick. Electrolytic double-cell method.
19 74c (393’)
82H
19 (2)
85s *
9.4.10 Nickel group metals Ni, Pd, Pt Ni
H H
2.0 * 10-l
61.96
1.7. 10-2
45.35
H H H H
1.1 * 10-3 1.5.10-2
35.70 44.38
2.0 - 10-J 2.3. lO-2
36.42 45.35
H H
1.0 * 10-a 4.5. 10-J
23.16 36.01
731.e. 871 473.s.773
Permeation method. Permeation method.
7510.. 1071
Permeation method. Permeation method.
20 (4
29H 32H
20 (7)
35E
52l.e. 673
Desorption method. Permeation method.
673.e.873 653-a. 1259
Absorption method. “Commercial purity” Ni; non-steady rate of desorption.
649...873 358 .-.438
23L 27B
36s 54L 55H
1
H
7.6. 1O-3
41.37
673...973
99.92% Ni. Desorption method.
55R
H
1.07.10-2
42.37
435..-769
High purity, commercial grade Ni. Desorption method.
57El
H
9.5.10-3
43.12
703.e.1123
99.4% Ni. Permeation method; no effect of plastic strain noted.
59G
H D
4.2 . 10-3 4.56. 1O-3
35.17 37.43
576...967
Spherical specimen. Desorption method.
H
5.73.10-3 3.02. 1O-3 4.15.10-3 2.99.10-3
40.19 37.26 40.19 37.26
523.s.623 623...873 523..-623 623...873
Ni membrane, 0.4 mm thick. Permeation time-lag method, using mass spectrometer. Break in Arrhenius plots at the Curie temperature.
H
3.8. 10-3
39.77
298 ... 348
Desorption method.
20 (10) 630
H
5.5. 10-3
37.35
1243 ... 1593
Desorption method.
64R
H D
6.7. 1O-3 4.8. 1O-3
39.78 38.52
658...893
Single-crystalline cylindrical specimen. Desorption method. Conclude H, D occupy octahedral sites.
65E
H
31.90
1353 ... 1669
Desorption method.
H
4.7. 10-3 4.4. 10-3
36.38
673...873
Desorption method.
66s 67D
H
5.22. 1O-3
40.03
473..-693
99.999% Ni single-crystal disc, 0.43 mm thick. Permeation time-lag method. No break at Curie point in Arrhenius plot. See [61B].
67El
H D
5.22. 1O-3 3.97.10-3
40.03 39.37
49O.q.690
See [67El]; measurements on isotope effect; DJDD < $; Results accounted for in harmonic approximation for octahedral-octahedral jumps.
67E2
H
5.39.10-a
40.00
423...1000
99.8 % Ni foils, 6.7 pm to 1.83 mm thick. Steady-state permeation and permeation time-lag methods.
67F
H
3.5. 10-3
43.31
273...328
Zone-refined Ni wires; 8 pm diameter; resistivity-recovery measured, following quench.
36O.e.377
See [67El]; find (DJDD) decreaseswith temperature, and becomes < 1 below x 364 K, in accord with theory in [67E2].
D
H D
20 VI
60E 61B
20 (if)
67s 68E (continued)
r
Solvent element Ni
Diffusant
H cont.
DO
10-4m2s-1
Q
kJmol-’
Fig.
Ref.
Temperature range K
Remarks
583-s-823
Permeation time-lag method. No break in Arrhenius plot observed at Curie point.
68V
(continued) H H
5.4 * 10-J
39.56
473-e-873
Cylindrical and spherical specimen. Absorption method.
69C
H
6.56. 1O-4
36.82
300.. .348
Electrochemical method.
70B
H
(1) 5.4.10-s (2) 5.05 .10-3 (3) 4.65 .10-J (4) 6.5. lo-’
38.11 40.32
473...873
(1) Cylindrical specimen. Absorption method. (2) Spherical specimen. Absorption method.
H
8.1 . lo-’
41.03
362.e. 573
Permeation method.
71Dl
H D T
7.04 * 10-3 5.27 - 1O-3 4.32 - 1O-3
39.47 38.67 38.08
673 ... 1273 773 ... 1273 773 -.. 1273
99.999% Ni single-crystal, spherical specimen. Desorption in UHV. Conclude harmonic approximation inadequate to account for diffusivity ratios of H, D, and T
71K
H
4.02. lo-’
39.31
293.0.673
99.98% Ni strip. Permeation time-lag method. No effect of grain size.
H
6.44. lO-3
40.24
273.e.1669
Best tit of literature data from permeation time-lag, absorption and desorption methods.
73R
H
5.2. 1O-3 9 * 10-4
40.61 29.73
63O.e.1123 523.s.630
99.98% Ni. Steady-state permeation method. Observed change in Do, Q at the Curie transition temperature.
74Bl
H
8.38. 1O-3
41.13
92O.e. 1170
41.50
(3) Cylindrical specimen. Desorption method.
38.59
(4) Spherical specimen. Desorption method.
20 (3, J-96)
20 (8)
70C
72R1, 72R2, 73R
7482
H D T
7.10-3 4.95.10-3 4.04 * 10-3
39.50
3oo.a. 550
99.98% and 99.995% Ni polycrystalline foils and rods. Permeation, desorption and absorption methods used for D and T, on annealed and on cold-rolled specimen. Suggest results represented byD”=(7~10-3/&?)m2s-1; Q = 39.50 kJ mol- ’ (M in atomic mass units).
H
6.87. 1O-3 4.76. 1O-3
40.52 39.56
T>T, T
Best fit of literature data. T, is the Curie point.
H
2.09. 1O-3
37.72
323...353
99.996% Ni strips, 0.2 mm thick. Diffusion-elastic method described and used (inverse of Gorsky-effect).
76C
2.14. 1O-3
37.18
190*..380
99.998% Ni wire, resistivity recovery following quench. Show diffusivities deduced are independent of wire diameter.
76Y1, 76Y2
423
Microcrystalline Ni (av. diameter x 100 A); containing x 3 at.% Al. Quasi-elastic neutron-scattering method used. Surface diffusion. D (Surface, 423 K) = 8 . IO-r2 m2 s-l.
77R
H
5 5.4.10-2 at.%
H
x 1 at.%
75L
20 75v (499)
*
H D
7.11 .10-3 4.52. 1O-3
44.77 43.51
573 ... 873
H
1.90 * 10-3
37.22
22O.e.370
99.998% Ni wire, diameter 0.02.. .0.075 mm. Quench recovery method (see [76Yl, 76Y2]). 2-stage recovery observed, lowest temperature stage due to trapping effects. Data agrees well with extrapolated curve from high temperature results [73R].
77Y1,79Y
H
7.85. 1O-3
40.80
400... 1600
Do, Q averaged from selected literature data.
78K
253
Deuterium implanted. Cont. profiles monitored with D (d, p) T reaction. D (253 K) x 1.5 . IO-l7 m2 s-l. Conclude implantation produces amorphous region.
78M2
540..*960
Thin, polycrystalline Ni membrane. Permeation, using novel pressure oscillation method described.
78M3 (continued)
D
H
5.98. 1O-3
40.48
77T
Solvent element Ni
Diffusant
H cont.
DO 10-4m2s-1
Q
kJmol-’
Temperature range K
Remarks
283.a.333
Polycrystalline sheet Ni, annealed and cold worked. Electrochemical permeation method. Diffusivity increases with grain size, decreasesas cold-working increases.
78Sl
Fig.
Ref.
(continued) H
H
4.8. 1O-3 6.9. 1O-3
39.37 40.52
22O.e.631 631... 1726
Best fit of data compiled from surface-independent methods.
78Vl
H
2.52.10-l
52.97
323...353
99.996% Ni strip clamped at one end. Diffusivity related to deflection of strip due to ingress of H from one side. See [76C].
79c
99.97% Ni strip, plastically deformed during cathodic charging. Effective diffusivity x 10m9m* s-l, compared with lo-l4 m* s-r in unstrained material.
79K2
99.97% Ni foils, 71 urn thick; grain size 50 urn. Electrochemical method.
8OA
H
H
6.44. 1O-3
40.17
298.0.363
H
6.7. IO-’
38.10
573***973
1.1 * 10-4 8.8 * 10-4
33.77 38.11
IlO... 165
H D
< 0.06 at.%
H
5.1 * 10-a
40.04
H
H D
6.6. 10-J 5.08 - lo-’
40.4 39.6
80T Ni specimen contained 2 at.% Fe. Do,Q determined from magnetic after-effect measurements. Arrhenius plot deviates from high-temperature results.
81H
Ni foil. (See [78M3].)
84C
393.a.703
99.9% Ni foils, 100 urn thick. Absorption and desorption time-dependence monitored.
84F
273-e-293
MARZ-grade Ni foils; 10 urn thick. Constant current permeation method and potentiostatic depletion method used. Results in good agreement with high-temperature data, contrary to [67S].
673.e.973
Permeation under oscillating pressure method. (See [78M3].)
H
*
20 (12)
84L
83T, 84T
H
x 0.08 at. %
H
Pd
u P
CL
333
99.996% Ni single crystals. Diffusion-elastic effect method (see[79C]). Diffusivity measured as a function of dislocation density Q. D (333 K, Q = lo8 m-‘) = 2.49. IO-l3 m2 s-l D (333 K, Q = 10” m-‘) = 2.52 . IO-l3 mz s-l D (333 K, Q = 1Ol4 m-‘) = 2.38 . IO-l3 m2 s-l D (333 K, Q = 101’ m-‘) = 1.33 . IO-l3 m2 s-l
85C
298
99.95% Ni foils, 0.076 ... 0.127 mm thick. Diffusion-elastic method (see[79C] [SSC]); bending measured by capacitance. D(298K)=7.10-‘4m2s-1.
85M
H
9.2. 10-3
41.40
26O.e. 1000
Electrochemical and gas permeation methods.
86H
H
3.86. 1O-3
36.0
5oo.e. 1000
Duplex membranes; Cu/Ni were used.
86T
H D
2.5. 10-3 8.5. 10-J
14.65 18.42
2ll.e.263
Ni single-crystal. Surface diffusion on (100) face measured using laser-induced thermal desorption.
87M
H
7.2. 1O-3
23.95
463 ... 673
Absorption method.
355
H D
8.43 +1O-3 6.70. 1O-3
24.07 24.07
H
4.3 . 10-3
23.53
473..*973
Permeation method.
54D
H
5.2. IO-’ (8.5. 10-3)
23.66 (22.82)
448..-648
58T
H
4.3. 10-3
23.45
486..-652
Permeation method. (Recalculated, using revised solubility data. See [70Hl.) 99.5% Pd tube. Permeation method.
H
1.9. 10-Z
23.86
303-s-373
Pd tube, 3 mm outside diameter, 0.1, 0.2 mm wall thickness. Steady state diffusion method.
64W2
300
99.8 % Pd membranes; surfaces precleaned by argon bombardment. Permeation method. D, (3OOK)= 1.6.10-“m2s-’ D, (300 K) = 1.5 .10-l’ m2 s-l
655
2730.0 323
Pd wire, 1 mm diameter; hydrogen absorbed from aqueous solution.
65s
H
5 3 at.% x 37 at.%
6.1 . 1O-3
25.08
*
405
60K
(continued)
Solvent element
Diffusant
H cone.
DO 10-4mZs-’
Q
kJmol-’
Temperature range Remarks K
Fig.
Ref.
Pd (continued) x 37 at.%
B
293 293.a.373
D, (293 K) = 2.7. lO-*o m* s-i.
66K
Pd foils, 0.1 ***0.2 mm thick. Gas-volumetric method. Reversed isotope dependence observed. See also [67H], [7lv].
67B
H D
5.7. 10-3 3.45 ’ 10-J
24.07 22.19
H D
1.1 . 10-t 8.10-3
25.54 23.86
273.a.353
Electrochemical method. Reversed isotope dependence noted.
67H
15.49
704
Inelastic neutron-scattering method. Concludes jumps are from octahedral to octahedral sites.
67s
533.e.873
Influence of an electric field on migrations of H and D studied.
68Kl
H
1.6...2.9 at.%
H D
5.5 * 10-3 4.45 * 10-3
24.70 23.86
H
4.94 * 10-J
24.05
Low pressure permeation method. Concluded D (grain boundary)/D (bulk) < 10’.
68K2,69K
20.86; 14.60 20.86; 12.10
99.9% Pd wire, charged with H. Elastic after-effect method. Two thermally activated processes contribute to the jump rates over 50-a. 300 K temperature range.
70A
H
38.e.45 at. %
D
17.58
3OO.a.333
Electra-chemical method.
70B
5.25. 1O-3 4.46. lo- 3
26.04 25.75
593.0.923
99.99%, electron-beam melted Pd. Permeation, time-lag method; for T> 923 K the observed Q for H and D increase.
70G
H
2.94 - 1O-3
22.02
533.e.913
99.9 + % Pd discs. Gas-volumetric time-lag method. (Found Q increased and Do decreased with increasing Ag additions.)
70H
a
H
4.10-3
24.07
273 ... 333
99.9 % Pd foils. Electra-chemical pulse, time-lag technique. (Q increased, Do decreasedwith increasing Ag content.)
a
H
2.6 - lO-3
22.19
e?
H
a
H
a
H D
a
Pd membranes (0.025 mm) supplied by Englehard Industries. Electrochemical time-lag method. D (299 K) = 1.95 * 10-i’ m’s-‘.
71Bl 7lB2
CL
H D
u
T
u
71B3
3.65. 1O-3 2.5. 1O-3
23.45 21.56
1.05 * 10-z
26.04
289.a.323
H D
2.5 +1O-3 1.7.10-3
21.81 19.88
233 . . .445 218...333
u
H
4.5. 10-3
24.07
273 ... 1273
CL
T
1.02~10--2
26.59
a
H
x 3 at.%
H D
40 at.%
U
CZO
623
2.5. 1O-3
21.23
100*~*500
x 25.9
573,623
2.93 * 10-3
23.43
453.e.793
2.1 . 10-3 5.4. 10-3
21.34 23.50
298
H H H T H D T
273...873
Tritium electrochemically injected on entrance side of membrane. Time-lag monitored on exit side, using B-activity; Tritium need not exit. Coiled, polycrystalline springs, wire diameter 0.5 mm. Quasi-static Gorsky-effect method. Reversed isotope effect confirmed (see [67B], [67Hl). Best fit from selected literature data.
71s
21(a)
71v
72Bl
See [71S].
72B2
Single crystal Pd. QENS method. Octahedral-octahedral jumps confirmed (see [67Sl). 99.99 % Pd bar; 0.08 x 1 x 15 mm3; large grain structure. Quasi-static Gorsky-effect method. Confirm isotope-reversal effect for T> 100 ... 500 K, but normal isotope-effect for Tz 60 K. Single crystal Pd. QENS method. D (573 K) = 2.92. IO-’ m2 s-r D(623K)=3.52.10-gm2s-1
72R
73R .
74c 75P
Frequency response method. Quasi-static Gorsky-effect method.
298
D (298 K) = 6.3 . 10-l’ m2 s-l D (298 K) = 6.8.10-” mzs-1
75s 75v 76Bl
7.2. 1O-3
23.80
273 ..a 323
See [71S]; additions of Ag, V increased Q; additions of Ni did not.
76B2
H
1.32. 1O-3
22.40
296..a341
77H, 79Hl
H D
3.44.10-3 2.46. 1O-3
22.56 21.26
273...313
99.95% Pd foil, 0.27 mm thick. Electrochemical method. Diffusivity decreasedslightly with increasing deformation. Frequency response method.
X0
77s (continued)
Solvent element
Diffusant
H cont.
DO 10-4m2s-1
Q
kJmol-’
Temperature range Remarks K
Fig.
Ref.
Pd (continued) CL
H
T
X0
H
296
99.94 at.% Pd membranes, 0.05***0.39 mm thick. Galvano-static method. D (296 K) = 3.4. lo-” m2s-r.
78E
7.2. 10-J
23.8
273.a. 325
Circular foils, 200 ... 300 pm thick. Method as in [71S]. Effect of alloy additions studied.
78H
6.0. lO-3
24.50
273 0..923
Q, Do averaged from literature data.
78K
113
Specimen loaded with D from gas phase. Nuclear reaction D(d, p) T used to determine deuterium profile. D (113K) = 1.15. 10-16m2s-1.
78M
D
a
H
2.90. lO-3
22.19
4730.. 1548
Best fit from literature data for surface-independent methods.
21 (b)
78V2 *
CL
H
2.83 - 1O-3
21.70
742.e.1219
MARZ-grade Pd foil, 940 urn thick. Permeation time-lag method. Break in Arrhenius plot for T> 923 K, reported in [70G] not observed.
21 @I
79K
a
H
0.001 .a*1 at.%
H
H
H
2.9. lo-’
22.20
10-4 to 1 at.%
12.54 20.26
(4
295
99.999% Pd foil. Electrochemical time-lag method, on annealed and deformed specimens. D (295 K, annealed) = 3.2 . IO- 11 mz s- l, independent of H cont.; D (deformed) decreases rapidly with decreasing H concentration.
302.e. 334
Several electrochemical methods used give excellent agreement with those from Gorsky-effect measurements.
295,322
99.999% Pd foils, annealed and cold-worked. Electrochemical method. Solubility is drastically enhanced at low concentration of H in deformed specimen while diffusivity decreases.
81K1, 81M2
130...220 220...270
99.98% Pd. foil, loaded to x 41 at.% with H (P-phase).Quasi-static Gorsky-effect method. Break observed in Arrhenius plot at x 220 K.
81Ml
80Kl
21 (b) (4
80K2
u
H
u
T
210-3
,%1.5. 10-3
21.48
279..-335
Annealed and cold-rolled specimens. Electrochemical method. Q independent of H concentration for both specimen conditions; Q (annealed) slightly lower than Q (cold-worked).
81S
x 17.50
283...323
Annealed and cold-rolled specimens. Tritium method [71S] to study influence of traps on H diffusivity. Conclude dislocation cores act as trap sites, with binding energy w 18 kJ mol- ‘.
83s
Mossbauer method, using “Fe. H diffusion in region of substitutional Fe impurity is measured.
84W
280.~. 365
Pd foil, 212 pm thick, annealed and cold-rolled. Improved electrochemical methods used. Diffusivity in deformed material decreaseswith decreasing H concentration.
842
570
Cylindrical specimen. Absorption rate measured with capacitance-dilatometer. D (570 K) = 2.95 . 10m9m2 s-l. No change on application of a 10T magnetic field.
85V
77 . . .300
PdHo.,, and PdD,.,, single crystals. Ultrasonic relaxation method. Inverse isotope effect noted.
86L
293
99.99% Pd foils, 0.05 mm thick. Galvanostatic permeation method. Dislocation density varied by CLp B transformations. D (293 K) z 4.2. IO-” m2 s-l.
87B
66G
at. %
P
H
u
H
37at.% 44 at.% 45 at.% lo-4...1
22.29 22.29 24.22 2.6. 1O-3
21.80
at. %
Pt
u
H
P
H D
u
H
22.38 21.13
H
(4.5. 10-y
40.19
323 ... 353
Pt foil, 0.02.. .0.05 mm thick. Electrochemical permeation time-lag method. D (343 K) = 3.4.10-l’ m2 s-l. Do value in parentheses is inferred from a single measurement of D at 343 K and from a measurement of Q.
H
6.0. 1O-3
24.70
600...900
99.999% Pt single crystal disc, 0.15 ... 1.9 mm thick, [IOO] orientation. Electrochemical permeation time-lag method. At 750 K, D (H)/D (D) = 1.16.
22 (2)
68E (continued)
Solvent element
Diffusant
H cont.
DO 10-4m2s-1
kJmol-’
Q
Temperature range K
2.25.10-s
105.1
773.a.873
Remarks
Fig.
Ref.
Pt (continued) H
303
H
H
6.47. 1O-3
26.3
H H
831 .a. 1209
279.e.333 0.05 at.%
8.41 . 1O-2
44.79
284.e. 330
78C “Technically pure” Pt strip, 0.2 mm thick. Diffusion-elastic method. D (303K) = 2.3. IO-l3 m2s-‘. MARZ grade Pt polycrystalline discs, 0.835 mm thick. Electrochemical permeation time-lag method. Pt membranes, galvanostatically charged. Electrochemical permeation method. MARZ grade Pt foils, 25 urn thick. Electrochemical pulse permeation method.
79c
22 (0
79K
81s 22 (3)
851
9.4.11 Noble metals Cu, Ag, Au cu
H
6.8. 10-s
47.31
523...800
99.92% Cu. Desorption method.
55R
H
1.10.10-2 1.15.10-s 6.2. lO-3
38.52
533...923
Desorption method.
40.82 37.85
698...913
99.999% Cu single crystal. Desorption method.
57E 65E
1253
Sievert’s cell. D (1253 K) = 2.32 . 10e8 m2 s-r. Calculated Q.
H D H H H
2.29.10-s
H D T H D
1.13 * 10-s 7.3 * 10-s 6.12. 1O-3 1.06. 1O-2 7.8. 1O-3
H H
5.75.10-J 1.69. lO-3
38.59 47.28 38.88 36.82 36.50 38.43 38.59 37.26 29.98
800... 1000 723..-1198 723 a.. 1073 723 ..a 1073 473.s. 573
99.999% Cu single crystal sphere. Desorption method. Permeation time-lag method.
23
66s 67N 68B 71K
72P, 73P 73K
773.a. 1073 Permeation method.
*
73s
1.06. lo-’ 1.1 . 10-Z
38.43 41.20
1.0. 10-Z
33.91 47.10
2.54. IO-’
75T
770... 1356 573...873
75v 76C, 77C
Permeation method.
43.40
273...300
99.999% Cu single crystal wire. Q determined from resistivity recovery measurements on quenched-annealed specimens.
76W
Do and Q values averaged from selected literature data.
78Kl
H
6.45. lo-’
35.60
555 ... 1356
H
1.1 . 10-Z
38.46
705 . ..924
H
1.1 . 10-Z
35.17
573..-973
Steady-state permeation method. Absorption enhanced by prior dissociation of H, molecules.
H
3.69. 1O-3
36.82
292*..339
Electrochemical permeation method. Cold-worked specimen exhibited higher Q.
300
99.999% Cu foil. Electrochemical method. D(300K)=2.3~10-‘3m2s-‘.
23 (4
79B 79K
23 (5)
82s 85D
H
2.11 .10-Z
44.53
299v.e323
99.9995% Cu foil, 25 urn thick; Pd-coated. Electrochemical pulse method. Do and Q obtained from least-squares fit to present results and those in [71K], [82S], [79B], [76P].
H
9.0. 10-a
43.5
260... 1000
Electrochemical and gas-phase permeation.
86H
H
1.96. 1O-3
28.8
500 ... 1000
Permeation through duplex-membranes.
86T
H
2.82. 1O-3
31.40
661 ... 873
Ag spherical specimen, 2 cm diameter. Desorption method.
373...973
“Super pure” Ag foil, 1 mm thick. Desorption of 4 . IO’l T ions/cm’ implanted at 40 keV; monitored by radioactivity measurements. Release rates lower than in undamaged material.
T
H H L
74G
Permeation method.
500*..740
H
Ag
473.~~873
x 0.05 at.%
23 (6)
24 (2)
851
58E 67M
8.55. 1O-3
30.11
947... 1123
MARZ grade Ag foils, 0.74 mm thick. Permeation time-lag method.
24 (1)
79K
8.4. 1O+5
77.10
28O.s.330
MARZ grade Ag foil, 75 urn thick. Electrochemical current-pulse permeation method.
24 (3)
851
Solvent element
Diffusant
Au
H
H cont.
DO
Fig.
Ref.
10-4m2s-’
kJ mol-’
Q
Temperature range Remarks K
5.6. 1O-4
23.61
773.+.1213
“Fine” Au polycrystalline spherical specimen, 1.6 and 3.0 cm diameter, grain size about 1 mm. Desorption method.
62E
54 . . .80
523.a.873
99.99% Au foils, 0.25 mm thick. Cold-worked as well as annealed foils measured by steady-state permeation and by desorption methods. Conclude deuterium interacts with lattice imperfections.
76C
298
Au membranes and rods. Absorption and electrochemical permeation. D(298K)=5~10-16m2s-*.
77Cl,77C2
D
H
H
1.4 * 10-J
20.51
523 ... 673
Au foils. Permeation time-lag method. H, is dissociated (“atomized”) in gaseous phase to avoid adsorption as rate determining step.
79K, 741
H
4.67. 1O-4
29.63
280-e. 330
MARZ grade foils, 25 urn thick. Electrochemical current-pulse permeation method.
8511
H
4.67. 1O-4
29.63
5.08.10+
22.74
99.9995% Au foil, 25 urn thick. Method as in [8511]. Foils quenched from 1248 K and subsequently aged show changes in Do, Q attributed to H-vacancy trap interactions.
4.42. 1O-4 1.11 .10-s 4.43.10-s 7.02.10+
35.60 26.58 27.71 23.78
Annealed (280 ... 335) Asquenched (280 ... 335) Aged at: 348 473 573 673
25
8512 *
9.4.12 Zinc group metals Zn, Cd, Hg Data available only for Zn. Zn
H
5.8 +1O-3 4.2. 1O-3
5.86 9.21
323.a.523 323 ... 523
99.99% Zn. 99.9% Zn.
68W
H
8.5. IO-*
18.62
298 . . a344
99.99% Zn single crystal. Diffusion perpendicular to c axis.
72K
9.4.13 Aluminum group metals Al, Ga, In, Tl Data available only for Al. Al
H
1.2. lo+5
140
673...773
99.99% Al. Desorption method.
55R
H
2.1 . 10-l
45.63
743...863
99.5 . . .99.994 % Al spheres and cylinders. Desorption method. No significant effect of specimen purity observed.
57E
H
1.1 . 10-l
40.95
673 ... 873
99.999% Al spheres and cylinders. Desorption method.
26 (2)
61E
H
2.of1o-2
50.24
843...903 (740 . . .870)
Al cylinders. Desorption method. (T-range values in parentheses are from Fig. 26, curve 5)
26 0
67M1, 69M
H
1.2. 10-i
60.71
723...873
Desorption and absorption methods on oxidized and unoxidized specimens.
75A
H
2.5. IO-’
90.0
723...863
99.8% Al rods, 12 mm diameter. Desorption method.
77P
H
4.58. lo-’
37.03
623.e.925
99.99% Al. Desorption method. D decreasedif specimens were melted and solidified in a mold prior to measurements. Attributed effect to voids.
T
(i) 2. 10m3 (ii) 9 . 10e3
(i) 42.6 (ii) 51.8
(i) 338 a..472 (ii) 423 . . .796
99.5 % Al cylinders, 6 mm diameter. Tritium tracer introduced by (i) recoil injection using 3He (n, p) T reaction, or (ii) absorption from gas. Diffusivities determined from (i) sectioning, (ii) desorption.
H
1.9. 10-i
40.0
730.~. 863
99.999% Al rods, 10 mm diameter. Hydrogen loaded by solidifying rods in air. Desorption method. Attributes discrepancy with earlier study [77P] to impurities.
26 (4
81P
H
1.01 .10-i
47.70
723..-898
99.995% Al cylinders, 1.25 cm diameter; grain size z 4 mm. Specimen H-charged, electro-polished prior to desorption measurements in UHV system.
26 (4)
820
26 (3)
791,801
81N
(continued)
Solvent element Al
Diffusant
H cont.
DO IOV4mZs-’
kJmol-’
Q
Temperature range Remarks K
2.6 . IO- *
58.86
573 ..a 673
8.5 . IO-’ 9.3 . 10-l 5.3 . 10-l
43.9 48.5 62.7
459.a.525 549.a.654 654.a.753
9.2 . lo- ’
55.25
285.e.296
Fig.
Ref.
26 (7)
83H
(continued) H
AI-U
T
wt.% Li 0.02 0.26 1.12
99.9999%, zone-refined Al discs, 50 *.- 500 urn thick. Both gas-phase and electrochemical charging methods used. Diffusivity calculated from time dependence of permeation rate, measured with a quadrupole mass spectrometer. Q value close to that for vacancy migration in Al, suggests H-vacancy complex at high temperatures. Alloys prepared from 99.99% Al. Foils 0.5 mm thick. Tritium introduced by recoil injection, using 3He(n, p) T and 6Li (n, CL)T reactions. Cont. profiles of T obtained by etch-sectioning and T &activity measurements used to determine diffusivity. 99.995% Al foil, 25 pm thick. Electrochemical pulse permeation time-lag method. Suggest that these results, along with [81P], [6IE], [57E] and [801] refute conclusion of H-vacancy interaction [83H].
83N
26 (8)
861 *
9.4.14 Group IVB metals Sn, Pb Data available only for Pb. Pb
298
H
Re-evaluation of literature data on permeation gives 1.2. 1O-1o 5 D (298 K) 5 8.7.10-l’ m’s-‘.
7oc
9.4.15 Actinide group metals AC, Th, Pa, U, Nb, Pu, etc. Data available for Th and U. Tha UU
H H
2.92. IO-3 I.95 * 10-2
40.82 46.32
573.a.1173 72O.e.940
B Y
::
3.3. 10-4 1.5. 10-J
Y
H
I.9 * 10-t
15.07 47.73 48.53
933 .a. 1023 1023 ... 1273 1020... 1250
Desorption and absorption method.
27
60P * 58M, 68M 68M
U spheres, I.22 mm radius; desorption method.
73P
Solvent element Al
Diffusant
H cont.
DO IOV4mZs-’
kJmol-’
Q
Temperature range Remarks K
2.6 . IO- *
58.86
573 ..a 673
8.5 . IO-’ 9.3 . 10-l 5.3 . 10-l
43.9 48.5 62.7
459.a.525 549.a.654 654.a.753
9.2 . lo- ’
55.25
285.e.296
Fig.
Ref.
26 (7)
83H
(continued) H
AI-U
T
wt.% Li 0.02 0.26 1.12
99.9999%, zone-refined Al discs, 50 *.- 500 urn thick. Both gas-phase and electrochemical charging methods used. Diffusivity calculated from time dependence of permeation rate, measured with a quadrupole mass spectrometer. Q value close to that for vacancy migration in Al, suggests H-vacancy complex at high temperatures. Alloys prepared from 99.99% Al. Foils 0.5 mm thick. Tritium introduced by recoil injection, using 3He(n, p) T and 6Li (n, CL)T reactions. Cont. profiles of T obtained by etch-sectioning and T &activity measurements used to determine diffusivity. 99.995% Al foil, 25 pm thick. Electrochemical pulse permeation time-lag method. Suggest that these results, along with [81P], [6IE], [57E] and [801] refute conclusion of H-vacancy interaction [83H].
83N
26 (8)
861 *
9.4.14 Group IVB metals Sn, Pb Data available only for Pb. Pb
298
H
Re-evaluation of literature data on permeation gives 1.2. 1O-1o 5 D (298 K) 5 8.7.10-l’ m’s-‘.
7oc
9.4.15 Actinide group metals AC, Th, Pa, U, Nb, Pu, etc. Data available for Th and U. Tha UU
H H
2.92. IO-3 I.95 * 10-2
40.82 46.32
573.a.1173 72O.e.940
B Y
::
3.3. 10-4 1.5. 10-J
Y
H
I.9 * 10-t
15.07 47.73 48.53
933 .a. 1023 1023 ... 1273 1020... 1250
Desorption and absorption method.
27
60P * 58M, 68M 68M
U spheres, I.22 mm radius; desorption method.
73P
Ref. p. 5561
9 The diffusion of H, D and T in solid metals (Figures)
549
Figures for 9
0.5
1.0
2.0 X?K-’
1.5 l/T-
2.5
Fig. 7. Be-T. Diffusion coefficient (T in Be) vs. reciprocal temperature [67J(Be)]. Desorption method.
2.1II-” 270 , ,
240 “C 210 II I
-T 180 I
150 I I
120 I I
2.10-8III 1.0
1.2
,o-,, 27O”C240 210 I I , I -7L I, I,,-,?7 6 .=l
90 I 1
2
1.8
.10-3K-’
2.2
-T 180 !
150 I ,
120 I ,
90 I
Lu-H,D
2
U-13
1o-13
(j&4 2.2
2.4
2.6 .10-3K-’ 2.8
1.8
l/T-
2.0
22
2.4
2.6 -lo-3 K’ 2.8
l/T -
Fig. 9(a). Lu-H. Diffusion coefficients (H in CL-Lu)vs. reciprocal temperature, parallel to the u-axis (D,), and parallel to the c-axis (D,) [87V (Lu)]. Quasi-static Gorsky-effect method.
Land&-B6rnstein New Series III/26
1.6 l/T-
Fig. 8. Ba-H. Diffusion coefticient (H in Ba) vs. reciprocal temperature [68P (Ba)]. Concentration profile obtained by sectioning, vacuum-fusion analysis.
4 -
4.10~“14 1.8 2.0
1.4
Fig. 9(b). Lu-H, D. Diffusion coefficients (H, D in a-L@ vs. reciprocal temperature, polycrystalline CL-Lu[87V(Lu)]. Quasi-static Gorsky-effect method.
Kidson
9 The diffusion of H, D and T in solid metals (Figures)
550
-1
1I 2x-s 1600 ,’ “C 800 d/s 10-s
SOC
[Ref. p. 557f.
-1
I200 ’
100
50
2e,o-,o80°C70
I
60
50
40
30
20
10
lll~/s lo-lo 1 6 -4
2
lo-” 2.8
3.0
3.2
3.1 JO-'K-' 3.6
Fig. 10(b). Ti-H. Diffusion coefficient (H in a-Ti) vs. reciprocal temperature [76B (Ti)]. Electrochemical pulse method.
lo-”
I
I
I\
1 \
II
\\
4
loq335 0.5
1.0
1.5
2.0 l/T-
Fig. 10(a). Ti-H, T. Diffusion coefticient (H, T (only curve 15) in a-Ti) vs. reciprocal temperature [83K (Ti)]. References to the numbered curves are: f: [54W (Ti)]; 2: [56K (Ti)]; 3: [58A(Ti)]; 4: (68P(Ti)]; 5: [69K(Ti)]; 6: [735(H)]; 7: [7582(D)]; 8: [75Sl (Ti)]; 9,IO: [76N(Ti); If: [76B(Ti)]; 12: [77P(Ti)J; 13: [77W (Ti)]; 14: [79D(Ti)]; 15: [83K (Ti)].
2.5
-1 lo-l'0
Zr-H
400 "C
300
250
200
150
m2/s 4 2
10-l' 8 6 t 4 Q 2
lo-" 6” 4 2
0 I
,o-‘31 1.4 1.6
I
1.8
I
I
2.0 l/l
2.2
I
.lO-'K-'
2.6
-
Fig. 12. Hf-T. Diffusion coefficient (fin a-Hf) vs. reciprocal temperature [83K (Hf)]. Concentration profiles determined by sectioning, counting B-activity.
2 1/r-
.10-3 K-1
4 Fig. 11. Zr- H. Diffusion coefficient (H in a-Zr) vs. reciprocal temperature [76M (Zr)]. Referencesto numbered curves are: I: [6OS2 (Zr)]; 2: (54s (Zr)]; 3: [57M (Zr)]; 5: [72K (Zr)]; 6: [76M (Zr)]; 7: [54G (Zr)]. Iandolt-BBmstein
New Series 111126
553
9 The diffusion of H, D and T in solid metals (Figures)
Ref. p. 558f.l
Pig. 13. V-H, D, T. Diffusion coefficients (H, D, T in V) b vs. reciprocal temperature [83Q (V)]. Quasi-static Gorskyeffect method.
-1 0 I
300 "C 100 I, II
4.10-* m2/s
-50 I
V- H,D,T
-140 I
-100 I
I
IO-" 3
12
4
6
5
40;3K-'
8
l/T-
10-a
300°C 100
-T -100
-50
0
-140
-160
-180
m2/s
10-g
4I 1o-l0
Fig. 14. Nb-H, D, T. Diffusion coefft- b lOA' cient (H, D, Tin cc-Nb)vs. reciprocal temperature. Quasi-static Gorsky-effect method. Taken from [83Q (Nb)] (T-diffusion) which includes also references for H, D diffusion (see table). v refers to lo-l2 12 [71S (Ta)].
3
5
4
6
7
8
1/T-
For Fig. 15 see next page.
10-B.
900 “C
-T 750 700 650 I I I *' 0% a,%8AO ,o A )
‘t-, . .
I 4 Q
800
l
600 I
500 I
MO-H ‘O
6
550 I ,
:
s.qA
‘\ ‘\_
2
1o-g 0.8
\.
. ‘\
0.9
1.0
1.1
1.2
.10-3K-' 1.3
l/T-
Fig. 16. MO-H. Diffusion coefficient (H in MO) vs. reciprocal temperature [82K(Mo)]. Permeation time-lag method. Different symbols refer to different specimens. Dashed curve from [60H (MO)]. Land&-Bhnstein New Series III/26
Kidson
9
10 .@K-'
12
9 The diffusion of H, D and T in solid metals (Figures)
552
300°C 100 I, II
KS*
m'h
0 -50 ,I I,
I
1 la-H,D,T
1o-l’,
-1 -100 I,
I
I
I
I
2
3
4
5
-1kO 1 I I
I
!
!
7
8
-160 I,
[Ref. p. 560f.
I
I
-180 11
I
I
9
10 *lo-3K" 12
\‘9,4 \
6 l/l-
Fig. 15. Ta - H, D, T. Diffusion cocfftcient (H, D, T in u-Ta) vs. reciprocal temperature. Quasi-static Gorsky-effect method. Taken from [83Q(Ta)] which includes further references(see table). Symbol v at x 300 K is from [71S(Ta)].
,o.72200 "C 1700
d/c
““a 6
..*
I’
1300
I
I.
1100 I
900 I
W -H
I t Qt
I
\.r\, ( h \ I
I
t ‘i -16 6 4
\
4.10-g 0.1
2
I
I
7
9
10-l’ 0.5
0.6
0.7
5
0.8 .10‘3K-' 0.9
11
13#
K-'36.1
l/T-
1/rFig. 17(a). W-H. Diffusion coefftcient (H in W) vs. reciprocal temperature [69F(W)]. References to numbered curves are: I: [69F (W)]; 2: [64R (W)].
Fig. 17(b). W-H, D. Diffusion coefticient (H, D on (110) surface of W) vs. reciprocal temperature [82D (W)]. 19is the fractional coverage of the (110) plane by the diffusants. Field emission, current-fluctuation method.
Kidson
Land&BBmsfein New Series 111126
Ref. p. 563f.l
9 The diffusion of H, D and T in solid metals (Figures) 1o-1 m2/s
-1 4.W" 1600 800 "C 400 , , II m2/s
200 II
II
100
I Q
50 II
II
I
I
0
I
lo-*
I
1o-g
2
I Q 10."O
IO-8 8 6
4.10-g 0.5
1.0
1.5
2.0 l/T-
2.5
3.0
.lO;jK-’
1o-12 0
4.0
Fig. 18(a). Fe-H. Diffusion coeffkient (H in a-Fe) vs. reciprocal temperature [82N (Fe)]. o: Gas permeation, time-lag method; l : Electra-chemical AC method. Deviation from linear plot for T < 293 K is attributed to trapping effects.
0.5
1.0
1.5
2.0 l/T-
2.5
1ur
I
m2/s
0.8
400 I ,
200 I
100 I
50 I
0 1
-40 I
Fe-H
1.2
1.6
2.0
2.4 l/T-
2.8
3.2
3.6
.10-j K-'
Fig. 18(b). Fe-H. Diffusion coeffkient (H in u-Fe) vs. reciprocal temperature measured by a variety of methods and showing the large disparities attributed to surface effects and/or trapping [83K (Fe)]. Referencesto the numbered curves are: I: [73N2(Fe)]; 2: [78QFe)]; 3: [50G(Fe)]; 4; [71D(Fe)]; 5: [63B(Fe)]; 6: [66W (Fe)]; 7: [81Y(Fe)]; 8: [75M (Fe)]; 9: [71M(Fe)]; 10: [58E(Fe)]; f1: [47S(Fe)]; 12: [74A3 (Fe)]; 13: [65M (Fe)]; [66B(Fe)]; 14: [79H(Fe)]; 15: [77K (Fe)]; 16: [74K2 (Fe)]; f 7: [61R (Fe)]; 18,18’: [70R2(Fe)]; 19, 19’: [77C(Fe)]; 20: [75Kl (Fe)]; 2f: [58Z(Fe)]; 22: [56S(Fe)]; 23: [60C(Fe)]; 24: [61L(Fe)]; 25: [6OJ (Fe)]; 26,26’, 26”: [69E2 (Fe)]; 27: [40B (Fe)]. Land&-B6rnstein New Series III/26
4.0
Fig. 19. Co-H. Diffusion coefficient (H, D in Co) vs. reciprocal temperature [85S(Co)]. Tc is the Curie temperature. References to numbered curves are: I: [66S(Co)]; 2: [85S(Co)]; 3,3’: [74C (Co)]. The dashed curve is an extrapolation of curve 2; the solid line is a best fit to combined data from [66S(Co)] and [85S(Co)]. Curves 3,3’ are for D diffusion, curves I,2 for H diffusion.
-1 A-c 800 "C
3.0 W3K-’
Kidson
9 The diffusion of H, D and T in solid metals (Figures)
[Ref. p. 566f.
-1 ,0-q 200 “C 100 I I I ’ m2/s X I
50
0
-25
I’ I-
I ’
I
-50 I(
I
---
2
lo-"0
,
I
”
6" I 4 M -
-2
lo-" 6
lo-'"I 2.0
I I
I I
r I
I I
I I
1.4
2.0
2.6
10 10-l)
“I”
3.0
3.5 1/r-
4.0
I ~10-~K-' 5.0
Fig. 21 (a). Pd-H. Diffusion coefficient (H, D in Pd) vs. reciprocal temperature [71V(Pd)]. Quasi-static Gorsky-effect method. Note the reversed isotope effect.
n\
h\b
I
0.8
2.5
8
3.2 .lO-jK-' 3.8
l/T-
Fig. 20. Ni - H. Diffusion coefticient (H in Ni) vs. reciprocal temperature [84L(Ni)]. References to the numbered curves are: I: [60E (Ni)]; 2: [29H (I%)]; 3,5,6: [7OC(Ni)]; 4,9: [75V(Ni)]; 7: [35E(Ni)]; 8: [72Rl (Ni)]; IO: [63O(Ni)]; If: [67S(Ni); 12: [84L(Ni)]. Curve 4(T> Tc) and 9(T < Tc) are the best fits to the data; Tc is the Curie temperature.
10-s 10-6 m21s 10-7
1.2
1.6
2.0
2.L
2.8
.lOV
Fig. 21 (b). Pd - H. Diffusion coefficient (H in Pd) vs. reciprocal temperature. References to numbered curves are: f: [79K (Pd)]; 3: [80K2(Pd)]. The dashed curve 2 is from the best fit of a compilation of results, taken from [78V2(Pd)].
10-s 10-s ~I lo-‘0 1o-” 10-12
10” 0.8
1.2
1.6
2.0 l/1-
2.1
2.8 .10-3K-' :
4 Fig. 22. Pt -H. Diffusion coefficient (H in Pt) vs. reciprocal temperature [85I(Pt)]. References to the numbered curves are: I: [79K (Pt)]; 2: [68E(Pt)]; 3: [85I (Pt)].
Kidson
Land&-BBmstein New Series III126
9 The diffusion
Ref. p. 571 f.]
555
of H, D and T in solid metals (Figures)
1o-7 m2/s 1o-E 10-g
I a
lo-"0 10-l'
0.8
0.8
1.2
1.6
2.0 l/T-
2.4
2.8
.@K-'
3.6
1.6
2.0 2.4 l/T-
2.8
.lOJK-'
3.6
Fig. 24. Ag-H. Diffusion coefficient (H in Ag) vs. reciprocal temperature [851(Ag)]. Referencesto the numbered plots are: I: [79K (Ag)]; 2: [58E (Ag)]; 3: [851(Ag)]. The disparities indicate the need for further studies over an extended temperature range.
Fig. 23. G-H. Diffusion coefficient (H in Cu) vs. reciprocal temperature [85I(Cu)]. References to the numbered curves are: f: [79B(Cu)]; 5: [82S(Cu)]; 6: [85I(Cu)]. The data points o are from [71K (Cu)]. Curve 6 was extrapolated beyond the measured T-range to show agreement with results from [71K (Cu)].
10-7 m*/s
24 tl-‘* m*/s
10-a
1O-l* 8 6
10-g
4
1o-l0
I a
1.2
aI 10-l'
2
lo-'*
lo-l3
4
2
IO-l4 2.9
3.0
3.1
3.2 3.3 l/T-
3.4
.10-3K-' 3.6
Fig. 25. Au-H. Diffusion coefficient (H in Au) vs. reciprocal temperature [8512(Au)]. Curve 1 is for an annealed specimen; curve 2 is for a quenched specimen. The decreasein D for the latter is attributed to trapping by vacancies.
Land&-BBmstein New Series III/26
0.8
1.2
1.6
2.0 l/T-
2.4
2.8
.105K'
3.6
Fig. 26. Al-H. Diffusion coefficient (H in Al) vs. reciprocal temperature [86I(Al)]. References to the numbered curves are: f: [81P(Al)]; 2: [61E(Al)]; 3: [8OI(Al)]; 4: [820(Al)]; 5: [67Ml (Al)]; 7: [83H (Al)]; 8: 1861(Al)]. (Curve 8 was extrapolated from the measured low temperature results; seetable).
Kidson
9.5 References for 9 (Be, Ba, Y, Lu)
556
00
0.5
1.0 1.0
1.5
2.0.10-k' 2.5
[Ref. p. 573
Fig. 27. Th -H. Diffusion coefficient (H in Th) vs. reciprocal temperature [60P(Th)]. o: Desorption method; v, A: Absorption method.
l/1-
9.5 References for 9 In this chapter 9 referencesare arranged separately for each substance, starting from Be. An asterisk (*) indicates the reference source of the parameters judged best to represent the intrinsic diffusion of hydrogen in a solvent. Be: 63P 64P 67J
Pemsler, J.P., Anderson, R.W., Rapperport, E.J.: Rep. ASD/TDR/62-1018, Pemsler, J.P., Rapperport, E.J.: Trans. Metall. Sot. AIME 230 (1964) 90. Jones, P.M.S., Gibson, R.: Rep. AWRE O-2/67, 1967.
1963.
Ba:
*68P y: 66C 12F 76F 79A 84A 87L
Peterson, D.T., Hammerberg, C.C.: J. Less-Common Met. 16 (1968) 457. Carlson, O.N., Schmidt, E.A., Peterson, D.J.: J. Less-Common Met. 10 (1966) 1. Frisius, F., Lamann, H.J., Mertins, H., Spalthoff, W., Wille, P.: Ber. Bunsenges. Phys. Chem. 76 (1972) 1216. Frisius, F., Hackbarth, H., Wille, P.: Atomkernenergie 27 (1976) 287. Anderson, D.L., Barnes, R.G., Nelson, SO., Torgeson, D.R.: Phys. Lett. 74A (1979) 427. Anderson, I.S., Heidemann, A., Bonnet, Ross,D.K., Wilson, S.K.P., McKergow, M.W.: J. Less-Common Met. 101 (1984) 405. Lichty, L., Schoeneberger,R.J., Torgeson, D.R., Barnes, R.G.: J. Less-Common Met. 129 (1987) 31.
Lu:
71B 79P 83V 86D 86V *87V
Barr&e, H., Tran, K.M.: C.R. Acad. Sci. 273B (1971) 823. Prakash, S., Bonnet, J.E., Lucasson, P.: J. Less-Common Met. 68 (1979) 1. Vajda, P., Daou, J.N., Moser, P.: J. Phys. (Paris) 44 (1983) 543. Daou, J.N., Vajda, P., Lucasson, P., Burger, J.P.: Philos. Mag. A53 (1986) 511. Vajda, P., Daou, J.N., Burger, J.P. Kai, K., Gscheider, K.A., Beaudry, J.P.: Phys. Rev. B34 (1986) 5154. Volkl, J. Wipf, H., Beaudry, B.G., Gscheider, K.A.: Phys. Status Solidi B 144 (1987) 315. Kidson
Landolt-Bornstem New Series III/26
9.5 References for 9 (Ti, Zr) Ti: 49G
50M 54w 56K 58A 60s 61s 65L 68P 69K 70Kl 70K2 70M 72P 73J 74B 75Sl 7532 *76B 76N 77P 77w 78K 79D 81B 82L 83K 85G
86Q 87s
Zr: 45s 54B 54G 54s 57M 59A 6OSl 6OS2 62C 63G 71P 72F *72K 74E 76F 76K 76M
557
Gulbransen, E., Andrew, K.: Trans. Metall. Sot. AIME 185 (1949) 741. McQuillan, A.D.: Proc. R. Sot. London A204 (1950) 309. Wasilewski, R.J., Kehl, G.L.: Metallurgia 50 (1954) 225. Kusamichi, H., Yagi, H., Yokawa, T., Noda, T.: Nihon Kinzoku Gakkaishi (J. Jpn. Inst. Met.) 20 (1956) 39. Albrecht, W.M., Mallett, M.W.: Trans. Metall, Sot. AIME 212 (1958) 204. Someno, N., Nagasaki, K.: Vat. Chem. 8 (1960) 145. Stalinski, B., Coogan, C.K., Gutowsky, H.S.: J. Chem. Phys. 34 (1961) 1191. Livanov, V.A., Bukhanova, A.A., Kolachev, B.A.: Hydrogen in Titanium. (Israel Progr. Sci. Transl.), Oxford: Pergamon Press, 1965. Papazoglov, T.P., Hepworth, M.T.: Trans. Metall. Sot. AIME 242 (1968) 682. Kolachev, B.A., Nazimov, O.P., Zhuralev, L.N.: Izv. Vyssh. Uchebn. Zaved. Tsvetn. Metall. 12 (1969) 104. Khazakov, D.N., Khokrin, V.M., Kunin, L.L., Ozhegov, P.I., Priselkov, Yu. A.: Zavod. Lab. 36 (1970) 441. Korn, C., Zamir, D.: J. Phys. Chem. Solids 31 (1970) 489. McQuillan, A.D.: J. Chem. Phys. 53 (1970) 156. Philips, I.I., Poole, P., Shrier, L.L.: Corros. Sci. 12 (1972) 855. Johnson, D.L., Nelson, H.G.: Metall. Trans. 4 (1973) 569. Brauer, E., Nann, E.: Werkst. Korros. 25 (1974) 309. Shah, K.K.: Thesis, Univ. Nebraska, USA, 1975. Sukhotin, A.M., Antonavskaya, E.J., Skibnev, E.V., Kornilov, I.I., Nartova, T.T., Magutova, T.V., Shulman, A.K.: Zashch. Met. 11 (1975) 430. Brauer, E., Doerr, R., Ziichner, H.: Z. Phys. Chem. NF 100 (1976) 109. Nazimov, O.P., Zhuralev, L.N.: Izv. Vyssh. Uchebn. Zaved. Tsvetn. Metall. 1 (1976) 160. Park, YK., Lee, L.J., Kim, C.H.: J. Korean Inst. Met. 15 (1977) 338. Waisman, J.L., Sines, G., Toosky, R.F.: Hydrogen in Metals (2nd. Int. Congr. Paris, 1977), Oxford: Pergamon Press, 4 (1977) No. 1 C 11. Katlinski, V.M.: Izv. Akad. Nauk SSSR., Neorg. Mater. 14 (1978) 1674. Doerr, R., Brauer, E., Gruner, R., Rauch, F.: Z. Phys. Chem. NF 116 (1979) 1. Brauer, E., Doerr, R., Gruner, R., Rauch, F.: Corros. Sci. 21 (1981) 449. Lin, L.Y, Huang, X.Y., Li, YK., Hsiao, C.M: Ser. Metall. 16 (1982) 1397. Kunz, W., Miinzel, H., Helfrich, U., Horneff, H.: Z. Metallkd. 74 (1983) 289. Grunner, R., Streb, B., Brauer, E.: Titanium: Scienceand Technology. (Proc. 5th. Int. Conf. on Ti.) 4 (1985) 2571. Quach-Kamimura, T.H., David, D.: J. Less-Common Met. 125 (1986) 59. Shoesmith, M.: unpublished. Schwartz, C.M., Mallett, M.W.: Trans. Am. Sot. Met. 41 (1945) 306. Belle, J., Cleland, B., Mallett, M.W.: J. Electrochem. Sot. 101 (1954) 211. Gulbransen, E.A., Andrew, K.F.: J. Electrochem. Sot. 101 (1954) 560. Schwartz, C.M., Mallett, M.W.: Trans. Am. Sot. Met. 46 (1954) 640. Mallett, M.W., Albrecht, W.M.: J. Electrochem. Sot. 104 (1957) 142. Albrecht, W.M., Goode, W.D.: Rep. Battelle Memorial Inst. BMI-1573 (1959) 10. Sawatzky, A.: J. Nucl. Mater. 2 (1960) 62. Someno, M.: Nihon Kinzoku Gakkaishi (J. Jpn. Inst. Met.) 24 (1960) 249. Cupp, C.R., Flubacher, P.: J. Nucl. Mater. 6 (1962) 213. Galezunas, V.L.: J. Electrochem. Sot. 110 (1963) 799. Paetz, P., Liicke, K.: Z. Metallkd. 62 (1971) 657. Frisius, F., Lahann, H.J., Mertins, H., Spalthoff, W., Willie, P.: Ber. Bunsenges. Phys. Chem. 76 (1972) 1216. Kearns, J.J.:J. Nucl. Mater. 43 (1972) 330. Elleman, T.S., Austin, J. H., Verghese, K.: J. Nucl. Mater. 51 (1974) 321. Frisius, F., Hackbarth, H., Willie, P.: Atomkernenergie 28 (1976) 225. Kubachewski, 0.: At. Energy. Rev. 6 (1976) 263. Mazzolai, EM., Ryll-Nardzewski, J.: J. Less Common Met. 49 (1976) 323.
Land&-Biirnstein New Series III/26
Kidson
558
9.5 References for 9 (Zr, Hf, V, Nb)
82K 87s
Kharatyan, S.L. et al.: Russ. Metall. 1 (1977) 39. Katlinskii, V.M.: Izv. Akad. Nauk SSSR., Neorg. Mater. 14 (1978) 1674. Greger, G.U., Miinzel, H., Kunz, W., Schwierczinski, A.: J. Nucl. Mater. 88 (1980) 15. Sawatzky, A., Ledoux, G., Tough, R.L., Cann, C.D.: Metal-Hydrogen Systems (Proc. Intl. Symp., Miami, 1981) T. Nejat Vezirdglu (ed.), Oxford: Pergamon Press, 1981. Kunz, W., Miinzel, H., Helfrich, U.: J. Nucl. Mater. 105 (1982) 178. Stem, A., Khatamian, D., Laursen, T.: J. Nucl. Mater. 148 (1987) 257.
Hf: *83K
Kunz, W, Miinzel, H., Helfrich, U., Horneff, H.: Z. Metallkd. 74 (1983) 289.
77K 78K 80G 8IS
v: 69C 7oc 70s 7ov 71D 72G 73B 74A 76B 76H 77E 77v 772 78F 78V 79s *83Q 83s 83W 8% Nb: 57P 59A 64R 66C 68SI 68S2 68V 69C 69M 7oc 70G 70R *7os *7ov 7ow 71c 71D 71K 710 71s
Cantelli, R., Mazzolai, EM., Nuovo, M.: Phys. Status Solidi 34 (1969) 597. Cantelli, R., Mazzolai, EM., Nuovo, M.: J. Phys. Chem. Solids 31 (1970) 1811. Schaumann, G., Volkl, J., Alefeld, G.: Phys. Status. Solidi 42 (1970) 401. Volkl, J., Schaumann, G., Alefeld, G.: J. Phys. Chem. Solids 31 (1970) 1805. Doremus, R.H.: J. Phys. Chem. Solids. 32 (1971) 2211. de Graaf, L.A., Rush, J.J.,Flotow, HF., Rowe, J.M.: J. Chem. Phys. 56 (1972) 4574. Boes, N., Ziichner, H.: Phys. Status Solidi 17A (1973) K 111. Abe, F., Hanada, R., Kimura, H.: Ser. Metall. 8 (1974) 955. Boes, N., Ziichner, H.: Z. Naturforsch. 31 A (1976) 760. Heller, R., Wipf, H.: Phys. Status Solidi 33 A (1976) 525. Eguchi, T., Morozumi, S.: Nihon Kinzoku Gakkaishi (J. Jpn. Inst. Met.) 41 (1977) 795. Viilkl, J., Bauer, H.C., Freudenberg, U., Kokkinidus, M., Lang, G., Steinhauser, K.A., Alefeld, G.: International Friction and Ultrasonic Attenuation in Solids (Proc. Int. Conf., Tokyo, 1977). Univ. of Tokyo Press, 1977, p. 485. Zeilinger, A., Pochman, W.A.: J. Phys. F 7 (1977) 575. Freudenberg, U., Volkl, J., Bressers,J., Alefeld, G.: Ser. Metall. 12 (1978) 165. Volkl, J., Alefeld, G.: Hydrogen in Metals I., Alefeld, G., Volkl, J. (eds.), Topics in Applied Physics, 28 (1978) 321. Schober, H.R., Lottner, V.: Z. Phys. Chem. NF 114 (1979) 203. Qi, Zh., Volkl, J., Lasser, R., Wenzl, H.: J. Phys, F 13 (1983) 2053. Suzuki, T., Namazue, H., Koike, S., Hayakawa, H.: Phys. Rev. Lett. 51 (1983) 798. Wipf, H.: DIMET-82 (Proc. Int. Conf., Tihany, Hungary, 1982) Kedves, F.J., Beke, D.L. (eds.), Diffusion and Defect Monogr. 7 (1983) 209. Sakamoto, Y, Baba, K., Suehiro, T.: Ser. Metall. 19 (1985) 871. Paxton, H.W., Sheehan, J.M.: Rep. No. NYO-8040 (A.E.C.), 1957. Albrecht, W.M., Goode, W.D., Mallett, M.W.: J. Electrochem. Sot. 106 (1959) 981. Ryabchikov, L.N.: Ukr. Fiz. Zh. 9 (1964) 293. Cannelli, G., Verdini, L.: Ric. Sci. 36 (1966) 246. Schiller, P., Schneiders,A.: Vacanciesand Interstitials in Metals (2nd. Int. Conf., Jiilich), 1968,p. 881. Schaumann, G., VBlkl, J., Alefeld, G.: Phys. Rev. Lett. 21 (1968) 891. Verdan, G., Rubin, R., Kley, W.: Neutron Inelastic Scattering (4th. I.A.E.A. Symp., Copenhagen) 1968, p. 223. Cantelli, R., Mazzolai, EM., Nuovo, M.: Phys. Status Solidi 34 (1969) 597. Mazzolai, EM., Nuovo, M.: Solid State Commun. 7 (1969) 103. Cantelli, R., Mazzolai, EM., Nuovo, M.: J. Phys. Chem. Solids 31 (1970) 1811. Gissler, W., Alefeld, G., Springer, T.: J. Phys. Chem. Solids 31 (1970) 2361. Rubin, R., Claessen,Y.: Solid State Commun. 8 (1970) 1321. Schaumann, G., Viilkl, J., Alefeld, G.: Phys. Status Solidi 42 (1970) 401. Volkl, J., Schaumann, G., Alefeld, G.: J. Phys. Chem. Solids 31 (1970) 1805. Wert, C., Thompson, D.O., Buck, 0.: J. Phys. Chem. Solids 31 (1970) 1793. Charlot, L.A., Westerman, R.E.: Rep. BNWL-1604, 1971, p. 72. Doremus, R.H.: J. Phys. Chem. Solids 32 (1971) 2211. Kistner, G., Rubin, R., Sosnowska, I.: Phys. Rev. L&t. 27 (1971) 1576. Ogurtani, T.0.: Metall. Trans. 2 (1971) 3035. Sicking, G., Buchold, H.: Z. Naturforsch. 26A (1971) 1973. Kidson
Land&-B6mstein New Series III/26
9.5 References for 9 (Nb) 72Bl 72B2 72C 72H 72Ll 72L2 72Sl 7282 72s 72v 72Wl 72W2 72W3 73A 73Bl 73B2 73B3 73s 74B 74c 74E 74K 74Ml 74M2 74P 74w 75A 75E 75H 751 75K 75s *75v 76A 76B 76Cl 76C2 76L 76R 76W 77B 77c 77E 77Ml 77M2 77R 77v 772
559
Birchall, J.H.L., Ross, D.K.: Hydrogen in Metals (Int. Conf., Ji.ilich), JUL-Conf-6. 1 (1972) 313. Birnbaum, H.K., Wert, C.A.: Ber. Bunsenges. Phys. Chem. 76 (1972) 806. Cotts, R.M.: Ber. Bunsenges. Phys. Chem. 76 (1972) 760. Hickman, R.G.: Rep. UCRL-74057 Rev. 2, 1972. Liitgemeier, H., Arons, R.R., Bohn, H.G.: J. Magn. Reson. 8 (1972) 74. Ltitgemeier, H., Bohn, H.G., Arons, R.R.: J. Magn. Reson 8 (1972) 80. Stump, N., Gissler, W., Rubin, R.: Phys. Status Solidi 54B (1972) 295. Stump, N., Gissler, W., Rubin, R.: Hydrogen in Metals (Int. Conf., Jiilich, 1972), JUL-Conf-6. 1 (1972) 375. Sussman, J.A., Weismann, Y: Hydrogen in Metals (Int. Conf., Jiilich, 1972) JUL-Conf-6. 2 (1972) 744. Volkl, J.: Ber. Bunsenges. Phys. Chem. 76 (1972) 797. Wipf, H.: Dissertation, Univ. of Mtinchen, FRG, 1972. Wipf, H.: Ber. Kernforschungsanlage Jtilich 6 (1972) 437. Wipf, H.: Hydrogen in Metals (Int. Conf., Jiilich, 1972), JUL-Conf-6. 2 (1972) 437. Abraham, P.M. et al.: Rep. ORO-3508-9, 1973. Baker, C., Birnbaum, H.K.: Acta Metall. 21 (1973) 865. Boes, N., Ziichner, H.: Phys. Status Solidi 17A (1973) K 111. Boes, N., Ziichner, H.: Ber. Bunsenges. Phys. Chem. 77 (1973) 708. . Sakamoto, K.: J. Iron Steel Inst. Jpn. (Tetsu to Hagane) 59 (1973) A153. Boes, N.: Dissertation, Univ. of Mtinster, FRG, 1974. Charlot, L.A., Johnson, A.B., Westerman, R.E.: AEC Symp. Ser 31 (1974) 970. Elleman, T.S., Verghese, K.: J. Nucl. Mater. 53 (1974) 299. Kutner, R., Sosnowska, I.: Acta Phys. Pol. 46A (1974) 755. Matusiewicz, G., Booker, R., Keiser, J., Birnbaum, H.K.: Ser. Metall. 8 (1974) 1419. Miinzing, W., Viilkl, J., Wipf, H., Alefeld, G.: Ser. Metall. 8 (1974) 1327. Pennington, C.W., Elleman, TX, Verghese, K.: Nucl. Technol. 22 (1974) 405. Wipf, H., Alefeld, G.: Phys. Status Solidi 23A (1974) 175. Alefeld, G., VBlkl, J., Wipf, H.: Ser. Metall. 9 (1975) 1095. Elleman, T.S., Verghese,K.: Tritium Technol. Relat. Fusion React. Syst. (Proc. Symp., 1974), Smith, W.H., Wilkes, W.R., Wittenberg, L.J. (eds.), 1975. Hanada, R.: Effect of Hydrogen on Behavior of Mater. (Int. Conf., Jackson Lake, Wyoming, 1975), New York: AIME, 1976, p. 676. Iijima, Y, Hirano, K.: Bull. Jpn. Inst. Met. 14 (1975) 599. Kehr, K.W.: Rep. JUL-1211, KFA Jtilich, 1975. Sakamoto, K.: Bull. Jpn. Inst. Met. 14 (1975) 333. Viilkl, J., Alefeld, G.: Diffusion in Solids; Recent Developments. Nowick, A.S., Burton, J.J.(eds.), New York: Academic Press, 1975, p. 231. Abraham, P.M., et al.: Rep. ORO-3508-10, 1976. Boes, N., Zi.ichner, H.: Z. Naturforsch. 31 A (1976) 760. Cantelli, R.: Metall. Ital. 68 (1976) 361. Chandra, D., Elleman, TX, Verghese, K.: J. Nucl. Mater. 59 (1976) 263. Lubchenko, A.F., Pavlovich, V.N., Fishchuk, 1.1.:Fiz. Met. Metalloved. 42 (1976) 1127. Phys. Met. Metallogr. (English Transl.) 42 (1976) 1. Richter, D., Tiipler, J., Springer, T.: J. Phys. F 6 (1976) L93. Westlake, D.J., Ockers, S.T., Regan, D.W: J. Less-Common Met. 49 (1976) 341. Birnbaum, H.K. et al.: Hydrogen in Metals. (2nd Int. Congr., Paris 1977), Oxford: Pergamon Press, 3 (1977) IBl. Cannelli, G., Cane& R.: Hydrogen in Metals (2nd Int. Congr., Paris, 1977), Oxford: Pergamon Press, 3 (1977) lB2. Eguchi, T., Morozumi, S.: J. Jpn. Inst. Met. 41 (1977) 795. Matusiewicz, G., Birnbaum, H.K.: J. Phys. F 7 (1977) 2285. Mazzolai, EM., France, R.: Hydrogen in Metals (2nd Int. Conf., Paris 1977), Oxford: Pergamon Press, 6 (1977) 2Cl. Richter, D., Alefeld, G., Heidemann, A., Wakabayashi, N.: J. Phys. F. 7 (1977) 569. VBlkl, J. et al.: International Friction and Ultrasonic Attenuation in Solids (Proc. 6th Int. Conf., Tokyo 1977), Tokyo: Univ. Tokyo Press, 1977, p. 485. Zeihnger, F., Pochman, WA.: J. Phys. F 7 (1977) 575.
Land&-Biirnstein New Series III/26
Kidson
9.5 References for 9 (Nb, Ta)
560
78Bl 78B2 78L
Bauer, H.C., Vblkl, J., Tretkowski, J., Alefeld, G.: Z. Phys. B29 (1978) 17. Bees, N., Wicke, E.: Ber. Bunsenges.Phys. Chem. 82 (1978) 356. Lottner, V. et al.: Neutron Inelastic Scattering (Proc. Symp. Vienna 1977), Vienna: IAEA, 2 (1978) 339.
78s *78V
Skiild, K.: Hydrogen in Metals I., Alefeld, G., Volkl, J. (eds.), Topics in Appl. Phys. 28 (1978) 267. Volkl, J., Alefeld, G.: Hydrogen in Metals I., Alefeld, G. Volkl, J. (eds.), Topics in Appl. Phys 28 (1978) 321.
79D 79E 79F 79Ll 79L2 79s 79v 8OP 8OZ 81W
82Q 82T *83Q 83Sl 8382 84Wl 84W2 85L 85M 85s 85T 85V 86K 87P 88s
Dais, S., Messer, R.: Z. Phys. Chem. NF 115 (1979) 177. Engelhard, J.: J. Phys. F 9 (1979) 2217. Fukai, Y, Kubo, K., Kazama, S.: Z. Phys. Chem. NF 115 (1979) 181. Lottner, V. et al: J. Phys. Chem. Solids 40 (1979) 557. Lottner, V., Heim, A., Springer, T.: Z. Phys. 32B (1979) 157. Schrober, H.R., Lottner, V.: Z. Phys. Chem. NF 114 (1979) 203. Viilkl, J., Alefeld, G.: Z. Phys. Chem NF 114 (1979) 123. Peterson, D.T., Jensen, C.L.: Metall. Trans. 11A (1980) 627. Zapp, P.E., Birnbaum, H.K.: Acta Metall. 28 (1980) 1523. Wipf, H., Magerl, A., Shapiro, S.M., Satija, S.K., Thomlinson, W.: Phys. Rev. Lett. 46 (1981) 947. Qi, Zh., Volkl, J., Wipf, H.: Ser. Metall. 16 (1982) 859. Tonks, D.L., Silver, R.N.: Phys. Rev. B 26 (1982) 6455. Qi, Zh., Volkl, J., Lassner, R., Wenzel, H.: J. Phys. F 13 (1983) 2053. Sherman, R., Birnbaum, H.K.: Metall. Trans. A 14A (1983) 203. Shirley, A.I., Hall, C.K., Prince, N.J.: Acta Metall. 31 (1983) 985. Wagner, F.E., Priibst, F., Wordel, R., Zelger, M.: Properties and Applications of Metal Hydrides. (Int. Symp. IV, Eilat, Israel), 1984. Wipf, H., Neumaier, K., Magerl, A., Heidemann, A., Stirling, W.: J. Less-Common Met. 101 (1984) 317. LHsser,R.: Z. Phys. Chem. NF 143 (1985) 23. Messer, R., Hopfel, D., Schmidt, C., Seeger,A., Zag, W., Liisser, R.: Z. Phys. Chem. NF 145 (1985) 179. Sakamoto, Y, Baba, K., Suehiro, T.: Ser. Metall. 19 (1985) 871. Teichler, H., Klamt, A.: Phys. Lett. 108A (1985) 281. Verbruggen, A.H., Lont, A., Griessen, R.: J. Phys. F 15 (1985) 1901. Klampt, A., Teichler, H.: Phys. Status Solidi B134 (1986) 533. Pusch. A., Fenzl, W., Peisl, J.: J. Less-Common Met. 129 (1987) 305. Sohn, K.S., Park, T.S., Kim, S.W.: Phys. Rev. B37 (1988) 1155.
Ta:
SOGI 50G2
5lG 58T 59c 60K 61H 61s 62M 65M 65P 66Cl 66C2 66M 67J
Garstens, M.A.: Phys. Rev. 79 (1950) 397. Gulbransen, E.A., Andrew, K.F.: Trans. Metall. Sot. AIME 188 (1950) 586. Garstens, M.A.: Phys. Rev. 81 (1951) 288. Torrey, H.C.: Nuovo Cimento Suppl. 9 (1958) 95. Cheselsky, F.J., Wallace, W.E., Hall, W.K.: J. Phys. Chem. 63 (1959) 505. Klyacho, Yu. et al.: Izv. Akad. Nauk SSSR 49 (1960) 1. Hall, W.K., Wallace, W.E., Cheselsky, F.J.: J. Phys. Chem. 65 (1961) 128. Spalthoff, W.: Z. Phys. Chem. 29 (1961) 258. Mallett, M.W., Koehl, B.G.: J. Electrochem. 109 (1962) 968. Makrides, A.C., Wright, M., McNeil, R.: Final Rep. Contract No. DA-49-186-AMC-136 (D), Harry Diamond Lab., 1965. Pedersen, B., Krogdahl, T., Stokkeland, O.E.: J. Chem. Phys. 42 (1965) 72. Cannelli, G., Verdini, L.: Ric. Sci. 36 (1966) 98. Cannelli, G., Verdini, L.: Ric. Sci. 36 (1966) 246. Merisov, B.A., Khotkevich, V.I., Karnus, A.I.: Fiz. Met. Metalloved. 22 (1966) 308; Phys. Met. Metallogr. (English Transl.) 22 (1966) 163. Jewett, D., Makrides, A.C.: Tyco Lab. Rep.; U.S. Dept. Comm. Clearinghouse, Fed. Sci. Techn. Info. No. N67-30359,
67s 692 70H
1967.
Stalinski, B., Zogal, O.J.: Colloq. Int. C.N.R.S. 157 (1967) 483. Ziichner, H., Wicke, E.: Z. Phys. Chem. NE 67 (1969) 154. Holleck, G.L.: J. Phys. Chem. 74 (1970) 1957. Kidson
Landolt-Btimstein New Series Ill/26
9.5 References for 9 (Ta) *7os 7lC 71H 71M 71s 72B 72Cl 72C2 72Gl 7262 7263 72H 72K 72V 72W 7221 7222 73Bl 73B2 73c 73Gl 7302 73Hl 73H2 73K 73R 74K 74Ml 74M2 74R 74T 742 75A 7511 7512 75K 75M 75v 76Bl 76B2 76C 76Hl 76H2 76W 77E 77H
561
Schaumann, G., Viilkl, J., Alefeld, G.: Phys. Status Solidi 42 (1970) 401. Cantelli, R., Mazzolai, EM., Nuovo, M.: J. Phys. (Paris) 32, Suppl. 7 (1971) C2:59. Herold, A., Mar&he, J.F., Rat, R.C.: C. R. Acad. Sci. C273 (1971) 1736. Merisov, B.A., Serdyuk, A.D., Falco, I.I., Khadzhay, G.Ya., Khotkevich, V. I.: Fiz. Met. Metalloved. 32 (1971) 604. Sicking, G., Buchold, H.: Z. Naturforsch. A26A (1971) 1973. Birnbaum, H.K., Wert, CA.: Ber. Bunsenges. Phys. Chem. 76 (1972) 806. Cantelli, R., Mazzolai, FM., Nuovo, M.: Hydrogen in Metals. (Int. Conf., Jiilich 1972) JUL-Conf-6 II (1972) 770. Cotts, R.M.: Ber. Bunsenges. Phys. Chem. 76 (1972) 760. Gissler, W: Ber. Bunsenges. Phys. Chem. 76 (1972) 770. de Graaf, L.A., Rush, J.J.,Flotow, H.E., Rowe, J.M.: J. Chem. Phys. 56 (1972) 4574. de Graaf, L.A., Rush, J.J.,Flotow, H.E., Rowe, J.M.: Hydrogen in Metals (Int. Conf., Jiilich 1972) JUL-Conf-6 I (1972) 301. Hanada, R., Suganuma, T., Kimura, H.: Ser. Metall. 6 (1972) 483. Kisch, D. et al: Hydrogen in Metals (Int. Conf., Ji.ilich 1972) JUL-Conf-6 II (1972) 400. Volkl, J.: Ber. Bunsenges. Phys. Chem. 76 (1972) 797. Wicke, E., Obermann, A.: Z. Phys. Chem. NF 77 (1972) 163. Ztichner, H.: Z. Phys. Chem. NF 82 (1972) 240. Ziichner, H., Boes, N.: Ber. Bunsenges. Phys. Chem. 76 (1972) 783. Boes, N., Zfichner, H.: Phys. Status Solidi 17A (1973) K 111. Boes, N., Westerboer, U., Ztichner, H.: Ber Bunsenges. Phys. Chem. 77 (1973) 708. Cantelli, R., Mazzolai, EM., Nuovo, M.: Appl. Phys. 1 (1973) 27. Garcia, E.A.: L’Hydrogene dans les Metaux (Congr. Intl., Paris 1972) Editions Scienceet Industrie 1(1973) 238. Guil, J.M., Hayward, D.O., Taylor, N.: Proc. R. Sot. A335 (1973) 141. Hanada, R.: Ser. Metall. 7 (1973) 681. Herold, A., Rat, J.C.: L’Hydrogene dans les MCtaux (Congr. Intl., Paris 1972) Editions Science et Industrie 1 (1973) 49. Katlinskii, V.M., Kotlik, L.L.: Metody Issled. Opred. Gazov Met. (Leningrad 1973) Petrov, A.A., Ivanova, T.F., Vitol, E.N. (eds.), 1973, p. 31. Rush, J.J., Livingston, R.C., de Graaf, L.A. Flotow, H.E., Rowe, J.M.: J. Chem Phys. 59 (1973) 6570. Kutner, R., Sosnowska, I: Acta Phys. Pol. A46 (1974) 755. Merisov, B.A., Khadzhai, G.Ya., Khotkevich, V.I.: Fiz. Met. Metalloved. 37 (1974) 1090; Met. Metallogr. (English Transl.) 37 (1974) 178. Miinzing, W!, Viilkl, J., Wipf, H., Alefeld, G.: Ser. Metall. 8 (1974) 1327. Rowe, J.M., Rush, J.J.,Flotow, H.E.: Phys. Rev. B9 (1974) 5039. Tretchowski, J.: Rep. JUL-1049FF, 1974. Ziichner, H., Boes, N.: Z. Phys. Chem. 93 (1974) 65. Alefeld, B., Kehr, K.W., Springer, T., Lottner, V., Heim, A., Wakabayashi, N.: Fiz. Nizk. Temp. 1 (1975) 638. Iijima, Y, Hirano, K.: Bull. Jpn. Inst. Met. 14 (1975) 599. Ivashina, Yu.K., Nemchenko, V.F., Charnetskii, V.G.: Fiz. Met. Metalloved. 40 (1975) 343; Phys. Met. Metallogr. (English Transl.) 40 (1975) 97. Kehr, K.W.: Rep. JUL-1211. KFA Jtilich, 1975, p. 149. Merisov, B.A., Khadzhai, G.Ya., Khotkevich, V.I.: Fiz. Met. Metalloved. 39 (1975) 324. Viilkl, J., Alefeld, G.: Diffusion in Solids; Recent Developments. Nowick, A.S., Burton, J.J. (eds.) New York: Academic Press, 1975, p. 231. Boes, N., Ziichner, H.: Z. Naturforsch. 31 A (1976) 754. Boes, N., Ziichner, H.: Z. Naturforsch. 31 A (1976) 760. Cantelli, R.: Metall. Ital. 68 (1976) 361. Hanada, R.: Effect of Hydrogen on Behavior of Materials (Proc. Int. Conf., Jackson Lake Lodge, Wyoming 1975) Thompson, A.W., Bernstein, I.M. (eds.), New York: AIME, 1976, p. 676. Heidemann, A., Kaindl, G., Salomon, D., Wipf, H., Wortmann, G.: Phys. Rev. Lett. 36 (1976) 213. Wipf, H.: J. Less-Common Met. 49 (1976) 291. Eguchi, T., Morozumi, S.: J. Jpn. Inst. Met. 41 (1977) 795. Hanada, R.: Ser. Metall. 11 (1977) 843.
Land&Bhstein New Series III/26
Kidson
562 171 r7K 17M 17V 172 18Bl 18B2 18L 18M 78Sl 78S2 78V 79E 79H 79L 79M 790 c79v 30H 30K
32Q ‘83Q Y3W 54F B5P BST BSW
B7P MO: 60H 61L 64M 65M 66J 67G 68F 68G 68V 7121 7122 720 73P 732 74G 74M 1 74M2 74s
9.5 References for 9 (Ta, MO) Ivashina, YuK., Nemchenko, V.F., Nemchenko, A.V.: Fiz. Met. Metalloved. 44 (1977) 212; Phys. Met. Metallogr. (English Transl.) 44 (1977) 189. Kokkinidis, M.: Dipl. Thesis, Tech. Univ. Miinchen, FRG, 1977. Mar&he, J.F., Rat, J.C., H&old, A.: Hydrogen in Metals, (2nd Int. Congr., Paris, 1977), Oxford: Pergamon Press, 3 (1977) 1 B 8. Volkl, J. et al.: International Friction and Ultrasonic Attenuation in Solids (Proc. 6th Int. Conf., Tokyo, 1977) Hasiguti, R.R., Mikoshiba, N. (eds.), Tokyo: Univ. Tokyo Press, 1977, p. 485. Zeilinger, A., Pochman, W.A.: J. Phys. F 7 (1977) 575. Bauer, H.C. et al.: Z. Physik B29 (1978) 17. Boes, N., Wicke, E.: Ber. Bunsenges.Phys. Chem 82 (1978) 356. Lottner, V., et al.: (Proc. Symp., Vienna 1977) Vienna: IAEA 2 (1978) 339. Merisov, B.A., Khadzhai, G.Ya., Khotkevich, V.I.: Fiz. Met. Metalloved. 45 (1978) 440; Phys. Met. Metallogr. (English Transl.) 45 (1978) 187. Skold, K.: Hydrogen in Metals I, Alefeld, G., Volkl, J. (eds.), Topics in Applied Physics 28 (1978) 267. Stoneham, A.M.: J. Nucl. Mater. 69-70 (1978) 109. Viilkl, J., Alefeld, G.: Hydrogen in Metals I, Alefeld, G., Volkl, J. (eds.), Topics in Applied Physics 28 (1978) 321. Engelhard, J.: J. Phys. F 9 (1979) 2217. Hornung, P.A., Khan, A.D., Torgeson, D.R., Barnes, R.G.: Z. Phys. Chem. NF 116(1979) 77. Lottner, V., Heim, A., Springer, T.: Z. Physik B32 (1979) 157. Merisov, B.A., Khadzhai, G.Ya., Khotkevich, V.I.: Fiz. Met. Metalloved. 39 (1979) 324; Phys. Met. Metallogr. (English Transl.) 39 (1979) 88. Orth, H., Diiring, K.P., Gladisch, M., Herlach, D., Maysenhiilder, W., Metz, H., Putlitz, G. zu, Seeger,A., Vetter, J., Wahl, W., Wigand, M., Yagi, E.: Z. Phys. Chem. NF 116 (1979) 241. Volkl, J., Alefeld, G.: Z. Phys. Chem. NF 114 (1979) 123. Hanada, R.: Hydrogen in Metals (Jpn. Inst. Met., Sendai), 1980, p. 185. Koiwa, M., Ishioka, S.: Solid State Commun. 35 (1980) 729. Qi, Zh., Volkl, J., Wipf, H.: Ser. Met. 16 (1982) 859. Qi, Zh., Volkl, J., Lasser, R., Wenzl, H.: J. Phys. F 13 (1983) 2053. Wipf, H.: DIMET-82 (Proc. Int. Conf., Tihany, Hungary, 1982) Kedves, F.J., Beke, D.L. (eds.), Diffusion and Defect Monogr. 7 (1983) 209. Fukai, Y: Jpn. J. Appl. Phys. 23 (1984) L596. Peichl, R., Weidinger, A., Ziegler, P.: Z. Phys. Chem. NF 143 (1985) 197. Teichler, H., Klamt, A.: Phys. Lett. 108A (1985) 281. Weiser, M., Kalbitzer, S.: Z. Phys. Chem. NF 143 (1985) 183. Peichl, R., Zeigler, P., Weidinger, A.: J. Less-Common Met. 129 (1987) 243. Hill, M.L.: J. Metals 12 (1960) 725. Lawley, A., Liebman, N., Maddin, R.: Acta Metall. 9 (1961) 841. Moore, G.E., Unterwald, EC.: J. Chem. Phys. 40 (1964) 2639. McNeil, M.B.: J. Appl. Phys. 36 (1965) 2382. Jones, P.M.S., Gibson, R., Evans, J.A.: Rep. AWRE 16166, 1966. Gibala, R., Wert, C.A.: Rpt. COO-1673-3, 1967. Frauenfelder, R.: J. Chem, Phys. 48 (1968) 3955. Gol’tsov, V.A., Gel’d, P.V., Vykhodets, V.B.: Phys. Met. Metallogr. 26 (1968) 144. Vykhodets, V.B., Gol’tsov, V.A., Gel’d, P.V.: Phys. Met. Metallogr. 25 (1968) 133. Zakharov, A.P., Sharapov, V.M.: Fiz. Khim. Mekh. Mater. 7 (1971) 54. Zakharov, A.P., Sharapov, V.M.: Fiz. Khim. Probl. Krist. 2 (1971) 194. Oates, W.A., McLellan, R.B.: Ser. Metall. 6 (1972) 349. Perkins, W.G.: J. Vat. Sci. Technol. 10 (1973) 543. Zhakarov, A.P., Sharapov, V.M., Evko, EL: Fiz.-Khim. Mekh. Mater. 9 (1973) 29; Sov. Mater. Sci. (English Transl.) 9 (1973) 149. Guthrie, J.W.et al.: J. Nucl. Mater. 53 (1974) 313. Maksumov, T.M., Petushkov, E.E.: Dokl. Akad. Nauk Uzb. SSR 31 (9) (1974) 32. Maksumov, T.M., Petushkov, E.E.: Dokl. Akad. Nauk Uzb. SSR 31 (10) (1974) 24. Sharapov, V.M., Zhakharov, A.P.: Vzaimodeistvie At. Chastits Tverd. Telom. (Dokl. Vses. Konf., 3rd, 1974). Chevepin, V.T. (ed.), Kiev: Naukova Dumka 2 (1974) 155. Kidson
Iandolt-Btimrtcin New Series Ill/26
9.5 References for 9 (MO, W, Fe) 7X 75Sl 75S2 7533 76s 77s 78Kl 78K2 78M 78Sl 7882 79K 792 *82K w: 57G 60H 62M 64M 64R 67A 68F *69F 73B 73P 732 78M 79K 79P 80D *82D 84M 84W 85T Fe: 20R 24E 27B 35s 40B 47s 50G 52C 54D 55J 56s 57B
563
Caskey, G.R., Louthan, M.R., Derrick, R.G.: J. Nucl. Mater. 55 (1975) 279. Sakamoto, K.: Bull. Jpn. Inst. Met. 14 (1975) 333. Sharapov, V.M., Zhakarov, A.P., Matveev, V.V.: Zhur. Tekh. Fiz. 45 (1975) 2002; Sov. Phys. Tech. Phys. (English Transl.) 20 (1975) 1262. Skrinichenko, T.M., Klibanov, E.L., Kashin, V.I.: Fiz. Khim. Obrabot. Mater. 1 (1975) 40. Sharapov, V.M., Zhakarov, A.P.: Zhur. Tekh. Fiz. 46 (1976) 611; Sov. Phys. Tech. Phys. (English Transl.), 21 (1976) 351. Sharapov, V.M., Zhakarov, A.P.: Hydrogen in Metals. (2nd Int. Congr., Paris 1977), Oxford: Pergamon Press, 3 (1977) lB12. Katlinskii, V.M.: Izv. Akad. Nauk SSSR, Neorg. Mater. 14 (1978) 1667; Inorg. Mater. (English Transl.) 14 (1978) 1299. Katlinskii, V.M., Kotlik, L.L.: Izv. Akad. Nauk SSSR, Met. 1978, p. 80; Russ. Metall. (English Transl.) 1978, p. 65. Mazaev, A.A., Avarbe, R.G.: Khimiya i Tekhnol. Neorg. Ftorsoedinenii, Tugoplavk., Lyuminestsentn. Mater. Komp. SOZH, 1978, p. 51. Sharapov. V.M., Zhakarov, A.P.: Zh. Tekh. Fiz. 48 (1978) 1213. Shaw, MS., Lane, N.F.: J. Nucl. Mater. 69-70 (1978) 576. Katlinskii, V.M.: Fiz. Khim. Svoistva Splavov Reniya, M., 1979, p. 138. Zhakarov, A.P., Gorodetsky, A.E., Sharapov, V.M.: Z. Phys. Chem. NF 117 (1979) 245. Katsuta, H., McLellan, R.B., Furukawa, K.: J. Phys. Chem. Solids 43 (1982) 533. Gomer, R., Wortman, R., Lundy, R.: J. Chem. Phys. 26 (1957) 1147. Hickmott, T.W.: J. Chem. Phys. 32 (1960) 810. Mallett, M.W, Koehl, B.G.: J. Electrochem. Sot. 109 (1962) 968. Moore, G.E., Unterwald, EC.: J. Chem. Phys. 40 (1964) 2639. Ryabchikov, L.N.: Ukr. Fiz. Zh. 9 (1964) 293. Aitken, E.A., Brassfield, H.C., Conn, P.K., Duderstadt, E.C., Fryxell, R.E.: Trans. Metall. Sot. AIME 239 (1967) 1565. Frauenfelder, R.: J. Chem. Phys. 48 (1968) 3955. Frauenfelder, R.: J. Vat. Sci. Technol. 6 (1969) 388. Birnbaum, H.F.: Ser. Metall. 7 (1973) 925. Perkins, W.G.: J. Vat. Sci. Technol. 10 (1973) 543. Zhakarov, A.P., Sharapov, V.M., Evko, EL: Fiz. Khim. Mekh. Mater. 9 (1973) 29; Sov. Mater. Sci. (English Transl.) 9 (1973) 149. Mazaev, A.A., Avarbe, R.G.: Khimiya Tekhnol. Neorg. Ftorsoedinenii, Tugoplavk., Lyuminestsentn. Mater. Komp. SOZH, 1978, p. 51. Katlinskii, V.M.: Fiz. Khim. Svoistva, Splavov Reniya. M. 1979, p. 138. Polizotti, RX, Erlich, G.: J. Chem. Phys. 71 (1979) 259. Di Foggio, R., Gomer, R.: Phys. Rev. Lett. 44 (1980) 1258. Di Foggio, R., Gomer, R.: Phys. Rev. B25 (1982) 3490. Macrander, A., Seidman, D.N.: J. Appl. Phys. 56 (1984) 1623. Wang, S.C., Gomer, R.: Surf. Sci. 141 (1984) L 304. Tringides, M., Gomer, R.: Surf. Sci. 155 (1985) 254. Ryder: Electronics 17 (1920) 161. Edwards: J. Iron Steel Inst. 60 (1924) 9. Borelius, Lindblom: Ann. Phys. 82 (1927) 201. Smithells, Ransley: Proc. R. Sot. 150A (1935)172. Barrer, R.M.: Trans. Faraday Sot. 36 (1940) 1235. Sykes, C., Burton, H.H., Gegg, C.C.: J. Iron Steel Inst. 156 (1947) 155. Geller, W., Sun., T.H.: Arch. Eisenhiittenwes. 21 (1950) 423. Chang, P.L., Bennett, W.D.G.: J. Iron Steel Inst. 170 (1952) 205. Demarez, A., Hock, G., Meuner, EA.: Acta Metall. 2 (1954) 214. Johnson, E.W., Hill, M.: Acta Metall. 3 (1955) 99. Stross, T.M., Tompkins, EC.: J. Chem. Sot. 159 (1956) 230. Baranowski, B., Smialowski, M., Szklarska-Smialowski, Z.: Bull. Acad. Pol. Sci. Ser. Sci. Chim. 5 (1957) 191.
Land&-Btirnstein New Series III/26
Kidson
564 57s 58B 58E 58F 58H 58R 582 59s 60C 605 61L 61P 61R 63B 63D 64D 64w 65K 65M 65s 66B 66C 66H 66s 66W 67B 67C 67Gl 6762 67L 67R 680 68W 69El 69E2 69G 69J 70B 7oc 70Dl 70D2 700 70R 1 70R2 70s 7OW 71c 71D 7IM 71s 72Bl 72B2 72C 72D 72E 72G
9.5 References for 9 (Fe) Shuetz, A.E., Robertson, W.D.: Corros. 13 (1957) 437 t. Bastien, P., Amiot, P.: Rev. Metall. 55 (1958) 24. Eichenauer, W., Kiinzig, H., Pebler, A.: Z. Metallkd. 49 (1958) 220. Frank, R.C., Swets, D.E., Fry, D.L.: J. Appl. Phys. 29 (1958) 892. Hobson, J.D.: J. Iron Steel Inst. 189 (1958) 315. Raczinski, W.: Arch. Hutn. 3 (1958) 59. Zitter, H., Krainer, H.: Arch. Eisenhiittenwes. 29 (1958) 401. Schenck, H., Taxhet, H.: Arch. Eisenhiittenwes. 30 (1959) 661. Carmichael, D.C.,Hornaday, J.R.,Morris, A.E.,Parlee,N.A.:Trans. Metall. Sot. AIME218 (1960)826. Johnson, E.W., Hill, M.L.: Trans. Metall. Sot. AIME 218 (1960) 1104. Lee, R.W., Swets, D.E., Frank, R.C.: Mem. Sci. Rev. Metall. 58 (1961) 36. Palczewska, W., Ratajczyk: Bull. Acad. Pol. Sci. Ser. Sci. Chim. 9 (1961) 267. Raczinski, W, Stelmach, S.: Bull. Acad. Pol. Sci. Ser. Sci. Chim. 9 (1961) 633. Bryan, W.L., Dodge, B.F.: Am. Inst. Chem. Eng. J. 9 (1963) 223. Devanathan, M.A.V., Stachurski, Z., Beck, W.: J. Electrochem. Sot. 110 (1963) 886. Devanathan, M.A.V., Stachurski, Z.: J. Electrochem. Sot. 111 (1964) 619. Wagner, R., Sizmann, R.: Z. Angew. Phys. 18 (1964) 193. Kuznietsov, V.V., Subbotina, N.I.: Electrokhimiya 1 (1965) 1096. McBreen, J.: Thesis, Univ. Pennsylvania, USA, 1965. Schwarz, W., Zitter, H.: Arch. Eisenhiittenwes. 36 (1965) 343. Beck, W., Bockris, J.O’M., McBreen, J., Nanis, L.: Proc. R. Sot. Ser. A290 (1966) 220. Coe, F.R., Moreton, J.: J. Iron Steel Inst. 204 (1966) 366. Heumann, T., Primas, D.: Z. Naturforsch. 21 A (1966) 260. Schenk, H., Lange, K.W.: Arch. Eisenhlttenwes. 37 (1966) 809. Wach, S., Miodownik, A.P., Macowiak, J.: Corrs. Sci. 6 (1966) 271. Boniczewski, T., Moreton, J.: Br. Weld. J. 1967, p. 321. Coe, F.R., Moreton, J.: Br. Weld. J. 1967, p. 313. Gibala, R.: Trans. Metall. Sot. AIME 239 (1967) 1574. Gonzalez, O.D.: Trans. Metall. Sot. AIME 239 (1967) 929. Lord, A.E.: Acta Metall. 15 (1967) 1241. Radhakrishnan, T.P., Shrier, L.L.: Electrochim. Acta 12 (1967) 889. Ono, K., Rosales, L.A.: Trans. Metall. Sot. AIME 242 (1968) 244. Wach, S., Miodownik, A.P.: Corros. Sci. 8 (1968) 271. Erdmann-Jesnitzer, F., Hieber, H.: Arch. Eisenhiittenwes. 40 (1969) 73. Evans, G.M. Rollason, E.C.: J. Iron Steel Inst. 207 (1969) 1484. Gonzalez, O.D.: Trans. Metall. Sot. AIME 245 (1969) 607. Jesnitzer, F.E., Hieber, H.: Arch. Eisenhiittenwes. 40 (1969) 73. Bockris, J. O’M., Genshaw, M.A., Fullenwider, M.: Electrochim. Acta 15 (1970) 47. Choi, J.Y.: Metall. Trans. 1 (1970) 911. Dillard, J.L.: Mem. Sci. Rev. Metall. 67 (1970) 767. Dillard, J.L.: C. R. Acad. Sci. C270 (1970) 669. Oriani, R.A.: Acta Metall. 18 (1970) 147. Raczinsky, W., Talbot-Besnard, S.: C. R. Acad. Sci. C270 (1970) 602. Reiermann, B.K.: Dissertation. Tech. Univ. Berlin D83 GDR, 1970. Salii, V.I., Gel’d, P.V., Ryabov, R.A.: Fiz. Khim. Mekh. Mater. 6 (1970) 96; Sov. Mater. Sci. (English Transl.) 6 (1970) 620. Wach, S., Miodownik, A.P.: Trans. Faraday Sot. 66 (1970) 2334. Chew, B.: Met. Sci. J. 5 (1971) 195. Domke, E.: Dissertation, Univ. Miinster, FRG, 1971. Maas, N.: Thesis, Univ. Miinster FRG, 1971. Subramanyan, P.K.: Thesis, Univ. Pennsylvania, USA, 1971. Bester, H., Lange, W.: Arch. Eisenhiittenwes. 43 (1972) 207. Bester, H., Lange, K.W.: Arch. Eisenhiittenwes. 43 (1972) 283. Cornet, M., Talbot-Besnard, S.: Corros. Trait. Prot. Finition 20 (1972) 523. Dresler, W., Froberg, M.G.: Hydrogen in Metals (Int. Conf., Jiilich 1972) JUL-Conf-6 2 (1972) 826. von Ellerbrock, H.G., Vibrans, G., Stiiwe, H.P.: Acta Metall. 20 (1972) 53. Gel’d, P.V., Ryabov, R.A., Salii, V.I.: L’Hydrogene dans les Metaux (Cong. Int., Paris 1972) Editions Science et Industrie 1 (1973) 167. Landok-BBmstcin New Series III!26
9.5 References for 9 (Fe) 72H 73A 73B 73c 73Dl 73D2 73D3 73G 73H 73K 73M 73Nl 73N2 73P 73Sl 7332 7333 7384 74Al 74A2 74A3 74D 74G 74Kl 74K2 74Sl 74S2 74s3 74v 74Y 75Al 75A2 751 75Kl 75K2 75M 75Sl 7582 7533 75v 76B 76F 76J 76K
565
Heumann, Th., Domke, E.: Hydrogen in Metals (Int. Conf., Jiilich 1972) JUL-Conf-6 II (1972) 492. Asano, S., Fujishima, Y, Ohtani, N.: J. Jpn. Inst. Met. 37 (1973) 301. Bouraoui, R., Cornet, M., Talbot-Bresnard, S.: C. R. Acad. Sci. C277 (1973) 231. Conophagos, E. et al.: L’Hydrogene dans les Metaux (Congr. Int., Paris 1972) Editions Science et Industrie 1 (1973) 97. Demin, V.B., Vykhodets, V.B., Gel’d, P.V.: Phys. Met. Metallogr. 35 (1973) 84. Dillard, J.L., Talbot-Besnard, S.: L’Hydrogene dans les Metaux (Congr. Int., Paris 1972) Editions Science et Industrie 1 (1973) 159. Dresler, W., Froberg, M.G.: J. Iron Steel Inst. 211 (1973) 298. Govindan Namboodhiri, T.K., Nanis, L.: Acta Metall. 21 (1973) 663. Hirano, K., Iijama, Y, Matsuyama, T.: J. Iron Steel Inst. Jpn. 59 (1973) A149. Krishtal, M.A., Snezhnoi, R.L.: Diffuz. Protsessy Met., 1973, p. 91. Mindyuk, A.K., Svist, E.I.: Fiz. Khim. Mekh. Mater. 9 (1973) 36; Sov. Mater. Sci. (English Transl.) 9 (1973) 34. Nanis, L., Namboodhiri, T.K.G.: Stress Corrosion Cracking and Hydrogen Embrittlement of Iron BaseAlloys. (Proc. Conf., Unieux-Firminy, France 1973) Houston, Texas: Nat. Asoc. Corros. Eng., 1977, p. 432. Nelson, H.G., Stein, J.E.: Rep. NASA TN D-7265, 1973. Perkins, W.G.: J. Vat. Sci. Technol. 10 (1973) 543. Sakamoto, K.: J. Iron Steel Inst. Jpn. 59 (1973) A153. Sidorenko, V.M., Sidorak, 1.1.: Fiz. Khim. Mekh. Mater. 9 (1973) 52; Sov. Mater. Sci. (English Transl.) 9 (1973) 50. Sidorenko, V.M., Sidorak, 1.1.: Fiz. Khim. Mekh. Mater. 9 (1973) 12; Sov. Mater. Sci. (English Transl.) 9 (1973) 372. Sidorenko, V.M., Kachmar, B.F., Borisova, N.S.: Fiz. Khim. Mekh. Mater. 9 (1973) 14; Sov. Mater. Sci. (English Transl.) 9 (1973) 500. Allen-Booth, D.M., Hewiit, J.: Acta Metall. 22 (1974) 171. Allen-Booth, D.M., Hewitt, J.: Ser. Metall. 8 (1974) 769. Asano, S., Hara, K., Nakai, Y, Ohtani, N.: J. Jpn. Inst. Met. 38 (1974) 626. Danauskas, A.V., Matulis, Yu.Yu., Bubyalis, Yu.S.: Liet. TSR Mokslu Akad. Darb., B2 (1974) 43. Gol’tsov, V.A., Podolinskaya, T.A.: Fiz. Khim. Mekh. Mater. 10 (1974) 8; Sov. Mater. Sci. (English Transl.) 10 (1974) 607. Kass, W.J.: Ser. Metall. 8 (1974) 763. Kumnick, A.J., Johnson, H.H.: Metall. Trans. 5 (1974) 1199. Safonov, V.L., Chene, J., Galland, J., Azou, P., Bastien, P.: C. R. Acad. Sci. C 278 (1974) 445. Salii, V.I., Ryabov, R.A.: Fiz. Khim. Mekh. Mater. 10 (1974) 45; Sov. Mater. Sci. (English Transl.) 10 (1974) 522. Sidorenko, V.M., Sidorak, 1.1.:Navod. Metall. Elektro-Khim. Prots., 1974, p. 27. Volkov, V.E. et al.: Fiz. Met. Ikh. Soedin 2 (1974) 3. Yoshizawa, S., Yamawaka, K.: Met. Corros. (Proc. 5th Int. Congr. 1972) Sato, N. (ed.), Houston, Texas: Nat. Assoc. Chem. Eng. 1974, p. 421. Alefeld, G., Wipf, H.: Fiz. Nizk. Temp. 1 (1975) 660; Sov. S. Low Temp. Phys. 1 (1975) 317. Allen-Booth, D.M., Atkinson, S., Bilby, B.A.: Acta Metall. 23 (1975) 371. Iijama, Y, Hirano, K.: Bull. Jpn. Inst. Met. 14 (1975) 599. Konig, H.J., Lange, K.W.: Arch. Eisenhtittenwes. 46 (1975) 237. Kiinig, H.J., Lange, K.W.: Arch. Eisenhtittenwes. 46 (1975) 269. Miller, RF, Hudson, J.B., Ansell, G.S.: Metall. Trans. A 6A (1975) 117. Sakamoto, K.: Bull. Jpn. Inst. Met. 14 (1975) 333. Shretsov, N.I., Levenchenko, V.P., Ryabov, R.A.: Metalloved. Term. Obrab. Met. 3 (1975) 50; Met. Sci. Heat Treat. (English Transl.) 17 (1975) 235. Sidorenko, V.M., Sidorak, I.I., Parkheta, R.G.: Fiz. Khim. Mekh. Mater. II (1975) 28; Sov. Mater. Sci. (English Transl.) II (1975) 642. Volkl, J., Alefeld, G.: Diffusion in Solids, Recent Development. Nowick, A.S., Burton, J.J.(eds.),New York: Acad. Press, 1975, p. 231. Bester, H., Lange, K.W: Arch. Eisenhiittenwes. 47 (1976) 333. Friedrich, K., Kusch, H.G.: Neue Hi.itte 21 (1976) 688. Jerome, M.: Colloqu. Metal1 (Diffus. Milieux Condens. Theor. Appl. 2), 19 (1976) 627. Kufudakis, A., Raczynski, W.: Czech. J. Phys. B26 (1976) 1360.
Land&-Biirnstein New Series III/26
566
9.5 References for 9 (Fe, Co, Ni)
80H 80K 81Y 82N +83K 83R 85H 85T 86T 87H
Louthan, M.R., et al.: Effect of Hydrogen on the Behavior of Materials (Proc. Int. Conf., Jackson Lake Lodge 1975) Thompson, A.W., Bernstein, I.M. (eds.), New York: AIME, 1976, p. 337. Quick, N.R.: Thesis. Cornell Univ., Univ. Microfilms, Mich.: Ann Arbor, No. 76-18, (1976) 191. Rieke, E.M.: Arch. Eisenhiittenwes. 47 (1976) 247. Rieke, E.M.: Reactivity of Solids (8th Int. Symp., Gothenburg, Sweden 1976), Gothenburg: Chalmers Univ of Technology, 1976, p. 298. da Silva, J.R.G.: Rpt. INIS-mf-4733, 1976. Volkov, V.E., et al.: Izv. V.U.Z. Fiz. 19 (1976) 18; Sov. Phys. J. (English Transl.) 19 (1976) 1399. Wipf, H.: J. Less-Common Met. 49 (1976) 291. Chene, J.: Met. Corros.-Ind. 52 No. 622 (1977) 203. Chene, J.: Met. Corros.-Ind. 52 No. 623-4 (1977) 262. Chene, J.: Met. Corros.-Ind. 52 No. 625 (1977) 291. Chene, J.: Met. Corros-Ind. 52 No. 626 (1977) 343. Chene, J. Galland, J., Azou, P.: Hydrogen in Metals (2nd Int. Congr., Paris 1977),Oxford: Pergamon Press 1 (1977) No. 1 A3. Kumnick, A.J., Johnson, H.H.: Acta Metall. 25 (1977) 891. Rieke, E.M.: Hydrogen in Metals (2nd Int. Congr., Paris 1977),Oxford Pergamon Press,5 (1977)No. 2 B8. Safonov, et al.: Izv. Akad. Nauk SSSR, Met. 3 (1977) 76; Russ. Metall. (English Transl.) 3 (1977) 62. Yamakawa, K., Tada, M., Fujita, F.E.: J. Phys. Sot. Jpn. 43 (1977) 102. Birnbaum, H.K., Au, J.J.:Acta Metall. 26 (1978) 1105. Katlinskii, V.M.: Izv. Akad. Nauk SSSR, Neorg. Mater. 14 (1978) 1667; Inorg. Mater. (English Transl.) 14 (1978) 1299. Quick, N.R., Johnson, H.H.: Acta Metall. 26 (1978) 903. Raczynski, W.: Phys. Status Solidi 48A (1978) K27. Rieke, E.: Arch. Eisenhiittenwes. 49 (1978) 509. Sabirzyanov, A.V. et al.: Fiz. Svoistva Met. i Splavov 2 (1978) 49. Shaw, M.S., Lane, N.F.: J. Nucl. Mater. 69-70 (1978) 576. Volkl, J., Alefeld, G.: Hydrogen in Metals I, Alefeld, G., Volkl, J. (eds.), Topics in Appl. Phys. 28 (1978) 321. Domke, E.: Dissertation, Univ. of Miinster, FRG, 1979. Hagi. H., Hayashi, Y., Ohtani, N.: Trans. Jpn. Inst. Met. 20 (1979) 349. Masui, K., Yoshida, H., Watanabe, R.: Trans. Iron Steel Inst. Jpn. 19 (1979) 547. Waelbroeck, F., Ali-Khan, I., Dietz, K.S., Wienhold, P.: J. Nucl. Mater. 85-86 (1979) 345. Hayashi, Y., Nagano, M., Ohtani, N.: J. Jpn. Inst. Met. 44 (1980) 48. Kumnick, A.J., Johnson, H.H.: Acta Metall. 28 (1980) 33. Yamakawa, K., Tsuruta, T., Yoshizawa, S.: Boshuko Gijutso 30 (1981) 501. Nagano,M., Hayashi, Y, Ohtani, N.: Ser. Metall. 16 (1982) 973. Kiuchi, K., McLellan, R.B.: Acta Metall. 31 (1983) 961. Raczynski, W.: Hydrogen in Metals (Int. Conf., Wroclaw, Poland), 1983. Hinotani, S., Ohmori, Y.: Trans. Jpn. Inst. Met. 26 (1985) 622. Tahara. A., Hayashi, Y.: Trans Jpn. Inst. Met. 26 (1985) 869. Tanabe, T., Sawada, K., Imoto, S.: Trans. Jpn. Inst. Met. 27(1986) 321. Hagi, H., Hayashi, Y: Nippon Kinzoku Gakkaishi 51 (1987) 591.
co: 66s 72D 72K 74c 76L 82H 85S
Schenck, H., Lange, K.W.: Arch. Eisenhtittenwes. 37 (1966) 809. Dander, W., Kronmueller, H.: Ber. Kernforschungsanlage Jiilich No. 6 (1972) 524. Khristova, I., Pangarov, N.: Izv. Otd. Khim. Nauki Bulg. Akad. Nauk 5 (1972) 387. Caskey, G.R., Derrick, R.G., Louthan, M.R.: Ser. Metall. 8 (1974) 481. Louthan, M.R., Caskey, G.R.: Int. J. Hydrogen Energy 1 (1976) 291. Hohler, B., Schreyer, H.: J. Phys. F 12 (1982) 857. Sutter, P., McLellan, R.B.: Ser. Metall. 19 (1985) 879.
Ni: 23L 27B 29H 32H
Lombard, V.: C. R. Acad. Sci. 177 (1923) 116. Borelius, G., Lindblom, J.: Ann. Phys. 82 (1927) 201. Hendricks, B.C., Ralston, R.R.: J. Am. Chem. Sot. 51 (1929) 3278. Ham, W.R.: J. Chem. Phys. l(l932) 476.
76L 76Q 76Rl 76R2 76s 76V 76W 77Cl 77c2 7X3 77c4 77CS 77K 77R 77s 77Y 78A 78K 78Q 78Rl 78R2 78Sl 7832 78V 79D 79H 79M 7911’
Kidson
Land&-B6mstein New Series III,/26
9.5 References for 9 (Ni) 35E 36s 38P 44G 54L 55H 55R 57El 57E2 59G 60E 61B 62M 630 63s 64R 65E 65s 66C 66s 67D 67El 67E2 67E3 67F 670 67s 68C 68E 68V 69C 70B 7oc 70s 71B 71Dl 71D2 71K 71L 72C
567
Euringer, G.: Z. Physik. 96 (1935) 37. Smithells, C.J., Ransley, C.E.: Proc. R. Sot. A 157 (1936) 292. Post, C.B., Ham, WR.: J. Chem. Phys. 26 (1938) 598. Glagley, H.L., Coleman, H.S.: J. Appl. Phy. 15 (1944) 125. Lieser, K.H., Witte, H.: Z. Phys. Chem. 202 (1954) 321. Hill, M.L., Johnson, E.W: Acta Metall. 3 (1955) 566. Ransley, C.E., Talbot, D.E.: Z. Metallkd. 46 (1955) 328. Edwards, A.G.: Brit. J. Appl. Phys. 8 (1957) 406. Eichenauer, W., Pebler, A.: Z. Metallkd. 48 (1957) 373. Grimes, H.H.: Acta Metall. 7 (1959) 782. Eichenauer, W: Mem. Sci. Rev. Metall. 57 (1960) 943. Belyakov, YuI., Ionov, N.I.: Sov. Phys. Tech. Phys. 6 (1961) 146. Marchand, A.: C. R. Acad. Sci. 254 (25) (1962) 4284. Olsen, K.M., Larkin, C.F.: J. Electrochem. Sot., 110 (1963) 86. Szklarska-Smialowski, Z., Smialowski, M.: J. Electrochem. Sot. 110 (1963) 444. Ryabchikov, L.N.: Ukr. Fiz. Zh. 9 (1964) 303. Eichenauer, W, Loser, W., Witte, H.: Z. Metallkd. 56 (1965) 287. Smialowski, M.: J. Electrochem. Sot. 110 (1965) 444. Cermak, J., Kufudakis, A.: Mem. Sci. Rev. Metall. 63 (1966) 767. Schenck, H., Lange, K.W.: Arch. Eisenhiittenwes. 37 (1966) 809. Dus, K., Smialowski, M.: Acta Metall. 15 (1967) 1611. Ebisuzaki, Y., Kass, W.I., O’Keefe, M.: J. Chem. Phys. 46 (1967) 1378. Ebisuzaki, Y, Kass, W.J., O’Keefe, M.: J. Chem. Phys. 46 (1967) 1373. Ebisuzaki, Y, Kass, W.J., O’Keefe, M.: J. Electrochem. Sot. 46 (1967) 1071. Fischer, W.: Z. Naturforsch. 22A (1967) 1581. Oriani, R.A., Gonzalez, O.D.: Trans. Metall. Sot. AIME 239 (1967) 1041. Scherrer, S., Lozes, G., Deviot, B.: C. R. Acad. Sci. B264 (1967) 1499. Cermak, J., Kufudakis, A.: Mem. Sci. Rev. Metall. 65 (1968) 375. Ebisuzaki, Y, O’Keefe, M.: J. Chem. Phys. 48 (1968) 1867. Vykhodets, V.B., Gol’tsov, VA., Gel’d, P.V.: Tr. Ural. Politekh. Inst. 167 (1968) 114. Combette, P., Azou, P.: C. R. Acad. Sci. C268 (1969) 677. Bockris, J.O’M., Genshaw, M.A., Fullenwider, M.: Electrochim. Acta 15 (1970) 47. Combette, P., Azou, P.: Mem. Sci. Rev. Metall. 67 (1970) 17. Sacris, E.M., Parlee, N.A.D.: Metall. Trans. 1 (1970) 3377. Beck, W., Bockris, J.O’M., Genshaw, M.A., Subramanyan, P.K.: Metall. Trans. 2 (1971) 883. Donovan, J.A., Derrick, R.G., Dexter, A.H., Louthan, M.R.: Rep. DPST (NASA) 71-2, 1971. Dresler, W.: Thesis, Tech. Univ. Berlin, FRG, 1971. Katz, L., Guinan, M., Borg, R.J.: Phys. Rev. B4 (1971) 330. Louthan, M.R., Derrick, R.G., Dexter, A.H.: Rep. DPST (NASA) 71-4, 1971. Combette, P., Renard, M., Grilhe, J.: Hydrogen in Metals (Int. Conf. Jiilich 1972) JUL-Conf-6 II (1972) 821. Dresler, W, Frohberg, M.G.: Z. Metallkd. 63 (1972) 204. Khristova, I., Pangarov, N.: Izv. Otd. Khim. Nauki, Bulg. Akad. Nauk 5 (1972) 387. Robertson, WM.: Ber. Bunsenges. Phys. Chem. 76 (1972) 825. Robertson, W.M.: Hydrogen in Metals (Int. Conf., Ji.ilich 1972) JUL-Conf-6 II (1972) 449. Stickney, R.E., Bradley, T.L., Levin, R.L.: Hydrogen in Metals. (Int. Conf., Jiilich 1972)JUL-Conf-6
72D 72K 72Rl 72R2 72Sl
1(1972) 231.
7282 73c 73D 73K 73P 73R 73Sl
Sussman,J.A., Weissman,Y: Hydrogen in Metals (Int. Conf., Jiilich 1972)JUL-Conf-6 II (1972) 821. Combette, P., Grilhe, J.: L’Hydrogene dans les Metaux (Congr. Int., Paris 1972), Editions Scienceet Industrie 1 (1973) 45. Denim, V.B., Vykhodets, V.B., Gel’d, P.V.: Fiz. Met. Metalloved. 35 (1973) 84; Phys. Met. Metallogr. (English Transl.) 35 (1973) 760. Kazakov, D.N., Kunin, L.L., Litvin0va;N.F.: Izv. Akad. Nauk SSSR, Met. 2 (1973) 91; Russ. Metall. (English Transl.) 2 (1973) 62. Perkins, W.G.: J. Vat. Sci. Technol. 10 (1973) 543. Robertson, W.M.: Z. Metallkd. 64 (1973) 436. Sidorenko, V.M., Sidorak, 1.1.: Fiz. Khim. Mekh. Mater. 9 (1973) 12; Sov. Mater. Sci. (English Transl.) 9 (1973) 372.
Land&-Biimstein New Series III/26
Kidson
568 MB1 74B2 74G 14L 74Sl 14S2 75A 75B 751 75K 75L 75s 75T *75v 76C 76G 76V 76W 76Yl 76Y2 77R 77T 77Yl 77Y2 78K 78Ml 78M2 78M3 78R 78Sl 78S2 78S3 78Vl 78V2 79B 79c 79G 79H 79Kl 79K2 79s 79T 79Y 8OA 80T 8OY
9.5 References for 9 (Ni) Barmin, N.I., Gel’d, P.V., Levchenko, V.P., Masharov, S.I., Ryabov, R.A., Shvetsov, NJ.: Dokl. Akad. Nauk SSSR 215 (1974) 567; Sov. Phys. Dokl. (English Transl.) 19 (1974) 151. Belyakov, YuI., Zvezdin, Yu.I., Kurdyumov, A.A., Nevdakha, G.G.: Zh. Tekh. Fiz. 44 (7) (1974) 1534. Gol’tsov, V.A., Podolinskaya, T.A.: Fiz. Khim. Mekh. Mater. 10 (1974) 8; Sov. Mater. Sci. (English Transl.) 10 (1974) 607. Louthan, M.R., Donovan, J.A., Caskey, G.R.: Ser. Metall. 8 (1974) 643. Shvetsov, N.I., et al.: Fiz. Met. Ikh. Soedin. 1 (1974) 3. Sidorenko, V.M., Sidorak, 1.1.:Navod. Metall. Elektro-Khim. Prots., 1974, p. 27. Alefeld, G., Wipf, H.: Fiz. Zhidk. Temp. l(l975) 660; Low Temp. Phys. (English Transl.) (1975) 317. Belyakov, Yul., et al.: Zh. Tekh. Fiz. 44 (1974) 1534; Sov. Phys. Tech. Phys. (English Transl.) 19 (1975) 956. Iijama. Y, Hirano, K.: Bull. Jpn. Inst. Met. 14 (1975) 599. Kehr, K.W.: Rep. JUL-1211, 1975. Louthan, M.R., Donovan, J.A., Caskey, G.R.: Acta Metall. 23 (1975) 745. Stafford, SW., McLellan, R.B.: Ser. Metall. 9 (1975) 1195. Tada, M., Yamkawa, K., Fujita, F.E.: Ser. Metall. 9 (1975) 743. Volkl, J., Alefeld, G.: Diffusion in Solids, Recent Developments. Nowick, AS., Burton, J.J.(eds.) New York: Acad. Press, 1975, 231. Cermak, J., Kufudakis, A.: J. Less-Common Met. 49 (1976) 309. Gol’tsov, V.A., Latyshev, V.V.: Fiz. Khim. Mekh. Mater. 12 (1976) 28; Sov. Mater. Sci. (English Transl.) 12 (1976) 484. Vykhodets, V.B., Demin, V.B., Gel’d, P.V.: Phys. Status Solidi A34 (1976) 787. Weiner, J.H.: Phys. Rev. B. B 14 (1976) 4741. Yamakawa? K., Tada, M., Fujita, F.E.: Jpn. J. Appl. Phys. 15 (1976) 769. Yamakawa, K., Tada, M., Fujita, F.E.: Ser. Metall. 10 (1976) 405. Renouprez, A., Fouilloux, P., Stockmeyer, R., Conrad, H.M., Goeltz, G.: Ber. Bunsenges. Phys. Chem. 81 (1977) 429. Tanabe, T., Miyata, Y., Imoto, S.: Technol. Rep. Osaka Univ. 27 (1977) 383. Yamakawa, K.: Jpn. J. Appl. Phys. 16 (1977) 1033. Yamakawa, K., Fujita, F.E.: Jpn. J. Appl. Phys. 16 (1977) 1747. Katlinskii, V.M.: Izv. Akad. Nauk SSSR, Neorg. Mater. 14 (1978) 1667; Inorg. Mater. (English Transl.) 14 (1978) 1299. Ma&he, J.F., Rat, J.C., Herold, A.: J. Chim. Phys. 75 (1978) 735. Miiller, W., Hufschmidt, M., Pfeiffer, Th.: Nucl. Instrum. Methods 149 (1978) 73. Morrison, H.M., Blackburn, D.A., Chui, K.M.: J. Nucl. Mater. 69-70 (1978) 578. Ragauskas, R.A., Danauskas, A.V., Matulis, Yu.Yu.: Liet TSR Mokslu Akad. Darb. Bl No. 104 (1978) 25. Sakamoto, Y, Miura, A.: J. Jpn. Inst. Met. 42 (1978) 331. Shaw, M.S., Lane, N.F.: J. Nucl. Mater. 69-70 (1978) 576. Stoneham, A.M.: J. Nucl. Mater. 69-70 (1978) 109. Varaksin, A.N., Puzanova, N.M., Volobuev, P.V.: Fiz. Met. Metallov. 46 (1978) 187; Phys. Met. Metallogr. (English Transl.) 46 (1978) 159. Volkl, J., Alefeld, G.: Hydrogen in Metals I. Alefeld, G., Viilkl, J. (eds.), Topics in Appl. Phys. 28 (1978) 321. Baskes, M.I., Melius, C.F.: Z. Phys. Chem. NF 116 (1979) 19. Cermik, J., Kufudakis, A., Redl, V.I.: Z. Phys. Chem. NF 116 (1979) 9. Gardavska, G., Lejcek, P.: Krist. Tech. 14 (1979) 285. Hauck, J.: Hydrogen in Metals (Int. Mtg. Miinster 1979), Preprints 1 (1979) 190. Katlinskii, V.M.: Fiz.-Khim. Svoistva Splavov Reniya, M., 1979, p. 138. Kurkela, M., Latanision, R.M.: Ser. Metall. 13 (1979) 927. Sakamoto, Y., Miura, A.: Nagasaki Daigaku Kogakubu Kenkyu Hokoku 13 (1979) 109. Tada, M., Fujita, F.E.: Hydrogen in Metals (Proc. 2nd JIM Int. Symp., Minakami, Japan 1979) Suppl. to Trans. Jpn. Inst. Met., 1979, p. 169. Yamakawa, K.: J. Phys. Sot. Jpn. 14 (1979) 114. Atrens, A., Mezzanotte, D., Fiore, N.F., Genshaw, M.A.: Corros. Sci. 20 (1980) 673. Telkov, V.I., Andreev, L.A., Malyutina, G.L.: Russ. J. Phys. Chem. 54 (1980) 1573. Yei, W.M., McLellan, R.B.: Acta Metall. 28 (1980) 1437. Kidson
Landoh-BBmstein New Series III/26
9.5 References for 9 (Ni, Pd) 8lH 81M 82H 83H 83L 83T 84C 84F 84L 84T 85C 85M 86H 86T *87M
569
Hohler, B., Kronmiiller, H.: Philos. Mag. A43 (1981) 1189. Meunier, G., Manaud, J.-P., de Valette, M.: J. Less-Common Met. 77 (1981) P47. Hohler, B., Schreyer, H.: J. Phys. F 12 (1982) 857. Hagi, H.: J. Jpn. Inst. Met. 47 (1983) 1029. Latanision, R.M., Kurkela, M.: Corrosion 39 (1983) 174. Tahara, A., Hayashi, Y: J. Jpn. Inst. Met. 47 (1983) 180. Cummings, D.L., Reuben, R.L., Blackburn, D.A.: Metall. Trans. A 15A (1984) 639. Furuya, Y., Hashimoto, E., Kino, T.: Jpn. J. Appl. Phys. 23 (1984) 1190. Lee, K.A., McLellan, R.B.: Ser. Metall. 18 (1984) 859. Tahara, A., Hayashi, Y: J. Jpn. Inst. Met. 48 (1984) 1152. Cermak, J., Gardavska, G., Kufudakis, A., LejEek, P.: Z. Phys. Chem. N.F. 145 (1985) 239. Matusiewicz, G., Duquette, D.J.: Acta Metall. 33 (1985) 1637. Hagi, H.: Trans. Jpn. Inst. Met. 27 (1986) 233. Tanabe, T., Sawada, K., Imoto, S.: Trans. Jpn. Inst. Met. 27 (1986) 321. Mullins, D.R., Roop, B., Costello, S.A., White, J.M.: Surf. Sci. 186 (1987) 67.
Pd:
1866G 28T 35J 40J 54D 54s 58T 60K 62D 63K 64B 64C 64s 64Wl 64W2 65C 65J 65K 65s 66K 66M 67B 67E 67H 67R 67s 68Kl 68K2 69B2 69K 69W 70A 70B 70G 70H 702 7lBl 71B2 7lB3 71s
Graham, F.: Philos. Trans. R. Sot. London 156 (1866) 415. Tamman, G., Schneider, D.: Z. Anorg. Chem. 172 (1928) 43. Jost, W., Widman, A.: Z. Phys. Chem. B29 (1935) 247. Jost, W., Widman, A.: Z. Phys. Chem. B45 (1940) 285. Davis, W.D.: USAEC Rep. KAPL-1227, 1954. Salmon, O.N., Randall, D.: USAEC Rpt. KAPL-984, 1954. Toda, G.: Hokkaido Univ, Res. Inst. Catalysis J. 6 (1958) 13. Katz, O.M., Gulbransen, E.A.: Rev. Sci. Instrum. 31 (1960) 615. Devanathan, M.A.V., Stachurski, Z.: Proc. R. Sot. Ser. A. 270 (1962) 90. Kiissner, A.: Z. Phys. Chem. NF 36 (1963) 383. Bohmbolt, B., Wicke, E.: Z. Phys. Chem. 42 (1964) 115. Castellan, G.W.: J. Electrochem. Sot. 111 (1964) 1273. von Stackelberg, M., Ludwig, P.: Z. Naturforsch. 19A (1964) 93. Wagner, R., Sizmann, R.: Z. Angew. Phys. 18 (1964) 193. Wicke, E., Bohmholdt, G.: Z. Phys. Chem. NE 42 (1964) 115. Charalambus, S., Goebel, K.: Z. Naturforsch. 20A (1965) 1085. Jewett, D.N., Makrides, A.C.: Trans. Faraday Sot. 61 (1965) 932. Kazanskii, V.B., Mardalishvili, R.E., Strunin, VP.: Zh. Fiz.-Khim. 30 (1965) 821. Simons, J.W., Flanagan, T.B.: J. Phys. Chem. 69 (1965) 3581. Kahrig, E., Kirstein, D., Lange, F.: Ber. Bunsenges. Phys. Chem. 70 (1966) 592. Makrides, A.C., Jewett, D.N.: Engelhard Ind. Tech. Bull. 7 (1966) 51. Bohmholdt, G., Wicke, E.: Z. Phys. Chem. NE 56 (1967) 133. Ebisuzaki, Y, Kass, W.J., O’Keefe, M.: Philos. Mag. 15 (1967) 1071. Holleck, G., Wicke, E.: Z. Phys. Chem. NE 56 (1967) 155. Rubin, L.R.: Engelhard Ind. Tech. Bull. 8 (1967) 18. SkBld, K., Nelin, G.: J. Phys. Chem. Sol. 28 (1967) 2369. Knaak, J., Eichenauer, W.: Z. Naturforsch. 23A (1968) 1783. Koffler, S.A., Hudson, J.B., Ansell, G.S.: J. Met. 20 (1968) 53. Bucur, R.: J. Electroanal. Chem. Interfacial Electrochem. 22 (1969) 127. Koffler, S.A., Hudson, J.B., Ansell, G.S.: Trans. Metall. Sot. AIME 245 (1969) 1735. Wicke, E., Meyer, K.: Z. Phys. Chem. 64 (1969) 225. Arons, R.R., Taminga, Y, de Vries, G.: Phys. Status Solidi 40 (1970) 107. Bockris, J.O’M., Genshaw, M.A., Fullenwider, M.: Electrochim. Acta 15 (1970) 47. Gol’tsov, V.A., Demin, V.B., Vykhodets, V.B., Kagan, G.Ye., Gel’d, P.V.: Fiz. Met. Metalloved. 29 (1970) 1305; Phys. Met. Metallogr. (English Transl.) 29 (1970) 195. Holleck, G.L.: J. Phys. Chem. 74 (1970) 503. Ziichner, H.: Z. Naturforsch. 25A (1970) 1490. Boes, N.: Dissertation, Univ. of Miinster, FRG, 1971. Breger, V., Gileadi, E.: Electrochim. Acta 16 (1971) 177. Buchold, H.: Dissertation, Univ. of Miinster, FRG, 1971. Sicking, G., Buchold, H.: Z. Naturforsch. 26A (1971) 1973.
Land&-BBmstein New Series III/26
570 71v 72Bl 72B2 72G 72R 722 73B 73D 73P 73R 73s 74B 74c 751 75M 75P 75s 75T 75v 76Bl 76B2 76D 76K 76M 76V 76W 77H 77K 77M 77s 78B 78E 78H 78K 78L 78M 78Vl *78V2 79B 79Hl 79H2 79K 80Kl 80K2 8lKl 81K2 81Ml 81M2 81s 82s
9.5 References for 9 (Pd) Volkl, J., Wollenweber, G., Klatt, K.H., Alefeld, G.: Z. Naturforsch. 26A (1971) 922. Birnbaum, H.K., Wert, C.A.: Ber. Bunsenges. Phys. Chem. 76 (1972) 806. Buchold, H., Sicking, G.: Hydrogen in Metals (Int. Conf., Jiilich 1972) JUL-Conf-6 Ii (1972) 391. Gol’tsov, V.A., Kagan, G.E.: L’HydrogZne dans les MCtaux (Congr. Int., Paris) 1972, p. 249. Rowe, J.M., Rush, J.J.,de Graaf, L.A., Ferguson, G.A.: Phys. Rev. Lett. 29 (1972) 1250. Ziichner, H., Boes, N.: Ber. Bunsenges. Phys. Chem. 76 (1972) 783. Boes, N., Westerboern, U., Ziichner, H.: Ber. Bunsenges. Phys. Chem. 77 (1973) 708. Demin, V.B., Vykhodets, V.B., Gel’d, P.V.: Fiz. Met. Metalloved. 35 (1973) 760; Phys. Met. Metallogr. (English Transl.) 35 (1973) 84. Perkins, W.G.: J. Vat. Sci. Technol. 10 (1973) 543. de Ribaupierre, Y, Manchester, ED.: J. Phys. C 6 (1973) L390. Samsonov, G.V.: Dokl. Akad. Nauk SSSR 208 (1973) 621. Balovne, Yu.A.: Zh. Fiz. Khim. 48 (1974) 719; Russ. J. Phys. Chem. (English Transl.) 48 (1974) 409. Carlile, C.J., Ross, D.K.: Sol. State Commun. 15 (1974) 1923. Iijima, Y., Hirano, K.: Bull. Jpn. Inst. Met. 14 (1975) 599. Mar&he, J.F., Rat, J.C., Herold, A.: C. R. Acad. Sci. C281 (1975) 449. Pugachev, V.A. et al: Zh. Fiz. Khim. 49 (1975) 1781; Russ. J. Phys. Chem. (English Transl.) 49 (1975) 1045. Sekine, K.: Chem. Lett. Jpn. 1975, 841. Takeris, S. et al.: Deposited Dot., VINITI 3479-75, 1975, p. 198. Volkl, J., Alefeld, G.: Diffusion in Solids: Recent Developments. Nowick, A.S., Burton, J.J.(eds.), New York: Academic Press, 1975, p. 231. Boes, N., Ziichner, H.: J. Less-Common Met. 49 (1976) 223. Buchold. H., Sicking, G., Wicke, E.: Ber. Bunsenges.Phys. Chem. 80 (1976) 446. Davis, et al.: Seereference 81s. Kley, Vv!, Drexel, W.: Rep. Comm. Eur. 5466e, 1976. Mar&he, J.F., Rat, J.C., H&old, A.: J. Chim. Phys. 73 (1976) 983. Vykhodets, V.B., Demin, V.B., Gel’d, P.V.: Phys. Status Solidi A34 (1976) 787. Wipf, H.: J. Less-Common Met. 49 (1976) 291. Hasegawa, H., Nakajima, K.: J. Jpn. Inst. Met. 41 (1977) 813. Katlinskii, V.M., Kotlik, L.L.: Splavy Blagorod. Met. 1977, p. 179. Ma&he, J.F., Rat. J.C., Herold, A.: Hydrogen in Metals. (2nd Int. Congr., Paris 1977), Oxford: Pergamon Press, 4 (1977) 1 C2. Sekine, K.: J. Res. Inst. Catalysis Hokkaido Univ. 25 (1977) 73. Balovnev, Yu.A.: Fiz. Met. Metalloved. 45 (1978) 1307; Phys. Met. Metallogr. (English Transl.) 45 (1978) 167. Early, J.G.: Acta Metall. 26 (1978) 1215. Huber, B., Sicking. G.: Phys. Status Solidi A47 (1978) K85. Katlinskii, V.M.: Izv. Akad. Nauk SSSR, Neorg. Mater. 14 (1978) 1667; Inorg. Mater. (English Transl.) 14 (1978) 1299. Labes. C., McLellan, R.B.: Acta Metall. 26 (1978) 893. Miiller, W., Hufschmidt, M., Pfeiffer, Th.: Nucl. Instrum. Methods 149 (1978) 73. Varaksin, A.N., Puzanova, N.M. Volubuev, P.V.: Fiz. Met. Metalloved. 46 (1978) 187; Phys. Met. Metallogr. (English Transl.) 46 (1978) 159. Viilkl, J., Alefeld, G.: Hydrogen in Metals I. Alefeld, G., Viilkl, J. (eds.), Topics in Appl. Phys. 28 (1978) 321. Banerjee, S., Lee, M.H.: J. Appl. Phys. 50 (1979) 1776. Hasegawa, H., Nakajima, K.: J. Phys. F 9 (1979) 1035. Hauck. J.: Z. Phys. Chem. NE 114 (1979) 165. Katsuta, H., Farraro, R.J., McLellan, R.B.: Acta Metall. 27 (1979) 11II. Kircheim, R.: Ser. Metall. 14 (1980) 905. Kircheim, R., McLellan, R.B.: J. Electrochem. Sot. 127 (1980) 2419. Kircheim, R.: Acta Metall. 29 (1981) 835. Kircheim, R.: Acta Metall. 29 (1981) 845. Mazzolai, EM., Ziichner, H.: Z. Phys. Chem. NE 124 (1981) 59. McLellan, R.B.: Ser. Metall. 15 (1981) 501. Sakamoto, Y, Tabaru, N.: J. Jpn. Inst. Met. 45 (1981) 1048. Sakamoto, Y, Kawachi, M., Hirata, S.: J. Jpn. Inst. Met. 46 (1982) 530. Kidson
Land&-BBmstein New Series III/26
9.5 References for 9 (Pd, Pt, Cu) 83s 84W 842 85B 85Sl 85V 85W 86B 86G 86L 87B
571
Sicking, G., Glugla, M., Huber, B.: Ber. Bunsenges. Phys. Chem. 87 (1983) 418. Wagner, F.E., Probst, F., Wordel, R., Zelger, M.: J. Less-Common Met. 103 (1984) 135. Ziichner, H., Schoneich, H.G.: J. Less-Common Met. 101 (1984) 363. Bucur, R.V.: Z. Phys. Chem. 146 (1985) 217. Schiineich, H.G., Bilitewsky, U., Ziichner, H.: Z. Phys. Chem. NE 143 (1985) 107. Verbruggen, A.H., Lont, A., Griessen, R.: J. Phys. F 15 (1985) 1901. Wicke, E.: Z. Phys. Chem. NE 143 (1985) 1. Bucur, R.V.: Electrochim. Acta 31 (1986) 385. Gillan, M.J.: J. Phys. C. 19 (1986) 6169. Leisure, R.G., Nygren, L.A., Hsu, D.K.: Phys. Rev. B33 (1986) 8325. Bucur, R.V., Indrea, E.: Acta Metall. 35 (1987) 1325.
Pt:
04R 66G 68E 72s 73D 73G 74P 78C 79c 79K 80H 81s 851 cu: 50H 55R 57E 65E 66s 67N 67T 68B 69s 70s *71K 72P 72s 73K 73M 73P 73s 74c 74G 75T 75v 76C
Richardson, O.W., Nicol, J., Parnell, T.: Philos. Mag. 8 (1904) 1. Gileadi, E., Fullenwider, M.A., Bockris, J. O’M.: J. Electrochem. Sot. 113 (1966) 926. Ebisuzaki, Y., Kass, W.J., O’Keefe, M.: J. Chem. Phys. 49 (1968) 3329. Stickney, R.E., Bradley, T.L., Levin, R.L.: Hydrogen, in Metals. (Int. Conf., Jtilich 1972)JUL-Conf6 1(1972) 231. Demin, V.B., Vykhodets, V.B., Gel’d, P.V.: Fiz. Met. Metalloved. 35 (1973) 760; Phys. Met. Metallogr. (English Transl.) 35 (1973) 84. Gol’tsov, VA., et al.: Metody Issled. Opred. Gazov Met., Petrov, A.A., Ivanova, T.F., Vitol, E.N. (eds.) Leningrad: Propag., 1973, p. 23. Podolinskaya, T.A., Mal’gin, A.V., Federov, G.O.: Tr. Ural Politekh. Inst. 231 (1974) 133. Chou, I.M., et al.: Geochim. Cosmochim. Acta 42 (1978) 281. Cermak, J., Kufudakis, A., Gardavska, G.: J. Less-Common Met. 63 (1979) P. 1. Katsuta, H., McLellan, R.B.: J. Phys. Chem. Solids 40 (1979) 697. Harvie, Ch., Weare, J.H., O’Keefe, M.: Geochim. Cosmochim. Acta 44 (1980) 899. Sakamoto, Y, Kamohara, H.: Nihon Kinzuko Gakkaishi, 45 (1981) 797 (J. Jpn. Inst. Met.). Ishikawa, T., McLellan, R.B.: Acta Metall. 33 (1985) 1979. Himmler, W.: Z. Phys. Chem. 195 (1950) 244. Ransley, C.E., Talbot, D.E.: Z. Metallkd. 46 (1955) 328. Eichenauer, W, Pebler, A.: Z. Metallkd. 48 (1957) 373. Eichenauer, W., Loser, W., Witte, H.: Z. Metallkd. 56 (1965) 287. Schenk, H., Lange, K.W.: Arch. Eisenhtittenwes. 37 (1966) 809. Nikulin, V.K., Potekhina, N.D.: Fiz. Met. Metalloved. 23 (1967) 563. Thomas, C.L.: Trans. Metall. Sot. AIME 239 (1967) 485. Belyakov, Yu.I., Zvezdin, Yu.1.: Uch. Zap. Leningrad Gos. Univ. Ser. Fiz. Nauk 345 (1968) 44. Sidorenko, V.M., Kripyakevich, R.I.: Fiz. Khim. Mekh. Mater. 5 (1969) 191; Sov. Mater. Sci. (English Transl.) 5 (1969) 145. Sacris, E.M., Parlee, A.D.: Metall. Trans. 1 (1970) 3377. Katz, L., Guinan, M., Borg, R.J.: Phys. Rev. B4 (1971) 330. Perkins, W.G., Begeal, D.R.: Ber. Bunsenges. Phys. Chem. 76 (1972) 863. Stickney, R.E., Bradley, T.L., Levin, R.L.: Hydrogen in Metals. (Int. Conf., Jtilich 1972)JUL-Conf-6 1(1972) 231. Kazakov, D.N., Kunin, L.L., Litvinova, N.F.: Izv. Akad., Nauk SSSR, Met. 2 (1973) 91; Russ. Metall. (English Transl.) 2 (1973) 62. McLellan, R.B.: J. Phys. Chem. 34 (1973) 1137. Perkins, W.G.: J. Vat. Sci. Technol. 10 (1973) 543. Sidorenko, V.M., Sidorak, 1.1.: Fiz. Khim. Mekh. Mater. 9 (1973) 12. Caskey, G.R., Pillinger, WL.: Hydrogen in Metals. (Proc. Int. Conf., Champion, PA., 1973) Bernstein, I.M., Thompson, A.W. (eds.), ASM, Metals Park, Ohio, 1974, p. 683. Guthrie, J.W., Bearis, L.C., Begeal, D.R., Perkins, WG.: J. Nucl. Mater. 53 (1974) 313. Talbot, D.E.J.: Int. Metall. Rev. 20 (1975) 166. Vyatkin, A.F., Andreev, L.A., Sharfstein, G.I.: Izv. Vyssh. Uchebn. Zaved. Chern. Metall. 7 (1975) 22. Caskey, G.R., Dexter, A.H., Holzworth, M.L., Louthan, M.R., Derrick, R.G.: Corrosion 32 (1976) 370.
Land&-Biirnstein New Series III/26
Kidson
9.5 References for 9 (Cu, Ag, Au, Zn)
572
76P 76V 76W 77c 78B 78Kl 78K2
Popovick, Z.D., Stott, M.J., Cabotte, J., Piercy, G.R.: Phys. Rev. B13 (1976) 590. Vykhodets, V.B., Demin, V.B., Gel’d, P.V.: Phys. Status Solidi A34 (1976) 787. Wampler, W.R., Schober, T., Lengeler, B.: Philos. Mag. 34 (1976) 129. Caskey, G.R., Derrick, R.G.: Metall. Trans. 8 A (1977) 511. Begeal. D.R.: J. Vat. Sci, Technol. 15 (1978) 1146. Katlinskii, V.M.: Izv. Akad. Nauk SSSR, Neorg. Mater. 14 (1978) 1667; Inorg. Mater. (English Transl.) 14 (1978) 1299. Kompaniets, T.N., et al.: Fiz. Tverd. Tela 20 (1978) 3533; Sov. Phys. Solid State (English Transl.) 20 (1978) 2043.
82s 83K 84D 85D 851 86H 86T
Varaksin, A.N., Puzanova, N.M., Volobuev, P.V.: Fiz. Met. Metalloved. 46 (1978) 187; Phys. Met. Metallogr. (English Transl.) 46 (1978) 159. Bugeat, J.P., Ligeon, E.: Phys. Lett. 71 A (1979) 93. Hauck, J.: Z. Phys. Chem. NE 114 (1979) 165. Kurakin, V.A., Kurdyumov, A.A., Lysnikov, V.N., Potapov, M.I.: Fiz. Tverd. Tela 21 (1979) 1060. Teichler, H.: Z. Phys. Chem. NE 114 (1979) 155. Kauer, R., Prakash, S.: J. Phys. F 12 (1982) 1383. Mitchell, D.J.: J. Vat. Sci. Technol. 20 (1982) 1048. Mitchell, D.J., Harris, J.M., Patrick, R.C., Boespflug, E.P., Beavis, L.C.: J. Appl. Phys. 53 (1982) 970. Sakamoto, Y, Takao, K.: J. Jpn. Inst. Met. 46 (1982) 285. Kiuchi. K., McLellan, R.B.: Acta Metall. 31 (1983) 961. Dhawan. L.L., Prakash, S.: J. Phys. E 14 (1984) 2329. DeWulf, D.W., Bard, A.J.: J. Electrochem. Sot. 132 (1985) 2965. Ishikawa, T., McLellan, R.B.: J. Phys. Chem. Solids 46 (1985) 445. Hagi. H.: Trans. Jpn. Inst. Met. 27 (1986) 233. Tanabe, T., Sawada, K., Imoto, S.: Trans. Jpn. Inst. Met. 27 (1986) 321.
Ag: 28s 57s 58E 67M 70M 70s 71s 74E 79K 83M 851
Steacie, E.W., Johnson, F.M.G.: Proc. R. Sot. London All7 (1928) 662. Siegelin, W., Lieser, K.H., Witte, H.: Z. Elektrochem. 61 (1957) 359. Eichenauer, von W., Kiinzig. H., Pebler, A.: Z. Metallkd. 49 (1958) 220. Matzke, H.: Z. Metallkd. 58 (1967) 573. Mindyuk, A.K.: Fiz. Khim. Mekh. Mater. 6 (1970) 60. Sacris, E.M., Parlee, N.A.D.: Metall. Trans. 1 (1970) 3377. Sicking. G., Buchold, H.: Z. Naturforsch. 26A (1971) 1973. Einziger, R.E., Huntington, H.B.: J. Phys. Chem. Solids 35 (1974) 1563. Katsuta. H.: Ser. Metall. 13 (1979) 65. Mahajan, S., Singh, N., Prakash, S.: J. Phys. F 13 (1983) 1449. Ishakawa, T., McLellan, R.B.: Acta Metall. 33 (1985) 1979.
78V
79B 79H 79K 79T 82K 82Ml 82M2
Au: 62E 73D 741 76C 77Cl 77C2 78B 79A 79K 83M 8511 *8512 Zn: 68W
Eichenauer, von W., Liebscher, D.: Z. Naturforsch. 17A (1962) 355. Demin, V.B., Vykhodets, V.B., Gel’d, P.V.: Fiz. Met. Metalloved. 35 (1973) 760; Phys. Met. Metallogr. (English Transl.) 35 (1973) 84. Ionov, N.I., Kompaneets, TN., Kostovanov, A.I., Kurdyumov, A.A.: Fiz. Tverd. Tela 16 (1974) 2541; Sov. Phys. Solid State (English Transl.) 16 (1975) 1654. Caskey, G.R., Derrick, R.G.: Ser. Metall. 10 (1976) 377. Chao, F., Costa, M.: Hydrogen in Metals (Proc. 2nd Int. Congr., Paris 1977), New York: Pergamon Press,9 (1977) 5 A8. Chao, F., Costa, M., Elkaim, P.: C. R. Acad. Sci. C284 (1977) 639. Begeal, D.R.: J. Vat. Sci. Technol. 15 (1978) 1146. Aziz, N.E.A., Kishk, S.S., Farag, N.: Indian J. Phys. A53 (1979) 292. Kurakin, V.A., Kurdyumov, A.A., Lyasnikov, V.N., Potapov, M.I.: Fiz. Tverd. Tela 21 (1979) 1060; Sov. Phys. Solid State (English Transl.) 21 (1979) 616. Mahajan, S., Singh, N., Prakash, S.: J. Phys. F 13 (1983) 1449. Ishikawa, T., McLellan, R.B.: Acta Metall. 33 (1985) 1979. Ishikawa, T., McLellan, R.B.: J. Phys. Chem. Solids 46 (1985) 1393. Wa_gman,D.D., Evans, W.H., Halow, I., Parker, U.B., Bailey, SM., Schumm, R.H.: NBS (U.S.) Tech. Note 270-3, 1968, p. 181. Kidson
Land&-B6mstein New Series Ill/26
9.5 References for 9 (Zn, Al, Pb, Th, U) 71M 72K
573
Moon, I.M.: J. Korean Inst. Met. 9 (1971) 158. Kim, I.B., Moon, I.M.: J. Corros. Sci. Sot. Korea 1 (1972) 51.
Al:
55R 57E 61E 67Ml 67M2 68E 69M 69Y 74A 75A 75v 76P 77P 79D 791 80E 801 81N 81P 81Y 820 83H 83K 83N 84C 85M 861
Ransley, C.E., Talbot, D.E.: Z. Metallkd. 46 (1955) 328. Eichenauer, von W., Pebler, A.: Z. Metallkd. 48 (1957) 373. Eichenauer, von W., Hattenbach, K., Pebler, A.: Z. Metallkd. 52 (1961) 682. Matsuo, S., Hirata, T.: Nihon Kinzoku Gakkaishi 31 (1967) 590; J. Jpn. Inst. Met. (English Transl.) 31 (1967) 590. Matzke, H.: Z. Metallkd. 58 (1967) 572. Eichenauer, von W.: Z. Metallkd. 59 (1968) 613. Matsuo, S., Hirata, T.: Trans. Nat. Res. Inst. Met. (Jpn) 11 (1969) 88. Young, J.R.: J. Vat. Sci. Technol. 6 (1969) 398. Andreev, L.A., Vyatkin, A.F., Zhukhovitskii, A.A.: Zh. Fiz. Khim. 48 (1974) 2359. Andreev, L.A., Vyatkin, A.F., Levchuk, B.V., Telkov, V.I., Rabinovich, A.L.: Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metall. 5 (1975) 123. Vyatkin, A.F., Andreev, L.A., Danilkin, V.A.: Izv. Vyssh. Uchebn. Zaved. Chern. Metall. 3 (1975) 23. Popovic, Z.D., Stott, M.J., Carbotte, J.P., Piercy, G.R.: Phys. Rev. B13 (1976) 590. Papp, K., Kovacs-Csetenyi: Ser. Metall. 11 (1977) 921. DBrr, R., Brauer, E., Gruner, R., Rauch, F.: Z. Phys. Chem. NF 116 (1979) 1. Ichimura, M., Imabayashi, M., Hayakawa, M.: Nihon Kinzoku Gakkaishi 43 (1979) 876. Edwards, R.A.H., Eichenauer, W: Ser. Metall. 14 (1980) 971. Ichimura, M., Imabayashi, M., Hayakawa, M.: Nihon Kinzoku Gakkaishi 44 (1980) 1045; J. Jpn. Inst. Met. (English Transl.) 44 (1980) 1053. Nakashima, M., Aratono, Y, Tachikawa, E.: J. Nucl. Mater. 98 (1981) 27. Papp, K., Kovacs-Csettnyi, E.: Ser. Metall. 15 (1981) 161. Yau, K.L.: Z. Metallkd. 72 (1981) 495. Outlaw, R.A., Peterson, D.T., Schmidt, EA.: Ser. Metall. 16 (1982) 287. Hashimoto, E., Kino, T’.: J. Phys. F 13 (1983) 1157. Kiuchi, K., McLellan, R.B.: Acta Metall. 34 (1983) 961. Nakashima, M., Saeki, M., Aratono, Y, Tachikawa, E.: J. Nucl. Mater. 116 (1983) 141. Choo, W.Y., Bernstein, I.M.: Metall. Trans. 15A (1984) 1953. Myers, S.M., Besenbacher, F., Nsrskov, J.K.: J. Appl. Phys. 58 (1985) 1841. Ishikawa, T., McLellan, R.B.: Acta Metall. 34 (1986) 1091.
Pb:
671 7oc
Ives, D.J.G., Smith, F.R.: Trans. Faraday Sot. 63 (1967) 217. Cadersky, I., Muju, B.L., Smith, F.R.: Can. J. Chem. 48 (1970) 1789.
Th: *6OP
Petersen, D.T., Westlake, D.G.: J. Phys. Chem. 64 (1960) 649.
u: 58M 68M 73P
Mallett, M.W., Trzeciak, M.J.: Trans. ASME 50 (1958) 981. Mueller, W.M., Blackledge, J.P., Libowitz, G.G.: Metal Hydrides, New York: Academic Press, 1968. Powell, G.L., Condon, J.B.: Anal. Chem. 45 (1973) 2349.
Land&-Biirnstein New Series III/26
574
10.1 ‘Mass dependence of diffusion
[Ref. p. 577
10 Mass and pressuredependenceof diffusion in solid metals and alloys 10.1 Mass dependence of diffusion When diffusion of two isotopes of the same element with different massesm, and mp is investigated in the samesolvent under identical conditions the pertaining diffusion coefficients D, and D, will be slightly different. This difference is usually denoted as isotope effect in diffusion. This effect is primarily of interest for more fundamental physical reasons.In particular it is sensitive to the atomistic mechanism of diffusion.
10.1.1 The isotope effect parameter It is common practice to characterize the isotope effect of solute atoms, which may be either self-atoms or foreign atoms, in a given solvent (metallic element or alloy) by the quantity
(10.1)
Ihis quantity is denoted as isotope effect parameter or as strength of the isotope efict. In the present chapter isotope effects of hydrogen diffusion will not be considered. Diffusion data for hydrogen isotopes are collected in chapter 9. This procedure is reasonable from a theoretical point of view as we!!since quantum effectsmay be important for diffusion of hydrogen isotopes, whereas for lithium and heavier diffusers quantum effects are negligible. If hydrogen diffusion is excluded the experimental values of E,., fall between the limits 0
(10.2)
The lower limit corresponds to a negligible mass dependence of the diffusion coefficient. The upper limit is obtained for the classical relationship (10.3)
Ihis limit can be reached when during the diffusion process of a solute (self-atoms or foreign atoms) only the atoms of the diffusing speciesundergo displacements. However, usually the diffusion of solutes involves correation and many-body effectsas we!!. As a consequencethe isotope effect parameter will normally have a value rmaller than unity. For details the reader is referred to [7OL, 75P].
10.1.2 Experimental methods Isotope effects in diffusion - except diffusion of hydrogen isotopes which is not considered in the present chapter - are small effects.Typically the quantity (D,/DP- 1) is less than a few percent. The smallness of this quantity and the fact that diffusion dependsstrongly on temperature have an impact on the method to measure isotope effects. In the best of scientific diffusion studies reproducibility of a few percent for the diffusion coefficients can be obtained in two independent diffusion experiments. Therefore, isotope effect experiments of solute diffusion are always performed in such a way that two isotopes are diffused simultaneously into the same sample. If this is done errors in the diffusion coefficients due to temperature measurement and profiling cancel each other and the diffusivities pertain to an identical solvent crystal. In practically a!! casesthin layer methods in combination with direct profile measurements (seesubsect. 1.6.1.2.1)are applied. Typical situations for isotope effect experiments are illustrated schematically in Fig. 1 for the casesof self- and impurity diffusion in pure metallic elements (a and b) and for self-diffusion of components in a binary alloy (c). The diffusion experiments are usually conducted in such a way that the thin-film solution of Fick’s second law is applicable. If this is the case it can easily be shown that the relation
Mehrer, Stolica
Land&-B6mstein New Series 111126
Ref. p. 5771
10.1 Mass dependence of diffusion
575
7
ln(:)=const-(2-l)
lnc,
(10.4)
where c, and cp denote the concentrations of the isotopes, must hold. Eq. (10.4)is fundamental for practically all isotope effect experiments. The ratio of the isotope concentrations has to be measured as a function of the tEoncentration of one isotope. The example shown in Fig. 2 illustrates the accuracy which can be obtained in 1practice [78H]. The relative difference in the diffusion coefficients (DJDP - 1) can be deduced from the slope of a plot of logarithm of (c&J versus logarithm of c,. In most isotope effect experiments radioisotope pairs are used as diffusors. The separation of the two isotopes after profiling can be based on the different half-lives of the isotopes, on the type of radiation, on energy ,discrimination in p- as well as y-counting using p- and NaI(T1) counters, on energy discrimination in Ge(Li) or 1intrinsic Ge y-spectrometers, or on combinations of these methods. In some isotope effect experiments stable isotopes are utilized as diffusors. The separation is then achieved 1by mass spectrometry or in a commercial SIMS device.
A*,A**
A”:p;“*or B*. B**
a b c Fig. 1. Schematic illustration of various isotope effectexperiments;(a)diffusionof isotopepair A*, A** in pure solventA (self-diffusion); (b) diffusion of isotope pair B*, B** in pure solvent A (impurity diffusion); (c) diffusion of isotope pairs A*, A** or B*, B** in binary AB alloy (self-diffusion in alloys). s ? 6 u’ z
Fig. 2. Simultaneous diffusion of the isotope pair “‘Au/ lg5Au in Au single crystals at various temperatures plotted according to Eq. (10.4)[78H].
Land&-Biimstein New Series III/26
‘Mehrer, Stolica
576
10.1 Mass dependence of diffusion
[Ref. p. 577
10.1.3 The isotope effect and correlation As already mentioned a measurement of the isotope effect can provide information about the atomic mechanism of diffusion. This is due to the fact that the isotope effect parameter can often be written as (seee.g. [7OL. 75P, 85P]) (10.5) E,,,=f,AK. In (10.5) f, denotes the so-called correlation factor of isotope CLand AK its kinetic energy factor. AK is the fraction of the kinetic energy at the saddle point, associatedwith motion in jump direction, that belongs to the diffusing atom. Hence AK is bound between zero and unity. The interest in isotope effect measurementsin solid state diffusion has been often motivated by the occurrence of the correlation factor in Eq. (10.5).Correlation factors by their definition are always bound between zero and unity. It is often of interest that correlation factors are not the same for different mechanisms of diffusion. For the caseof self-diffusion this can be seenfrom Table 1. If more than one mechanism contributes to self-diffusion and for foreign atom diffusion the correlation factor will be temperature dependent. A measurementof E,., can provide information regarding the value of the correlation factor in any material for which a suitable pair of isotopes is available and provided that (10.5) is applicable. It has been shown (for details see,e.g.,[7OL, 75P, 85P]) that (10.5) is indeed valid for some frequently observed diffusion mechanisms in somecubic structures. For example (10.5)holds for the direct interstitial and for the monovacancy mechanism in fee, bee and diamond structures and for the divacancy mechanism in the fee lattice. Nevertheless it should be noted that (10.5)is an equation of limited validity. Some of the limitations can be found in the literature (see,e.g., [7OL, 73M, 76M, 85P, 8711). Table 1. Correlation factors for self-diffusion in the fee and bee lattices. Mechanism of diffusion
Monovacancy Divacancy Interstitial
Correlation factor fee
bee
0.781 0.468 1
0.727 0.346...0.487 1
10.1.4 Use of the isotope effect tables and figures In the tables and figures of the present chapter mainly isotope effect data for diffusion of sohrte atoms (self-atoms or foreign atoms) in solid metals and alloys are presented.The few available isotope effect data for the semiconducting elements Si and Ge have been also included for reasonsof completeness.Data on diffusion of hydrogen isotopes are presented in chapter 9. The data are reported for elements in section 10.2 and for (binary) alloys in section 10.3 in terms of the isotope effect parameter E,., defined in (10.1).Experimental errors are listed in brackets in the column ‘isotope effect parameter E,, B’as well. The digits in brackets refer to the last digits of E,,,. E,,, and E,,, are not equal, but E,,, can be calculated from E,,, for given isotope masses.On the other hand in most isotope effect experiments the relative massdifferences between the isotopes of the isotope pair used are of the order of a few percent or less. If this is the case Em,pand E,,, are almost equal. Lithium is the only metal for which isotope effects of the soleent have been reported as well. The isotope inter-diffusion was studied for tracers of 6Li in 7Li as solvent as well as for tracers of ‘Li in 6Li as solvent. In this case the ratio of the two diffusion coefficients will bc reported. The order oft/~ eler~lerltsaccording to which the isotope effect data for diffusion in solid metals are compiled in the tables is the same as in the chapters 2 and 3. If data for several diffusors (self-atoms and foreign atoms) in the same element are available self-diffusion will be listed first. The foreign atom diffusors are then listed according to their position in the periodic table, like in chapter 3. For bimry nllo~~ only relatively few isotope effect measurementsare available. The data are compiled in the same order as the diffusion data for binary alloys in chapters 4 and 5. The column ‘Isotope poir/Rmnrks in the isotope effect tables usually contains the following information: (i) The isotope pair is stated in the order ~1,p. In most casesradioisotopes have been used. If stable isotopes were utilized this is stated explicitly. Mehrer, Stolica
Landolt-BGmslein New Series III!26
10.2.1 Isotope effect tables for diffusion in alkali metals
Ref. p. 5981
577
(ii) The use of single- or polycrystals is stated. The grain size of polycrystals is indicated whenever this information is available. (iii) The nominal purity of the samples is stated. For alloys the purity of components used for the alloy preparation is stated. (iv) The sectioning technique (lathe, microtome, grinder, sputtering, . . .) used for the diffusion profile determination is stated. (v) The separation scheme of isotopes is stated. (vi) Some optional information may be stated as well. Central to the present chapter are the tables. From the tables reference is made to the figures. For all materials where E, p is measured over a whole temperature range a diagram of the isotope effect parameters as a function of temperature has been included in the figure section. In figures pertaining to metallic elements the melting temperature T, is indicated. Several metals undergo allotropic transformations which transform one crystal structure into another when the temperature is changed. The transformation temperatures are indicated in the figures as well. The values of the transformation and melting temperatures are taken from [73H].
10.1.5 References for 10.1 Le Claire, A.D.: Correlation Effects in Diffusion in Solids, in: “Physical Chemistry - An Advanced Treatise,” Vol. X, Ch. 5, Eyring, H., Henderson, D., Jost, W. (eds.),New York, London: Academic Press 1970. Hultgren, R., Desai, ED., Hawkins, D.T., Gleiser, M., Kelley, K.K., Wyman, D.D.: SelectedValues of the Thermodynamic Properties of the Elements, Metals Park, Ohio: American Society for Metals, 1973. Mehrer, H.: Korrelation bei der Diffusion in kubischen Metallen, Habilitationsschrift, Universitat Stuttgart, 1973. Peterson, N.L.: Isotope Effects in Diffusion, in: “Diffusion in Solids -Recent Developments,“Nowick, A.S., Burton, J.J.(eds.),New York, London: Academic Press, 1975, p. 115. Mehrer, H., Seeger,A., Steiner, E.: Phys. Status Solidi (b) 73 (1976) 131. Herzig, C., Eckseler, H., BuBmann, W., Cardis, D.: J. Nucl. Mater. 69/70 (1978) 61. Philibert, J.:Diffusion et Transport de Mat&e dans les Solides, Paris: Les Editions de Physique, 1985. Ishioka, S., Nakajima, H., Koiwa, M.: Philos. Mag. A 55 (1987) 359.
7OL 73H 73M 75P 76M 78H 85P 871
10.2 The isotope effect tables for diffusion in solid metallic elements Diffusor
Temperature K
D’Li(6Li)/ DeLi(‘Li)
Method/Remarks
Ref.
10.2.1 Isotope effects in alkali metals Li, Na, K, Rb, Cs, Fr Lithium (Li) Li self-diffusion
308.65 314.65 334.35 334.85 356.25 381.45 393.05 406.65 427.05 435.15 438.65 448.75
1.33 1.31 1.40 1.37 1.14 1.30 1.35 1.26 1.24 1.22 1.25 1.32
Isotope interdiffusion of 6Li in ‘Li and of 7Li ind 6Li 7OL studied; purity of Li and the use of poly- or single crystals not specified; the symbol DeLi(‘Li) denotes the diffusion coefficient of trace amounts of 6Li in isotopically pure ‘Li solvent; D7Li(6Li) is vice versa
(continued) Land&-BBmstein New Series III/26
Mehrer, Stolica
578
[Ref. p. 598
10.2.2, 3 Isotope eff. tables for diff. in alkaline earth, SC group, rare earth metals
Diffuser
Temperature K
Isotope effect Isotope pair/Remarks parameter Em,D
Ref.
Lithium (Li), continued Na
423.15
0.19 (1)
cu
420.65
0.11 (3)
k
423.15
0.26 (1)
“Na, 24Na; presumably polycrystal (not specified in 73Ml [73Ml]); 99.98%; sectioning by razor; half-life separation of isotopes; isotope effect of Ag in Li also studied 64Cu, 67Cu; presumabl y p 01ycr ystal, (not specified in 73M2 [73M2]); 99.98%; sectioning by razor; separation of isotopes by y-counting and half-life ‘lonAg, losAg; presumably polycrystal (not specified 73Ml in [73Ml]); 99.98%; sectioning by razor; separation of isotopes by y-counting and half-life; isotope effect of Na in Li also studied Sodium (Na)
313.15 Na self-diffusion 328.05 336.35 345.15 357.15 362.75 365.75 368.85 370.35 Na
247.65
jelf-diffusion 3t ambient pressure
273.25
Na
307.85
313.15 353.05 357.35 369.05 287.95
0.3643 0.3868 0.3665 0.3553 0.3620 0.3081 0.2474 0.2249
(130) (290) (400) (90) (360)
0.3845 0.3890 0.3755 0.3733 0.3396 0.3148 0.2586 0.4025 0.3530 0.3440 0.3351 0.3351 0.2833 0.2991 0.2653
(90) (70) (40) (40) (40) (90) (40) (90) (220) (220) (40) (40) (70) (90) (70)
22Na, 24Na; polycrystals (grain size 3 mm); 99.95% ; microtome sectioning; y-counting and half-life separation of isotopes; see Fig. 3
66M
22Na, 24Na; polycry stals; 99.9995%; microtome settioning; half-life separation of isotopes; see Fig. 3
71M
(110) (40)
(130) 0.2991 (70)
Potassium, rubidium, cesium, francium No data available.
10.2.2 Isotope effects in alkaline earth metals Be, Mg, Ca, Sr, Ba, Ra There are no reported isotope effect measurementsfor alkaline earth metals.
10.2.3 Isotope effects in scandium group and rare earth metals SC,Y, La, etc. There are no reported isotope effect measurementsfor scandium group and rare earth metals,
Mehrer, Stolica
Land&-B6mstein New Series III,/26
Ref. p. 5981 Diffusor
10.2.4 Isotope effect tables for diffusion in titanium group metals Temperature K
Isotope effect Isotope pair/Remarks parameter E,, B
579 Ref.
10.2.4 Isotope effects in titanium group metals Ti, Zr, Hf Titanium (Ti) Sn in P-Ti
co in a-Ti
1245 1388 1481 1581.7 1798 889.3 984.5 1097.2 888.0 984.7 1097.6 1097.2
0.18 (3) 0.22 (2) 0.31 (2) 0.36 (2) 0.37 (3) 11c axis : 0.089 (14) 0.078 (12) 0.073 (14) I c axis: 0.317 (13) 0.293 (12) 0.317 (15) polycrystal 0.265 (7)
‘13Sn, ‘21mSn;polycrystals of bee P-phase; 99.97%; lathe sectioning; separation of isotopes by P-rspectroscopy; see Fig. 4
77J
6oCo 57Co; single crystals ]I and I hexagonal c axis 85N an& polycrystals; 99.97% ; lathe sectioning; separation of isotopes by y-spectroscopy; seeFig. 4
Zirconium (Zr) Zr 1215 self-diffusion 1459 in p-Zr 2057 2088 Zr 1189 self-diffusion 1245 in j3-Zr 1330 1444 1512 1592 1592 1771 1871 2000 Hf 1190 in j3-Zr 1278 1378 1590 1695 1906 1972 co 1214 in j3-Zr 1258 1335 1386 1561 1741 1199 Ag in p-Zr 1239 1406 1582 1749 Land&-Bhmstein New Series III/26
-0.03 (7) 0.00 (3) 0.06 (14) 0.00 (6) 0.285 (23) 0.324 (12) 0.354 (8) 0.352 (19) 0.370 (13) 0.375 (17) 0.368 (11) 0.408 (17) 0.396 (10) 0.411 (24) 0.450 (25) 0.454 (12) 0.463 (12) 0.435 (18) 0.437 (22) 0.445 (30) 0.406 (15) 0.266 (12) 0.233 (11) 0.245 (14) 0.191 (6) 0.224 (21) 0.215 (12) 0.436 (21) 0.355 (19) 0.334 (20) 0.389 (24) 0.361 (28)
8gZr gOZr; polycrystals of bee P-phase(5 to 7 mm 70G grain size); 99.85%; lathe and microtome sectioning; separation of isotopes by y-spectroscopy; not included in Fig. 5 g5Zr, 8sZr; polycrystals of bee P-phase(1 to 3 mm 79H2 grain size); 99.96% (detailed specification of purity in Table 1 of [79H2]; lathe sectioning; separation of isotopes by y-spectroscopy; seeFig. 5
175Hf, 181Hf; polycrystals (3 to 4 mm grain size); 99.99% and 99.9 % ; lathe sectioning; separation of isotopes by y-spectroscopy; seeFig. 5
87Hl
6OCo,57Co; polycrystals (1 to 3 mm grain size);
87H2
99.99% ; lathe sectioning; separation of isotopes by y-spectroscopy; seeFig. 5
“‘Ag, losAg; polycrystals of bee P-phase; purity specified in [79H2]; lathe sectioning; separation of isotopes by y-spectroscopy; seeFig. 5
Mehrer, Stolica
82Ml
580
10.2.5 Isotope effect tables for diffusion in vanadium group metals
Diffusor
Temperature K
Isotope effect Isotope pair/Remarks parameter E,. B
[Ref. p. 598 Ref.
Hafnium @If) Hf 2012 self-diffusion 2086 in g-Hf 2133 2201 2201 2288 2351
0.36 (I) 0.35 (2) 0.32 (1) 0.31 (2) 0.32 (2) 0.28 (3) 0.29 (2)
82HI “‘Hf, “‘Hf; polycrystals (2 to 3 mm grain size); 97 % (main impurity Zr); lathe sectioning; separation of isotopes by y-spectroscopy; seeFig. 6
10.2.5 Isotope effects in vanadium group metals V, Nb, Ta Vanadium (V) Fe
1282 1570 1618 1688 1778 1918 2090
0.681 (47) 0.695 (61) 0.704 (41) 0.574 (38) 0.421 (74) 0.374 (55) 0.296 (82)
68C “Fe, “Fe; single crystals; lathe sectioning at high and chemical sectioning at low temperatures; separation of isotopes by y-counting; see Fig. 7
Niobium (Nb) Nb 1929 self-diffusion 1974 2075 2086 2212 2319 2341 2480 2555 2579 2605 2648 2656 2673 Fe 1888 2168
0.430 (26) 0.431 (23) 0.485 (12) 0.433 (23) 0.458 (23) 0.455 (14) 0.435 (27) 0.369 (20) 0.398 (20) 0.374 (12) 0.400 (I 1) 0.417 (14) 0.398 (1I) 0.346 (10) 0.049 (40) 0.025 (66)
“Nb, “Nb; single crystals; 99.9% (z 500 at. ppm C, 81B x 60 at. ppm 0); microtome sectioning; separation of isotopes by y-spectroscopy; seeFig. 8
“Fe 5gFe; polycrystals; 99.9 % (detailed specification 76A, of’purity); lathe sectioning; separation of isotopes 77A by y- and X-ray counting; similar data in [76A]; seeFig. 8 Tantalum (Ta)
No data available.
Mehrer, Stolica
Land&-BCmsfein New Series III!26
Ref. p. 5981 Diffusor
10.2.6, 7, 8 Isotope effect tables for diffusion in Cr, Mn, Fe group metals Temperature K
581 Ref.
Isotope effect Isotope pair/Remarks parameter E,, B
10.2.6 Isotope effects in chromium group metals Cr, MO, W Chromium (Cr) 1714 Cr self-diffusion 1765 1805 1996 2024 2060 2083
0.52 (2) 0.41 (2) 0.45 (3) 0.41 (4) 0.35 (2) 0.38 (3) 0.31 (2)
51Cr 48Cr; single crystals; 99.95% ; grinder sectioning; 76M2 seiaration of isotopes by y-counting; see Fig. 9
Molybdenum (MO) No data available. Tungsten (W) Cr
MO
2084 2157 2195 2308 2411 2461 2529 2596 2658 1909 2084 2157 2195 2411 2529 2596 2658
0.128 (13) 0.159 (14) 0.115 (37) 0.131 (14) 0.132 (16) 0.137 (13) 0.140 (8) 0.156 (11) 0.112 (12) 0.156 (40) 0.179 (50) 0.178 (37) 0.213 (29) 0.280 (25) 0.348 (22) 0.349 (36) 0.299 (24)
stable isotopes 5oCr, 54Cr; single crystals; “high purity”; SIMS-analysis; preliminary data in [87K]; see Fig. 10
89K
stable isotopes “MO, g8Mo, ll”Mo; single crystals; “high purity”; SIMS-analysis; seeFig. 10
89K
10.2.7 Isotope effects in manganese group metals Mn, Tc, Re There are no reported isotope experiments for manganese group metals.
10.2.8 Isotope effects in iron group metals Fe, Ru, OS Iron (Fe) 1444 Fe self-diffusion 1461 1509 in y-Fe 1559 1579 1622
0.661 (43) 0.474 (43) 0.644 (69) 0.599 (58) 0.572 (81) 0.494 (72)
55Fe 5gFe; pblycrystals (2 to 5 mm grain size); 99798% ; lathe sectioning; separation of isotopes by y- and gas flow counting; seeFig. 11
68H
(continued)
Land&-Biimstein New Series III/26
Mehrer, Stolica
10.2.9 Isotope effect tables for diffusion in Co group metals
582 Diffuser
Temperature K
[Ref. p. 598 Ref.
Isotope effect Isotope pair/Remarks parameter E., B Iron (Fe), continued
Fe 1168 ;elf-diffusion 1168 In u-Fe 1169 1169 ielf-diffusion 1641 In y-Fe 1641 self-diffusion 1683 in &Fe 1683 1685 1685 1706 1706 1733 1733 993 Fe self-diffusion 1043 1142 in a-Fe self-diffusion 1611 in y-Fe self-diffusion 1725 in &Fe 1051.5 Fe self-diffusion 1051.5 in a-Fe 1051.5 1174 1174 1174 828 Fe self-diffusion 869 in a-Fe 953 1005 1023 1042 1052 1079 1107
0.431 (15) 0.502 (49) 0.382 (21) 0.459 (25) 0.529 (13) 0.531 (13) 0.340 (4) 0.338 (5) 0.342 (5) 0.332 (5) 0.337 (5) 0.340 (5) 0.337 (7) 0.328 (7) 0.40 (15) 0.51 (6) 0.69 (14) 0.79 (5)
69W 59Fe, 52Fe; polycrystals (grain size not specified in [69Wj); 99.95% ; lathe sectioning for y- and &runs, and grinder sectioning for a-runs; half-life separation of isotopes by y-counting; see Fig. 11
69G 55Fe, 59Fe; polycrystals (3 to 4mm grain size); 99.999%; microtome or lathe sectioning; separation of isotopes by y-counting; see Fig. 11
0.71 (6) 0.44 0.42 0.41 0.47 0.50 0.41 0.60 (2) 0.59 (2) 0.60 (5) 0.59 (4) 0.55 (1) 0.51 (4) 0.48 (4) 0.48 (3) 0.46 (5)
721 55Fe 59Fe; single crystals of cl-Fe; three different p&ties studied - no dependence of E observed; microtome sectioning; separation of isotopes using y-counting and a gas flow counter; seeFig. 11; isotope effects in dilute Fe 0.09 at. % V, Fe 0.11 at. % Ti and Fe 0.27 at. % Cu also studied “‘Fe, 59Fe; polycrystals (grain size about 6 mm); high 881 purity electrolytic iron; sputter sectioning; separation of isotopes by y-counting; seeFig. 11
Ruthenium (Ru) No data available. Osmium (OS) No data available.
10.2.9 Isotope effects in cobalt group metals Co, Rh, Ir Cobalt (Co) 1451 co self-diffusion 1465 1538
0.684 (11) 0.691 (11) 0.681 (17)
6oCo, 57Co; polycrystals (grain size 2 to 3 mm); 99.99%; lathe sectioning; separation of isotopes by y-counting; seeFig. 12 (continued) Mehrer, Stolica
Land&-Bbmstein New Series III/26
Ref. p. 5981 Diffuser
583
10.2.10, 11 Isotope effect tables for diffusion in Ni group and noble metals Temperature K
Ref.
Isotope effect Isotope pair/Remarks parameter E., p Cobalt (Co), continued
1611 1718 1737 1745
79B
0.648 (25) 0.640 (15) 0.655 (9) 0.649 (10) Rhodium (Rh)
No data available. Iridium (Ir) No data available.
10.2.10 Isotope effects in nickel group metals Ni, Pd, Pt Nickel (Ni) 1473 Ni self-diffusion 1673
0.7 (1) 0.6 (1)
76Ml 57Ni, 63Ni; single crystals; 99.997%; sectioning by precision milling; separation of isotopes by p-counting at different energies Palladium (Pd)
1725.7 Pd self-diffusion 1725.7 1775.8 1775.8
0.8096 (441) 0.8275 (352) 0.8148 (445) 0.8026 (457)
lozPd i12Pd; single crystals; 99.999%; lathe sectioning: half-life separation of isotopes; Em,@values recalculated as mean values of 4 counting runs
64P
Platinum (Pt) No data available.
10.2.11 Isotope effects in noble metals Cu, Ag, Au Copper (Cu) 1167.6 cu self-diffusion 1219.1 1219.9 1271.5 1333.9 1220 cu self-diffusion 1250 1282 1346 1351 1220 1250 1282 1316 1346 1351
0.673 (19) 0.695 (18) 0.690 (11) 0.695 (7) 0.668 (8) 0.74 (3) 0.74 (5) 0.63 (7) 0.54 (7) 0.58 (3) 0.71 (3) 0.74 (4) 0.61 (5) 0.59 (5) 0.60 (3) 0.61 (3)
67Cu, 64Cu; single crystals; 99.999%; lathe sectioning; 69R half-life separation of isotopes; see Fig. 13
‘j7Cu 64Cu; single crystals; 99.999%; microtome set- 90F tiohing; separation of isotopes by y-spectroscopy
‘j7Cu Wu; material and procedure like for 67Cu/64Cu pa&
(continued)
Land&-Biirnstein New Series III/26
Mehrer, Stolica
10.2.11 Isotope effect tables for diffusion in noble metals
584 Diffusor
Temperature K
[Ref. p. 598 Ref.
Isotope effect Isotope pair/Remarks parameter E., s Copper (Cu), continued
Mn
1195
990.0 1040.5 1200.6 1329.2 1329.2 1130 1130 1130 1138 1138 779 839 968 1130 1130 1142 1142 1167.7 1219.6
0.312 (29)* 0.275 (43) 0.310 (15)* 0.325 (27) 0.296 (21)* 0.308 (56) 0.320 (23)* 0.314 (37) 0.590 (53) 0.650 (28) 0.679 (43) 0.681 (36) 0.742 (52) 0.833 (11) 0.818 (18) 0.795 (13) 0.828 (19) 0.827 (17) 0.768 (60) 0.792 (65) 0.773 (80) 0.801 (35) 0.830 (17) 0.802 (27) 0.797 (40) 0.410 (4) 0.410 (10)
983 1025 1077 1089 1226 1274 1295 1309 1125 1126
0.13 (5) 0.22 (7) 0.22 (10) 0.24 (7) 0.30 (8) 0.28 (7) 0.33 (16) 0.31 (10) 0.043 (28) 0.083 (19)
1215.5 1226.4 1227.7 1230.4 1263.0
0.532 (34) 0.550 (34) 0.593 (34) 0.522 (30) 0.574 (32)
1197 1201 1202 Fe
co
Ni
Au
Zn
Cd
In
Ga
83R 52Mn 54Mn; single crystals; 99.999%; microtome secioning; separation of isotopes by y-spectroscopy; values for Ea,awith asterix were corrected for tracer evaporation; see Fig. 13; data also in [83H2]
5gFe, “Fe; single crystals; 99.998%; lathe sectioning; 61M separation of isotopes using absorber techniques and GM tube; see Fig. 13; isotope effects of Fe in Ag also studied 78E 57Co 6oCo; single crystals; 99.999%; microtome sectioning; separation of isotopes by y-spectroscopy; see Fig. 13; isotope effects of Au in Cu also studied
stable isotopes 5*Ni, 64Ni; single crystals; 99.99%; SIMS analysis; see Fig. 13
76s
“‘Au “‘Au; single crystals; 99.999%; microtome sectfoning; half-life separation of isotopes; see Fig. 13; isotope effect of Co in Cu also studied
78E
6sZn, 6gZn; single crystals; 99.999%; lathe sectioning; 67Pl half-life separation of isotopes; seeFig. 13; isotope effects in ordered and disordered CuZn alloys also studied 8282 llSmCd, “‘Cd; polycrystals (2 to 4 mm grain size); 99.998%; grinder sectioning; separation of isotopes by y- and p-counting; see Fig. 13
* i ‘In l 14mIn; single crystals; 99.999%; microtome 81H seciioning; half-life separation of isotopes; see Fig. 13; similar data in [83H2]; isotope effects of Sn in Cu, Zn in Au, Ga in Au, In in Au and Sn in Au also studied 88Sl stable istopes ‘jgGa, ‘lGa; single crystals; purity not specified; SIMS analysis; data taken from Fig. 6 of [88Sl]; seeFig. 13 (continued)
Mehrer, Stolica
Land&BBmskin New Series III/26
Diffusor
585
10.2.11 Isotope effect tables for diffusion in noble metals
Ref. p. 5981
Temperature K
Isotope effect Isotope pair/Remarks parameter E,, p
Ref.
Copper (Cu), continued Ge
Ge
Sn
1234
0.423 (27)
1236 1244
0.478 (43) 0.451 (43)
1239 1239 1239 1239 1106 1106 1128 1128
0.462 (17) 0.478 (32) 0.493 (66) 0.571 (65) 0.159 (15) 0.128 (15) 0.119 (9) 0.116 (11)
68Ge, 77Ge; coarse grain polycrystals; 99.999%; lathe 77H sectioning; separation of positrons and electrons emitted by the two isotopes in a magnetic spectrometer; see Fig. 13; isotope effects in CuGe alloys also studied 79Hl 70Ge, “jGe. 72Ge, “jGe1 single crystals; 99.999% ; SIMS analysis 73Ge 76Ge. of stable Ge isotopes, seeFig. 13 74Ge: 76Gej I l13Sn 117mSn;single crystals; 99.999%; microtome 81H seciioning; separation of isotopes by y-spectroscopy; seeFig. 13; similar data in [83H2]; isotope effects of In in Cu, Zn in Au, Ga in Au, In in Au, and Sn in Au also studied Silver (Ag)
913.6 949.9 1001.3 1019.7 1052.8 1120.6 1210.1 1227.7 946 Ag self-diffusion 1071 1097 1210 1213 1220 1227 1203 Ag self-diffusion
0.7050 (78) 0.7180 (84) 0.7180 (111) 0.7180 (110) 0.6570 (116) 0.6700 (106) 0.6390 (113) 0.6390 (128) 0.72 (7) 0.69 (7) 0.67 (9) 0.64 (17) 0.64 (6) 0.59 (7) 0.58 (8) 0.6590 (14)
1038 self-diffusion 1038
0.696 (35) 0.687 (34)
Ag self-diffusion
Ag Ag
self-diffusion
Mg
Land&-Biimstein New Series III/26
625.5 671 726 773.5 782 830 874.5 880 1085.7
0.86 (13) 0.72 (10) 0.76 (11) 0.77 (12) 0.77 (12) 0.74 (11) 0.68 (10) 0.74 (11) 0.08 (10)
losAg, llom.4g; single crystals; 99.999%; lathe sectioning; separation of isotopes by y-counting; seeFig. 14
70R
losAg, “OrnAg; single crystals; 99.999%; microtome 72R sectioning; separation of isotopes by their half-lives; seeFig. 14
losAg ‘11Ag; single crystals; 99.999% ; lathe 73P sectioning; separation of isotopes by p- and y-counting; seeFig. 14; isotope effects for Ag in AgCl and AgBr also studied losAg, “OrnAg; polycrystals; 99.999%; microtome 74Hl sectioning; separation of isotopes by y-spectroscopy; see Fig. 14; isotope effects of Ag in Au also studied 82M2 losAg, ’ ““Ag; single crystals; 99.999% ; sputter sectioning; separation of isotopes by y-spectroscopy; see Fig. 14
stable isotopes 25Mg, 26Mg; polycrystal; 99.9999%; 74H2 electron microprobe analysis of diffusion profile; separation by mass spectrometry; seeFig. 14 (continued)
Mehrer, Stolica
10.2.11 Isotope effect tables for diffusion in noble metals
586 Diffusor
Temperature K
[Ref. p. 598 Ref.
Isotope effect Isotope pair/Remarks parameter Em.,, Silver (Ag), continued
998.6 1070.5 1153.7 1153.7 1200.7 970 1018 1058 1153 1166 1197 1225 1008.2 1084.2 1110.7 1114.2 1114.2 1140.7 1145.2 1158.2 1179.2 1179.2 1060 1060
0.757 (78) 0.615 (60) 0.487 (70) 0.487 (87) 0.751 (68) 0.413 (18) 0.447 (9) 0.473 (9) 0.490 (9) 0.516 (9) 0.499 (9) 0.482 (18) 0.742 (82) 0.676 (76) 0.686 (53) 0.663 (97) 0.671 (84) 0.676 0.664 0.667 0.613 (64) 0.598 (48) 0.373 (14) 0.372 (11)
In
1063 1065
0.330 (26) 0.315 (23)
Sn
1042 1043
0.418 (12) 0.434 (9)
Sn
1119.0 1128.8 1130.1 1152.3 1176.9
0.444 (29) 0.491 (49) 0.449 (21) 0.576(18) 0.636 (22)
Fe
Zll
Cd
Cd
“Fe 5gFe; single crystals; 99.99%; lathe sectioning; se;aration of isotopes by absorber techniques; see Fig. 14; isotope effects of Fe in Cu also studied
1
61M
65Zn 6gZn; single crystals; 99.999%; lathe sectioning; 67R haif-life separation of isotopes; seeFig. 14; ’ ‘OAg diffusion in dilute AgZn alloys also studied
llSmCd, “‘Cd; single crystals; spectroscopical purity; mechanical sectioning; separation of isotopes by Sand y-counting; seeFig. 14; diffusion of “OrnAg in dilute AgCd alloys also studied
77B
115mCd,logCd; single crystals; 99.999%; microtome sectioning: separation of isotopes by y-spectroscopy; seeFig. 14; similar data also in [83H2] l 14mIn,l* ‘In; single crystals; 99.999%; microtome sectioning; separation of isotopes by y-spectroscopy; see Fig. 14; similar data also in [8382]; isotope effects of Sn in Ag also studied l 13Sn l 17mSn;single crystals; 99.999%; microtome sec;ioning; separation of isotopes by y-spectroscopy; seeFig. 14; similar data also in [83H2]; isotope effects of In in Ag also studied stable isotopes ’ ’ %n, ’ “Sn, lzOSn; single crystals; purity not specified; SIMS analysis; data taken from Fig. 6 of [88Sl]; seeFig. 14
84R2
84R1
84R1
88Sl
Gold (Au) AU 1041 self-diffusion 1041 1116 1119 1119 1123 1127 1127 1317 1319 1321
0.706 (26) 0.703 (15) 0.667 (19) 0.721 (29) 0.724 (30) 0.682 (35) 0.720 (27) 0.722 (22) 0.637 (17) 0.624 (23) 0.656 (25)
lggAu lg5Au; single crystals; 99.999%; microtome sectioning; separation of isotopes by y-spectroscopy; seeFigs. 2 and 15; isotope effects of Co in Au also studied
78H
(continued)
Mehrer, Stolica
Landolt-BBmstein New Series III/26
10.2.11 Isotope effect tables for diffusion in noble metals
Ref. p. 5981 Diffusor
Temperature K
Isotope effect Isotope pair/Remarks parameter E,, p
587 Ref.
Gold (Au), continued 1323 1327 1328 1329 1030 1031 1109 1184 1245 1272 1304 1321 1325 1004 1072 1072 1177 1177 1274 1274 1323 1125 1125 1125 1269
0.685 (24) 0.647 (32) 0.676 (19) 0.651 (19) 0.706 (13) 0.698 (16) 0.715 (22) 0.708 (12) 0.685 (14) 0.646 (10) 0.645 (17) 0.632 (13) 0.617 (12) 0.456 (18) 0.469 (18) 0.480 (39) 0.499 (20) 0.510 (25) 0.495 (29) 0.512 (33) 0.455 (18) 0.125 (9) 0.132 (12) 0.120 (17) 0.134 (24)
Ga
1066
0.119 (21)
In
1075 1075 1177 1177
0.223 (34) 0.250 (34) 0.256 (30) 0.214 (18)
Sn
1098.7
0.14 (2)
Sn
1046 1046
0.121 (12) 0.176 (11)
,co
Zn
Land&-BGmstein New Series III/26
57Co 6oCo; single crystals; 99.999%; microtome sectioning; separation of isotopes by y-spectroscopy; see Fig. 15; isotope effects of Au in Au also studied
78H
losAg, llomAg; single crystals; 99.999%; microtome sectioning; separation of isotopes by y-spectroscopy; see Fig. 15; isotope effects of Ag in Ag also studied
74Hl
65Zn, 6gmZn;single crystals; 99.999%; microtome settioning; separation of isotopes by y-spectroscopy and by half-life; seeFig. 15; similar data also in [83H2]; isotope effects of In in Cu, Sn in Cu, Ga in Au, In in Au, Sn in Au and Zn in AuZn alloys also studied 67Ga 72Ga; single crystals; 99.999%; microtome sectioning; separation of isotopes by y-spectroscopy; seeFig. 15; similar data also in [83H2]; isotope effects of In in Au, Sn in Au, Zn in Au, In in Cu, Sn in Cu and Zn in AuZn alloys also studied “‘In, 114mIn;single crystals; 99.999%; microtome sectioning; half-life separation of isotopes; see Fig. 15; similar data also in [83H2]; isotope effects of Ga in Au, Sn in Au, Zn in Au, In in Cu, Sn in Cu and Zn in AuZn alloys also studied l17Sn, l14Sn; crystals; electron microprobe analysis of diffusion profile; separation of stable Sn isotopes by mass spectrometry; see Fig. 15 l13Sn, 117mSn;single crystals; 99.999%; microtome sectioning; separation of isotopes by y-spectroscopy; see Fig. 15; similar data also in [83H2]; isotope effects of In in Cu, Sn in Cu, Ga in Au, In in Au, Zn in Au and Zn in AuZn also studied
81H
Mehrer, Stolica
81H
81H
72H
81H
588
10.2.12, 13 Isotope effect.tables for diffusion in Zn group and Al group metals
Diffusor
Temperature K
[Ref. p. 598 Ref.
Isotope effect Isotope pair/Remarks parameter Ea.B
10.2.12 Isotope effects in zinc group metals Zn, Cd, Hg Zinc (Zn)
Zn self-diffusion 562.5 589.5 621.8 655.6 670.3 684.5 691.1 562.5 589.5 621.8 655.6 670.3 684.5 691.2 Zn self-diffusion 656.0 684.8 656.0 684.8 Cd 616.9 683.2 616.9 683.2
11c axis: 0.693 (10) 0.677 (10) 0.696 (IO) 0.723 (26) 0.729 (10) 0.670 (13) 0.693 (13) 1 c axis: 0.752 (16) 0.755 (10) 0.714 (13) 0.763 (13) 0.785 (13) 0.700 (13) 0.736 (13) 11c axis: 0.646 (25) 0.691 (23) 1 c axis: 0.707 (29) 0.667 (15) 11c axis: 0.449 (23) 0.507 (34) 1 c axis: 0.273 (34) 0.317 (32)
6’Zn 69Zn; single crystals; 11and 1 c axis; 99.999%; 67P2 lathe sectioning; half-life separation of y-activities of isotopes; see Fig. 16
65Zn, 69Zn; single crystals; 11and 1 hexagonal c axis; 67B 99.999%; lathe sectioning; half-life separation of isotopes; seeFig. 16; E,,, values represent averages over 6 measurements;isotope effects of Cd in Zn also studied r15Cd, “‘Cd; single crystals; 11and 1 hexagonal c axis; 99.999%; lathe sectioning; half-life separation of isotopes; seeFig. 16; isotope effects of Zn in Zn also studied
67B
Cadmium (Cd) Zn 472.5 472.5
11c axis: 0.438 (49) 1 c axis: 0.683 (102)
‘j5Zn 69Zn; single crystals; 11and 1 hexagonal c axis; 72M 99.999%; lathe sectioning; separation of isotopes by y-counting Mercury (Hg)
No data available.
10.2.13 Isotope effects in aluminum group metals Al, Ga, In, Tl Aluminum (Al) cu
857.9 930.0
0.890 (50) 0.814 (50)
67Cu 64Cu; single crystals: 99.999%; microtome sec- 78P tioning; half-life separation of isotopes; seeFig. 17; isotope effects of Zn in Cu also studied (continued)
Mehrer, Stolica
Land&-Bhstein New Series Ill!26
Ref. p. 5981 Diffusor
10.2.12 Isotope effect tables for diffusion in aluminum group metals Temperature K
Isotope effect Isotope pair/Remarks parameter Em,, p
589 Ref.
Aluminum (Al), continued
cu
Ag
Fe
Zn
862 873 893 893 909 833 877 893 909 913 926 643 643 738 738 827 827 910.7 910.7 924 924 865.2 883.7 908.2 915.1 922.2 923.4 687.9 689.8 723.5 724.2 752.4 787.2 829.0 840.6 898.9 926.5 928.0
0.57 (3) 0.55 (3) 0.51 (3) 0.53 (3) 0.46 (3) 0.34 (6) 0.31 (4) 0.25 (4) 0.25 (3) 0.22 (3) 0.19 (3) 0.437 (23) 0.396 (24) 0.525 (9) 0.487 (1) 0.543 (25) 0.556 (33) 0.566 (14) 0.582 (17) 0.649 (14) 0.643 (27) 1.07 (25) 1.01 (14) 0.99 (16) 0.54 (9) 0.50 (7) 0.43 (5) 0.366 (8) 0.343 (7) 0.488 (20) 0.396 (12) 0.416 (10) 0.465 (9) 0.472 (8) 0.432 (19) 0.508 (5) 0.584 (9) 0.614 (14)
67Cu 64Cu; single crystals; 99.999% ; microtome sectioning; separation of isotopes by y-spectroscopy
90F
67Cu 61Cu; material and procedure like for 67&f64Cu pair
90F
‘iomAg losAg; single crystals; 99.999%; microtome 75B sectioning; separation of isotopes by y-counting; see Fig. 17
55Fe 5gFe; large grains (2 or 3 grains observed on enh surfaces of samples); 99.995%; microtome sectioning; separation of isotopes by y-counting; preannealing at T < 923K to reach solubility limit inside the solvent; see Fig. 17
89B
65Zn 6gZn* single crystals; 99.999%; microtome sectioning; half-life separation of isotopes; seeFig. 17; isotope effects of Cu in Al also studied
78P
Gallium (Ga) No data available. Indium (In) No data available. Thallium (Tl) No data available.
Land&-Biimstein New Series III/26
Mehrer, Stolica
590
10.2.14, 15 Isotope effect tab. for diff. in group IVB elements, actinide group metals
Diffusor
Temperature K
[Ref. p. 598 Ref.
Isotope effect Isotope pair/Remarks parameter E,, B
10.2.14 Isotope effects in group IVB elements Si, Ge, Sn, Pb Isotope effect data for the semiconducting elements Si and Ge have been also included. Silicon (Si) Ga
Ge
1373 1433 1473 1262 1323 1422 1498
0.31 (3) 0.27 (3) 0.27 (4) 0.28 (IO) 0.32 (8) 0.33 (14) 0.23 (6)
stable isotopes 6gGa, 7’Ga; single crystals; high spec- 82L tral purity; sputter sectioning; SIMS analysis stable isotopes 70Ge, 72Ge, 73Ge,74Ge, 76Ge; single crystals; sputter sectioning; SIMS analysis; similar data also in [83S]
88S2
Germanium (Ge) 1173.5 Ge self-diffusion 1173.9 1197.1 1198.0 1040 Ga 1097
0.246 (6) 0.275 (6) 0.293 (6) 0.312 (9) 0.244 (50) 0.244 (65)
7’Ge 77Ge; single crystals; high purity; sectioning by chemical etching; half-life separation of isotopes
75c
stable isotopes ‘jgGa, 7’Ga; single crystals; specific re- 86s sistivity 60 Qcm; sputter sectioning; SIMS analysis Tin (Sn)
No data available. Lead (Pb) cu
594.7
0.23 (8)
Ag
573 573
0.91 (15) 1.22 (26)
Ag
423.3 569.6 573.2 576.3 569.5 562 562 570 570 521.1
0.31 (2) 0.25 (1) 0.19 (I) 0.30 (I) 0.26 (2)* 0.300 (66) 0.226 (43) 0.246 (43) 0.246 (42) 0.119 (37)
498 570
0.23 (4) 0.23 (5)
Au
Cd
Hg
64Cu 67Cu; single crystals; 99.9999%; microtome sec- 74M tioking; half-life separation of isotopes; seeFig. 18 71H losAg ’ * ‘Ag; polycrystals (0.3 to 0.8 cm grain size); 99.6995%; microtome sectioning; separation of isotopes by half-lives and P-y-spectroscopy 73M3 “‘Ag ‘lomAg; single crystals; 99.999%; microtome secioning; separation of isotopes by half-lives and y-counting; seeFig. 18; *value refers to a Pb 0.08 at.% Ag alloy lg5Au, rggAu; polycrystals (2 mm grain size); 8284 99.999%; microtome sectioning; half-life separation of isotopes; see Fig. I8 logCd llsmCd; single crystals; 99.9999%; microtome sectioning; separation of isotopes by l3- and X-ray counting using g-filter; seeFig. I8 lg7H f5 ‘03Hg; polycrystals (3 mm grain size); 99.999%; microtome sectioning; separation of isotopes by half-lives and y-spectrometry; seeFig. I8
69M
8283
10.2.15 Isotope effects in actinide group metals AC, Th, Pa, U, Np, Pu, etc. There are no reported isotope effect measurementsfor actinides.
Mehrer, Stolica
landolbB6mstein New Series III,/26
10.3 Isotope effect tables for diffusion in binary alloys
Ref. p. 5981
10.3 The isotope effect tables for diffusion in binary alloys Diffusor
Composition
Temperature Isotope effect parameter E,, B K
Isotope pair/Remarks
Ref.
Au Zn alloys Au
48.37 at.% Zn 876 876 48.59 878 49.10 874 49.40 878 49.41 875 49.47 757 49.78 874 49.83 757 50.27 875 50.70 875 50.73 814 50.92 875 51.01
Zn 49.18 at.% Zn 49.35 50.20 50.43 51.85
916 928 835 837 810
0.22 (2) 0.30 (3) 0.41 (4) 0.24 (3) 0.32 (2) 0.21 (6) 0.37 (4) 0.20 (3) 0.23 (2) 0.25 (3) 0.29 (3) 0.35 (3) 0.36 (3) CsCl-structure 0.228 (17) 0.186 (13) 0.090 (35) 0.101 (13) 0.053 (10)
83Hl “‘Au iggmAu; polycrystals (2 to 3 mm grain size); lathe sectioning; separation of isotopes by y-spectroscopy and half-lives
65Zn, 6gmZn;polycrystals; microtome 81H, sectioning; separation of isotopes by 83H2 y-spectroscopy and half-lives; isotope effects of In in Cu, Sn in Cu, Ga in Au, In in Au, Sn in Au and Zn in Au also studied
CoFe alloys 20
12 at.% Co
Fe
49 to 50 at.% Fe
1003 1034 1077 1091 1137 1171 1175 1185 928 956 975 994.7 1068 1150 1175 1217.7
co
Land&-Biirnstein New Series III/26
1285 1335 1400 1434 1333
0.85 (2) 0.82 (3) 0.82 (4) 0.81 (8) 0.80 (4) 0.70 (4) 0.69 (3) 0.68 (6) CsCl-structure 0.06 (20) 0.30 (20) 0.16 (20) 0.30 (15) bee 0.54 (8) 0.46 (8) 0.64 (10) 0.55 (8) fee 0.67 (8) 0.71 (8) 0.65 (8) 0.61 (8) 0.773 (100)
Mehrer, Stolica
5’c!o 6oCo; polycrystals of 3 to 4 mm 89L grain size; prepared from 99.97% Fe and 99.97% Co; sputter sectioning; separation of isotopes by y-counting and y-spectroscopy
55Fe, 5gFe and ‘j°Co, 57Co; large grain 70F polycrystals of equiatomic CoFe alloy with CsCl-type ordered, bee and fee phases; prepared from 99.99% Fe and 99.99% Co; lathe and grinder sectioning; separation of isotopes by y- and X-ray counting; seeFig. 19
70F
10.3 Isotope effect tables for diffusion in binary alloys
592 Diffusor
Composition
Temperature Isotope effect K parameter E., B
[Ref. p. 598 Ref.
Isotope pair/Remarks
Cr 80% Ni alloy /Cr
80 at.% Ni
1518
stable isotopes “Cr, 54Cr; polycrystals; purity not specified; electron microprobe analysis of concentration profile; mass spectrometry
0.5
66H
CuGe alloys Ge
4.81 at.% Ge 9.45
1228 1155
0.422 (42) 0.461 (46)
6*Ge, “Ge; coarse grain polycrystals; 77H 99.999% Cu; lathe sectioning; separation of positrons and electrons emitted by the two isotopes in a magnetic spectrometer; isotope effects of Ge in Cu also studied
CuZn alloys cu 3.6 at.% Zn 29.8
1169.6 1166.1
46.8
683.1
46.2
835.8
Zn 4.89 at.% Zn 30.6
1169.9 1169
41.2
683.8
49.0
833.5
64Cu, 67Cu and 65Zn, (j9Zn; single 7OP a-brass crystals of u-CuZn alloys and of 0.699 (7) ordered and disordered B-brass; pre0.632 (9) pared from 99.999% Cu and Zn; ordered P-brass lathe sectioning; half-life separation 0.325 (10) disordered P-brass of y activities of isotopes; data for E of Zn in p-brass from [67Pl] 0.325 (9) u-brass 0.389 (10) 0.446 (8) ordered P-brass 0.20 disordered P-brass 0.24 Fe 3% Si alloy
Fe
3 at.% Si
980 996 1008 1016 1023 1039 1062 1076 1083 1128 1175
0.336 (48) 0.339 (45) 0.336 (44) 0.343 (45) 0.339 (41) 0.343 (38) 0.346 (37) 0.349 (36) 0.346 (35) 0.377 (34) 0.397 (40)
55Fe, 59Fe; single crystals; “high pm-i- 71G ty”; grinder sectioning and measurement of residual activity; separation of isotopes by y- and gas flow counting; seeFig. 20
ScZr alloys Zr
6.7 at.% SC 13.6
1300 1380 1680 1416 1519 1589 1826
0.397 (10) 0.397 (10) 0.375 (10) 0.351 (20) 0.400 (13) 0.379 (17) 0.372 (10)
95Zr, 88Zr; polycrystals (ca. 2 mm grain size); prepared from MARZ quality Zr and 99.99% SC; lathe sectioning; separation of isotopes by y-spectrometry
Mehrer, Stolica
87H3
Land&BBmstein New Series 1rr,lza
Ref. p. 5981 The isotope effect for diff. in solid metallic
elements and binary
alloys (Figs.)
593
Figures for 10.2 and 10.3
0.42
Solvent Na n a 0.38 I
v . na
I
0.34
Ll
0.30
VW1 . NaL66Ml A NoI7lMl (ambient pressure1 v tjaf71M 1 (pc0.7GPa)
CUE
I .;, E
O.Z?
360 320 340 lFig. 3. Na. Isotone effectuarameter for diffusion of Na [66M, 7&I] in sodium ia. temperature. J
260
200
300
380 K 41
0.6
0.5 0.4 -
OX
I
cu
I
~ 0.3-
0.3
0.2
0.2-
0.1
0.1-
0 800
1000
1200
1400 TM
1600
1800 K 2000
Fig. 4. Ti. Isotope effectparameters for diffusion of Co [85N] and Sn [7751in titanium vs. temperature. pc: polycrystal.
Landolt-BCrnstein New Series III/26
O1000
1200
1400
1600 I-
1800
2000 K 2200
Fig. 5. Zr. Isotope effect parameters for diffusion of Zr [79H2], Ag [82Ml], Co [87H2] and Hf [87Hl] in zirconium vs. temperature.
Mehrer, Stolica
[Ref. p. 598
The isotope effect for diff. in solid metallic elements and binary alloys (Figs.)
594
0.8 0.7 I 0.6 I 0.31 0.32 u
Lu 0.5 06 0.3
0.26
1900 2000 2100 2200
2300
2kOO 2500 K 2600
0.2 1200
l-
Fig. 6. Hf. Isotope effect parameter for diffusion of Hf [82Hl] in j-hafnium vs. temperature.
1800
2000
2200
2600
1400
1600 I-
1800
2000 K 2200
Fig. 7. V. Isotope eflect parameter for diffusion of Fe [68c] in vanadium vs. temperature.
2600 K 2800
0.38 0.381
l-
I
I
I
Solvent W
Fig. 8. Nb. Isotope effectparameters for diffusion of Nb [81B] and Fe [77A, 76A] in niobium vs. temperature.
0.34
I .
I
I
l
0.30 0.30
I 0.26
I
41
0.22
0.18 0.38
1700
1800
1900
2000
2100 K 2200
1800
00
c
o.lo_ 0.10 2000
2200
2400
2600 K 2800
l-
l-
Fig. 9. Cr. Isotope effectparameter for diffusion of Cr [76M2] in chromium vs. temperature.
Fig. 10. W. Isotope ellect parameters for diffusion of Cr [89K] and MO [89K] in tungsten vs. temperature.
Mehrer, Stolica
Landok-BGmsfein New Series III:26
Ref. p. 5981 0.9 -
The isotope effect for diff. in solid metallic elements and binary alloys (Figs.) I
I
Solvent Fe 0.8 -
cql
I
I
I
Cl J
! FeI68Hl
700
900
1100
I
Fei7211
I
Fe169Gl -
’
1300 T-
1500
1
1650 1700 1750 K 1 ’ TFig. 12. Co. Isotope effectparameter for diffusion of Co [79B] in cobalt vs. temperature.
1700 K 191
1450
Fig. 11. Fe. Isotope effectparameter for diffusion of Fe [68H, 721,69G, 69W, 8811in iron vs. temperature Tc: Curie temperature.
1500
1550
1600
0.9
Solvent Cu 0.8
bo PA n
n
0.7
.
0
0.6
"
~>.
O !I 0,
. %
t 0.5 - .l AuI78El Cu[69Rl
.
l .*:-
OS 0 700
800
900
1000 T-
1100
1200
1300 K 1400
Fig. 13. Cu. Isotope effect parameters for diffusion of Cu [69R], Au [78E], Cd [82H2], Co [78E], Fe [61M], Ge [77H, 79Hl], In [81H], Mn [83R], Ni [76S],Sn [81H], Zn [67Pl] and Ga [88Sl] in copper vs. temperature.
Land&-Biirnstein New Series III/26
595
Mehrer, Stolica
I
596
The isotope effect for diff. in solid metallic elementsand binary alloys (Figs.)
[Ref. p, 598
0.6 I 0.5 I Lu 0.4 0,3--a 0.3 q
+ I D
0.20.1 0.1 -.
0
0 0. 600
A
Cd f77Bl Cd 18LR21 Fe 161Ml In 184Rll Mg174H21 Sn I84Rll ln 167Rl Sn 188511 I
700
+ +
I =I E &I
x
800
900
1000
1100
1200 K 1300
l-
Fig. 14. Ag. Isotope elkct parameters for diffusion of Ag [70R, 72R, 73P, 74H1, 82M2], Cd [77B, 84R2], Fe [61M], In [84Rl], Mg [74H2]. Sn [84Rl, 88Sl] and Zn [67R] in silver vs. tempcraturc.
0.7 I 0.6 LJ 0.5
0.2 560
580
600
620
6LO
660
680 K 7
I-
l-
-ig. 15. Au. Isotope effect paramctcrs for diffusion of Au 78HJ.Ag (74HlJ. Co [78H], Ga (81H], In (81H]. Zn [81H] and in [72H, 81H] in gold vs. tempcraturc.
Fig. 16. Zn. Isotope effect parameters for diffusion of Zn [67P2, 67BJand Cd [67B] in zinc vs. temperature.
Mehrer, Stolica
Land&Bkmfein New Series 111:X
Ref. p. 5981
0.9
The isotope effect for diff. in solid metallic elements and binary alloys (Figs.)
I
I
0
I
597
I I
b
0.3 I 600
400
2 700
800 T-
900
K
1000
Fig. 17. Al. Isotope effect parameters for diffusion of Fe [89B], Ag [75B], Cu [78P] and Zn [78P] in aluminum vs. temperature.
Soivent Phi
L50
500
1
/
550
600
1
K
650
T-
Fig. 18. Pb. Isotope effect parameters for diffusion of Ag [73M3], Au [82H4], Cd [69M], Cu [74M] and Hg [82H3] in lead vs. temperature.
0.39 0.38 I 0.37 cu 0.36 0.35
0.33I 950
1050
1100
I 1150 K 1200
TW
T-
Fig. 19. CoFe (equiatomic). Isotope effectparameters for diffusion of Fe and Co [70F] in CoFe alloy vs. temperature.
Land&Biirnstein New Series III/26
1000
Fig. 20. Fe 3 % Si. Isotope effectparameter for diffusion of Fe [71G] in Fe 3 % Si alloy vs. temperature.
Mehrer, Stolica
598
References for 10.2 and 10.3
Referencesfor 10.2 and 10.3 61M 64P 66H 66M 67B 67Pl 67P2 67R 68C 68H 69G 69M 69R 69W 70F 70G 7OL 7OP 70R 71G 71H 71M 72H 721 72M 72R 73Ml 73M2 73M3 73P 74Hl 74H2 74M 75B 75c 75P 76A 76Ml 76M2 76s 77A 77B 77H 775 78E 78H 78P 79B 79Hl 79H2 81B
Mullen. J.G.: Phys. Rev. 121 (1961) 1649. Peterson, N.L.: Phys. Rev. 136 (1964) A 568. Heumann. Th., Reerink, W.: Acta Metall. 14 (1966) 201. Mundy, J.N., Barr, L.W., Smith, EA.: Philos. Mag. 14 (1966) 785. Batra, A.P.: Phys. Rev. 159 (1967) 487. Peterson, N.L., Rothman, S.J.: Phys. Rev. 154 (1967) 558. Peterson, N.L., Rothman, S.J.: Phys. Rev. 163 (1967) 645. Rothman, S.J., Peterson, N.L.: Phys. Rev. 154 (1967) 552. Coleman, M.G., Wert, C.A., Peart, R.F.: Phys. Rev. 175 (1968) 788. Heumann, T., Imm, R.: J. Phys. Chem. Solids 29 (1968) 1613. Graham, D.: J. Appl. Phys. 40 (1969) 2386. Miller, J.W.,Edelstein, W.A.: Phys. Rev. 188 (1969) 1081. Rothman, S.J., Peterson, N.L.: Phys. Status Solidi 35 (1969) 305. Walter, C.M., Peterson, N.L.: Phys. Rev. 178 (1969) 922. Fishman, S.G., Gupta, D., Lieberman, D.S.: Phys. Rev. B2 (1970) 1451. Graham, D., Hanes, E.R.: NASA Technical Note D 5905, 1970. Lodding. A., Mundy, J.N., Otto, 0.: Phys. Status Solidi 38 (1970) 559. Peterson, N.L., Rothman, S.J.: Phys. Rev. B2 (1970) 1540. Rothman, S.J., Peterson, N.L., Robinson, J.T.: Phys. Status Solidi 39 (1970) 635. Gonzalez, C.O., de Reca, N.E.W.: J. Phys. Chem. Solids 32 (1971) 1067. Herzig. Ch., Heumann, Th., Wolter, D.: Z. Naturforsch. A26 (1971) 1477. Mundy, J.N.: Phys. Rev. B3 (1971) 2431. Heumann, Th., Kueper, H., in: “Atomic Transport in Solids and Liquids”, Lodding, A., Lagerwall, T. (eds.), Tiibingen: Verlag der Z. Naturforsch., 1971, p. 241 Irmer, V., Feller-Kniepmeier, M.: J. Appl. Phys. 43 (1972) 953. Mao, C.: Phys. Rev. B5 (1972) 4693. Reimers, P., Bartdorff, D.: Phys. Status Solidi (b) 50 (1972) 305. Mundy, J.N., McFall, W.D.: Phys. Rev. B7 (1973) 4363. Mundy, J.N., McFall, W.D.: Phys. Rev. B8 (1973) 5477. Miller, J.W.,Mundy, J.N., Robinson, L.C., Loess, R.E.: Phys. Rev. B8 (1973) 2411. Peterson, N.L., Barr, L.W., Le Claire, A.D.: J. Phys. C6 (1973) 2020. Herzig, Ch., Wolter, D.: Z. Metallkde. 65 (1974) 273. Heumann, Th., Kohl, J.G.: Acta Metall. 22 (1974) 21. Mundy, J.N., Miller, J.W.,Rothman, S.J.: Phys. Rev. BlO (1974) 2275. Bartdorff, D., Reimers, P.: Phys. Status Solidi (a) 28 (1975) 433. Campbell. D.R.: Phys. Rev. B12 (1975) 2318. Peterson, N.L.: Isotope Effects in Diffusion, in: “Diffusion in Solids-Recent Developments”, Nowick, A.S., Burton, J.J.(eds.), New York, London: Academic Press, 1975, p. 115. Ablitzer, D.: La Diffusion dans les Milieux Condenses, 19’ Colloque de MCtallurgie. Saclay, Vol. 1 (1976) p. 73. Maier, K., Mehrer, H., Lessmann, E., Schiile, W.: Phys. Status Solidi (b) 78 (1976) 689. Mundy, J.N., Tse, T.W., McFall, W.D.: Phys. Rev. B13 (1976) 2349. Seran. J.L.: Acta Metall. 24 (1976) 627. Ablitzer, D.: Philos. Mag. 36 (1977) 391. Bharati, S., Sinha, A.P.B.: Phys. Status Solidi (a) 44 (1977) 391. Hehenkamp, Th., Schlett, V.: Acta Metall. 25 (1977) 1109. Jackson, MS., Lazarus, D.: Phys. Rev. B15 (1977) 4644. Eckseler, H., Herzig, Ch.: Phys. Status Solidi (b) 85 (1978) 185. Herzig. Ch., Eckseler, H., BuBmann, W., Cardis, D.: J. Nucl. Mater. 69/70 (1978) 61. Peterson, N.L., Rothman, S.J.: Phys. Rev. B 17 (1978) 4666. BuBmann, W., Herzig, Ch., Remp, W., Maier, K., Mehrer, H.: Phys. Status Solidi (a) 56 (1979) 87. Hehenkamp, Th., Lodding, A., Odelius, H., Schlett, V.: Acta Metall. 27 (1979) 829. Herzig. Ch., Eckseler, H.: Z. Metallkde. 70 (1979) 215. Bunmann, W., Herzig, Ch., Hoff, H.A., Mundy, J.N.: Phys. Rev. B23 (1981) 6216.
Mehrer, Stolica
Landoh-BBmctein New Series 111j26
References for 10.2 and 10.3 81H 82Hl 82H2 82H3 82H4 82L 82Ml 82M2 83Hl 83H2 83R 83s 84Rl 84R2 85N 86s 87Hl 87H2 87H3 87K 881 88Sl 88S2 89B 89K 89L 90F
599
Hilgedieck, R.: Dr. rer. nat. thesis, Universitat Miinster, FRG, 1981. Herzig, Ch., Manke, L., BuDmann, W, in: “Point Defects and Defect Interactions in Metals”, Takamara, J.I., Doyama, M., Kiritani, M. (eds.), University of Tokyo Press, 1982, p. 578; [also: BuBmann, W: Doktorarbeit, Universitat Miinster, FRG, 19821. Hoshino, K., Iijima, Y., Hirano, K., in: “Point Defects and Defect Interactions in Metals”, Takamara, J.I., Doyama, M., Kiritani, M. (eds.), University of Tokyo Press, 1982, p. 562. Herzig, Ch.: DIMETADiffusion in Metals and Alloys, Kedves, F.J.,Beke, D.L. (eds.), Diffusion and Defect Monograph Series 7 (1983) 330; [also: Rokosch, H.-J.: Diplomarbeit, Universitat Miinster, FRG, 19791. Herzig, Ch.: DIMETADiffusion in Metals and Alloys, Kedves, F.J.,Beke, D.L. (eds.), Diffusion and Defect Monograph Series 7 (1983) 330; [also: Stracke, E.: Doktorarbeit, Universitat Miinster, FRG, 19791. Lodding, A., Odelius, H., Sodervall, U.: SIMS III, Benninghoven, A., Giber, J., Laszlo, J., Riedel, M., Werner, H.W. (eds.), Springer Ser. Chem. Phys. 19 (1982) 351. Manke, L., Herzig, Ch.: Acta Metall. 30 (1982) 2085; [also: Manke, L.: Diplomarbeit, Universitit Miinster, FRG, 19791. Mehrer, H., Hutter, F.: in “Point Defects and Defect Interactions in Metals”, Takamara, X-I., Doyama, M., Kiritani, M. (eds.), University of Tokyo Press, 1982, p. 558. Hilgedieck, R., Herzig, Ch.: Z. Metallkde. 74 (1983) 38. Herzig, Ch., Rockosch, H.J., Hilgedieck, R.: DIMETADiffusion in Metals and Alloys. Kedves, F.J., Beke, D.L. (eds.), Diffusion and Defect Monograph Series 7 (1983) 330. Rockosch, H.J., Herzig, Ch.: Phys. Status Solidi (b) 119 (1983) 199. Siidervall, U., Roll, U., Predel, B., Odelius, H., Lodding, A., Gust, W.: DIMETADiffusion in Metals and Alloys. Kedves, F.J., Beke, D.L. (eds.), Diffusion and Defect Monograph Series7 (1983) 492-499. Rockosch, H.J., Herzig, Ch.: Philos. Mag. A49 (1984) 717. Rockosch, H.J., Herzig, Ch.: Acta Metall. 32 (1984) 503. Nakajima, H., Ishioka, S., Koiwa, M.: Philos. Mag. A52 (1985) 743. Sijdervall, U., Odelius, H., Lodding, A.: Philos. Mag. A54 (1986) 539. Herzig, Ch., KBhler, U.: Materials ScienceForum 15-18 (1987) 301; [also: Schulten, R.: Diplomarbeit, Universitat Miinster, FRG, 19821. Herzig, Ch., Neuhaus, J.,Vieregge, K., Manke, L.: Materials ScienceForum 15-18 (1987) 481; [also: Manke, L.: Diplomarbeit, Universitat Miinster, FRG, 1979. Herzig, Ch., KBhler, II.: Acta Metall. 35 (1987) 1831. Klotsman, S.M., Osetrov, S.V., Polikarpova, L.P., Tatarinova, G.N., Timofeev, A.N., Shepatkovskiy, O.P.: Fiz. Met. Metalloved. 64 (1987) 148. Iijima, Y, Kimura, K., Hirano, K.: Acta Metall. 36 (1988) 2811. Sodervall, U., Lodding, A., Odelius, H.: Surf. Interface Anal. 11 (1988) 529. Sodervall, U., Odelius, H., Lodding, A.: Scanning Microsc. 2 (1988) 1343. Beke, D.L., God&y, I., ErdClyi, G., Kedves, F.J., Felszerfalvi, J.: DIMETA 88 - Diffusion in Metals and Alloys, Kedves, F.J., Beke, D.L. (eds.), Diffusion and Defect Forum 66-69 (Pt. 1) (1989) 421. Klotsman, S.M., Koloskov, V.M., Osetrov, S.V., Polikarpova, L.P., Tatarinova, G.N., Timofeev, A.N.: DIMETA 88 - Diffusion in Metals and Alloys, Kedves, F.J., Beke, D.L. (eds.), Diffusion and Defect Forum 66-69 (Pt. 1) (1989) 439. Lee, C.-G., Iijima, Y, Hirano, K.I.: DIMETA 88 - Diffusion in Metals and Alloys, Kedves, F.J., Beke, D.L. (eds.), Diffusion and Defect Forum 66-69 (Pt. 1) (1989) 433. Fujikawa, S., Ushino, S.: private communication.
Mehrer, Stolica
600
10.4 Pressure dependence of diffusion
[Ref. p. 624
10.4 Pressure dependence of diffusion In the remaining part of chapter 10 data are compiled for diffusion under high pressure in solid elements (section 10.5),in homogeneous binary alloys (section 10.6)and for interdiffusion in binary alloys (section 10.7). Becausethe pressure dependenceof diffusion is not treated in the “General introduction” (chapter 1) the main concepts are briefly covered in section 10.4. Some remarks about the use of the tables and figures will also be made in 10.4.
10.4.1 Introduction When diffusion is investigated at different hydrostatic pressuresthe pertaining diffusion coefficients will be different. The effect of hydrostatic pressure on diffusion can be seen from the Arrhenius-Boltzmann type of equation for the diffusion coefficient (see,e.g., [83L, 85P, 89K]): D=gfa*v,
(10.6)
exp(- AG/kT).
In (10.6) g denotes a geometrical constant, f a correlation factor, a the lattice parameter and v,, an attempt frequency. AC is the isothermal, isobaric work (increment of Gibbs free energy) required to surmount the diffusion barrier, k denotes the Boltzmann’s constant and T absolute temperature. As usual the Gibbs free energy can be decomposed according to AG=AU+pAV-TAS
(10.7) where p denoteshydrostatic pressure,AU the activation energy, AS the activation entropy and AY the activation volume. Using (10.6) the diffusivity can be written in the form D=gfa*v,
exp(AS/k) exp(-AU/kT)
exp(-pAV/kT).
(10.8)
For positive values of the activation volume D decreaseswith pressure. In very few casesD increases with increasing pressure which implies a negative activation volume. For zero pressure (10.8) reduces to the wellknown Arrhenius relation (seesection 1.8 of the “General introduction”) D=D” exp(- Q/kT)
(10.9)
Do = gfa’ v. exp(AS/k)
(10.10)
Q=AU.
(10.11)
where the preexponential factor is given by and the activation energy Q is for all practical purposes identical with the activation enthalpy at ambient pressure since the term pAV becomessignificant only at much higher pressures:
10.4.2
The activation volume
Using a well-known thermodynamic relationship one can define the activation volume according to (10.12) The activation volume is the isothermal change in volume of a crystal associated with a diffusive jump. This quantity is of interest for technological and for more fundamental physical reasonsas well. Like the value of the activation enthalpy the activation volume provides a fingerprint of the diffusion process and its underlying mechanism. The microscopic interpretation of AV depends on the microscopic mechanism of diffusion (seesection 1.5 of the “General introduction”). We illustrate this by two examples: (i) Diffusion in solids often involves thermally generated defects.The activation volume like the other activation quantities (seechapter 1) is then composed of a defect formation and a defect migration term. In the caseof seljl&@rsion, which is of particular interest since many experimental data for AV concern self-diffusion, we have Al’= VF+ I’” (10.13) where YF is denoted as formation volume and V” as migration volume of the defect involved.
Mehrer, Stolica
Landok-BBmstein New Series W/26
10.4 Pressure dependence
Ref. p. 6241
601
of diffusion
Theformation volumes for a vacancy, a divacancy and for a self-interstitial are illustrated schematically in Fig. 21. The formation volume corresponds to the volume change upon forming a defect in the crystal. The microscopic significance of the formation volume can be envisaged in the following way: The formation of a defect in a “rigid” crystal would change its volume by z Q (Q = atomic volume; e.g.: z = + 1 for a vacancy, z = + 2 for a divacancy, z = - 1 for a self-interstitial). Since the real, finite crystal relaxes one must add a relaxation volume when an outward relaxation occurs and subtract a relaxation volume when an inward relaxation occurs. The migration volume corresponds to the volume change of the crystal between the saddle point configuration and the equilibrium configuration of the jumping atom. An attempt to illustrate the migration volume for an atom which exchanges its site with a vacancy is shown in Fig. 22 a. Iii) For the case of direct interstitial diffusion of foreign atoms the activation volume according to (10.14)
AV= VM contains no formation Fig. 22b.
term. A schematic illustration
of the activation
volume for this case is shown in
Inward relaxation
a
+Q
I/F= + J2- Vrel
Inward relaxation w
a
1
S
2
b
1
s
2
Schematic illustrations of migration volumes Y”: (a) migration volume of a vacancy; (b) migration volume of an interstitial diffusor. Open circles represent solvent atoms. Full circles represent an atom that exchangessites from equilibrium position 1 to equilibrium position 2 by crossing the saddle point configuration S. V Mcorresponds to the volume difference between configuration S and 1 or 2, respectively. Fig. 22.
b
t2i-2
C
-0
vF=+29-l/,,1
vF=-Q+V,,,
Fig. 21. Schematic illustrations of formation volumes VF for various defects: (a) formation volume of a monovacancy; (b) formation volume of a divacancy; (c) formation volume of a self-interstitial. D denotes the atomic volume and 1/;.,the volume changes due to relaxation. qC, is different for different defects.
Land&Biirnstein New Series III/26
Mehrer, Stolica
10.4 Pressure dependence of diffusion
602
[Ref. p. 624
10.4.3 Experimental methods The pressure dependence of the diffusivity is seen by differentiating the logarithm of D in eq. (10.6) with respect to pressure p at constant temperature T: (10.15) Using the definition (10.12) we get for the activation volume (10.16)
Equation (10.16)is the basis for the experimental determination of AV by measuring the pressure variation of the diffusivity at constant temperature. The second term on the right hand side of Eq. (10.16)is a small correction term which is usually estimated using the isothermal compressibility K and Griineisen’s constant yGaccording to [72M, 85P]
kTaIn(da’vo) =k 7-K)',. ap The correction term is typically not more than a few percent of the atomic volume. High hydrostatic pressuresare usually obtained by using an inert gas (mostly argon) or an inert liquid as pressure transmitting medium. For the determination of the activation volume measurementsof D at different pressuresare necessary.For the measurementof D in principle any of the direct and indirect methods described in section 1.6 of the “General introduction” can be used in combination with high hydrostatic pressure: (i) The most commonly applied and the most dependable method is the thin layer method in combination with radiotracers (seesubsection 1.6.1.2.1).As an example Fig. 23a shows penetration curves of 195A~ measuredin AI at three different pressuresunder identical conditions of temperature and time. A semilogarithmic plot of the diffusivities of the samediffusor 19’Au in Al as a function of pressureaccording to [89B] is shown in Fig. 23 b. The diffusion coefficient decreaseswith increasing pressure indicating that AV (as usual) is positive. (ii) In some casesthe thin layer method was used in combination with stable isotopes and SIMS measurements of the diffusion profile (seesubsection 1.6.1.2.1).In one case Rutherford backscattering (RBS) has been used for depth profiling (seesubsection 1.6.1.2.2). (iii) Diffusion couple methods (seesubsection 1.6.1.2.2)in combination with electron microprobe analysis of the diffusion profiles have been applied in the few interdiffusion studies available for binary alloys. (iv) Creep rate measurements (seesubsection 1.6.1.2.5)have been used in a few self-diffusion studies under hydrostatic pressure. (v) Among the indirect methods relaxation methods (seesubsection 1.6.2.1)and NMR (seesubsection 1.6.2.2 have been used.
L
0
I 1
I
I
2
3 .1DeLcm2 4
x2-
Fig. 23a. Semilogarithmicplot of the activity of ‘95A~ in aluminum single crystalsafter diffusion at three different pressures[89B].Temperatures and timesof the diffusion anneal arc the samein all threecases.
Mehrer, Stolica
Landok-B6mstein New Series IIIl26
Ref. p. 6241
10.4 Pressure dependence of diffusion
Fig. 23 b. Semilogarithmic plot of the diffusion coefficient of lg5Au in Al vs. pressureat three different temperatures [89B]. 8: atomic volume.
0
603
2
6 .108Pa
8
10.4.4 Use of the pressure effect tables and figures In the tables and figures of the following parts of chapter 10 pressure effect data for diffusion in solid elements are presented in section 10.5.The few available pressure effect data for the semiconducting elements Si and Ge and for P have been also included in section 10.5for reasonsof completeness.The few data available for diffusion in homogeneous binary alloys are presented in section 10.6 and those for interdljjfusion in binary alloys in section 10.7. The order of the elements according to which the data are compiled in the tables is the sameas in chapters 2 and 3. If data for several diffusors (e.g.self-atoms and foreign atoms) are available self-diffusion will be listed first. The foreign atom diffusors are then listed according to their position in the periodic table, like in chapter 3. For binary alloys the data are compiled in the same order as the ambient pressure diffusion data for binary alloys in chapters 4 and 5. The column “Activation volume” of the pressure effect tables for elements (section 10.5) contains the value of the activation volume in units of the molar volume V, (atomic volume). If the data in the original paper contained AI/’ in units of cm3mol- ’ the quantity AVIV, was calculated by the present authors using the values of the atomic volumes given in [64G]. For foreign atom diffusion V, of the solvent was used as well. In the pressure effect tables of homogeneous alloys (section 10.6) the activation volumes are listed also in units of V,, which is then specified in the column “Pressure range/Method/Remarks”. In the pressure effect tables for interdiffusion (section 10.7) the activation volume is listed in units of cm3mol-‘. The column “Pressure rangefMethod/Remarks” usually contains the following information: (i) The pressure range of the experiments is stated. (ii) The experimental method is briefly characterized. This has been done in the sameway as in chapter 2 (see 2.1.2).
(iii) (iv) (v) (vi)
The nominal purity of the samples will be stated whenever this information is available. The use of single- or polycrystals will be stated. For uniaxial crystals it will be indicated which crystallographic direction has been investigated. For a metal which undergoes (an) allotropic transformation(s) a statement will be included, which crystal structure(s) has (have) been investigated in this particular reference. (vii) Usually reference is made to the pertaining figure. The column “Pressure range/Method/Remarks” may also contain some optional information which concerns the following items: (viii) Remarks on the interpretation of the data by the authors. (ix) If in the same paper additional experiments have been performed this will be indicated as well. Central to the sections 10.5 to 10.7 are the tables. From the tables reference is made to the figures.
Land&-Bihstein New Series III/26
Mehier, Stolica
10.51, 2 Pressure effect tables for diffusion in alkali and alkaline earth metals
604
[Ref. p. 624
10.5 Pressure effect tables for diffusion in solid elements 1Diffusor
Temperature K
Activation volume AV/V,
Ref.
Pressure range/Method/Remarks
10.5.1 Pressure effects in alkali metals Li, Na, K, Rb, Cs, Fr There are reported data for Li, Na and K. Lithium (Li) 0...0.7 GPa; NMR; spin-spin relaxation time T2; dispersed particles (about 20 pm) in silicon fluid; 99.995%; pressure dependenceof Na self-diffusion also studied
0.286 0.282 0.281 0.267 0.288
Li 309.8 self-diffusion 323.2 329.8 344.0 351.2
62H
Sodium (Na) Na 363.2 self-diffusion
0.53...0.31
223.2 Na self-diffusion 228.2 231.0
0.395 0.421 0.409
not specified Na self-diffusion Na 263 self-diffusion 288.0 364.5
0.418
0.. . I .2 GPa; Z2Na; diffusion couples of radioactive and nonactive sodium; purity not specified; microtome sectioning; pressure isotherm curved; seeFig. 24 b 0 .+*0.4 GPa; NMR: spin-spin relaxation time T2; dispersion of particles in silicon fluid; 99.99%; see Fig. 24 b; pressure dependenceof Li self-diffusion also studied 0 ..* 0.1 GPa; tensile creep measurementsunder hydrostatic pressure 0...0.95 GPa; 22Na, 24Na; polycrystal; 99.9995%; mechanical sectioning; pressure isotherms curved; interpretation in terms of two processes (seealso [78M]); seeFigs. 24 a and 24 b
0.41 0.48 0.52
52N
62H
65R 71M
Potassium (K) 288...303 K self-diffusion K self-diffusion
O...O.I GPa; tensile creep measurementsunder hy- 65K drostatic pressure; similar data in [65R] O...O.I GPa; tensile creep measurementsunder hy- 67K drostatic pressure for various creep rates E: * at E<7.10-7s-1; ** at E> 10-6s-’
0.55 (I) 0.55* 0.97**
10.5.2 Pressure effects in alkaline earth metals Be, Mg, Ca, Sr, Ba, Ra There are reported data for Be and Mg. Beryllium (Be) Be 966 self-diffusion 966
1 c: I.2 (1) 11c: 1.2 (1)
0...0.8 GPa; 1 and 11hexagonal c axis investigated: 7Be; single crystals; purity not specified; mechanical sectioning; pressure effects on AI selfdiffusion also studied
Mehrer, Stolica
70B
LandckB6mstein New Series Ill!26
605
Ref. p. 6241 10.5.3, 4 Pressure effect tables for diff. in SCgroup, rare earth, Ti group metals Diffusor
Temperature K
Pressure range/Method/Remarks
Activation volume AVIV,
Ref.
Magnesium (Mg) 771
Cd
0.. .0.8 GPa; I and ]I hexagonal c axis investigated: electron microprobe analysis of Cd profiles; sample purity not specified
I c: 1.04 (10) 11c: 1.10 (9)
72C3
10.5.3 Pressure effects in scandium group and rare earth metals SC,Y, La, Ce, etc. There are reported data for La, Ce and Yb. Lanthanum (La) 1167 La self-diffusion in y-La
0.10
76B2 0. .. 0.56 GPa; bee y-La investigated: 140La; polycrystals; purity not specified; mechanical sectioning Cerium (Ce)
Ce self-diffusion in 6-Ce Ce self-diffusion in y-Ce
1003 1028
- 0.08 - 0.09
948 (or 930)
-0.15
0 ... 1 GPa; bee 8-Ce investigated: 141Ce;polycrys- 74L tals, 99.9% ; mechanical sectioning with measurement of residual activity O... 1 GPa; fee y-Ce investigated: 141C!e;polycrys- 76M tals; 99.9% ; mechanical sectioning; two contradieting statements of temperature in [76M] Ytterbium (Yb)
1003 Yb self-diffusion 1033 1073 in y-Yb
0.590 0.575 0.605
O... 1 GPa; bee y-Yb investigated: 16’Yb; polycrystals; 99.9%; mechanical sectioning
75F
10.54 Pressure effects in titanium group metals Ti, Zr, Hf There are reported data for Ti. Titanium (Ti) Ti 1273 self-diffusion in P-Ti 1175 Fe
Land&-BGmstein New Series III/26
0.33 (9) -
0.03 ... 0.65 GPa; bee P-Ti investigated: 44Ti; poly- 715 crystals; 99.97% . . .99.99 % ; lathe sectioning; similar data in [7lL] 0 ... 0.4 GPa; 5gFe; single crystals; purity not speci- 67P Red; mechanical sectioning; D increases nonlinear with pressure; attributed to diffusion along sub-grainboundaries and segregation; pressure effects of Fe diffusion in Ti 10 at.% Fe also studied
Mehrer, Stoka
10.55, 6, 7, 8, 9 Pressure effect tables for diff. in V, Cr, Mn, Fe, Co group metals
606
Diffusor
Temperature K
[Ref. p. 624
Activation Pressure range/Method/Remarks volume 111//I&
Ref.
10.55 Pressure effects in vanadium group metals V, Nb, Ta There are reported data for V. Vanadium (V) N
429.8 436.2 356.2 364.9 371.2
0
0.146 (15) 0.123 (15) 0.206 (8) 0.226 (9) 0.176 (7)
0.. .0.8 GPa; N induced stress relaxation in V investigated 0. .. 0.9 GPa; 0 induced stress relaxation in V investigated
61T 61T
10.56 Pressure effects in chromium group metals Cr, MO, W There are no reported pressure effect measurementsfor chromium group metals.
10.5.7 Pressure effects in manganese group metals Mn, Tc, Re There are no reported pressure effect measurementsfor manganesegroup metals.
10.5.8 Pressure effects in iron group metals Fe, Rh, OS There are reported data for Fe. Iron (Fe) 234.1
0.052 (47)
238.8 246.0 250.0 253.2
-0.062 -0.062 -0.082 -0.024
:-Fe) E-Fe)
(49) (48) (49) (49)
0...0.3 GPa; N induced magnetic aftereffect in bee 57B cc-Feinvestigated 0.. .0.3 GPa; C induced magnetic aftereffect in bee 60B u-Fe investigated
10.59 Pressure effects in cobalt group metals Co, Rh, Ir There are reported data for hcp Co. Cobalt (Co) ;-co,
348 348
-0.254 (300) -0.072 (30)
0 ... 0.6 GPa; C induced magnetic aftereffect in hcp 71W2 Co investigated; pressure dependence of magnetic aftereffect for C in Ni and Fe 1.4 wt.% Si also studied
Mehrer, Stolica
Land&-BBmsfein New Series Ill/26
Ref. p. 6241 10.5.10, 11 Pressure effect tables for diffusion in nickel group and noble metals Diffusor
Temperature K
Activation volume AVIV,
Pressure range/Method/Remarks
607 Ref.
10.5.10 Pressure effects in nickel group metals Ni, Pd, Pt There are reported data for Ni. Nickel (Ni) C
383
-0.182 (25)
0.. .0.4 GPa; C induced magnetic aftereffect in Ni 71W2 investigated; pressure dependence of magnetic aftereffect for C in Co and Fe 1.4 wt.% Si also studied
10.5.11 Pressure effects in noble metals Cu, Ag, Au Copper (Cu) cu
973
self-diffusion 1023 1073 1173 not specified cu self-diffusion Au 693 765 833 Zn 1256 1286 1313
1.09 (31) 1.03 (29) 0.96 (8) 0.93 (2) 0.6 0.963 (50) 0.920 (37) 0.928 (40) 0.77 0.77 0.88
O... 1 GPa; (j4Cu; single crystals; “pure” copper; 68B2 lathe sectioning; AV recalculated in [89F] using data of [68B2]; seeFig. 25; similar data in [68Bl]; pressure dependence of self-diffusion in Ag and Al also studied 0.. .0.9 GPa; 64Cu; single crystals; purity not spec- 69M ified; serial sectioning 89F 0 ... 0.55 GPa; lg8Au; single crystals; 99.999%; sputter sectioning; see Fig. 25 0 ... 3.2 GPa; diffusion couples of pure Cu and CuZn (4.9 at.%) alloys; electron microprobe analysis of diffusion profiles; seeFig. 25
88Y
Silver (Ag)
Ag
1179
0.865
Ag
1173
0.88
self-diffusion
self-diffusion
594 Ag self-diffusion 683 766 885 994 In 1179
0.66 (2) 0.68 (2) 0.72 (2) 0.77 (2) 0.86 (2) 0.81
Sb
0.765
Land&-B6mstein New Series III/26
1179
0...0.9 GPa; ‘lomAg, lllAg; single crystals; 65B2 99.99%; lathe sectioning; see Fig. 26; pressure effects on In and Sb diffusion in Ag also studied 0.. .0.8 GPa; 1‘OrnAg;single crystals; “pure” silver; 68Bl lathe sectioning; seealso [65Bl, 67B]; seeFig. 26; pressure effects on self-diffusion of Cu, Au and Al and of Cu, Ag and Au in Al also studied 0 ... 0.6 GPa; “OrnAg; single crystals; 99.999%; 82R sputter sectioning; seeFig. 26; pressure dependence of self-diffusion in Au at 692 K also studied 0...0.8 GPa; ‘141n; single crystals; 99.99%; lathe sectioning; seeFig. 26; pressure effects of Sb and Ag in Ag also studied 0 . . .0.8 GPa; lz4Sb; single crystals; 99.99%; lathe sectioning; seeFig. 26; pressure effects of In and Ag in Ag also studied
Mehrer, Stolica
65B2
65B2
608
10.512 Pressure effect tables for diffusion in zinc group metals
Diffuser
Temperature K
Activation volume AVIV,
[Ref. p. 624 Ref.
Pressure range/Method/Remarks
Gold (Au) Au 1133 self-diffusion 1183 1233 Au 973 self-diffusion 1023 1073
0.60 (8) 0.75 (5) 0.61 (14) 0.81 0.68 0.67
Au 692 self-diffusion
0.73 (2)
Au 603 self-diffusion 660 701 760 800 823
0.73 0.74 0.75 0.76 0.76 0.77
0 ... 0.9 GPa; lg8Au; single crystals; 99.99%; lathe sectioning; seeFig. 27
65D
68B2 O... 1 GPa; rg8Au; single crystals; 99.99%; lathe sectioning; AV/V, calculated from data of [68B2]; similar data in [68Bl]; see Fig. 27; pressure effects of Cu and Al self-diffusion also studied 0...0.6 GPa; “*Au; single crystals; 99.999%; sput- 82R ter sectioning; seeFig. 27; pressure dependence of Ag self-diffusion also studied 0...0.6 GPa; lg8Au; single crystals; 99.999%; sput- 83W ter-sectioning; see Fig. 27
10.512 Pressure effects in zinc group metals Zn, Cd, Hg There are reported data for Zn and Cd. Zinc (Zn)
Zn self-diffusion Zn self-diffusion
683 683 574.1 623.9 674.0 574.1 623.9 674.0
1 c: 0.630 (57) 11c: 0.404 (44) I c: 0.392 (10) 0.428 (10) 0.469 (15) 11c: 0.406 (9) 0.433 (5) 0.467 (3)
0...0.9 GPa; 1 and ]I hexagonal c axis investigat- 67s ed.. 65Zn; single crystals; serial sectioning 0...0.9 GPa; 1 and I] hexagonal c axis investigat- 72C2 ed. 65Zn; single crystals; 99.999%; lathe sectioning; see Fig. 28; similar data in [71G2]
Cadmium (Cd) Cd 524 self-diffusion 549 574 592 524 549 574 592
1 c: 0.530 (10) 0.540 (7) 0.575 (11) 0.590 (15) 11c: 0.530 (10) 0.550 (11) 0.590 (7) 0.580 (11)
0...0.8 GPa; 1 and I] hexagonal c axis investigated. “‘Cd, single crystals; 99.999%; lathe sectioning; see Fig. 29; similar data in [71Gl]
Mehrer, Stolica
73B
Land&BCmstein Ncn Series 111’26
Ref. p. 6241 Diffusor
10.5.13 Pressure effect tables for diffusion in aluminum group metals Temperature K
Activation volume AVIV,
Pressure range/Method/Remarks
609 Ref.
10.5.13 Pressure effects in aluminum group metals Al, Ga, In, Tl There are reported data for Al and In. Aluminum (Al) Al self-diffusion Al self-diffusion Al self-diffusion
not specified
1.35
‘.. 562
0.44 . . .0.87
803 843 883
1.23 (7) 1.29 (7) 1.35 (7)
Al 667 self-diffusion 681 681 684 684 708 711 719 721 722 803 cu 843
0.62 0.75 0.52 0.97 0.66 0.65 0.64 0.76 0.87 0.65 1.16 1.16
Ag
843 853
1.19 1.19
Au
803
1.18
Au
785 823 873
0.93 0.91 1.04
Fe
856 896
1.61 1.56
Zn
884
1.09 (10)
863 913
1.00 1.11
787.5
0.87 (1)
Sn
LandolGB6mstein New Series III/26
0 . . . 0.1 GPa; tensile creep measurement under hydrostatic pressure 0 ... 6 GPa; TEM observation of dislocation loop annealing 0 ... 0.8 GPa; 26AI; single crystals; “pure” aluminum; lathe sectioning; similar data in [68Bl, 70B]; seeFig. 30; pressure dependence of self-diffusion in Cu and Au also studied 0 . . .0.2 GPa; NMR: spin-spin relaxation time T,; 325 mesh filings; 99.99%
65R
0.. .0.8 GPa; 64Cu; single crystals; purity not specified; lathe sectioning; pressure effects on self-diffusion of Cu, Ag, Au and Al and of Ag and Au in Al also studied 0.. .0.8 GPa; “OrnAg; single crystals; purity not specified; lathe sectioning; pressure effects on self-diffusion of Cu, Ag, Au and Al and of Cu and Au in Al also studied 0 . . ‘0.8 GPa; lg8Au; single crystals; purity not specified; lathe sectioning; pressure effects on self-diffusion of Cu, Ag, Au and Al and of Cu and Ag in Al also studied 0 . . .0.8 GPa; lg5Au (implanted); single crystals; 99.9995%; microtome sectioning; seeFigs. 23 and 30; pressure effects on diffusion of Fe and Zn in Al also studied 0 . . .0.8 GPa; “Fe (implanted); single crystals; 99.9995%; microtome sectioning; seeFig. 30; pressure effects on diffusion of Au and Zn in Al also studied 0 .. .1.288GPa; ‘j5Zn; single crystals; microtome sectioning 0 .. .0.8 GPa; 65Zn; single crystals; 99.9995%; microtome sectioning; seeFig. 30; pressure effects on diffusion of Au and Fe in Al also studied 0...0.735 GPa; lr3Sn (implanted); single crystals; 99.9995% microtome sectioning
68Bl
Mehrer, Stolica
66N 68B2
71E
68Bl
68Bl
89B
89B
83E 89B 90E
[Ref. p. 624
10.514 Pressure effect tables for diffusion in group IVB elements
610 Diffuser
Temperature K
Activation volume Al’/V,
Pressure range/Method/Remarks
Ref.
Indium (In) 243...388 In self-diffusion In 391.8 self-diffusion 406.1 422 369.3 385.5
AiT
0.76 0.516 (64) 0.529 (25) 0.490 (38) 1 and ]] c axis 0.41 (4) 0.41 (4) 1 and I] c axis
0.08 ..* 5.5 GPa; tensile creep measurements; single crystals; 99.999% O... 0.9 GPa; 1 and ]] tetragonal c axis investigated: 114mIn;single crystals; 99.999%; microtome sectioning
67C
O..* 0.9 GPa; 1 and 11tetragonal c axis investigated: r ’ OrnAg.single crystals; 99.999% ; microtome sectioning
7102
7101
10.514 Pressure effects in group IV B elements Si, Ge, Sn, Pb Data on the semiconducting elements (Si and Ge) have been also included. Silicon (Si) B
Ga
Ge
As
1323 1443 1503 1323
0.29 (30) 0.31 (30) -0.12 (20) -0.85 (25)
1323 1443 1503 1123 1173 1223 1273
-0.52 (20) -0.47 (15) -0.27 (10) -0.475 (192) -0.617 (83) -0.425 (100) -0.391 (108)
O..+1.5 GPa; B implanted in {Ill) Si wafer; SIMS analysis; pressure effects on Ga and Ge diffusion in Si also studied O..+1 GPa; Ga film on (111) Si wafer; SIMS analysis; pressure effects on B and Ge diffusion in Si also studied O... 1.5 GPa; Ge film on {ill} Si wafer; SIMS analysis; pressure effects on B and Ga diffusion in Si also studied O..* 3 GPa; As implanted (5.10” cm-‘) into (111) wafers; RBS profiling; see Figs. 31a and 31b; similar data in [85N2]
89s
89s
89s
85Nl
Germanium (Ge) Ge self-diffusion
Li
876 916 973 1025 1086 573...823
0.24 0.28 0.35 0.36 0.41 0.05 (3) 0.28
0 ... 0.6 GPa; 7’Ge; single crystals; intrinsic materi- 85W al; sputter sectioning; see Fig. 32; doping dependence of self-diffusion and of activation volume at 973 K also studied 0...4.5 GPa; pn junction-depth method; single crystals; Ga doped (1.8.10’6 cme3)
72V
Tin (Sn) Sn 273...330 self-diffusion Sn self-diffusion 465.2 482.0 498.8 465.2 482.0 498.8
0.33 1 c axis: 0.362 (31) 0.319 (15) 0.304 (23) 11c axis: 0.329 (18) 0.321 (18) 0.326 (23)
0 ... 1 GPa; tensile creep measurementsunder hydrostatic pressure O...l GPa; 1 and )I c axis investigated; r*3Sn; single crystals; 99.999%; microtome sectioning; similar data in [65N]
Mehrer, Stolica
63D2 64C
Laodolt-B?rnstein New Series Ill!26
Ref. p. 6241 Diffusor
611
10.5.14 Pressure effect tables for diffusion in group IVB elements Temperature K
Activation volume AVIV,
Pressure range/Method/Remarks
Ref.
Lead (Pb) 526.2 Pb self-diffusion 574.2 Pb 383 self-diffusion
0.843 (98) 0.712 (44) 0.80
476 Pb self-diffusion 526 574 588 599 667 769 273...330 Pb self-diffusion
0.572 0.599 0.615 0.632 0.637 0.670 0.715 0.69 (13)
538.4 Pb self-diffusion 568.3 598.7 Ni 298 600 700
Pd
298 600 700 600
0.728 (17) 0.728 (17) 0.728 (17) at p = 0: 0.111 0.131 0.137 at p = 5 GPa: 0.072 0.092 0.099 0.124*(13)
cu
600
0.04 (3)
Ag
556 588 625 667 714 769 427... 584
0.381 (28) 0.377 (29) 0.376 (30) 0.381 (31) 0.380 (33) 0.387 (34) 0.37
Ag Au
298 523 600
Au
Land&-Bihstein New Series III/26
623 623 473
at p = 0: 0.324 (22) 0.290 (30) 0.280 (30) atp=3GPa: 0.31 (5) 0.42 (7) 0.28 (3)
0 ... 0.8 GPa; “‘Pb; single crystals; 99.999%; microtome sectioning 0 ... 0.1 GPa; tensile creep measurement under hydrostatic pressure; polycrystalline wires; 99.9999% 0.. .4 GPa; ” ‘Pb; single crystals; 99.9999%; electrochemical sectioning; non-linear pressure isotherms (seeFig. 33)
0 ... 1 GPa; tensile creep measurement under hydrostatic pressure; polycrystalline samples; 99.999% 0 .. .I GPa; method and material not specified
59N 61B
61H
63Dl
75B
0 ... 5 GPa; 63Ni; single crystals; 99.9999%; micro- 73C tome sectioning; see Figs. 34 and 35
0...4 GPa; logPd; single crystals; 99.9999%; microtome sectioning; seeFigs. 34 and 36; * average value calculated by present authors 0.. .5.6 GPa; 64Cu; single crystals; 99.9999%; microtome sectioning; seeFigs. 34 and 37 0.. .3.9 GPa; ‘lomAg; single crystals; 99.999%; microtome sectioning; activation volume for ~>I.19 GPa; see Figs. 34 and 38
0...0.86 GPa; ‘lomAg; single crystals; 99.998%; microtome sectioning 0 . . .4.6 GPa; “*Au (n activation); single crystals; 99.9999% ; microtome sectioning; see Figs. 34 and 39
75D
73c 65C
74A 71Wl
76Bl 0 . . .0.7 GPa; “‘Au; single crystals; 99.999%; microtome sectioning (continued)
Mehrer, Stoka
612 10.5.15,16 Press. effect tables for diff. in group V B semimetals and actinide group metals [Ref. p. 624 Diffusor
Temperature K
Ref.
Pressure range/Method/Remarks
Activation volume AV/V,
Lead (Pb), continued Zn
600
0.212 (6)
Cd
600
0.317 (10)
&
600
0.516 (6)
Sn
600
0.517 (25)
0.. .4.7 GPa; 65Zn; single crystals; 99.9999%; microtome sectioning; seeFigs. 34 and 40; saturation solubility as a function of pressure also studied 0...4 GPa; lo9Cd; single crystals; 99.9999%; microtome sectioning; seeFigs. 34 and 41; pressure effects on diffusion of Hg in Pb also studied 0...4 GPa; 203Hg; single crystals; 99.9999%; microtome sectioning; seeFigs. 34 and 42; pressure effects on diffusion of Cd in Pb also studied 0 ... 2.9 GPa; 1*3Sn; single crystals; 99.9999%; lathe sectioning; seeFig. 43
77Dl
77V
77v
77D2
10.5.15 Pressure effects in group V B semimetals P, As, Sb, Bi There are reported data for white P. Phosphorus (P) P 303.2 self-diffusion 314.5
0.44
P 300..*314 self-diffusion
0.44
0 .. *0.4 GPa; white P investigated; 32P; polycrystals (average grain size 0.01 cm); diffusion couples of inactive P and P doped with 32P; microtome sectioning; pressure isotherm at 314.5 K curved (seeFig. 44) 0.. .0.6 GPa; white P investigated in creep measurements
55N
64D
10.5.16 Pressure effects in actinide group metals Th, Pa, U, Np, Pu, etc. There are reported data for y-U and E-Pu. Uranium (U) 1173 U self-diffusion in y-U
-
O... 1 GPa; bee y-U investigated; diffusion couples 65Bl of natural U and U enriched 20 wt.% with 235U; purity not specified; lathe sectioning; anomalous variation of the diffusion coefficient with pressure observed (seeFig. 45) Plutonium (Pu)
Pu 788 self-diffusion 811 in E-PU 823 849
-0.329 -0.35 -0.347 -0.33
O... 1.4 GPa; bee E-PUinvestigated: 240Pu; polycrystals; 99.9% (detailed specification of purity and isotopic composition is given in [71C]); mechanical sectioning and measurement of residual activity; similar data in [72Cl]
Mehrer, Stolica
71c
Landolt-Barnstein New Series Ill!26
Ref. p. 6241
10.6 Pressure effect tables for diffusion in homogeneous binary alloys
613
10.6 Pressure effect tables for diffusion in homogeneous binary alloys There are reported data for the following alloys: Ag - Au, Ag - Zn, Au - Zn, Co-Fe, Fe - Si and Fe - Ti. Diffusor
Temperature K
Activation volume AVIV,
Pressure range/Method/Remarks
Ref.
Ag - Au (34 at.%) Ag
1133 1183 1233
0.807 0.700 0.593
Au
1133 1183 1233
0.808 0.721 0.672
0...0.83 GPa; llomA g, lg8Au; crystal grown from 99.99% Au and 99.99% Ag; lathe sectioning; V,(Ag)=10.27 cm3mol-’ V,(Au)=10.22 cm3mol-’
64A
Ag - Zn (30 at.%) Ag and Zn
Composition at. %
383.2 394.1 403.6 414.3 424.2 Diffusor
0.561 (22) 0.536 (7) 0.523 (10) 0.523 (8) 0.557 (10) Temperature K
0.. .0.9 GPa; anelastic relaxation due to stressinduced ordering investigated on wires of a-Ag - Zn; Vm(Ag-Zn (30 at.%))=10cm3mol-’ Activation volume AV/V,
Pressure range/Method/Remarks
59T
Ref.
Au-Zn 49% Zn 50% Zn 51.2% Zn Diffusor
Au Zn Au Zn Au Zn Temperature K
814.9 814.9 814.9 814.9 814.9 814.9
0.296 (148) 0.370 (63) 0.995 (159) 0.857 (105) 0.360 (169) 0.391 (169)
Activation volume A V/V,
0 . . .0.524 GPa; ordered CsCl structure investigated; ig5Au, 65Zn; single crystals; lathe sectioning; V, = 9.45 cm3mol - ’ ; seeFig. 46
Pressure range/Method/Remarks
Co-Fe (50 at.%) Fe
1218
0.60 (12)
O... 0.45 GPa; equiatomic FeCo alloy investigated: “Fe; large grain po 1ycrystals grown from 99.99% Fe and 99.99% Co; lathe sectioning
71F
Fe - Si (1.4 wt.%) C
Land&Bkmstein New Series III/26
252 252
0.042 (42) -0.084 (127)
0 . . .0.4 GPa; C induced magnetic aftereffect investigated; V,(Fe)=7.094 cm3mol-‘; pressure dependence for magnetic aftereffect of C in Ni and a-Co also studied
Mehrer, Stolica
71W2
10.7 Pressure effect tables for interdiffusion
614 Diffusor
Temperature K
Activation volume AVIV,
[Ref. p. 624
in binary alloys
Ref.
Pressure range/Method/Remarks Fe (90 at.% Ti)
1081
Fe
0.56 (10)
67P 0...0.4 GPa; “Fe; bi-crystal of Ti-Fe (10 at.%) alloy; serial sectioning; &(Ti) = 10.64cm3mol - ’
10.7 Pressure effect tables for interdiffusion in binary alloys There are reported data for the following alloys: Ag - Al, Al - Mg, Al - Zn, Cu - Zn, Fe -Ni and Fe-V. Composition Temperature K range
Ref.
Activation Pressure range/Method/Remarks volume [cm3mol - ‘1 Ag-AI
0 . . .2.07 at.% Ag
786 832 865 895
786 832 865 895
1.1 at.% Ag: 7.8 7.8 7.8 7.9 2.01 at.% Ag: 8.1 8.0 7.9 7.8
729 731 815 858 873
6.1 7.3 7.7 8.0 7.7
786 832 865 895
d-phase
0 at.% Ag: 7.8 7.7 7.7 7.7
0. ** 3.24 GPa; diffusion couples of Al (99.996%) 84Ml and Al-2.07 at.% Ag alloy (produced of 99.996% AI and 99.999% Ag); electron microprobe analysis of diffusion profiles; activation volumes for further compositions between 0 and 2.07 at.% Ag listed in [84Ml]; 1/,(Al) = 10.0cm’mol-’
0 ... 3 GPa; diffusion couples of AI (99.996%) 84M2 and Ag (99.999%); electron microprobe analysis of diffusion profiles; activation volumes of &phase growth also studied AI-Mg
0 . . .4.06 at.% Mg
737 783 818 848 871 737 783 818 848 817
0 at.% Mg: 8.5 8.6 8.6 8.7 8.7 1 at.% Mg: 8.5 8.5 8.6 8.6 8.6
0. .. 3.3 GPa; diffusion couples of pure Al and Al-4.06 at.% Mg alloys (produced of 99.996% AI and 99.95% Mg); electron microprobe analysis of diffusion profiles; vm(Al) = 10.0 cm3mol- ’
83M
(continued)
Mehrer, Stolica
Landoll-B6mstan New Series III!26
10.7 Pressure effect tables for interdiffusion
Ref. p. 6241
Composition Temperature K range
737 783 818 848 877 737 783 818 848 877 737 783 818 848 877
in binary alloys
Activation Pressure range/Method/Remarks volume [cm3mol- ‘1 2 at.% Mg: 8.5 8.6 8.6 8.6 8.7 3 at.% Mg: 8.6 8.7 8.6 8.6 8.5 4.06 at.% Mg: 8.5 8.6 8.6 8.7 8.7
615 Ref.
Al - Mg, continued
Al-Zn 0 ... 3.5 at.% 767 Zn 809 849 881 767 809 849 881
0 at.% Zn: 9.4 9.0 8.7 8.4 3.5 at.% Zn: 9.0 8.7 8.2 8.1
0 ... 3.5 GPa; diffusion couples of pure Al and Al-Zn (3.5 at.%) alloy (produced of 99.996% Al and 99.996% Zn); electron microprobe analysis of diffusion profiles; for comparison: V,(Al)= 10.0 cm3mol-‘; see Fig. 47
82M
Cu-Zn 0...21 at.% Zn
1108 1138 1168 1198 1223 1108 1138 1168 1198 1223 1108 1138 1168 1198 1223
0...4.9 at.% Zn 1256 1286 1313
Land&-Biirnstein New Series III/26
0 at.% Zn: 4.5 4.7 5.3 5.0 5.0 9 at.% Zn: 4.4 4.5 5.1 5.0 4.6 15 at.% Zn: 3.9 4.1 4.4 4.3 4.2 0 at.% Zn: 5.51 5.51 6.26
0 *++3.26 GPa; diffusion couples of pure Cu and 84T Cu base alloys of 24.6 and 28.5 at.% Zn (produced of 99.99% Cu and 99.996% Zn); electron microprobe analysis of diffusion profiles; V,(Cu) = 7.1 cm3mol-‘; seeFigs. 48 a and 48 c
0 ... 3.2 GPa; diffusion couples of pure Cu and Cu-Zn (4.9 at.%) alloys (produced of 99.99% Cu and 99.996% Zn); microprobe analysis of diffusion profiles; V,(Cu) = 7.1 cm3mol-‘; see Figs. 48 b and 48c Mehrer, Stolica
88Y
616
Pressure effect for diff. in solid elements and (homogeneous) binary alloys (Figs.)
Composition Temperature K range
[Ref. p. 624
Activation Pressure range/Method/Remarks volume [cm3mol- ‘1
Ref.
Fe-Ni x 6...7;
O... 100 at.% 1427 Ni (y-phase) 1506
0 .*. 4 GPa; diffusion couples of pure Fe and Ni; 65G electron microprobe analysis of diffusion profiles; seeFigs. 49 a and 49 b; f$(Fe) = 7.1 cm3mol-r; f$,(Ni) = 6.59 cm3mol-‘; Kirkendall effect also studied Fe-V
0.7 . . .30 at.% V
1373...1623
y-phase 0.7% v: 5.5 u-phase 8% v: 4.8 10% V: 4.6 15% v: 3.4 20% V: 3.2 25% V: 3.4 30% v: 3.3
0. .. 4 GPa; diffusion couples of iron-vanadium alloys; electron microprobe analysis of diffusion profiles; seeFigs. 50a and 50b; V,(Fe) = 7.1 cm’mol-‘; Kirkendall effect at 0 and 4 GPa also studied
65H
Figures for 10.5 to 10.7 t
1
**No in No
0.8 0.7 w
364.5K
I 0.6 =’ 0.5 =I 0.4
288K
0.4
0.6
0.2 200
0.82
280
320
360 K 400
P-
Fig. 24 a. Na. Semilogarithmic plot of the self-diffusion coefficients of 22Na vs. pressure for two temperatures [71M].
Fig. 24b. Na. Activation volumes of self-diffusion in sodium vs. temperature [52N, 62H, 71M]. AV,, and AV,, denote activation volumes for mono- and divacancy mechanism according to [78M, 78P].
Mehrer, Stolica
Landok-BBmslein NW Series III/26
Ref. p. 6241
Pressure effect for diff. in solid elements and (homogeneous) binary alloys (Figs.)
0.3 0 600
700
800
900
Cu [68821 -71 v Au[89Fl A Zn I88Y 1 7~1 I 1100 1200 1300 K 1400
1000 T-
Fig. 25. Cu. Activation volumes vs. temperature for diffusion of @Cu [68B2], lg8Au [89F] and Zn [My] in copper.
I
0.9-v
I
z 0.8~ 14
Ag 165821 A Ag 168El I 0 A Agf82Rl . In Sb 165821 I65821
0 :
’
0
’
0
0.7
0
c 0.6 500
600
700
800
900
1000
ti .z 1200 K 1300
1100
Fig. 26. Ag. Activation volumes vs. temperature for diffusion of ‘lomAg [65B2, 68B1, 82R], l141n [65B2] and lz4Sb [65B2] in silver.
I
1 Au 1
I
I
I
I
I
I
0.9
I
1’
$j 0.7
.
. I
I
0.6 0.5 500
v
v
0.8
600
700
,,* I
n
I aAuL6501 v Au [68821 o Au [82Rl . Au [83Wl
800
900
I
I v
v
n
1000
1100
Fig. 27. Au. Activation volumes of self-diffusion in gold vs. temperature [65D, 68B2, 82R, 83WJ. Land&-B&m&n New Series III/26
Mehrer, Stolica
I v
1200 K 1300
617
Pressureeffect for diff. in solid elementsand (homogeneous)binary alloys (Figs.)
618
8.51
[Ref. p. 624
I
6.5 I I I 625 650 675 K i lrig. 28. Zn. Activation volumes vs. temperature for self-difusion 1 and (1to the hexagonal c axis of zinc [72C2]. I 600
I 575
3.251 550
1.8
6.0 520
510
560
580
K
61
Fig. 29. Cd. Activation volumes vs. temperature for self-d fusion 1 and 11to hexagonal c axis of cadmium [73B].
I
Al
0
1.5 1.2
.
.
.
z 0.9 2 3
I
6
v A
n
I I I
p
I I r: .
26AI
01 750
in Al 168821 I 800 850
900
K
4 Fig. 30. AI. Activation volumes vs. temperature for diffusic of 26Al [68B2], 5gFe [89B], lg5Au [89B] and 65Zn [89B] 950 aluminum.
I-
10“” m2/s
I
I
As in Si
I 0
0.5
1.0
1.5
2.0
2.5
3.0GPO:
P-
Fig. 31a. Si. Semilogarithmic plot of As diffusion coefficient in silicon vs. pressure at four different temperatures [85Nl].
I
I
’ 385,9kJ/mol ’
0.83 0.85 0.87 40 l/l Fig. 31b. Si. Semilogarithmic plot of As diffusion coeffkil in silicon vs. reciprocal temperature at three different pr sures [8SNl].
Mehrer, Stolica
3
0.81
Land&-Bhstein New Series III/26
Ref. p. 6241 Pressure effect for diff. in solid elements and (homogeneous) binary alloys (Figs.) 10-17 m2/s L
4.
1 I
l
619
T=l086K
Ge intrinsic
I 1O-2o
916
,o.2~--fj++= 0
0.1
0.2
0.3 P-
0.4
0.5 GPa
Fig. 32. Ge. Semilogarithmic plot of self-diffusion coefficient of 71Gein intrinsic Ge vs. pressure for various temperatures [85w].
1o-'OoJ
4
GPO 5
P-
Fig. 33. Pb. Semilogarithmic plot of self-diffusion coefticierIt of ‘rOPb in lead vs. pressure for various temperatures [61HI.
lo-g m2/s lo-"0
10-l'
II 10-12 Q 10-1'3
IO“5
10-16 0
1
2
3
4
GPO
1.2
Fig. 34. Pb. Semilogarithmic plot of the diffusivity vs. pressure at 600 K for Cu, Pd, Au, Ni, Zn, Ag, Cd, Hg, and Pb in lead [75D].
1.8
1.6
2.0 .W3 K-' 2.2
Fig. 35. Pb. Semilogarithmic plot of the diffusion coefficient of 63Ni in lead vs. reciprocal temperature for ambient pressure (0.1 MPa) and 4 GPa [73C].
L
Land&-B&stein New Series III/26
1.4
l/T -
P-
Mehrer, Stolica
Pressure effect for diff. in solid elements and (homogeneous) binary alloys (Figs.)
620 10 9m5‘s . 6
I TIPI+
[Ref. p. 624
4 Fig. 36. Pb. Semilogarithmic plot of the diffusion coeffkient of ro9Pd in lead vs. reciprocal temperature for various prcssures [75D].
logid in Pb’
&
10-8
I
m2’s @‘Cuin Pb I
.lO _
p=hGPo 10-q ---z-y -
1 Q 10-10
-11
1.2
1.4
1.6
2.0 .lo'J K' 2.2
1.8
10 m2
lo-" 1.2
1.4
1.6
1.8
2.0 .10-3K-' 2.2
l/lFig. 37. Pb. Semilogarithmic plot of the diffusion coefficients of “4Cu in lead vs. reciprocal temperature for ambient pressure (0.1 MPa) and 4 GPa [73C].
10
I
Q
10
10 1.1
1.3
1.5
1.7 l/l-
1.9
2.140-3K-'2.3
Fig. 38. Pb. Semilogarithmic plot of the diffusion coefficients of ‘romAg in lead vs. reciprocal temperature for various
Q
10“" m2/s 6 4
1.4
1.6
2.0
1.8
2.2 W3K-'
l/7-
Fig. 39. Pb. Semilogarithmic plot of the diffusion coefticients of rp8Au in lead vs. reciprocal temperature for various pressures[71Wl]. 6
10-l" 1.2
1.4
1.6
1.8 l/l
-
2.040-3K-' 2.2
4 Fig. 40. Pb. Semilogarithmic plot of the diffusion coefficients of 65Zn in lead vs. reciprocal temperature for various pressures[77Dl].
Mehrer, Stolica
Land&-BBmslein New Series III,/26
Ref. p. 6241 Pressure effect for diff. in solid elements and (homogeneous) binary alloys (Figs.) -12 _
ICI-'* m2/s
IO
m2/s
IO-13
621
_
lo-l3
t 23
t Q IC,-14
_
IC,-15 1.2
10-15 1.2
1.4
1.6
1.8 l/l
Fig. 41. Pb. Semilogarithmic plot of the diffusion coefficients of ‘@‘Cd in lead vs. reciprocal temperature for various pressures[77VJ.
10-1'2 m2/s
J
2.0 *lU"K' 2.2
-
Fig. 42. Pb. Semilogarithmic plot of the diffusion coefticients of zo3Hg in lead vs. reciprocal temperature for various pressures [77v].
I
‘13Sn in Pb IO-'3
I
I
I
m21s 1.97GPoI
i
,o-l?
lo-l4
%
I Q
p = 0.1MPo 1o-l4
,0-l!
,o-lF
v
,
1.4
1.8
1.6
\
10-lf
2.0 .105 K-'
0.2
0.3
0.4
GPO 0.5
P-
l/T -
Fig. 43. Pb. Semilogarithmic plot of the diffusion coefficients of “?Sn in lead vs. reciprocal temperature for various pressures [77D2].
Land&Biirnstein New Series III/26
303K
I a
Fig. 44. P. Semilogarithmic plot of the self-diffusion coefficients in white phosphorus vs. pressure at ttio temperatures. [55N
Mehrer, Stolica
Pressureeffect for diff. in solid elementsand (homogeneous)binary alloys (Figs.) [Ref. p. 624
622
4 Fig 45. U. Semilogarithmic plot of the self-diffusion coefftcients of 235U in y-uranium vs. pressure at 1173K [65Bl]. lOA'2 m2/s
(~I lo-l3
0
0.2
0.4
0.8 GPO 1.0
0.6
10-l'
0.13
cm3 ii3
0.825
0.850
.@ K-'
0.9
Fig. 48 a. Cu - Zn alloy. Semilogarithmic plot of interdiffusion coefficients vs. reciprocal temperature for three different pressuresfor an alloy with 15 at.% Zn [84T].
10.0
I
1.5 1 22 5.0
48.5
0.875
49.0
49.5
50.0
50.5
- 3.2GPo.1286K
51.5
at%
Zn Fig. 46. Au-Zn alloy. Activation volumes for self-diffusion of both components vs. composition at 814.9 K [72J].
1
10-l
m*/r
2
ln Fig. 48 b. Cu -Zn alloy. Semilogarithmic plot of interdiffusion coefficients at 1283and 1286K for three different pressures vs. composition [88yl.
10-l
1.0 0.9 I 9 2 d
t 10-l a
0.8 0.7 0.61 1050
10”
I1100
I 1150
I 1200 l-
I 1250
I I 1300 K 1350
Fig. 48~. Cu -Zn alloy. Activation volume of interdiffusion in dilute Cu-Zn alloys vs. temperature [84T, 88yl. lo-
<
1.15
1.20
1.25 l/1 -
I
40.)K-'
I 4 Fig. 47. Al-Zn alloy. Semilogarithmic plot of interdiffu._ s'ton coefficients vs. reciprocal temperature for two compositions at three different pressures[82M]
1.4~
Mehrer, Stolica
Iandolt-BCmslein New Series III/26
Ref. p. 6241 Pressureeffect for diff. in solid elementsand (homogeneous)binary alloys (Figs.)
623
1cl-l4 IOl-cm3 mol 8
I~I US""
6 _. I 2
1IYE
4
2 ,o-li 0
I
I
I
20
40
60
I
80 at% 100
0
I
I
I
20
40
60
I
Ni -
NI -
Fig. 49a. Fe-Ni alloy. Semilogarithmic plot of interdiffuCon coefficients vs. composition at two temperatures and pressures[65G].
I
80 at% 100
Fig. 49 b. Fe-Ni alloy. Activation volume of interdiffusion vs. composition at 1458K [65G]
lOA1 m2/s
I2
10-l I !Q
10-l3-
4 GPO 10-l4 ! I1.60
0.64
0.68
0.72 l/T -
0.76
^ .lO”K-
0.84
Fig. 50a. Fe-V alloy. Semilogarithmic plot of the interdiffusion coefficient in cc-phasevs. reciprocal temperature at 10 at.% V and for three different pressures [65H].
Land&-Biirnstein New Series III/26
lo-‘( 0.
0.64
0.68
0.72
0.76
.W3K
Fig. 50b. Fe-V alloy. Semilogarithmic plot of the interdiffusion coefficient in the y-phase vs. reciprocal temperature at 0.7 at.% V and for three different pressures [65H].
Mehrer, Stolica
624
References for 10.4 to 10.7
References for 10.4 to 10.7 52N 55N 5lB 59N 59T 60B 61B 61H 61T 62H 63Dl 63D2 64A 64C 64D 64G 65Bl 65B2 65C 65D 65G 65H 65K 65N 65R 66N 67B 67C 67K 67P 67s 68Bl 68B2 69M 70B 71c 71F 71E 71Gl 71G2 715 71L 71M 7101 7102 71Wl 71W2 72CI 72C2 72C3
Nachtrieb, N.H., Weil, J.A., Catalano, E., Lawson, A.W: J. Chem. Phys. 20 (1952) 1189. Nachtrieb, N.H., Lawson, A.W.: J. Chem. Phys. 23 (1955) 1193. Bosman, A.J., Brommer, P.E., Rathenau, G.W.: Physica 23 (1957) 1001. Nachtrieb, N.H., Resing, H.A., Rice, S.A.: J. Chem. Phys. 31 (1959) 135. Tichelaar, G.W, Lazarus, D.: Phys. Rev. 113 (1959) 438. Bosman, A.J., Brommer, P.E., Eijkelenboom, L.C.H., Schinkel, C.J., Rathenau, G.W.: Physica 26 (1960) 533. Butcher, B.M., Ruoff, A.L.: J. Appl. Phys. 32 (1961) 2036. Hudson, J.B., Hoffman, R.E.: Trans. Metall. Sot. AIME 221 (1961) 71. Tichelaar, G.W., Coleman, R.V., Lazarus, D.: Phys. Rev. 121 (1961) 748. Hultsch, R.A., Barnes, R.G.: Phys. Rev. 125 (1962) 1832. DeVries, K.L., Baker, G.S., Gibbs, P.: J. Appl. Phys. 34 (1963) 2254. DeVries, K.L., Baker, G.S., Gibbs, P.: J. Appl. Phys. 34 (1963) 2258. Albrecht, E.D., Tomizuka, C.T.: J. Appl. Phys. 35 (1964) 3560. Coston, C., Nachtrieb, N.H.: J. Phys. Chem. 68 (1964) 2219. DeVries, K.L., Gibbs, P., Miles, H., Staten, H.S.: J. Appl. Phys. 35 (1964) 536. Gschneider, K.A.: Solid State Phys. 16 (1964) 275. Beyeler, M., Adda, Y.: in “Physics of Solids at High Pressures”, Tomizuka, C.T., Emrick, R.M. (eds.), New York, London: Academic Press, 1965, p. 349. Bonanno, F.R., Tomizuka, C.T.: Phys. Rev. 137 (1965) A1264. Curtin. H.R., Decker, D.L., Vanfleet, H.B.: Phys. Rev. 139 (1965) A1552. Dickerson, R.H., Lowell, R.C., Tomizuka, C.T.: Phys. Rev. 137 (1965) A613. Goldstein, J.I., Hanneman, R.E., Ogilvie, R.E.: Trans. Metall. Sot. AIME 223 (1965) 812. Hannemann, R.E., Ogilvie, R.E., Gatos, H.C.: Trans. Metall. Sot. AIME 223 (1965) 691. Kohler, C.R., Ruoff, A.L.: J. Appl. Phys. 36 (1965) 2444. Nachtrieb, N.H., Coston, C.: in “Physics of Solids at High Pressures”, Tomizuka, C.T., Emrick, R.M. (eds.), New York, London: Academic Press 1965, p. 336. Ruoff, A.L.: in “Physics of Solids at High Pressures”, Tomizuka, C.F., Emrick, R.M. (eds.), New York, London: Academic Press, 1965, p. 378. Norris, D.I.R.: Acta Metall. 14 (1966) 291. Beyeler, M., Pernot, B., Adda, Y.: Rapport C.E.A. No. 3316,1967. Chevalier, G.T., McCormick, P., Ruoff, A.L.: J. Appl. Phys. 38 (1967) 3697. Kohler, C.R., Ruoff, A.L.: J. Mater. 2 (1967) 20. Peart, R.F.: Phys. Status Solidi 20 (1967) 545. Styris, D.L.: Ph. D. Thesis, Arizona State University 1967. Beyeler, M.: These, Universite de Paris, 1968. Beyeler, M., Adda, Y.: J. Phys. (Paris) 29 (1968) 345. McArdle, P.A.: Bull. Am. Phys. Sot. 13 (1969) 489. Beyeler, M., Lazarus, D.: Mem. Sci. Rev. Metall. 67 (1970) 395. Cornet, J.A.: J. Phys. Chem. Solids 32 (1971) 1489. Fishman, S.G., Jeffery, R.N.: Phys. Rev. B12 (1971) 4424. Engardt, R.D., Barnes, R.G.: Phys. Rev. B3 (1971) 2391. Gilder, H.M., Buescher, B.J., Chhabildas, L.C.: in “Atomic Transport in Solids and Liquids”, Lodding. A., Lagerwall, T. (eds), Tiibingen: Verlag der Zeitschrift fur Naturforschung, 1971, p. 331. Gilder, H.M., Chhabildas, L.C.: Phys. Rev. Lett. 26 (1971) 1027. Jeffery, R.N.: Phys. Rev. B3 (1971) 4044. Lazarus, D., Yoon, N.N., Jeffrey, R.N.: Z. Naturforsch. A26 (1971) 56. Mundy, J.N.: Phys. Rev. B3 (1971) 2431; and private communication. Ott, A., Norden-Ott, A.: J. Appl. Phys. 42 (1971) 3745. Ott, A.: Phys. Status Solidi (b) 43 (1971) 213. Weyland. J.A., Decker, D.L., Vanfleet, H.B.: Phys. Rev. B4 (1971) 4225. Wuttig. M., Keiser, J.: Phys. Rev. B3 (1971) 815. Calais, D., Cornet, J.A.: Mem. Sci. Rev. Metall. 69 (1972) 493. Chhabildas, L.C., Gilder, H.-M.: Phys. Rev. BS (1972) 2135. Combronde, J.: Ser. Metall. 6 (1972) 801. Mehrer, Stolica
Landolf-Bhslein New Series III/26
References for 10.4 to 10.7
625
Jeffery, R.N., Gupta, D.: Phys. Rev. B6 (1972) 4432. Mehrer, H., Seeger,A.: Cryst. Lattice Defects 3 (1972) 1. Vanfleet, H.B., Decker, D.L., Curtin, H.R.: Phys. Rev. B 12 (1972) 4849. Buescher, B.J., Gilder, H.M., Shea, N.: Phys. Rev. B7 (1973) 2261. Candland, C.T., Vanfleet, H.B.: Phys. Rev. B7 (1973) 575. Ascoli, A., Filoni, L., Poletti, G., Rossi, S.L.: Phys. Rev. B 10 (1974) 5003. Langiiille, A., Calais, D., Fromont, M.: J. Phys. Chem. Solids 35 (1974) 1373. Baker, A.G., Gilder, H.M.: Bull. Am. Phys. Sot. 20 (1975) 442. Decker, D.L., Candland, CT., Vanfleet, H.B.: Phys. Rev. B 11 (1975) 4885. Fromont, M.: J. Phys. Chem. Solids 36 (1975) 1397. Barbfi, A.: in: “La Diffusion dans les Milieux Condenses”, 19” Colloque de Metallurgic, Saclay Vol. 1 (1976) p. 155. Boidron, M., Fromont, M., Marbach, G.: J. Phys. (Paris) Lett. 37 (1976) 115. Marbach, G., Fromont, M., Calais, D.: J. Phys. Chem. Solids 37 (1976) 689. Decker, D.L., Ross, R.A., Evenson, W.E., Vanfleet, H.B.: Phys. Rev. B 15 (1977) 507. Decker, D.L., Weiss, J.D., Vanfleet, H.B.: Phys. Rev. B16 (1977) 2392. Vanfleet, H.B., Jorgensen, J.D., Schmutz, J.D., Decker, D.L.: Phys. Rev. B15 (1977) 5545. Mehrer, H.: J. Nucl. Mater. 69/70 (1978) 38. Peterson, N.L.: J. Nucl. Mater. 69/70 (1978) 3. Minamino, Y, Yamane, T., Koizumi, M., Shimada, M., Ogawa, N: Z. Metallkde. 73 (1982) 124. Rein, G., Mehrer, H.: Philos. Mag. A 45 (1982) 767. Erdelyi, G., Beke, D.L., Gbdeny, I., Gergely, L., Kedves, F.J.: DIMETA 82 - Diffusion in Metals and Alloys, Kedves, F.J., Beke, D.L. (eds.), Defect Monograph Series7 (1983) 398. Lazarus, D.: DIMETA 82 - Diffusion in Metals and Alloys, Kedves, F.J., Beke, D.L. (eds.), Diffusion and Defect Monograph Series 7 (1983) 134. Minamino, Y, Yamane, T., Shimomura, A., Shimada, M., Koizumi, M., Ogawa, N.: J. Mater. Sci. 18 (1983) 2679. Werner, M., Mehrer, H.: DIMETA 82 - Diffusion in Metals and Alloys, Kedves, F.J., Beke, D.L. (eds.), Trans. Tech. Publications, 1983, p. 393; [also: Werner, M.: Dr. rer. nat. Thesis, Universitat Stuttgart 1984, FRG]. Minamino, Y, Yamane, T., Shimomura, A., Shimada, M., Koizume, M., Ogawa, N.: J. Jpn. Inst. Light Met. 34 (1984) 174. Minamino, Y, Yamane, T., Ueno, S., Koizumi, M., Ogawa, N., Shimada, M.: Met. Sci. 18 (1984)
72J 72M 72V 73B 73c 74A 74L 75B 75D 75F 76Bl 76B2 76M 77Dl 77D2 77v 78M 78P 82M 82R 83E 83L 83M 83W
84Ml 84M2
419.
85P
Takahashi, T., Kato, M., Minamino, Y, Yamane, T., Azukizawa, T., Okamoto, T., Shimada, M., Ogawa, N.: Z. Metallkde. 75 (1984) 440. Nygren, E., Aziz, M.J., Turnbull, D., Hays, J.F., Poate, J.M., Jacobson, D.C., Hull, R.: in: “Impurity Diffusion and Gettering in Silicon”, Fair, R.B., Pearce, C.W., Washburn, J. (eds.), Mater. Res. Sot. Symposia Proc. 36 (1985) p. 77. Nygren, E., Aziz, M.J., Turnbull, D., Hays, J.F., Poate, J.M., Jacobson, D.C., Hull, R.: Appl. Phys. Lett. 47 (1985) 105. Phillibert, J.: Diffusion et transport de mat&e dans les solides, Les editions de physique, Paris,
85W 88Y
Werner, M., Mehrer, H., Hochheimer, H.D.: Phys. Rev. B32 (1985) 3930. Yamane, T., Mori, N., Minamino, Y, Miyamoto, Y., Koizumi, M., Takahashi, T.: Metall. Trans.
89B
Becker, Ch., Erdtlyi, G., Hood, G., Mehrer, H.: DIMETA 88 - Diffusion in Metals and Alloys, Kedves, F.J., Beke, D.L. (eds.), Diffusion and Defect Forum 66-69 (Pt. 1) (1989) 409. Fujikawa, S., Werner, M., Mehrer, H., Seeger,A.: DIMETA 88 - Diffusion in Metals and Alloys, Kedves, F.J., Beke, D.L. (eds.), Diffusion and Defect Forum 66-69 (Pt. 1) (1989) 421. Kedves, F.J., Erdtlyi, G.: DIMETA 88 - Diffusion in Metals and Alloys, Kedves, F.J., Beke, D.L. (eds.), Diffusion and Defect Forum 66-69 (Pt. 1) (1989) 174. Siidervall, U., Lodding, A., Gust, W: DIMETA 88 - Diffusion in Metals and Alloys, Kedves, F.J., Beke, D.L. (eds.), Diffusion and Defect Forum 66-69 (Pt. 1) (1989) 415. Erdelyi, G., Freitag, K., Mehrer, H.: Philos. Mag. Lett., in press.
84T 85Nl
85N2
1985.
19A (1988) 467.
89F 89K 89s 90E
Land&Biirnstein New Series III/26
Mehrer,
Stolica
626
11.I Introduction;
11.2 Methods of measurement
[Ref. p. 629
11 Diffusion in dislocations 11.1 Introduction The rate at which atoms in solids migrate in grain boundaries, over surfaces and along dislocations is ;eneral!y very much greater, often by several orders of magnitude, than their rate by volume (or bulk) diffusion :hrough the crystal lattice. Diffusion in grain boundaries is dealt with in chapter 12, diffusion over surfacesin :hapter 13. In this chapter we deal with dislocation diffusion. Reviews of the subject are given in [70B], [7362], :84L] and [85L]. Several methods have been employed to measuredislocation diffusion rates, most of which give directly only the product D,a2, a being the effective radius of the dislocation “pipe” within which the mean effective diffusion :oeflicient is D,. When, as in heterodiffusion, there is segregation of the diffusant to the dislocations, it may be the product D,a2s that is measured, s being the segregation coefficient. To obtain the dislocation diffusion zoetlicient D, itself therefore requires knowledge of a and, where relevant, of s. Since these quantities are mostly unavailable it is usual to report just the directly measuredD, a2 or D, u2s. (The value a = 5. IO- lo m is sometimes assumedfor illustrative calculation of Dd.) Most measurementsare, of course, made with single crystals to avoid the effects of grain boundaries.
11.2 Methods of measurement 11.2.1 Dislocation tail method (Method I) Material may be transported by dislocation diffusion to much greater distances into single crystals than is reached by lattice diffusion alone, some of it at the same time diffusing out of the dislocations into adjacent diffusant-free lattice regions. At such distances the mean concentration E differs, of course, from the appropriate Fick solution expression describing purely volume diffusion. Thus, for example, penetration plots of In Cversus x2, drawn to determine D by the thin layer method (subsection 1.6.1.2.1),frequently for this reason depart from linear at large distances (> 4 or S(Dt)“‘) and curve upwards, a feature known as a “dislocation tail”. In this dislocation tail region In Cvaries linearly with x and from the gradient, which is independent of the anneal time, D,02s can be calculated from the relation (11.1)
D,a2s=DAZ(d !nE/dx)-2.
A is a known constant [81L] that depends very weakly on the ratio a2/fi but that for most practical purposes lies between 0.5 and 0.8. This is probably the most reliable and accurate method for determining D,a2 s. It requires that the diffusion length L (= (D r)‘12)should remain less than the average spacing 2 R between dislocations.
11.2.2 Bulk diffusion enhancement method (Method II) When L %2 R, diffusing atoms enter and leave many dislocations and crystal regions during the diffusion anneal. The averageconcentration, at least at not too great distances,is then still described by the Fick solution for bulk diffusion but with an effective and enhanced diffusion coefficient Dell, given by a weighted mean of D and D,, (11.2) D,,,=D(l -js)+DJs where j is the fraction of sites on dislocations. It follows, since D,$D,
that
D, a2 s = (D,,, - D)/nd
(11.3)
where d is the line density of dislocations - number crossing unit area. If d is not known, but constant, at least ihe activation energy for dislocation diffusion can be determined by this method.
11.2.3 “Type C” diffusion method (Method III) When times are so short that (Dt)“2 @a, diffusion is almost wholly within the dislocations with negligible loss into the surrounding crystal. A thin layer experiment performed under such conditions will show Inc varying linearly with x2 but with a slope determined by D, alone. Thus D, is directly determined without the Le Claire
Land&BBmslein New Series III/26
11.3 Presentation of results
Ref. p. 6291
627
need to know a2. These conditions are difficult to realise becauseof the very short distances involved and the method has only very occasionally been used.
11.2.4 Permeation method (Method IV) In this method one measuresthe rate of permeation of radioactive diffusant across thin single crystal wafers deformed so as to generate dislocations of known configuration and density. If (D t)“’
11.2.5 Low angle grain boundary method (Method V) Low angle grain boundaries have the structure of a linear array of individual dislocations with a spacing 1 determined by the angle. It may be assumed,provided that (D t)“’ 9 1, that such an array is equivalent in its diffusion properties to some uniform boundary slab of width 6. The methods for studying grain boundary diffusion can then be applied to give a value for the product “Dgb“6. “Dgb” is the diffusion coefficient in the equivalent slab and is related to D, by the equation D, na2 = “Dgb” 6 1. Thus D, a2 can be calculated from (11.4)
D, a2 =<‘Dgb)l 6 Lfn.
Some of the earliest studies of dislocation diffusion were made by this method.
11.2.6 Defect annealing methods (Method VI) There are methods occasionally employed entailing the microscopic observation of the behaviour on annealing of various types of defects.Thus, for example, there have been studies of the shrinkage of micro-pores attached to dislocations, of the shrinkage of dislocation loops and of the break-up on annealing of quenched-in dislocation dipoles. From the rates of such processescan often be determined again the product D,a’.
11.3 Presentation
of results
D, and s both vary in the usual Arrhenius manner and it is convenient to write D,a2s=(D,a2s)’
exp(- Q/R T).
(11.5)
In self-diffusion s = 1 and Q’- Qdr the activation energy for dislocation diffusion. With segregation, s =l=1 and Q’= Qd- v where k’ is the binding energy of the diffusing solute to the dislocations. The tables report for self-diffusion (subsect.11.3.1)either individual values of D,a2 or the associatedpair of terms (Dda2)’ and Qd. For heterodiffusion (subsect.11.3.2)the corresponding quantities are D,a2 s or the pair (Dda2 s)’ and Qd- v Column 6 reports what information may be available on the nature of the dislocations in the samples studied, some of it quoted from the discussions in [70B]. The following abbreviations are used in column 6: E - edge dislocation. S - screw dislocation. U - undissociated dislocation. D - dissociated dislocation. b - Burgers vector, a - lattice constant.
11.3.1 Self-diffusion in dislocations System (D,a2)’ m4se1 Nb Fe
D,a2=1.6.
1.25.10-l’ D,=3.3...6.4*
Ni
3.10-26 9.9 . 10-24 2.1 . 10-23
Qd
kJ mol-’ 1O-34’)
Method Dislocations
Ref.
1273
I
Not specified
70R
I III
973 .** 1373 873 ... 1243 873 ... 1243
v V V
Not specified Not specified 1 E, U, b=a(lOO) or a/2(110) E, D, b=a/2 (110) S, D, b=a/2 (110) I
773 ... 873
IV
E, D, b = a/2 (110)
240 595...926 10e21 m2se1 569 104.2 170.4 188.3
154 1.8. 1O-2o D”=2. 10e3 m2s-lc) d Land&-Biimstein New Series III/26
Temperature range [K]
> Le Claire
88M 58U 69C 66W (continued)
528
11.3 Presentation of results
System (D, ~7~)~ m4s-’
Temperature range [K]
Method Dislocations
Ref.
82.5
673...800
V
54T
49.4 x 126 x126
673...829 623.a.772 575.e.766 738 . ..826 723
V V II II IV
E,U,b=a(lOO) or a/2(110); tilt boundaries 9 .+*28” 16” tilt boundary, E, U,b=a(lOO) 18” tilt boundary, E,D,b=u/6(112) Not specified Not specified E, b=a(lIO)
10-34a) 10-35”) 116 D,n*=7. 10-32”) 1.9. 10-25”) 110.1
625 628 633 ... 1032 696 520..+570b)
I I II I I
Not specified Not specified Not specified Not specified E,D, b=a(211)
70G 68W 71M 71M 73GI
2.2. 10-25 5.8. 10-25d)
323 . ..453 w413
VI VI
Mixed E and S, D, b=a/2(110) Not specified
7IV 78R
Qd
kJ mol-’
3.3. 10-24c)
43
1.5.10-26 w4.10-20 7.6. IO-24 D,a*=1.8. Au
1O-2a5
D,a*=1.15. D,a*=9.6.
Al
[Ref. p. 629
82.1 84
I 72R 7OL 73BI 54H
‘) Derived from graphical data not analysed by the authors, or previous results recalculated, using the procedure of [81L]. “) Additional measurementsat higher temperatures (589, 625 K) depart, from the Arrhenius line. Set figure 1. ‘) The unique analysis employed by [66w] leads to separate values for a (z 3 . 10Y9m) and D,. d, Theoretical estimate. ‘) Recalculated by [72R] using the Whipple solution.
;:I:” 10~‘7 10.” 10-29 10.” lo-” u) I 10.” “0 0” 10-31 10.” 10-35 10-M lo-” 10“s 1.0
1.2
IA
1.6
1.8 2.0 &/l--t
2.2
2.4
Ik Claire
2.6
4 Fig. 1. Self-diNusion and heterodiNusion in dislocations in metals. D,a*s vs. T,/T (T, = host melting point). Broken lines = lattice self-diffusion coenicient 2.8 in Ni and Ag times a*, with a=S.lO-“m. Landolf-BCmsfein New Series III!26
11.4 References for 11
11.3.2 Hetero-diffusion System Nb in Ta
D,a2s=2.2.
Ruin Cu
3.2. IO-” 8.3. lO-22
Ni in Cu
Method
Dislocations
Ref.
1523
I
Not specified
65P
151
1030~~~1175
138
945...1113
II I
Not specified Not specified
73Bl 73B2
738...
889
I
Not specified
73B2
758... 758
898
II I
Not specified Not specified
65M
917... 1000
II
Not specified
73Bl
kJ mole1 10-32a)
176
2.10-21
Ag in Cu
%144 D,a2s=2.
Fe in Ag
10-31a)
2.9. 1O-23
in dislocations
Temperature range [K]
Qct-V
(D, a’)’ m4se1
629
67
“) See footnote a) of Table 11.3.1.
11.4 References for 11 54H 54T 58U 65M 65P 66W 68W 69C
70B 70G
7OL 70R 71M 7lV
72R 73Bl 73B2 73Gl 7362
78R 8lL 84L 85L 88M
Hendrickson, A.A., Machlin, ES.: J. Met. 6 (1954) 1035. Turnbull, D., Hoffman, R.E.: Acta Metall. 2 (1954) 419. Upthegrove, W.R., Sinnot, M.J.: Trans. A.S.M. 50 (1958) 1031. Morrison, H.M.: Philos. Mag. 12 (1965) 985. Pawel, R.E., Lundy, T.S.: Acta Metall. 13 (1965) 345. Wuttig, M., Birnbaum, H.K.: Phys. Rev. 147 (1966) 495. Whitton, J.L., Kidson, G.V.: Can. J. Phys. 46 (1968) 2589. Canon, R.F., Stark, J.P.: J. Appl. Phys. 40 (1969) 4366. Ball&i, R.W.: Phys. Status Solidi 42 (1970) 11. Gupta, D., Tsui, T.C.: Appl. Phys. Lett. 17 (1970) 294. Lai, C.T., Morrison, H.M.: Can. J. Phys. 48 (1970) 1548. Reuther, TX., Achter, M.R.: Metall. Trans. 1 (1970) 1777. Morrison, H.M., Yuen, V.L.S.: Can. J. Phys. 49 (1971) 2704. Volin, T.E., Lie, K.H., Ballufi, R.W.: Acta Metall. 19 (1971) 263. Robinson, J.T., Peterson, N.L.: Surface Science 31 (1972) 586. Bernardini, J., Cabane, J.: Acta Metall. 21 (1973) 1561. Bernardini, J., Cabane, J.: Acta Metall. 21 (1973) 1571. Gupta, D.: Phys. Rev. B 7 (1973) 586. Gjostein, N.A.: in “Diffusion”, Chpt. 9, American Sot. Metals, Ohio, 1973. Ronander, E., Kritzinger, S.: J. Appl. Phys. 49 (1978) 3980. Le Claire, A.D., Rabinovitch, A.: J. Phys. C 14 (1981) 3863. Le Claire, A.D., Rabinovitch A.: in “Diffusion in Crystalline Solids”, Murch, Nowick (eds.),Chpt. 5, New York: Academic Press Inc. 1984. Le Claire, A.D.: in “Solute-Defect Interactions - Theory and Experiment”, p. 251 Saimoto, Purdy, Kidson (eds.),Oxford, New York: ‘Pergamon Press, 1985. Mehrer, M., Ltibbehusen, M.,: DIMETA 88 Int. Conf., Diffusion in Metals & Alloys, Hungary, 1988. Defect and Diffusion Forum 66-69 (1990) 591. EJ. Kedves, D.L. Beke (eds.),Liechtenstein: Sci. Tech Publ. 1990.
Land&-Biirnstein New Series III/26
Le Claire
12.1 Introduction
630
[Ref. p. 708
12 Grain and interphase boundary diffusion 12.1 Introduction 12.1.1 General remarks Internal surfaces,such as grain boundaries (i.e. the region of transition between crystals of different crystallographic orientation in contact with each other) in uniphase materials and interphase boundaries in a multiphase material, are almost invariably present in real metallurgical specimens.Being, in general, highly disordered atomic structures as compared to the adjoining crystal lattices, theseboundaries act as fast diffusion paths for the host as we!! as impurity atoms; the boundary diffusion properties of a given material depending upon a number of parameters characterizing the boundary and the diffusing species.The fast-diffusion character of grain and interphase boundaries results in many discontinuous solid-state reactions being boundary-diffusion controlled. In thin-film microelectronic devices short-circuit diffusion (the commonly used expression in this field for fast diffusion along internal surfacesand dislocations) among various components of the multilayered structures forms one of the principal modes of device failure. Thus, the importance of a knowledge of grain and interphase boundary diffusion data in genera! does not need to be emphasized. This chapter presents an extensive review of the various grain and interphase boundary diffusion data available in literature. The most important information is reproduced in the form of tables along with Arrhenius diagrams. These are preceded by a brief introduction to those theoretical aspectsof grain and interphase boundary diffusion which are mainly of relevance to the following tables and diagrams.
12.1.2 Mathematical
analysis of grain boundary diffusion
In a!! the mathematical models of grain boundary diffusion the boundary is assumedto be an isotropic, thin (thickness of atomic dimensions) rectangular slab, the diffusivity D, inside which is much larger than that (D) inside the crystal (Fig. 1).Upon diffusion from a surface normal to the boundary, material transport takes place along the boundary as we!! as in the bulk of the grains. D, being much larger than D, diffusion along the boundary persists to much larger penetration depths than in the bulk. As a result, beyond a certain depth depending on D the material diffusing along the boundary starts “leaking” laterally into the adjoining grains by volume diffusion. The extent of this lateral leakage determines the kinetics of diffusion under the given experimental conditions and the type of mathematical analysis required for evaluation of the diffusion data. Three types of kinetic behaviour (Fig. 2) may be distinguished, as first classified by Harrison [61H]. 1. Type-A kinetics. This refers to the limiting caseof long diffusion anneal times, small grain size and/or D not much smaller than D,, so that the volume diffusion length is much larger than the spacing between the boundaries and the leakage fields from the various boundaries overlap each other extensively. Under these conditions the diffusant does not remain confined to one particular boundary. After migrating some distance along one boundary it diffuses out into the bulk and enters another boundary, continuing this processthroughout the diffusion anneal. If the extent of overlapping is large, each diffusant atom would have moved along a number of boundaries as we!! as in the grains before any experimental measurement is made. This means that on a macroscopic scalethe atomic transport is characterized by a single effective diffusion coefficient (Deff)which represents an average of D and D, weighted by the ratios of the corresponding volume fractions. Since on the whole the system appears to obey Fick’s law with penetration depth proportional to ~‘1’ as for volume diffusion in a homogeneous medium, Dcffmay be determined in the sameway as D. Dcffis related to D, and D through Hart’s equation:
Deff=gDb+(l-g)D,
(12.1)
where g is the volume fraction of grain boundaries in the specimen.This equation shows that for large values of g (i.e. extremely small grain size) in the temperature range of grain boundary diffusion (i.e. D, 9 D), the specimen behaves as a homogeneous medium with D, as the effective diffusion coefficient. On the other hand, for small values of g Deffis approximately equal to D, unless D, is so much larger than D that g D, is comparable to D.
Kaur, Gust
Land&BBmstein New Series Ill./26
12.1 Introduction
Ref. p. 7081
631
2. Type-C kinetics. This refers to the limiting caseon the other extreme of ,/& scalewhere the sideways volume diffusion is negligible to the extent of fi being much smaller than the grain boundary width 6 (about 0.5 **. 1 nm), so that the diffusion process remains confined to within the boundaries only. Thus the diffusion coefficient is D, inside the boundaries and zero outside them. This allows an evaluation of D, (or the interphase boundary diffusion coefficient Di) in the samemanner as D, except for methods requiring measurementsof the absolute concentration, such as the permeation method, where a knowledge of grain boundary volume fraction (x 6/d) is also required in addition. 3. Type-B kinetics. This is the normally encountered situation under the real experimental conditions. Here too diffusion along the boundary is accompanied by lateral leakage of the diffusant by volume diffusion as in the caseof type-A kinetics, but the extent of this leakage is limited to distances much smaller than the grain size so that no overlapping of the diffusion fields from the neighbouring boundaries occurs and the boundaries can be considered as essentially isolated. Under these conditions the mathematical solutions for volume diffusion are not applicable, since on a macroscopic scale the system apparently does not obey Fick’s laws even though individually the boundary phase and the bulk phase obey these laws. The mathematical solutions for this case of coupled boundary and volume diffusion are obtained by solving simultaneously the diffusion equations for the boundary and the bulk phases and subjecting the solution to the additional boundary conditions at the boundary/bulk interface. This yields the well-known Fisher, Whipple and Suzuoka solutions for the diffusant distribution in a specimen containing isolated grain boundaries. Three methods are available for evaluating the grain boundary diffusivities s 6 D, (s: segregation factor, s = 1 for self-diffusion) from the concentration distribution measured after subjecting the initially diffusant-free specimen to radiotracer diffusion anneal treatment; the most reliable and the most commonly employed one being the sectioning method, the other two being the penetration-depth measurement method and the contour-angle measurement method. The corresponding mathematical relations for the evaluation of the triple product sSD, are summarized below. It may be mentioned that experiments in the type-B kinetics regime can yield only the product sSD, (or SSDi) and not independently the boundary diffusion coefficient D, (or Di). Db>> 0 cg >c, >c, >c,>c,
z=rj=o cg
Diffusion source : co = const
z
J-
6
p-1 I (Dbt)“2
I
-.
Fig. 1. Typical isoconcentration contours according to Fisher’s approximate solution for diffusion from a constant source. The b value is the same for all these isoconcentration contours [89Kl]. GB: grain boundary. Fig. 2. Schematic illustration of type-A, B and C diffusion b kinetics in a polycrystal containing uniformly spaced grain boundaries. Becauseof the limited space it is not possible to illustrate the condition (Dt)“’ % d for type-A kinetics on a proportionate scale [89Kl]. d: spacing between boundaries; 6: grain boundary width. Land&-Bknstein New Series III/26
TypeB
A.-.-
zcrf””
1006c(Df)“2
‘1;1--;
Type c
Kaur, Gust
‘1’2, O
ZK f”2
20(Df)“2<6
*
12.1 Introduction
632
[Ref. p. 708
12.1.2.1 Analysis of the sectioning measurements The classical radiotracer method, also called the sectioning method, involves removal of thin sections of the specimen after diffusing into it a suitable radioactive isotope of the diffusant element and measuring the radioactivity of each of these sections. A concentration distribution curve as a function of the penetration depth can thus be established. According to the approximate solution of Fisher [51Fl] for boundary diffusion from a constant source, logarithm of the measured average concentration E at a depth z in the specimen decreases linearly with z, the slope - alogc/az being related to sSD, through the equation
sSD, = 2(D/t)*‘2 (- alnqaz)-27t-1’2.
(12.2)
Some other approximate solutions used in the literature for evaluating grain boundary diffusion data from sectioning measurements,such as the ones after Borisov et al. [58B2] and Borisov and Golikov (cited after [59Bl]), end up being more or less the same as Fisher’s solution except probably for some difference in the constant factor. The former is referred to as BV (Borisov’s eq.) and the latter as BG (Borisov-Golikov’s eq.) in the tables. Later on Levine and MacCallum [6OLl] showed using a different approach that IogE vs. z615variation is much closer to being linear than IogF vs. z variation. This was confirmed by the exact mathematical analysis of Suzuoka [61Sl] for diffusion from a thin-film source. He showed the sameto hold true also from Whipple’s exact solution [54Wl] for diffusion from a constant source. In fact, he went a step further to show that not only the variation IogFversus z6/’ is linear irrespective of the type of diffusion source,even the magnitude ofthe slope - a log qaP is more or less the same. This lends a very special character to the sectioning method when applied to boundary diffusion measurements that the results are almost (within k 10%) insensitive to the boundary conditions at the specimen/source interface. This is not true for volume diffusion studies. Assuming 6 = 5.10-i’ m, Suzuoka provided the following relation for the evaluation of D, (in m’/s) from sectioning measurements(z in m and t in s) [89Kl]: 0.973 log (D,/D - 1) = 8.513 - 1.644 log (- a log Z/az6”) - log (D t)1’2.
(12.3)
The original form of Whipple’s exact solution for diffusion from a constant source was too complex to be of much usefor routine applications. It was only later that Le Claire [63Ll] reduced it to a very simple and useful form for the evaluation of sSD,: sSD, =
2(D/t)112(-aln@~6/5)-5/3(0.78)s/3.
(12.4)
In fact, Le Claire formulated an extremely useful and mathematically exact expression for s6D,, which is valid in general for any type of diffusion source and to which all the above-mentioned solutions can be reduced. This in a generalized form deduced by [89Kl] is
~so,=2(D/t)*‘~(-aa1n~/az”)-~‘“[-aIn~/a(~~-~’~)”]~‘”
(12.5)
where q = z/2(Dt)“2,
/3 = sS(D, - D)/2D3’2t”2
x ~60,/2D~‘~t”~.
n and [ - a log F/a(tlj-“2)“] are numerical constants. It is only in the values of these two that the various solutions differ from each other. Equation (12.5) may further be simplified and written in an extremely condensed form as follows: s6D, = KDmt-“(-alogE/azP)-q,
(12.6)
where the values of the constant K and the exponents m, u, p and q are as summarized in Table 1 of this section. Accordingly, the various equations for the evaluation of sSD, may be formulated in a very lucid and convenient form as follows. The same solutions have been applied in literature for interphase boundary diffusivity (saDi) where D, and D, are the volume diffusion coeflidetermination simply by replacing fi by (&, + &)/2, cients on the two sides of the interphase boundary. Fisher’s equation
SaD, = 0.2128(D/t)“‘(-
a10gqaz)-2.
(12.7)
Whipple - Le Claire equation SSD, = 0.3292(D/t)‘12 (- a log E/az6’5)-5’3.
Kaur, Gust
(12.8)
LandoMi6mstein New Series III/26
633
12.1 Introduction
Ref. p. 7081 Suzuoka’s equation sag,
= 02585
09t/t94t-103/194(_a,,,~/a~6/5)-500/291
(12.9)
for 10 < fi < 100, and SOD, = 0.2807 D1*‘37t-‘9’37(-
,,,,$=J~6’5)-125’74
(12.10)
for lo2 < /.I < 104. Levine - MacCallum equation s6 D, = 0.4848(D/t)“’ (- a log E/?Iz~‘~)-5’3
(12.11)
for 16 D t/d2 I 10m2(i.e. d 2 4O(D t)“2), and (12.12)
s 6D, = 0.4704(D/t)l’” ( - Cllog @z6”) - s’3 for 16 D t/d2 = 0.1 (i.e. d x 13 (D t)‘12).
Table 1. Values of the constant K and the exponents m, u, p and q for various grain boundary diffusion solutions. Solution
K
m
Fisher
0.2128
w
l/2
1
2
Approx., constant source
Whipple-Le Claire
0.3292
112
w
615
513
Exact, constant source
Suzuoka
0.2585
911194
Suzuoka
0.2807
18137
Levine-MacCallum
0.4848
112
Levine-MacCallum
0.4704
112
P
U
1031194 615
Remarks
9
5001291 Exact, instantaneous source, for 10 < j < 100
19137
615
125174
112
615
513
112
615
513
for lo2 < j < lo4 Polycrystal, constant source, for 16 Dt/d2 I 10M2 for 16 Dt/d2 = 0.1
12.1.2.2 Analysis of the autoradiographic measurements The concentration distribution of a radioactive tracer diffused into the specimen may also be measured by directly imaging it onto a photographic plate by the technique of autoradiography, instead of sectioning the specimen.For quantitative investigations the autoradiograms are normally taken at a surface perpendicular to both the diffusion source plane and the grain boundary plane. Mapping of the concentration in this plane yields isoconcentration contours of the form depicted in Fig. 1, from the geometry of which the grain boundary diffusivities can be evaluated. One can, for example, measure the contour angle ($) which makes a particular isoconcentration contour with the boundary/bulk interface. The penetration depth (zo) along the grain boundary must also be measured for a more accurate analysis. Accordingly, the following expressions are available for the evaluation of sSD,: s6D, = 2(7~t)~‘~D3’2cot2 I,+
(12.13)
s 6 D, = 8 t”’ D312cot3 Il//qo
(12.14)
after Fisher’s approximate solution, and after Whipple’s asymptotic solution. Here lo = z,(D t)- 1/2 is the reduced penetration depth along the grain boundary. One can also combine penetration-depth measurements with grain boundary concentration (c,, = (cJrZo) measurements instead of contour-angle measurements. (Here (c,)+~ represents the grain bulk concentration at depth zo). In that case the following equation is available for the evaluation of SSD,: s6D, = where the factor q. j- ‘I2 must be determined graphically from Fig. 3, first by assuming fi > 10 and then later using the trial and error method. Land&-Bhnstein New Series III/26
Kaur, Gust
12.1 Introduction
634
[Ref. p. 708
Grain boundary diffusivity may also be determined from autoradiograms taken at surfacesparallel to the diffusion source plane. In this case two autoradiograms taken at different depths z, and z2 are required. Bokshtein et al. [58Bl] have derived the following expression for the evaluation ofsaD, from the optical density measurementson these autoradiograms: - e2z1Y
ssD = 1.32D%~, b (I21 -
e212
(12.16)
.
F2
1
\
l-
10‘
l-
2 G Fig. 3. Variation of the diffusant concentration at the edge (5 = 0) of the grain boundary as a function of ~~fi-‘/~ (qO = q at 5 = 0) for various values of B after Le Claire [63Ll]. The concentrations are expressed in units of cO, the source concentration.
10-3-----
Whipple’s exact Whipple’s asymptotic Fisher’s opproximote
10.c 0
12.1.3 Mathematical analysis of penetration kinetics measurements In case of thin specimens,where the thickness is comparable to the grain boundary diffusion length, the mathematical solutions described in the preceding section become invalid. Moreover, accurate sectioning of such thin specimensposesmany experimental difficulties unless some special microsectioning techniques, such as radio-frequency sputtering, are employed. For thin specimens one therefore resorts to methods avoiding sectioning, such as the surface accumulation method. This involves monitoring of the diffusant accumulated at the back surface of the specimen after traversing its thickness and is particularly suitable in the type-C kinetics region where the temperatures are low enough to allow the assumption of zero volume diffusion. Obviously, unlike the sectioning method, in this casethe boundary conditions at the back surface of the specimenenter the mathematical analysis in addition to those at the source surface. For the caseof a constant diffusion source of concentration c0 at the z = 0 surface and an infinite sink at the back surface z = h (h: specimen thickness), Hendrickson and Machlin [54Hl] derived the following equation for diffusion under steady-state conditions: (12.17) D, = Q,(t)h/g Cor assuming that the time required to set-up the steady-state concentration gradient is much smaller than t. Here Q,(t) is the total amount of diffusant accumulated at the back surface per unit area in time t and g is the fractional area of this surface that is occupied by grain boundary terminations.
Kaur, Gust
Land&-Biimsfcin New Series III/26
Ref. p. 7081
635
12.1 Introduction
A more elaborate analysis for grain boundary diffusion acrossthin-film specimenswas carried out by Hwang and Balluffi [79H2]. Similar to the analysis of Hendrickson and Machlin (Eq. (12.17)),this analysis too is valid in the temperature region of zero volume diffusion only (i.e. type-C kinetics). Under the practically realizable conditions of(i) fast surface diffusion at the accumulation surface,(ii) quasi-steady state in the grain boundaries and (iii) film thickness much smaller than the grain boundary diffusion length, the following equation was shown to describe the accumulation kinetics: (12.18)
15,= c,[l -exp(-Z&1@)],
where ?$is the average diffusant concentration at the accumulation surface and 1 is the grain boundary length per unit area of this surface. It may be mentioned that segregation effects are assumed to be negligible in this case.Also, the thickness of the accumulation surfaceis assumedequal to the grain boundary thickness. For large t (t $ h/&L), this equation reduces to a form similar to that of Hendrickson and Machlin (Eq. (12.17)). Another simple method commonly used for boundary diffusion measurementson thin films is the so-called first-appearance measurements.A rough estimate of D, can be obtained simply by equating the time t, for first appearance of the diffusant at the back surface to h2/D,. For the caseof a constant source and an infinite sink Hall and Morabito [76Hl] prepared a nomograph (Fig. 4) for directly extracting D, from first-appearance measurementscarried out on thin-film diffusion couples under type-C kinetics conditions using surface analytical techniques like AES (Auger electron spectroscopy), XPS (X-ray photoelectron spectroscopy) and SIMS (secondary-ion massspectrometry). In calculation of this nomograph the following values were assumed:5 at.% for detection limit, 1 nm for escapedepth, 1 nm for grain boundary width and 50 at.% for concentration at the original interface between the two components of the diffusion couple. It may be mentioned that such measurements with diffusion couples yield in principle the chemical, and not the tracer, diffusivities. Db in m*/s
1D, f, I"* in pm - 0.01
r lo-l6 -5
h inpm ,0.01
i 0.02
-2 f0
E- 0.03
yeors
- 0.04 1 0.05 r 0.06 = 0.08 : 0.1
: 5
F 0.2 5 1 :
0.3 0.4 0.5 0.6
= 0.8 : 1.0 F 1.5 = 2.0
Fig. 4. Nomograph for obtaining grain boundary diffusion coefficient (D,) from first-appearance measurementson thin films assuming a detectivity limit of 0.1 monolayer and a grain boundary width 6 of 1 nm, after Hall and Morabito [76Hl]. d: grain size, h: film thickness and t, : time for first appearance.
hours 0.1 0.2 0.5
1 2 5
:oo 50 100 200 500 1000 2000 5000 10000
: 10-17 -5 -2 r lo-'* -5 -2 rlO-'9 -5 -2 r 10-20 -5
:: 50 100I
-2 I-10-*' 15 -2 _10-** 15 -2 -10-23
Landolt-B6mstein New Series III/26
Kaur, Gust
636
12.1 Introduction
[Ref. p. 708
12.1.4 Determination of grain and interphase boundary diffusivities from the kinetics of discontinuous solid-state reactions A large number of discontinuous solid-state reactions in real metallurgical materials are controlled by chemical diffusion of the atomic speciesinvolved in the reaction along the migrating reaction front, which is invariably a large-angle grain boundary or an interphase boundary. The various solid-state reactions from the kinetics of which boundary diffusion data have been evaluated and reported in literature are: Discontinuous precipitation (DP), discontinuous dissolution (DD), discontinuous coarsening (DC) and eutectoid decomposition (ED). In the same category falls the process of diffusion-induced grain boundary migration (DIGM). The common characteristic of all these reactions is that they are initiated at a large-angle grain boundary, which therefore plays the role of a reaction front (RF), i.e. the abrupt migrating interface separating the reaction product (RP) formed behind it and the initial material (I,) in front of it (Fig. 5). The same holds true also for DIGM, which implies the migration of a grain boundary in a pure metal (or a solid solution) upon chemical diffusion of a solute into (or out of) the material along the boundary, leading to the formation of an alloyed (or dealloyed) zone behind the migrating boundary. The diffusivities obtained from the kinetics of these processes therefore refer to chemical diffusion along the migrating grain boundaries (or interphase boundaries, depending upon whether the RP is partly uniphase with I, or not).
Fig. 5. A schematic representation of a discontinuous solidstate reaction in a material (1,) (a) before and (b) after the reaction.OGB: original positionof the grainboundary (GB), RF: reaction front, and RP: reaction product [89Kl].
All these discontinuous solid-state reactions as well as DIGM are basically of the samenature as far as their relation to boundary diffusion is concerned, and therefore follow the same dependenceon kinetic parameters. The only distinguishing features are the initial state (I,,) of the material and the reaction product (RP), the only consequenceof which is a different constant of proportionality between the boundary diffusivity and the kinetic parameters.For example, in DP reaction I, representsa homogeneous supersaturated solid solution u0 and RP represents a 2-phase structure u + p consisting of the depleted solid solution OLuniphase with u0 and the precipitated p phase. The growth of the p precipitates occurs by chemical diffusion of the solute and solvent atoms along the migrating u/o(~interface, which is nothing but a grain boundary in the original u0 phase. The fine lamellar structure formed as reaction product in this reaction can becomeI, for the second reaction of DC in the samespecimen.The RP in this reaction is simply a coarselamellar structure of u + p. On the other hand, if a specimen that has undergone DP is subjected to temperatures near the solvus point, the precipitates start dissolving by reversemigration of the DP reaction front into the 2-phaselamellar structure, leaving behind in its wake a solid solution as the reaction product. This represents the DD reaction. It may, however, be mentioned that the solid solution (a-) formed in this reaction is in general not homogeneous and exhibits residual concentration fluctuations. The only difference of the ED reaction from the DP reaction is that both components of the lamellar structure u + p formed in the reaction are of different phase compared to the original parent phase. Table 2 shows a summary of the characteristics of the various processesinvolving boundary diffusion along migrating boundaries. Kaur, Gust
Iandoll-BBmstein New series III,/26
12.1 Introduction
Ref. p. 7081
637
Table 2. Characteristics of the various solid-state reactions and DIGM. Reaction/Process Discontinuous precipitation Discontinuous coarsening Discontinuous dissolution Eutectoid decomposition DIGM
Initial state (Id
Reaction product (RP)
Z+ Phine a+P Y Pure metal Solid solution
a+P (a + PLoarse uu+P Alloy Depleted alloy
homogeneous supersaturated solid solutions in the c1-and y-phase, respectively. depleted solid solution uniphase with ~1~. precipitated P-phase. P: CL-: solid solution (in the cl-phase)exhibited residual concentration fluctuations. CL+ B: 2-phase lamellar structure. ao, Y:
u:
The dependenceof the boundary diffusion characteristics on the kinetics of any of theseprocessesis basically the same for all, the chemical boundary diffusivity being given by sdd, = K,l,Zv x KA=v,
(12.19)
where v is the boundary migration velocity, 1, is the width of the a-phase in the 2-phase lamellar structure and 1 is the interlamellar spacing. K is a proportionality constant the value of which differs for different models. For example, for discontinuous precipitation K = x,/(x,
- x,) (in [58Tl])
or K = x0/2(x0 - x,) (in [55Tl])
according to Turnbull’s model, ,,/?? tanh(1/2 &
= 0.5 (x0 - x1Mxo - 4
according to Cahn’s model [59Cl], and K = R7’/(-8AG)
according to Petermann-Hornbogen’s model [68Pl]. Here x0 is the solute concentration in the parent a,-phase, x1 is the average concentration in the depleted a-phase formed in the reaction, x, is the equilibrium concentration of the a-phase, AG is the change in Gibbs free energy associated with the reaction (AG < 0), R is the gas constant, and Tis the absolute temperature. By.making appropriate substitutions in the expressions for K, the samemodels can be applied to discontinuous coarsening, discontinuous dissolution and DIGM, too. In the case of eutectoid decomposition, in addition, b, must be replaced by the chemical interphase boundary diffusion coefficient bi along the U/Yinterface. Cheetham and Ridley [71Cl] supplied an independently derived expression for this case: 1 xp-x, SSQ = -.-
4x2 x; - x,p
PV,
where xp is the equilibrium composition of the 8 lamellae, and x,” and xt are the y-phase compositions at the tips of the advancing lamellae. Aaronson and co-workers [68A2, 69B2, 70Gl] developed a method to estimate grain and interphase boundary chemical diffusivities from the growth kinetics of the O-phasegrain boundary precipitates in the a-phase Al-3.93 wt.% Cu alloy. The earlier analysis of Aaron and Aaronson [68A2] (AA analysis) assumedthe solute concentration ci in the ~$3 interphase boundary to be equal to that (c,,) in cl-phase at the a/0 interface (i.e. ci = c,,), and the shape of the precipitates to be constant. The modified analysis of Brailsford and Aaron [69B2, 70Gl] (BA analysis) took into account the variable shape of the precipitates, and assumed instead ci = (c,, + c&/2, where c, is the concentration in the precipitated B-phase.
Land&-B&rut& New Series III/26
Kaur, Gust
638
12.1 Introduction
[Ref. p. 708
12.1.5 Grain boundary diffusivities from creep and sintering experiments It is a well-known fact that in tine-grained specimensdiffusiona! creep at low temperatures is controlled by diffusion of vacancies along the grain boundaries. One may therefore determine grain boundary diffusivities from creep measurements.Coble [63Cl] derived the following expression for 60,:
6D,= Ek Td3/147caR,
(12.20)
where d is the creep rate; k, the Boltzmann constant; d,the grain size; 0, the applied stress;62,the atomic volume and T is the absolute creep temperature. Strictly speaking, this equation is valid only for pure metals. It was shown by Gordon [73Gl] that for a compound M,N, in the above equation the grain boundary diffusivity 6 D, has to be replaced by a complex diffusivity ~amp,ergiven by
a"DM.cSNDN PCO+- = m ah,Drb+ n 6Nb DT;’’
(12.21)
where aMand aNare the effective widths of the Mm+ and N”- ions along the grain boundaries and 0: and 0: are the corresponding grain boundary diffusion coefficients. Similar to creep, the process of sintering is also under certain conditions controlled by the diffusion of vacancies along grain boundaries in the initial as we!! as final sintering stages.This allows the determination ofgrain boundary diffusivities from measurementsof the sintering kinetics. According to the analysis of Johnson and Cutler (63511the fractional linear shrinkage AI/&, is proportional to t ’ 31,the slope of this line being related to 6D, through the expression
6D, = [-a(Al/~,)/at0.3’]“03’
(7rrkTr,4/50@),
(12.22)
where rp is the particle radius and y the specific surface energy (or surface tension). This equation was later modified by Johnson and Clarke [64Jl] and the following improved expression given for the evaluation of 6 D,: 6 D, = (A1/1,)2,’[d(Al/l,)/dt] (2rrk Tr;/yO).
(12.23)
Having briefly introduced the reader to the main methods and equations referred to in the following tables, a review of the data on grain and interphase boundary diffusion in the form of tables and Arrhenius plots is presented below.
12.1.6 Use of tables and figures In this subsection a brief explanation regarding the use of tables and figures is given. Firstly, it may be noted that for many diffusion systemsthere are shown in the tables two different setsof Arrhenius parameters,namely, “Reported” and “Real”. This happens in those caseswhere the Arrhenius parametersgiven in the original works fail to reproduce the Arrhenius line fitted to the measurement points so much that in some cases the line calculated from the given values of (sSDb)Oand Qb lies a couple of orders of magnitude away from the actual experimental line. In these caseswe have derived graphically a new set of Arrhenius parameters from the fitted Arrhenius line and referred to them as “Real” to distinguish them from the “Reported” ones. Here, the term “Real” is used only in the sensethat these parameters are consistent with the reported values of T and SSD,, or the measurement points in the plot; these may not be the same as the “true” or “correct” parameters, e.g.due to faulty measurementsor faulty calculations. In some casesit was felt more convenient to evaluate the “Real” parameters by least-squaresanalysis instead of the graphical determination from the plot. These values are referred to as “RLSF” (recalculated least-squares fit) in the table. Only in few casesthe given information was complete enough to enable us a thorough cross-check of the data involving (i) checking of the validity of the equation employed under the given experimental conditions, (ii) checking the quality of the concentration profiles and their consistency with the reported diffusivity values and (iii) checking of consistency between the reported Arrhenius parameters and the fitted Arrhenius line. If either one or both of the first two checks gave negative results, we have labelled these data as “Questionable”, “Unreliable” or “Incorrect”, depending upon a number of factors which add to the overall picture of the publication. Only in rare casesdid all the three checksestablish unambiguously the absenceof any inconsistency in the work and hence correctness of the reported data; in these caseswe have shown the Arrhenius parameters in boldface type along with simply a dash in the “Remarks” column (unless some other experimental variables needed a mention here). Boldface type printing of the Arrhenius parameters is also used against “Real” in the “Remarks” column in caseswhere consistency is found to be lacking only in the last of the three checks.
Kaur, Gust
LandolbB6mstein New Series III/26
Ref. p. 7081
12.1 Introduction
639
In all other caseswhere the quality of the data could not be unequivocally established, the “Remarks” column in the table shows simply a dash mark along with the (s6 D,)’ and Qbcolumns in ordinary nonboldface type. The dash mark in other columns indicates the absence of the corresponding information in the original publication, e.g. a dash in the Do and Q columns implies that no information is available in the original publication about the volume diffusion data used for the evaluation of the grain boundary diffusivities. Similarly, a dash in the “Eq.” column implies that no mention is made in the original publication as to which equation was employed for evaluating the reported grain boundary diffusion data. A blank space,on the other hand, in any column signifies that the information here is the same as in the previous line. The ditto mark has been intentionally avoided to give the tables a clean and uncrowded look. However, a blank in the “Ref.” column in the table indicates that the corresponding values in the (s6 Db)’ and Qb columns have been calculated by us. And now a word about the figures. In those caseswhere the “Reported” Arrhenius parameters do not yield a line fitting the measurement points, the Arrhenius lines drawn in the figures correspond to the “Real” or the “RLSF” parameters.
12.1.7 Concluding remarks The following values of the conversion factors have been used throughout in this chapter. They are based on the physical constants given in the Document IUPAP-25 (Symbols, units, nomenclature and fundamental constants in physics, 1987 Revision) 1 eV = 1.60217733. 10-lgJ 1 eV * NA = 96.4853kJmol-’ = 23.0605kcal mol-’ 1 cal = 4.18400J The cal referred to here is the thermochemical calorie. In the following tables, the most reliable Arrhenius parameters are printed in bold.
Land&-BBmstein New Series III/26
Kaur, Gust
12.2 Data for grain and interphase boundary diffusion Matrix
Tracer
Purity (matrix)
Method
Eq. T K
(6 W” m3s-*
Qb
Remarks
Fig.
Ref.
kJ mol-’
DO
Q
Ref.
m’s-’
kJ mol-’
12.2.1 Data for grain boundary self-diffusion in pure materials Abbreviations used are explained at the end of the table Ag PC
“‘Ag
“‘Ag ‘9 BC (001) TiGB
> 3N7
SS
F
752 . . .647
> SN
SS
F
748 ... 627
> 3N8
SS
F
797.s.722 773.s.698 797...673 773-a-673
“‘Ag Ag BC (hkl) TwGB Ag PC
Ag 16” (001) TiGB Ag 18”(112)TiGB Ag PC Al PC
SN
ss
SN > 3N7 >4N
ss NA SS
6N
ss
“‘Ag
6N
ss
793 ... 693 793, 743 743, 693 F 771.~. 563 LMS’ 694 ..a 614 W 829 .a. 623 S 829 ..a 623 W 829 ..a 674 S 829.e.674 W 771 ea.623
‘l”Ag Al
SN -
ss TE
S -
“‘Ag
“‘Ag
F
905 ... 554 -
1.so~10-‘5 1.29. lo-l5 6.00. IO- ls 5.76.10-” 2.00~10-‘6
84.52 84.43 89.96 89.31 71.55
Reported aReal Reported aReal e=9
6 6 6
SIHI
8.95. IO-’
192.3
SlHl
SlHl
8.9S.1O-s
192.3
SlHl
54Tl
7.24.10-’
190.4
54Tl
1.40. IO-l6 5.46. IO-l6 1.20~10-1s 8.83. IO- l6 9.60. IO- l4 1.06. IO-l3 2.70. IO- l3 8.00. IO-= 3.10*10-”
68.62 76.44 80.33 78.12 101.3 101.3 133.9 136.0 75.31
0 = 13”, reported “Real 8 = 16”, reported “Real 0 = 23”, reported aReal c$= 6”, bincorrect 4 = 24”, bincorrect bIncorrect
54Tl
7.24. lo-’
190.4
54Tl
54Tl
7.24.10-’
190.4
54Tl
54Tl
7.24.10-’
190.4
54Tl
63L2 63L2 63L2 68Kl 68S1,2 72Rl 72Rl 72Rl 72Rl 72Rl
8.9Se1O-s 8.95*10-S 8.95 11O-s 2.78 +lo-’ 4.00.10-’ 6.70.10-’
192.3 192.3 192.3 181.5 184.1 189.1
SlHl SlHl SlHl 68Kl 61S2 69Rl
6.70.10-’
189.1
69Rl
6.70.10-’
189.1
69Rl
78Gl 74H2
1.00 * 10-4 -
191.2 -
78Gl -
1.16*10-‘6
63.60
-
3.1S~10-1s 1.30.10-‘” 8.60*10-‘6 3.40.10-‘7
79.08 76.99 74.48 49.37
bUnreliable -
3.10*10-‘7
49.37
-
-
x126
-
6 6 6 6 6 6 6 6 -
3.79.10-l” 80.77 ~f9.S~10-1s x60.2
-
6 -
Al,o,
ssc
PC CP SP PSP
‘4l3+ 020202-
>3N 2N7 2N8 -
ISS ssc ssc
C JC C C
2023 ... 1923 ... 2073 ... 1798 ...
PC
02-
-
OK
-
-
Au SCTF
19’Au
> 5N
ss
S
625 ... 521
PC TF
l95AU 19’Au
> 5N > 5N
ss ss
S S
717...640 450...390
“Cd
2N5
ss
F
420.., 324
llsmCd
5N5
ss
S
408 ... 324
14C
> 6N
SW)
W
CH,C - COOH SGB
14C
6N
ss
CN - C,H, - CN SGB
14C
4N5
co PC
‘Co
Cd PC
C,oH,,
Cr PC cu PC
SGB
1463 1473 1573 1623
-
8.60.10-‘0 w 2.5. 1O-4 4.00.10-6 4.38. 1O-7 8.48. 1O-7 1.00~10-6 “4.30.10-12 d1.40.10-‘6
418.4 z 594* 564.8 439.3 439.3 385.0 “231.0 d61.00
1 at.% Fe-doped 2 at.% Fe-doped 3 at.% Fe-doped 0.7 at.% Ti-doped 0.7 at.% Ti-doped
3.80. lo-l6 3.32. lo-l6 3.10*10-‘6 x 9.10-‘6 2.37. IO-l5
111.9 110.6 84.91 x 96 95.92
Reported aReal Reported aReal
5.00~10-14 5.30.10-14 3.35.10-14
54.39 54.04 46.02
Reported aReal -
476...403
1.70~lo-‘3 1.48. lo-l5
49.00 48.34
Reported aReal
S
297 ... 281
3.00.10-9 3.40*10-9
47.00 46.94
Reported aReal
ss
S
288...253
2.70.10-10 4.84.10-l’
44.00 40.84
Reported aReal
2N2
S(R)
V
973 . ..773
6oCo
4N
ss
F
1023 ... 723 693...623
f7.50.10-I5 ‘3 52.10-16 2.00.10-14 1.20.10-‘4
163.2 141.2 117.2 117.2
Reported aReal cl-phase E-phase
“Cr
3N5
AR
B
1623 ... 1373 ;70.
192.5 152.5
Reported aReal
7 7 7 7 8 8 8 9 9 IO 10 10 11 11 11 12
110.0 107.2 120.0 102.1 104.6
Reported, from T, Recalculated From low T A@‘,, see [69M2] Aflv, see [65Gl]
12 12 12 -
cu
> 3N8
ssc
C
1092..- 833
-
TE
-
-
lo-I3
4.00. lo- I4 2.35*10-‘4 8.80 * 10-14 1.05.10-‘4 1.20.10-14
-
-
8OC2 63Jl 74Vl 77Ll 77Ll 8OWl 8OWl 8OWl
-
-
-
7363
9.10.10-6
174.6
57Ml
7302 74Gl
9.10. IO-l6 9.10.10-6
174.6 174.6
57Ml 57Ml
55Wl
-
-
55Wl
69Gl
-
-
55Wl
77Bl
3.62
142.5
77Bl
81B2
4.90.10-4
59.00
81B2
86Bl
6.80.10-4
57.00
86Bl
5962
Not required
75Bl 75Bl
1.10~10-~
242.7
75Bl
57B2
g7.09. 1O-7
g258.4
57B2
70Bl
3.40. 10-5 200.0 2.00. 10-5 197.2 Not required -
74H2 74H2
54Kl 55Kl -
Matrix
Fe PC
Tracer
“Fe
59Fe
Purity (matrix)
Method
2N6
AR
< 2N
55*59Fe 2N7
“Fe
Eq.
B
T
@QJ"
Qb
K
m3sq1
kJ mol-’
-
9.03**0-‘3 7.77.10-14 3.71 . lo- l4 1.12~10-‘~ 2.02.10-‘2
x 128 165.0 222.9 141.2 141.0 143.9 167.4 159.3 174.5 x 167 x 172 172.3 167.4 172.3 104.6 96.94 139.7 143.9 = 163 174.0 z 163 180.5 159.0 158.3 173.6 177.1
y-Fe, reported RLSF RLSF RLSF Reported, UR RLSF, UR u-Fe, reported “Real a-Fe, DFP y-Fe, reported y-Fe, reported aReal y-Fe, reported “Real y-Fe, reported aReal a-Fe, reported aReal y-Fe, reported aReal y-Fe, reported aReal y-Fe, reported aReal Reported, UR “Real, UR
1.78. lo-l5 9.06.10-*’ 2.34. IO-l4 8.35.10-‘* 5.00. lo- l4 1.66.10-” 5.55~10-‘4 7.55.10-l’
74.48 ** 82.41 81.17 60.02 82.84 69.16 88.70 87.60
Reported, UR RLSF, UR Reported, UR RLSF, UR Reported, UR RLSF, UR Reported, UR RLSF, UR
1473 ... 1273
S(R)
F BG V
1473 ... 1273 1473 .a. 1273 953 a.. 803
ss
F
929...853
3N6 2N7
ss SW AR
4N
SW
F 924.e. 805 F 1289... 1196 F PD 1310...834 1289...1196 F 1287.e. 1191
EG
AK
B-G 13750.. 1223 1125...975
s5*s9Fe 2N7 4N -
Fe SP, 90% TD 94% TD 97% TD 97% TD, stabilized
55*59FE > 2N
S(R)
W
1289...1196
SW
W
1287-e. 1191
SW
SW
Fs’
1432e.e 1222
Fs’
955 . . .774
Fs’
1373 ... 1223
5.25 * lo- l3 9.18. IO-” 5.38. IO-l5 ‘1.80.10-” ‘2 91*10-” 6.;0. IO-” 2.39.lo-l3 4.33.10-13 i&*0-‘3
1.00~10-‘~ 1.84~1o-‘J 1.04~10-‘5 5.73*10-‘6 2.40. lo- l3 3.26.10-l’ 6.79.10-l’
Remarks
Fig.
Ref.
DO
Q
Ref.
4.45.10-5
281.5
57Bl
9.22.10-6
191.5 268.2
57Bl 57Bl
m2s-’ 57Bl
13 13 13 13 13 13 13 13 -
1.40~10-5
kJ mol-’
59Gl
Not required
59Ll
g1.80. IO-’
*266.2
59Ll
59Ll 59L2 59L2
g1.80-10-3 1.85.1O-‘j -
*266.2 251.0 x 260
59Ll 59L2 59L2
59L2
1.85+10+
251.0
59L2
64Bl
-
-
-
64Bl
-
-
-
6503
1.85 .lO+
251.0
59L2
6563
1.85.IO+
251.0
59L2
6551
1.05. lO-4
283.7
6551
6551
2.75. lO-3
254.0
65Sl
75Ml
1.10*10-s
265.7
75Ml
75Ml 75Ml 75Ml
-
TE
-
-
ss S(R) ss
S S S
1023 ... 836 1083 1.. 873 1109...873
1311-
3N7 3N8 3N7 -
ss
W
798...553
1311-
-
ss
W
834... 625
Ni BC
63Ni
3N5
AR
F PD 1373 ... 973
Ni PC
63Ni
4N 3N8
ss ss
V F
1023 ... 853 1358 ... 1202
HP
S(R) AR ss
FS’ V F
1373...1123 1473 ... 1073 923...748 1244.e.873 1243 ... 873 1353 ... 1083
Fe 36.9” (001) (013) TiGB Fe PC
IUPC BC
w-Fe, Z = 5
13
81Bl
165.8 91.00
a-Fe cl-Fe a-Fe, y-Fe
82Bl 85Hl 86Hl
x 50 49.30 x 105 102.5
Reported RLSF Reported RLSF
w 109 180.8 140.3 115.2 108.1 102.4 102.2 102.8 108.3 116.5 143.7 111.3 127.2 362.9 118.0 108.7 114.6 116.9 170.3 187.9 x 234 233.2 131.0 134.0 129.3 129.6 114.6 187.0
Reported RLSF, 0 = 5” RLSF, 0 = IO” RLSF, 6’ = 20” RLSF, 0 = 30” RLSF, 0 = 40 RLSF, 0 = 45” RLSF, b’ = 50” RLSF, 0 = 60” RLSF, 0 = 70” RLSF, 0 = 80” bIncorrect Reported, UR RLSF, IC bIncorrect Reported RLSF IO” (112) TiGB IO” <112> TwGB Reported aReal Reported RLSF Reported RLSF -
13 13 13 14 14 15 15 15 15 15
-
5gFe
-
BC
63Ni
3N7
AR
W
PC
63Ni
4N
S(R)
W
2N5
GGK
4N
GGK
-
1323...1173
3N7 4N8
ss ss
BV S
1373 ... 823 1324.e. 641
1323...1173
3.40.10-12 1.74.10-16 See Fig. 13 3.05.10-l’ 7.58.10-l’ 3.05.10-14 1.40.10-‘5 4.56. lo-l6 4.81. IO-l6 3.68.10-16 3.70.10-16 3.78.10-16 4.60. IO-l6 4.43.10-16 1.87.10-15 f8.00~10-‘g 2.96. 1O-6 8.75.10-16 f1.84.10-20 3.50.10-15 5.48.10-15 2.20. lo- l4 2.60. IO-l4 ;91.10-‘1 3.10.10-14 1.19.10-‘4 4.05.10-14 2.00.10-‘4 4.00.10-‘5 4.40. IO--”
W
Q(T)
82Bl 85Hl 77Hl
102.1
62Cl
4.93.10
102.8
62Cl
58Ul
1.27. 1O-4
279.5
56Hl
61Gl 63Sl
Not required 2.59. 1O-4 290.8
63Sl
64Ll 6502 65Wl
1.39.10-4 275.7 Not required 1.90.10-4 279.5
64Ll
69Cl 69Cl 74Al
1.10.10-4 1.10~10-4 1.60.10-4
277.8 277.8 259.4
69Cl 69Cl 74Al
75Dl 15 75Dl 15 85Bl 15 15,53 88Nl
4.70.10-S
274.9
75Dl
1.50.10-4
284.5
75Dl
3.62. 1O-4 9.00.10-5
284.2 278.0
85Bl 76Ml
268.2 292.0
62Cl
1.80.10-3 2.86. 1O-2 D”(T) 4.05.10-s
62Cl
65Wl
r
Matrix
Tracer
3N8 4N5
Pb PC
210Pb
3N5
ss ss ss
Pb BC
TiGB
210Pb
> 5N
AR
1.00 - lo- ” 3.00*10-1’
192.5 171.7
SGB LAGB
8.10. lo-l4 3.66010-‘~ 2.26. IO- ” 4.05. lo- l8 3.13.10-‘* 1.78.10-l’ 8.46.10-l’
65.69 71.86 z 33.5 32.53 cz 24.1 23.88 x 17.2 17.42 x 19.7 20.23 z 38.2 38.14
Reported aReal 0 = IO”, RLSF 0 = 14”, RLSF 13= 20”, RLSF 0 = 30”, RLSF Reported RLSF Reported “Real -
m3 s-l
W w
1073**.795 1073***773
F
533..*474
F PO 493 .** 393
63Ni 63Ni
Remarks
@DJ"
Method
NiO SC PC
Qb
T K
Purity (matrix)
Eq.
Fig.
reported reported reported reported
2.20 * 10-6 2.20.10-6
246.4 247.0
79Al 81Al
5401
1.17 * 1o-4
107.5
5401
66Sl
6.26.10-’
103.2
60Hl
19
80Gl
1.60.10-’
100.3
72Ml
17 17 18 18 -
68Hl 68Hl
3.00-10-5 3.00~10-s
159.0 159.0
65Cl 65Cl
66Fl
Not required
79Hl
2.62. lo4
841.3
79Hl
79Hl
1.97.104
836.5
79Hl
19 -
62Ll 76Sl 84Sl
7.80.10-5 95.40 Not required 1.69.10-3 108.6
61Ll
71Kl
3.50 * 10-s
625.5
71Kl
86Sl
Not required
66F2
4.50.10-E
176.6
66F2
67Fl 68Fl
2.80*10-’ 1.10*10-s
185.1 150.6
67Fl 68Fl
> SN
AR
F po 493 ..* 393
lo3Pb
SNS
ss
w
473.0.344
6.10. lo- l5 5.87. lo-Is
44.38 43.99
Sb PC
124Sb
3N4 6N
F F
821... 573 841 ea.658
2.94.10-l’ 1.50. 10-l’
%.65 92.88
SIC HPP
C4+
98.2%
S(R) WV CE
C
2473.~. 2173
14C4+
HP
ss
S
2374s.. 2128
F
2374.e. 2128
7.00 * lo- t4 6.64. lo-l4 2.22.10-6 1.38.10-’ 6.35. lo-’ 3.19.10-6
305.4 303.1 563.5 600.7 551.9 584.6
ss LS LS
F V LM
483.e. 404 486-e-415 334-a. 272
3.22.10-” ‘5.5o~lo-‘e 2.45. lo-l3
39.96 44.77 48.96
ss
F
2318..-2119
8.00. 1O-2o -
156.1
Reported ’ Real Reported ’ Real Reported ’ Real bQuestionable bQuestionable -
x 390
-
18 -
1.60. lo-” 9.05. lo- l2 3.00.10-” l.OO.lO-” 3.24.10-”
185.4 189.7 191.6 178.7 186.6
a-U, reported RLSF P-U y-U, reported RLSF
20 20 20
TbO, SGB
4N
llgrnSn llgSn
6N 6N
22fq-j,4+
_
TIC PSP
c
-
CE
C
1773 ... 1473
u PC
235U
3N
SW
F
903.a.773
2N8
SW
F
1023.a.963 1323-a. 1123
kJ mol-’
79Al 81Al
*l”Pb
113.123~~
Q
Ref.
m2s-’
DO
16 16 -
Pb IO” (001) TwGB Pb PC
so PC TF
Ref.
kJ mol-’
66Sl 66Sl 66Sl 66Sl
84Sl
UC PC UC,.,, PC uo, SP
PSP
233u4+
_
233u4+
_
233u4+
RG
237u4+
_
tJ4+
RG
ss ss ss
W, S 2473 ... 1473
7.20. IO-l5
313.4
W, S 2473 ... 1473
1.43 * lo-I3
287.4
-
S
1923 ... 1750
ss
S
2423.‘. 2173
FSS
F -
2423...2173 1973 1.. 1623
4.00. lo- I5 3.11~ lo-= R5.19.10-‘5 1.71. lo-” 4.3o~lo-l2 1.50.10-I3 1.34.10-13 7.05 * 10-16 1.79. lo-l6 R6.90.10-16 3.36. IO-” -
292.8 294.2 197.5 351.0 335.4 290.0 290.4 338.9 323.9 R239.0 373.4
Reported RLSF Incorrect Recalculated Recalculated Reported aReal Reported aReal CCS(IC) Corrected
21
75Rl
21 22 22
75Rl
g6.09- 1O-4 -
586.1 -
67Vl -
66Al
4.00~10-1’
292.9
66Al
66Yl
5.82.10-’
304.2
66Yl
72Bl
Not required
72Wl
Not required
79Rl
Not required
Reported, x = 0.106 Reported, x = 0.045 DFP, x = 0.10 22
70Ml 70Ml
355.6 355.6 355.6 468.6
69Ml 69Ml 69Ml
-
22 22 22
CP
U4+
-
ISS
JC
1373 ... 1173
PSP
IJ4+
RG
CE
C
1723 ... 1523
eu4+
-
ss
S
1923 ... 1548
4.55. IO-l2
x 285 x 193 281.8
2423 .+. 1670 2423 ... 1670 2423 ... 1973
3.33. lo-l3 1.24. lo-l3 2.30 . IO- I2
384.9 378.7 380.7
SGB LAGB -
23 23 23
67Kl 67Kl 81B4
1.43 * 10-6 1.79.10-6 7.96.10-* 5.00. IO+
U&+x
PC
w SPC
185~
>4N > 3N5
S(R) SW
F F S
WC HPP
14C
4N
ss
S F
2643 ... 2238 2643 ... 2238
2.29. lo-” 7.85. IO- I4
297.1 309.6
bIncorrect DFP, bincorrect
-
71Bl
g2.59. 1O-6
g240.2
71Bl
w,c
14c
-
S(R)
F S
1773 a.. 1573 1773 ... 1573
6.54.10-l’ 1.80.10-10
280.3 287.9
-
18
81Tl 81Tl 54W2 54W2 66Bl
382.8 382.8 93.51
81Tl 81Tl
24 24 24
1.83.10-3 1.83.10-3 1.50.10-5
-
67Bl
Not required
PC
zu PC
65Zn
5N 4N -
ss ss ss
F F F
460... 350 428 ... 354 496.e.333
1.10 * lo- l4 1.90. lo- l4 5.50.10-‘4
59.83 61.09 54.39
Zr PC
Zr
3N5
CE
C
893.s.793
z 7.5.10-14
x 112
a
AK AR b
These Arrhenius parameters (derived by us) from the original Arrhenius plot correspond to the actual Arrhenius line drawn there; the reported ones yield a much different line lying away from the experimental data points. Absorption kinetics. Autoradiography. For reasons discussed in detail in [89K2], these data are considered incorrect, unreliable or questionable.
B . BC BG B-G BV ’ C
NTAP
65Al 65Al 81B4
53Sl 62Hl
Bokshtein’s equation. Bicrystal. Borisov-Golikov equation [57Bl] for sectioning method. Borisov-Golikov analysis for absorption kinetics. Borisov’s equation (very similar to Fisher’s equation). Assuming precipitation to be occurring. Coble’s equation. (continued)
Footnotes for 12.2.1, continued CCS(IC) CE CP CVD d DFP Do, Q e EG f F F FF FSS B GGK WI) HP HPP IC KS JC LAGB LMS’ NA NTAP OK PC PCTF PSP
Evaluated from combined creep [79Rl] and sintering [72Bl] measurements. (These data are incorrect, because the sintering data taken from [72Bl] for Arrhenius parameters determination are in error by an order of magnitude.) Indirect estimation from creep experiments. Powder compacts. Chemical-vapour-deposition grown. Assuming precipitation to be absent. Arrhenius parameters derived by us from the original Arrhenius plot. Volume diffusion data used for the evaluation of grain boundary diffusion data. Radioactive, but the particular isotope used is not specified. Electrolytic grade. From the reported, recalculated or derived (from the Arrhenius plot) value of 0: assuming a value of 6 = 0.5 nm for the grain boundary width. Fisher’s equation. Fisher’s solution for application to penetration-depth measurements. Fisher’s equation; stated incorrectly in the original work. Indirect estimation from final-stage sintering kinetics. Evaluated by us from the reported D values or from the corresponding Arrhenius plot. Indirect estimation from grain growth kinetics. (OOI), (011) and (111) directions. High purity. Hot-pressed polycrystal. Incorrect; for reasons discussed in detail in [89K2]. Indirect estimation from initial-stage sintering kinetics. Johnson-Cutler equation. Large-angle grain boundary. Levine-MacCallum equation; stated incorrectly in the original work. Nuclear absorption. No tabular data and no Arrhenius plot given in the original work. Indirect estimation from the oxidation kinetics. Polycrystal. Polycrystalline thin film. Partially-sintered polycrystal.
R
Reported. Reactor grade. Recalculated least-squares tit. Suzuoka’s equation. Single crystalline thin-film containing dislocation networks. Subgrain boundaries. Sintered polycrystal. Swaged polycrystal. Sectioning combined with residual-activity measurements. Serial sectioning. Indirect estimation from steady-state creep measurements. Absolute temperature. Temperature of transition from volume diffusion-controlled creep to grain boundary diffusion-controlled creep. Theoretical density. TD Theoretical estimation. TE Thin film. TF Tilt grain boundary. TiGB Twist grain boundary. TwGB Unreliable; for reasons discussed in detail in [89K2]. UR Analogous to homogeneous volume diffusion. V The Do value [76Ml] used is incorrectly cited in [89#2]: 9.00 . 10e4 m2 s-i W instead of 9.00. 10m5m2 s-i. Thus, the suggestedvalues [89K2] of j?at 1324 and 641 K are not the true ones. The corresponding p values given in the original work [88Nl] are more or less correct. Whipple-Le Claire equation. W (6 D,)', Qb Arrhenius parameters for grain boundary self-diffusion. Activation enthalpy for migration of monovacancies in the lattice. Afl” Reciprocal density of the coincident sites relative to the crystal lattice. sites. z Tilt angle. Twist angle. i * The corresponding value in eV is misprinted in [89K2] as 7.16 in place of 6.16. ** The corresponding value in eV is misprinted in [89K2] as 0.7919 in place of 0.7719. RG RLSF S SCTF SGB SP SPC SW ss ssc T T.
Figs. 6 to 24, see p. 676ff.
Matrix
Tracer
Purity (matrix)
Method
Eq.
T
(~64)~
K
m3 s-l
Qt,
Remarks
Fig.
Ref.
kJmol-’
DO
Q
m2se1
kJ mol-’
Ref.
12.2.2 Data for grain boundary tracer impurity diffusion in pure materials Ag PC
“‘Cd 114mIn 124Sb “‘Sn i2’Te
"OrnAg
Al SP PC
5gFe
5N 5N 5N 5N 5N >4N
Abbreviations
used are explained at the end of the table 3.55*10-‘6 3.90*10-‘6 6.70*10-16 6.00. lo-l6 1.70.10-‘5 1.00~10-9
S(R) S(R) SW S(R) ss
F F F F W
772... 557 764+..469 77l.e.471 776...527 970...650
;SR,
V W
893 ... 523 774... 523
1.98~10~*
BC
W
723 ... 523
67Ga 65Zn
5N 4N >4N
SW ss ss
V F F W
468 . ..404 572.+. 373 633 . ..493 604...425 593...428
ZIl
5N5
EPMA
W
613.e.523
F, W 613 ... 523
AI,03
L
F
613...523
PC
“‘Ag
2N7.
S(R)
S
1733 ... 1100
SP
“Cr3+
4N5
S(R)
-
1773 ... 1473
1.00~10-” 5.85. lo-l2 “2.00~10-‘0 9.30*10-i’ 1.60.10-‘5 3.10.10-‘5 1.60+10-” 6.30. IO-l4 1.00~10-9 See Figs. 27...29 See Figs. 30 . . .33 See Figs. 34 . . .38
2.10.10-a 3.10.10-3 5.00.10-‘2 1.10. lo-”
64.56 63.55 57.11 59.87 42.00 z 58.6 135.1 147.6 100.3 95.18 101.3 31.92 49.79 49.21 90.70 59.82 118.7
392.0 392.0 341.0 350.4
SGB, reported SGB, areal LAGB, reported LAGB, ‘areal TCK LAGB’ LAGB” SGB 31~~~55”(111) TiGBs 10***45” (001) TiGBs 14...45” (001) TwGBs, 31...58” (111) TwGBs Reported “Real Reported aReal
25 25 25 25 25
69Kl 67K2 67K3 69K2 87Gl
5.04.10-5 5.50-10-5 2.34.10-5 4.72. 1O-5 2.10.10-5
176.6 174.8 163.5 170.9 154.7
69Kl 67K2 67K3 69K2 87Gl
26 26 26 26 26 26 26 26 27... 29 30 ... 33 34... 38
69Hl 86B2
Not required 8.20. 1O-3 186.2
85B2
4.90.10-5 1.10~10-4 2.45. 1O-5 2.45. IO- 5
122.3 129.3 119.5 119.5
7OPl 59Hl 83Bl 83Bl
-
-
-
1.40.10-4
128.9
6001
80Al
1.40.10-4
128.9
6001
86Ml
2.40.10-4
331.0
86Ml
84Ll
6.93. IO-”
266.0
83Ll
39 39
86B2 86B2 86B2 75Vl 74Hl 86Gl 87B2 87B2 87B2 76A1, 78A 77Al
Matrix
AW,
6” (0112)TiGB
Tracer
Purity (matrix)
s1Cr3+ 3N4 sgFe3+ 4N5
Method
Eq.
S(R) SW
W
T
(~~4s)~
Qb
Remarks
K
m3s-l
kJmol-’
4.00. lo-is 1.01. IO- l4 2.14. IO- l4
z 170 212.0 225.4 264.0
bUnreliable Reported aReal bUnreliable
39 -
9.50. IO- r6 3.90. IO- ‘* 3.90. lo- l9 “2.00. IO-‘s =1.10~10-” 8.60. IO- l7 1.11 -IO-l6 8.03. IO-‘*
67.78 59.82 59.82 62.72 69.60 104.6 106.1 x 87 87.48+
bQuestionable Upper limit Lower limit Reported aReal Reported ’ Real Reported RLSF
40 40 40 40
75KI 7982 7982 8IVI
169.0 8.00. IO-6 Not required
76H3
-
-
75KI -
76Hl
-
-
-
41
72SI
1.20.10-6
82.01
72SI
42 42 42 -
65A3 61GI 69LI
239.3 4.00.10-6 Not required 259.4 4.00~10-6
65A3
76M2
Not required
43 43 43 43 43 43
60Gl 62Bl
Not required 197.2 7.18.10-’
6OL2
70B2
6.10.10-’
194.6
70B2
79Sl 70KI 69C2
Not required 176.3 2.02.10-s 178.2 3.00.10-6
70Kl 69C2
-
61RI 8IGI
Not required 1.30*10-4 193.5
72GI
1873 a.. 1473 1773 *a* 1473
Ni*+ -WA 30” (001) TiGB
4N6
EPMA
F
1643-e. 1483
Au PC
4N -
SW AES
F HB
809a.e 548 542a.0303
-
ERM
*
423.0.289
Cr
-
AES
-
566-a-484
cu
-
AES
-
473-e. 373
TF
ii”Ag Ag
Cd PC
l lomAg 4N
S(R)
F
473-o. 413
7.40. IO- l5
44.35
co PC
“Fe 63Ni l=W
3N7 2N2 -
S(R) S(R) ss
S V F
1273...1110 1023 ... 853 1073..*913
5.60. lo-l5 “9.50. lo-l5 7.74. IO-l4
131.0 190.8 165.3
CrTF
Au
-
RBS
V
907.e.551
cI.00~IO-24
65.61
NPTAP RLSF -
cl’ PC cu BC(OOI)TiGB
ll”Ag ‘l”Ag
SN 5N4
SW AR
V F
723 ... 523 1067 *.. 790
cl’ PC
‘l”Ag
> 4N4
SW
F
891 a.. 671
CU BC(OOl>TiGB Cu TF PC
“‘Ag
SN
AR
S W
891 ..a 671 1030*.. 816
& 13As dam
5N
RBS S(R) ss
HB F S
573.a.498 816...609 973.a.673
‘lsCd “JIn, 11%1
SN -
AR SIMS
V S
773...613 819,773
c1.55.10-‘g 2.20 * lo- l1 2.80.10-” 7.10*10-‘6 7.96. lo-l6 2.30. IO-” 7.50 * lo- 13 9.39.10-13 ‘1.05 - lo-*’ 7.90.10-‘6 5.00. IO- l6 1.47*10-i* ‘2.57. IO-** x 1.2*10-‘4
71.96 133.9 133.4 134.0 75.31 75.31 75.31 108.8 109.3 60.07 51.67 83.68 39.11 48.53 x 86
b Questionable 0 = 45”, reported “Real, UBC “Real, SBC Reported ’ Real t9 = 45”, reported ’ Real RLSF Reported “Real, UR bUnreliable bUnreliable
BC
Fig.
-
Ref.
8482 84Ll
DO
Q
Ref.
m*s-’
kJmol-’
-
-
3.64 * 10-9
300.0
83LI
-
-
77H4
75KI
Not required
70B2 70RI
69Ll
-
‘l3In ‘IsIn 63Ni
-
SIMS SIMS AR
S 973..-773 S 973..-773 F PD 1098 .a. 923
cu BC(001) (013) TiGB
Ni
5N 4N6
AR EPMA
S T?
1123 ... 1023 1048...948
cu PC
32P
2N8 3N 3N2 5N 5N
ss ss ;;Rj AR
W, S W, S W, S W SpD
984... 847 976... 847 959 ... 847 1098...783 994... 878
4N >4N
W-9 W-9
F w
874.a.614 933.a.773
gCd
-
AES
V
800...500
“Cd
-
AES
V
“‘HP+
3N4
S(R)
-
3N7
S(R)
-
cu BC(OOl)TiGB
35S
cu
124Sb
45” TiGB cu PC 65Zll
CuInSe, PC
Er,O,
PC
2.18.10+ 4.93 * 10-7 7.97.10-S 2.40. IO-” 2.67. IO-l2 1.47. IO-l2 1.20. IO-l2 1.05. IO-l2 3.28. IO-l3 3.24. IO-l3 4.50.10-‘4 x 2.0.10-12 x 5.6.10-13 x 8.5.10-14 z 3.3.10-14 c 7.1 .lO-” z 1.3.10-15 z ‘5.4.10-15 x 8.3.10-16 8.58~10-‘3 1.16. lo- l3 3.16. lo-l5 1.00. IO-I2 1.15. IO-I2 8.03. IO-l3 6.00 * lo- I’ 3.10. IO-l4 3.72. IO- l4
210.5 203.2 278.4 200.7 174.9 165.2 162.6 162.4 157.3 164.6 108.8 x 147 x 136 x 119 z 110 z 98 z 84 z 94 x 78 81.06 78.56 53.25 81.59 87.86 83.66 60.25 96.65++ 98.68
0 = 45” 1bunreliable bUnreliable 0 = IO”, RLSF 8 = 20”, RLSF f3 = 30”, RLSF 0 = 40”, RLSF 0 = 45”, RLSF f3 = 50”, RLSF 0 = 60”, RLSF 8 = 70”, RLSF 8 = 450 Z = 5, 0 = 36.87” Q = 36.68” e = 37.330 e = 37.970 0 = 38.00” f3 = 38.08” 0 = 38.30” 0 = 38.80” DFP DFP DFP Reported RLSF Reported aReal
-
761 ..a 500
c5.30~10-‘3 “3.05. IO-I2 “4.20. IO-”
144.7 154.6 111.0
Reported aReal -
2243 .-a 1874
l.21f10-9
544.8
bQuestionable
43 45 45 45 45 45 43 43 43 43 43 43 43 46 46 -
1966, 1886
6.70. 1O-4
714.6
bQuestionable
-
44 44 44 44 44 44 44 44
84Gl 84Gl 55Yl 55Yl 55Yl 55Yl 55Yl 55Yl 55Yl 55Yl 70Rl 86Al 86Al 86Al 86Al 86Al 86Al 86Al 86Al 7882 7882 7832 73Ml 70Rl
2.19 * 10-5
178.0
83Gl
‘6.32. 1O-3
268.2
55Yl
1.10~10-4 1.70.10-3
225.9 231.5
70Rl7921
7.02. 7.98. 4.38. 2.30. -
lo-’ IO-’ lo-’ lo-’
138.0 138.9 138.0 207.1 -
7882 7832 7882 73Ml 70Rl
69K3 77H2
7.30 * 10-s 3.40.10-s
198.7 190.8
69K3 57Hl
77Kl
Not required
79Kl
Not required
78Sl
i7.70.1012 ‘1.15.10-10 1.48. IO-”
‘1172 ‘248.5 295.4
78Sl 78Sl 78Sl
78Sl
Matrix
Tracer
Fe PC
Purity (matrix)
Method
Eq.
800 ppm 0, 100 ppm S
c2.50.10-14 =5.95*10-‘5 2.50.10-‘4 2.61. lo-l4 2.33.10-13 1.80~10-10 6.02+10-” 4.40. lo- l4 2.25. lo-l4 3.20.10-‘* 4.54.10-‘2 4.27.10-l3 ‘1.46.10-” 3.85. lo- l4 3.23.10-‘* 2.13*10-‘* 2.00~10-‘* 2.11.10-‘2 2.50. IO-‘* 3.47. lo-” 1.21~10-‘* 1.27.10-‘” 3.30*10-‘5 7.05*10-‘5 2.30.10-” 6.00. lo-l6 3.03*10-9
196.6 178.5 138.1 138.3 173.6 217.6 217.7 117.2 123.5 177.8 178.0 167.8 6.355 152.3 181.2 177.8 173.6 173.0 186.2 215.4 176.2 177.6 92.47 93.77 78.66 74.31 218.0
Reported RLSF Reported RLSF bUnreliable Reported aReal Reported, a-Fe aReal Reported, y-Fe ’ Real bQuestionable No APs Reported aReal Reported RLSF Reported RLSF Reported RLSF 190 ppm C, reported “Real 40 ppm C, reported ’ Real -
47 47 47 47 47 47 47 47 47 47 47
2.05. IO-” 2.05.10-” 2.05.10-” 2.20. lo- l2 1.50 - 10-12 1.21*10-‘2
130.5 130.5 130.5 113.0 96.65 96.86
-
973...838
2N7
V
3N8
S
3N5 -
Fs’ S
968 a.. 773 995...885
> 3N
BV
1141 ee.980
H 9wb 63Ni
3N6 TG 3N7 3N5
SW FAM ss SW ss
S V S Fs’ Fs’
1483 .+. 1378 1073 ... 573 1075 *** 993 1403 ..a 1213 969.e.805
Ni
2N6
SA
F
1473 ... 1273
3N8
SA
F
1473 ... 1273
63Ni
3N6
SW
S
156O.e. 1426
3*P
3N6
S(R)
S
1139.a.950
3N2
S(R)
S
1125...925
3N8
S(R)
W
1153...1018
EG
S(R)
S
1098...798 1098 -a- 838 1098...953 1159...963 1025...812
3%
Remarks
(~~4.)~ m3s-*
1310*** 1200
Fe PC, 20 mm 0, 20 ppm S
Qb
T K
Fig.
Ref.
kJ mol-’
DO m2sm1
Q
Ref.
kJmol-’
5962
Not required
61S1,3
1.25.10-4
305.0
61S1,3
65J 67Hl
7.19 * 10-4 2.53. 1O-4
259.5 240.6
65Jl 67Hl
7OLl
5.90. 1O-4
246.9
7OLl
71Ll
9.20~10-~
301.2
71Ll
77Ml 73Sl 85Gl 64Ll 65Jl
4.16~10-~ Not required 5.02 * 10-3 4.40.10-S 1.40*10-4
305.0
77Ml
252.0 278.7 245.6
85Gl 64Ll 6551
70K2
9.00.10-5
270.7
70K2
70K2
1.25. 1O-4
283.3
70K2
77H3
1.09.10-4
296.7
77H3
72R2
7.10.10-’
167.4
63Gl
72R3
7.10. lo-’
167.4
63Gl
83Ml
‘2.87. IO-* “‘13.8 1.35 * 10-4
‘271.0 m332.0 202.5
83Ml 83Ml 60Al
68Rl 68Rl 68Rl 68Al 68Al
Fe PC
H,O PC
35s
3N6
‘13Sn
4N5 3N7
SS SS
S
1073...973 1023 ... 890
65Zn
3N7
SS
S
993...873
137cs+
-
ss
F
267...248 267... 254
1.26. 1O-2 5.01.10-4
64.02 54.39
+&,+
-
ss
F
267...249
4.95.10-3 -
z 67 66.36 w 75
7.96. IO-’ -
76.85 % 77
1.88 -
78.09 w 87
160 -
86.91 x 89 92.01 -
S
1525 ... 1393 1335... 1172
96.23 113.0 117.2 135.1 153.5 125.7
1.10. lo-” 2.20.10-12 3.86. lo- l2 1.91.10-12 4.76. lo-I2 1.55.10-13 See Fig. 47
SW
InSb PC
l13Sn
-
ss
FS’
785...663
2.66. IO3 -
Kc1 BC(OOl)TiGB
&+
5N5
MH
F
923...473
x 10-14
x 51
Ca2+
5N5
MH
F
923...473
z 5.10-14 2.10-I’
z 51 z 23
Tl+
5N5
MH
F
893...523
w 2.10-15 w 3.10-16
w 23 w 38
Tl+
5N5
MH
F
873 . ..473
w
z 46
KI BC (OO1)TiGB
3.10-15
bUnreliable Reported, UR “Real, UR Reported RLSF No APs Pure ice ImM CsCl-doped ice Reported, pure ice RLSF Reported, 1 mM NaCl-doped RLSF Reported, 2 mM NaCl-doped RLSF Reported, 5 mM NaCl-doped RLSF Reported, 10 mM NaCl-doped RLSF No APs fl = 12s.. 14”, NTAP 0 = 1 . . .2”, NTAP ~9= 12... 14”, NTAP 6= l...2”,NTAP 6’ = 12e.e 14”, NTAP t’ = 12.e. 14”, NTAP
47 47 47
71Hl 71Hl
1.70.10-S
221.8
71Hl
7202 82Bl
3.46. 1O-3 5.40 * 10-4
231.4 232.2
7262 82Bl
85H2
Q0”)
81Rl
“56.15 “19.53
63Dl 63Dl
e 56.40
63Dl
48 48
7051 7051
Do CT) “2.50. 1O-4 “3.12. IO-’ “2.85. 1O-4
-
71Jl
48 -
7151
48 -
71Jl
-
7151
-
7151
48 -
61S4
5.50. IO- l2
72.36
61S4
-
67G2
-
41
6702
-
6801 6762
-
19
6762
-
68Gl 6762
-
42
66Dl
-
6762
-
39
6564
-
-
Matrix
Tracer
Purity (matrix)
Method
Eq.
T
W4J"
K
m3s-’
‘8 00. 1O-21 131 2 ‘3:67. lo-” 132:8 x 180
MgO PC
coz+
“95%
RP
-
1373 ... 1073
WS’
‘lCr3+
3N3
S(R)
W
1723 ... 1470
Qb
BC(001)TiGB
MgO PC
Ni2+
“95%
MO PC
14C 51Cr 13’Cs
3N5 3N5 2N7 3N7
“Fe
-
0 ‘SSW
3N5
K+
5N5
SP PC
NaCl
RP
DK AR SW EPMA
3.94.10-13 -
173.7 x 165
2.78. lo-” -
167.7 x 180
2.54. lo-l3 -
165.2 z 185
4.63. lo-l3 c5.95*10-20 ‘4.60. lo-”
182.2 166.0 164.9 297.9 171.1 310.5 230.1 233.8 175.7
-
1373*..1073
S BV BV V
1513...1203 1423 .a. 1273 1373e.e 1273 1873e.e 1408
S
1478.e. 1231
2.24. 1O-6 1.52.10-” 1.81. lo-lo cl.lO~lO-lg c1.70~10-1g 9.00. lo- *a
F S
1743a.o 1423 2173...2023 2423-e. 1973
1.13. lo-l3 c3.90~10-12 5.50.10-12 1.00~10-‘2
179.6 270.0 322.2 318.0
F
923-s-673
z 5.10-15
x 60
923.s.473
x 8.10-”
x 60
~4.10-‘~ y;P-‘e”
x60 38.92 x 23
BC(OOl)TiGB
22Na+
-
ss
Ni2+
5N5
MH
W F
696.s.623 923 s.0473
Remarks
Fig.
Ref.
kJ mol-’ Reported ’ Real 49 e = 5”, Diffusion 11(001) *Real 50 8 = Y, Diffusion I(OO1) *Real 50 e = w, Diffusion (( (001) aReal 50 e = 15”, Diffusion I(OO1) ’ Real 50 Reported aReal 49 300 ppm C Reported RLSF 300 ppm C, reported ’ Real 15.6 at.% 0 bQuestionable NPTAP 8 = 12-m. 14”, NTAP 0 = 12...14”, NTAP 8= l...2”,NTAP 0 = lo”, DFP, UR 6’ = 12.e. 14”, NTAP
51 51 51 51,60 -
DO
Q
m2 s-l
kJ mol-’
Ref.
-
85B3 8301
8301
-
-
-
8301
8301
-
-
-
-
85B3 76Ll 71Ml 71Ml 80G3
4.16.10-s 381.6 1.40*10-a 309.2 1.80.10-3 313.4 Not required
76Ll 71Ml 71Ml
74Ll
3.70.10-7
291.6
74Ll
51 51 51 -
84Nl 65Bl 81B4
-
-
3.18. 1O-4 5.00. lo- ‘I
472.4 380.7
65Bl 81B4
6762
-
48
6762
-
68Gl
-
-
-
68Gl 76H2 6702
-
-
‘4.73. 1O-9 -
=87.02 25
76H2 6702
NbPC
Ni PC
13’Cs <2N
S(R)
V
1718 ..a 1373
“3Sn
-
ls5W
3N
F S
2123 ... 1233 2423 .-.I973
“‘Ag
2N3
S(R) W-9 SW
F
1162.e.973
W
1162.e.973
lo%iioAg “‘Au
3N8 5N
141C!e 4N *Co 4N
PC, BC PC foil
Pb PC
F
ss
S
1257.e.945 1073 ... 973
ss ss
w, s 1143.e.793 V 973.e.773
*Fe
4N
S(R)
V
l14’“In 14’Nd *Sn
3N8 4N 2N8
ss ss
S 1166...609 W, S 1148.e.773 B 1373 .** 973
‘13Sn NiO PC foil PC, BC PC foil
S(R)
4N
AR ss
S
973 ... 823
1182.a.912 793 ... 673
13gCe4+ HP 6oCo2+ 5N “Co’+ HP
ss ss ss
V W w
‘lC!r3+ “C!r3+
ss ss
W 1476e.e 1179 w, v 1373..a973
114mIn 5N llgmSn 4N8
ss PK
w V
453-a. 334 363 ... 307
5N5
ss
w
473 *** 344
SN HP
1373***973 1316... 1075 1073 ... 773
c1.50. IO-l9 “4.53. IO-*’ 3.50.10-15 1.70.10-10
221.8 207.7 181.6 359.8
Reported RLSF NPTAP
80G3 52,60 52 79Fl 52 81B4
Not required 3.2O.lO-‘j 1.60. IO+
302.1 364.0
79Fl 81B4
3.63. IO-l5 9.00. IO-l5 1.64. lo- l5 1.60. IO-l4 2.88. lo-l5 2.86. IO-l5
96.23 104.6 95.67 104.6
282.1
75Tl
79Vl
8.94. 1O-4
279.2
79Vl
94.67
53 53 53 53 53 53 53 53 53 -
2.25+10-3
1.76.10-"
Reported Reported aReal Reported aReal Reported RLSF Reported RLSF Reported RLSF Reported RLSF bQuestionable aReal bUnreliable
68Cl
2.35. IO+
220.0
68Cl
71Pl 5962
6.60 * 10-5 254.4 Not required
5962
Not required
89Nl 71Pl 59Bl
1.10*10-4 4.40.10-5 1.37.10-4
250.0 250.3 248.4
8lG2 71Pl 59Bl
87Nl 87Nl
4.56. 1O-4
267.0
79v2
86A2 8OCl 82Al
Not required 9.12.10-7 226.7 2.50. 1O-6 234.5
72Cl 82Al
80Cl 86A2
8.60.10-’ 8.60.10-7
8662 8OG4
2.20.10-4 110.0 Not required
8662
82Kl
4.10.10-5
77Dl
1.50. IO-l3 3.45.10-‘* 5.50*10-” “I oo*10-16 “1:70~10-‘5 c1.15~10-‘4 “4.00. IO-l3
95.67. 99.66 125.5
167.7 123.6 133.9 158.7 188.3 213.6
l.oo~lo-'" lo-l5 -
177.0 119.6
2.06. lo-l6 3.60. lo-l2 1.20.10-10
152.0
“3.15.10-l’ 3.84. lo-l3 P6.50. lo-’
193.0 z 172 179.7 P193.0
Reported RLSF Qb X Q -
-
1.20.10-11 “5.50.10-” ‘5.65.10-” 7.30. IO-l5 8.45.10-15 9.88*10-15
66.57 45.35 45.26 39.56 39.22 40.19
b Questionable Reported, UR “Real, UR Reported DFP RLSF
54
3.50.
x 127 128.7 182.0
e,=
Q
75Tl 76Tl 76Tl
L
4282.0 9282.0
99.38
7lPl
73Cl 73Cl
Matrix
PtTF
Tracer
Au
Cr Si TF
Al 16As
Purity (matrix)
Method
-
AES
-
AES
T
(sbW"
Qb
K
m3sm1
kJ mol-’
623 ... 523 892...765
9.00.10-‘6
x 93 159.2
V HB
850...700 848 ... 770
“5.10~10-‘6 2.80. IO-”
163.1 132.6
V W
698...623 1323... 1223
=6.50.10-’ 9.40.10-14
V
9.19*10-‘4 1523.e. 1223 ‘6.85. IO-” ‘4.30~10-” =1.61~10-” c2.57.10-19 2.77.10-l’ 5.90.10-” 6.00.10-‘* 2.20*10-‘9 1.27.10-19 4.87.10-lo 1.90.10-1’ 2.75.10-”
254.7 247.0 245.9 ** x 222 223.9 376.3 370.7 x 157 159.5 x 188 189.2 135.1 276.9 80.08 72.69 279.8 279.8 287.2
bQuestionable Reported ’ Real Reported aReal Reported ’ Real Reported aReal Reported “Real Reported ’ Real Reported Reported ’ Real
1.95.10-‘6 2.59. lo-l6 6.70. lo- l4 4.18. lo-i4
28.16 29.16 33.89 32.02
Reported aReal Reported RLSF
Eq.
-
bQuestionable
-
55 -
124Sb
-
ss
l*%b
-
ss
W,S 1423...1203
“‘Ag
5N5
ss
F
422-a. 340
204n
5N
ss
F
489...410
S(R)
V
1743 ... 1573
‘3.10~10-‘* ‘1.61.10-‘*
292.9 286.8
Reported RLSF
SS, S(R)
S
1188...789
1.34.10-21 1.11. 1O-23
50.17 27.02
TF/poly Si/SiO,/Si TF/SiO,/Si
57 57
-
-
AES S(R) EBIC RBS
V
1223-e. 1023
EBIC
V
1473***1173
WFTJ1373*.*1174 32P
-
Ta PC
13’CS 2N8
TaSi, TF
33P
-
ss
Ref.
DO m*s-’
W 1373...1173 W,S 1423...1173 W 1373...1173
P
Sn PC
Fig.
56 56 56 56 56 56 56 56 54 54 60
As
PC
Remarks
Q
Ref.
kJmol-’
76Cl 78H1, 78Ml 75D2 78Hl
‘7.60. 1O-4 ‘254.8 ‘3.30. IO-’ ‘263.6 Not required Not required
80Hl 75Cl
Not required 5.10.10-5 340.6
81B3
Not required
82Sl
Not required
81B3
Not required
82B2
-
82Ll 8682 82Ll
60Ml 61Bl
75Cl
-
-
8.00. lo-’ -
277.9 -
8632 -
85Sl 8632
1.35 * 10-J
376.3
85Sl
66B2
1.18.10-*
58.83
66B2
69B2
1.20.10-’
61.50
69B2
80G3
Not required
83Pl 83Pl
4 21 *lo-l6 3:50.10-i6
64.64 60.79
83Pl 83Pl
-
The,
233pa4+
SP
_
-
6.66.10-1’7 1.83. IO-l6 2.35. IO-l5 7.80. IO-l5
128.0 145.4 200.4 220.2
Reported, UR “Real, UR Reported, UR “Real, UR
68F2
2.91. 1O-5
315.5
68F2
-
68F3
1.10~10-*
319.7
68F3
2073 ... 1670 2047.~. 1573 2083 ... 1573
9.00.10-“7 3.00~10-‘5 3.50.10-l*
159.0 142.3 125.5
NPTAP NPTAP NPTAP
58 58 58
6682 6632 6682
1.40.10-1’ 1.20. IO-” 1.15~10-1’
179.9 242.7 175.7
6682 6682 6682
Reported RLSF bQuestionable Reported RLSF Reported RLSF b Questionable Reported aReal Thoriated W, ERDGB
60
80G3
Not required
59 59,60 59 59 59.
88Ll 88Ll 80G3
4.30. 1O-4 418.0 4.30.10-4 418.0 Not required
88Ll 88Ll
71Tl
1.15.10-3
45Ll
74Kl 71B2
Not required 1.34.10-4 527.0
34Ll
Not required
S
2273 ... 2073
ss
S
2273 ... 2073
ss
237u4+
_
q,f(p
-
ss
95Nb5+
-
ss
g5zr4+
-
ss
F F F
VPC
137Cs
2N8
SW
V
1258... 1148
“2.50. lo-” c 1.71 .10-2O
163.2 158.5
WPC
5’co
3N8
SS
S
13’Cs
3N5
S(R)
V
1673 ... 1470 1273...963 2183 ... 1523
5gFe
3N8
SS
F
1998 ... 1798
BC
56Fe MO
-
SIMS EPMA
V S
2318 ... 1218 2363...2113
PC
Th
-
EE
-
2400... 1900
4.40.10-12 3.10~10--‘6 c1.25.10-‘5 c9.30.10-‘7 6.30.10-1’ 7.67.10-l’ “9.00~10-‘5 1.20.10-“7 c3.71f10-14
269.0 198.0 376.6 343.0 338.9 344.0 323.8 w 113 111.1 376.6
YPC
14C
93.4%
S(R)
BV
1117...619
2.00. lo-lo 7.01. lo-”
138.1 135.6
Reported aReal
57
59Dl
-
-
-
Zr SP
C
97.4%
EPMA
F
1973 ... 1373
69Sl
F, W 773 ... 623
57
125.5
WV
Reported, UR “Real, UR -
1.40.10-10
> 3N
100.8 107.1 50.00
69Sl
51Cr
3.76. IO-l3 5.01.10-13 9.65.10-l9
65A2
1.19. IO--‘2
75.31
65A2
uco.95 PC
PC
a
AES AR b B BC BV
These Arrhenius parameters derived by us from the original Arrhenius plot correspond to the actual Arrhenius line drawn there; the reported ones yield a much different line lying away from the experimental data points. Auger electron spectroscopy (for first-appearance, accumulation or sectioning measurements). Autoradiography. For reasons discussed in detail in [89K2], these data are considered incorrect, unreliable or questionable. Bokshtein’s equation. Bicrystal. Borisov’s equation (very similar to Fisher’s equation).
c
d DFP DK Do, Q e
585.8
71B2
From the reported, recalculated or derived (from the Arrhenius plot) value of 0,” assuming a value of 6 = 0.5 nm for the grain boundary width and s = 1 for the segregation factor. Radioactive, but the particular isotope used is not specified. Arrhenius parameters derived by us from the original Arrhenius plot. Indirect estimation from the deoxidation kinetics. Volume diffusion data used for the evaluation of grain boundary diffusion data. Evaluated by us from the reported D values or from the corresponding Arrhenius plot. (continued)
Footnotes for 12.2.2, continued P Quoted in [86A2] as 282.7 kJ mol- ‘. Electron beam-induced conductivity measurements of p-n junction formed r Reported in [78Ml]. between the B-doped p-type Si matrix and the As (or P)-doped n-type diffuRutherford backscattering spectroscopy. RBS sion source. Recalculated least-squares tit. RLSF Indirect estimation from electron emission studies. EE Indirect estimation from the kinetics of ripening of the second phase precipiRP Electrolytic grade. EG tates of COO. Electron probe microanalysis. EPMA (saDdo, QbArrhenius parameters for grain boundary impuritiy diffusion. ERDGB Earliest reported data on grain boundary diffusion. Suzuoka’s equation. S Electrical resistivity measurements. ERM I Suzuoka’s solution for application to penetration-depth measurements. S Misprinted in the original work as 5.40. lo- “. Spectral analysis of the layers removed by sectioning. ST F Fisher’s equation. Strained bicrystal. SBC Fisher’s solution for application to penetration-depth measurements. F $Y Subgrain boundaries. SGB Fisher’s equation; stated incorrectly in the original work. Secondary-ion mass spectrometry. SIMS First appearance measurements. FAM 8 Sintered polycrystals (for Al(SP) containing finely divided Al,O, particles: SP Cd from CdS source. h oxide content 6%). Cd from elemental Cd source. Sectioning combined with residual-activity measurements. Hwang-Balluff equation. HB S(R) Serial sectioning. ss High purity. HP t 1 Reported in [78Hl] for the same data. For T > 2103 K; these are the values derived by us from the reported ArrheAbsolute temperature. T nius line, the given values of 2.91 . lo-” m’/s and 986 kJmol-’ failing to From type-C kinetics regime. TCK yield this line. Thin film. TF For T < 2103 K. Technical grade (Armco Fe). TG This is the real value corresponding to the reported Arrhenius line; the given Tilt grain boundary. TiGB value of 545 kJ mol- ’ seemsto have arisen due to a printing error because Twist grain boundary. TwGB the former is equivalent to about 103 kcalmol-’ and the latter Unstrained bicrystal. UBC 130 kcalmol-i. Unreliable; for reasons discussed in detail in [89K2]. UR For diffusion in the paramagnetic region, i.e. T > 1043 K. Analogous to homogeneous volume diffusion. V LAGB I,11 Large-angle grain boundaries of type I and type II. m Whipple-Le Claire equation. W For diffusion in the ferromagnetic region, i.e. T < 1043 K. Whipple’s solution for application to penetration-depth measurements. Microhardness measurements for establishing the isoconcentration conMH WPD Reciprocal density of the coincident sites relative to the crystal lattice sites. c tours. n Tilt angle. 0 With 5% COO. * D,r* = 0.1 h*, where T* is the time for initial fall in resistance and h is the No APs No Arrhenius parameters were evaluated. film thickness. NPTAP No concentration profiles, no tabular data and no Arrhenius plot given in ** The corresponding value in eV is misprinted in [89K2] as 2.540 in place of the original work. 2.548. No tabular data and no Arrhenius plot given in the original work. NTAP t P Misprinted in [89K2] as 87.5 Best estimates of 0,” and Q,, from a combination of measurements in type-B tt Misprinted in [89K2] as 96.68. and type-C kinetics regimes obtained assuming s = exp (44.4 kJ mol- ‘/RT) and 5 = 1 nm. Polycrystal. PC Figs. 25 .-a60, seep. 681ff. Penetration kinetics. PK
EBIC
Matrix
Tracer
Method
Eq.
T K
W'J" m3 s-I
Qb
Remarks
Fig.
Ref.
kJmol-’
DO m2s-’
Q
Ref.
kJ mol-l
-
-
-
12.2.3 Data for grain boundary tracer diffusion in alloys Abbreviations Ag-0.007
at.% S PC
Ag-26.85
wt.% Sn PC ‘03Hg
(Al-O.1 wt.% Y),O,
35s
2.90.10-I3
77.33
-
518.~~323
1.78. IO-”
33.14
aUnreliable
-
1773 ... 1473
7.90.10-‘6 2.54. IO-” 2.00. IO-” 7.81.10-I2 7.10.10-‘7 5.80. IO-” 2.20. IO-” 3.30.10-I7 6.10. IO-‘-= 2.10. IO-” 1.80. IO-I4 1.80. IO-l4
199.0 213.3 270.0 287.2 34.31 29.71 22.18 23.01 33.89 40.58 47.91 47.91
Reported b Real Reported b Real -
62 62 63 63 63 63 63 63 63 63
5.00 - lo- l3 x IO-IS 4.06. lo- l6
121.6 x 116 110.8
LAGB Reported, b Real
RLSF RLSF RLSF “Unreliable “Unreliable Same in [70B2], UR. Reported b Real
SW
W
971...751
S(R)
S -
SP “Cr3+
S(R)
“Fe3+
S(R)
Al-2 at.% Zn PC Al-4.33 at.% Zn PC Al-7.90 at.% Zn PC Al-g.39 at.% Zn PC A-16.7 at.% Zn PC Al-36.9 at.% Zn PC A-49.4 at.% Zn PC Al-62.9 at.% Zn PC
6=Zn 6=Zll 65Zn -==zn =zn 6sZn 65Zn 6sZn
ss ss SS ss ss SS SS SS
F F F F F F F F
678 . ..487 613 ..-493 654...487 613...493 673...563 659...582 642... 588 605...563
Au-l.2
“‘AU
SS
W
667...477
at.% Ta PC
used are explained at the end of the table
1773 ... 1473
co-5% w PC Co-19.6% W PC Co-31.89% W PC
lSSW ls=w lSSw
ss ss ss
1073...913 1273 ... 773 1273...913
2.67. IO-I4 5.94. IO-l3 3.36. IO- I2
159.9 196.9 215.5+
Cu-0.1 at.% Ag PC Cu-0.1 at.% Cd PC Cu-0.8 wt.% Cr PC
y%&
2;)
“‘Ag
S(R)
723...523 771... 613 891...667
“8 50.10-16 v:12. 1o-2o 1.81 . lo-I4 1.33.10-‘3
71.34 66.11 88.16 101.9
Cu-0.6 wt.% Te PC
“‘Ag
S(R)
884...738
1.10~10-‘~ 5.82. IO-l3
113.0 108.2
S
61
SGB
79A2, 80A2 7601
1.87. lo-’
34.52
7601
84Ll
6.93. IO-”
266.0
83Ll
84Ll
3.64. 1O-g
300.0
83Ll
69H2 69H2 69H2 69H2 69H2 69H2 69H2 69H2
-
-
59Hl 59Hl 59Hl 59Hl 59Hl 59Hl 59Hl 59Hl
64 64
75Gl 75Gl
1.40.10-7
142.8
75Gl
65 65 65
69Ll 69Ll 69Ll
8.00. IO-‘= 1.5O.1O-s 2.26. IO-’
267.7 280.3 285.3
69Ll 69Ll 69Ll
66 -
60Gl 61Rl 70B2 70B2
Not required Not required 4.09.10-4 211.6
70B2
66
70B2
1.61. lo-’
70B2
176.8
Matrix
Tracer
Method
Eq.
T K
(~~4)~ m3s-’
Qb
Remarks
1.30~10-12 2.11 . IO-” 1.80. IO-l4 9.60. IO-” 6.46. IO-l3
121.3 128.1 78.24 129.7 126.4
Reported b Real Reported b Real
66 67 66
‘2.05. IO-l6 ‘1.74. IO-l6 ‘1.80. IO-l6 ‘4.76. IO-l6 ‘3.80. IO-‘* c2.86.10-19 6.00. IO-” 3.96. IO- *’ 1.56. 1O-9 2.12.10-8
155.6 156.0 155.6 162.9 138.1 117.4 202.1 196.6 222.2 244.2
-
-
3.73 * 10-13 3.16.10-15 3.28.10-15 5.72. IO- l4 1.48.10-l’
164.0 111.3 110.6 200.8 250.1
Reported RLSF 68 Reported RLSF 68 Reported RLSF 68 Reported b Real 69 Reported b Real 69 u-phase, No APs y-phase, No APs 69 Reported b Real 69 Reported b Real 84
4.30*10-‘6 3.40.10-‘6 2.30. lo-l6 l.lo~lo-s 4.51 . to-14 1.23.10-9 3.24. lo-’ 9.00.10-16 ‘6.15.10-‘*
105.3 117.0 132.2 x 289 303.8 x 155 147.0 x 272 243.9 x 289 283.4 108.8 11.55
NPTAP NPTAP NPTAP m-phase, reported b Real y-phase, reported b Real aPR, 19ppm C b Real aPR, 60 ppm C b Real y-phase “Questionable
Cu-0.1 wt.% Ti PC
“‘Ag
S(R)
S
884.a.738
Cu-30 at.% Zn PC Zr PC Cu-O.l2wt.%
65Zn “‘Ag
S(R) S(R)
W S
831...627 884...734
Fe-O.27 wt.% Al PC
59Fe
S(R)
V
953...803
Fe-O.39 wt.% Al PC
s9Fe
S(R)
V
953 ..a 803
Fe-l.7 wt.% Al PC
59Fe
SW
V
1023 ..a 823
Fe-O.0018 wt.% B PC
59Fe
AK
B-G 1373 ... 1223 1123...973
Fe-O.003 wt.% B PC
64cu
SW
Fe-90 ppm C PC Fe-O.04 wt.% C PC
59Fe 59Fe
SW AK
1074...980 1303 ... 1200 S 1023...883 B-G 1273 ... 1203
Fe-9.7 Co-9.5 W4.1 0-2.1 v0.94 c (%) PC Fe-O.72 wt.% Cr PC Fe-l.85 wt.% Cr PC Fe-2.45 wt.% Cr PC Fe-2.9 wt.% Cr PC
lssW
S(R)
-
1054***957
S
1360...896
59Fe
S(R)
-
S
1076...931 1088 ... 896
Fe-S.1 wt.% Cr PC
H
FAM
V
1343.e.1187 1133*..573
Fig.
DO m2sw1
Q
70B2
6.10. 1O-5
194.6
70B2
77H2 70B2
7.30.10-s 3.90. 1O-4
170.3 213.4
57Hl 70B2
59Gl
Not required
59GI
Not required
5962
Not required
64Bl
-
-
-
64Bl
-
-
-
7OLl 7OLl 85Hl 79Gl
1.12.10-3 5.80. 1O-3 2.86. IO-’ -
255.2++ 297.1 292.0 -
7OLI 7OLI 85HI -
6921 -
2.40. IO-’
224.3
6921
7OSl 7OSl 7OSl 69H3
9.60.10-* 2.56.10-’ 2.88. IO-’ 5.50.10-4
200.8 213.4 225.9 246.9
7OSl 7OSI 7OSI 69H3
69H3
I.90*10-5
261.5
69H3
73Hl
7.87. lo-’
300.5
73Hl
5.15.10-7 246.5 Not required
69H3
Ref.
kJ mol-*
70 70 71 71 71 -
Ref.
kJ mol-’
73Hl 69H3 74Sl
Fe-6.8 wt.% Cr PC
59Fe
S(R)
1076...925
Fe-7.8 at.% Cr PC
59Fe
S(R)
1074...926
8.20 +IO-” 1.04.10-9 1.20.10-” 1.30~10-‘*
234.3 234.8 169.5 79.50
138.1 x 205 206.6 137.2
Fe-8.2 wt.% Cr PC
59Fe
W-9
1047...894
7.70. lo-l5 9.86.10-l* 7.70. IO-l4
Fe-8.9 wt.% Cr PC
59Fe
SW
1084...926
-
-
z 2.6. IO-*
S(R)
1360+..896 6.86.10-9 5.09.10-‘3 x 7.9. 1O-9 2.00. IO-l6 “6.60. lo-l8 2.45.10-15 4.12. lo-l5 3.50. lo-l4
w 393 73 259 249.8 w 182 174.0 x 252 102.5 11.72 122.2 126.1 152.3
5.30.10-‘3 3.39 * lo- l5 4.40. IO-l* 2.00.10-10 6.94. lo-l6 3.10. lo-l3 2.07. IO- l3 2.96. IO- l3 R9 53.10-10 6.89.10-10 3.36. IO-’ 1.58.10-’ 1.83.10-l’ 1.96.10-8
177.4 131.1 189.0 245.0 114.0 205.0 200.5 203.5 R275.0 272.1 307.0 301.5 231.0 296.0
1328...1174 1044...931
Fe-g.1 wt.% Cr PC
Fe-18.15 wt.% Cr PC Fe-6.94 Cr-0.034 C (wt.%) PC Fe-17 Cr-12 Ni (wt.%) PC
Fe-18 Cr-10 Ni (wt.%) PC
51Cr
59Fe
S(R)
H 59Fe
FAM AK
1048...900 1073 ... 573 B-G 1273...1153
51Cr
ss
W
1323 ... 849
59Fe 63Ni 51Cr
ss S(R) S(R)
W W S
59Fe
S(R)
S
1306...870 1523 ... 876 1323...973 1323...1173 1123...973 1273...993
1344... 1069
1273 ... 1018 1273 ... 1123 1083, 1018 ‘j3Ni
S(R)
S
1273 ... 1003
uPR b Real 71 a-phase, 50ppm C 71 d-phase, 71 50ppmC (martensite) y-phase, 5OppmC 71 uPR, 19ppm C b Real 71 a-phase, 71 100 ppm C a-phase, No APs DFP a-phase, reported b Real 70 z-phse, reported 70 y-phase, No APs DFP a-phase 71 aQuestionable Reported b Real 71 72
73Hl
HP 70 ppm S-doped 70 ppm S-doped HP, reported aReal HP 70 ppm S-doped bReal 70 ppm S-doped bReal HP 70 ppm S-doped
73 74 72 72 72 73 73 73 74 74
0.356 5.00~10-6
309.6 209.2
73Hl 69H3
69H3 74H3
‘2.19. 1O-3
‘269.8
74H3
73Hl
2.50. IO-’
182.0
73Hl
73Hl
0.111
305.5
73Hl
69H3
84.9
355.6
69H3
69H3
3.20. IO-’
221.8
69H3
69H3
1.88.10-8
326.3
69H3
69H3 74Sl 79Gl
3.95.10-s 200.8 Not required -
69H3
73P2
1.30~10-5
264.0
73P2
73P2 73Pl 8451 8451 8451 7851
3.70.10-5 8.80-10-7 1.44-10-9
279.5 251.0 153.0
73P2 73Pl 8451
4.40.10-5
280.0
7851
4.40.10-5
280.0
84Jl
3.94.10-7
230.0
84Jl
69H3 69H3
8451 84Jl
-
8451 84Jl 84Jl
Tracer
Matrix
Fe-20 0-x
Ni
59Fe
Method
SW
Eq.
W
T
W4J"
Q,,
K
m3s-’
kJ mol-’
1323.e.1123
1.60.10-” 2.16. IO-” 2.00~10-‘6 1.43 * 10-16 4.00. to-15 6.80. to-14 4.00*10-‘3 6.82. IO-l5 3.20.10-” 3.67.10-” 1.00*10-‘0 9.60.10-” 2.95.10-‘* 9.68.10-l’ 1.40*10-‘5 1.05*10-‘5 1.60.10-9 2.00*10-9 2.40.10-l3 2.02.10-13 l.60~10-10 6.51 . lo- *’ 4.00. IO-” 1.62.10-l’
71.13 73.19 104.6 99.52 177.8 168.0 148.5 136.7 234.3 234.3 253.1 247.1 71.13 58.69 142.3 138.8 284.5 285.7 184.1 180.8 253.1 245.4 253.1 228.6
(wt.%) PC
63Ni
SW
W
1373...1173
Remarks
x = 10, RLSF x = 30, RLSF x = 45, RLSF x = 55, RLSF x = 65, RLSF x = 75, RLSF x = 10, RLSF x = 30, RLSF x = 45, RLSF x = 55, RLSF x = 65, RLSF x = 75, RLSF
Fig.
reported reported reported reported reported reported reported reported reported reported reported reported
73 73 73 74 74 74 74 74 74
DO
Q
m2s-’
kJmol-’
7364
2.50. lo-’
217.6
7304
7364
1.00. 1O-4
278.2
7364
7364
1.20.10-4
255.2
7364
7364
4.50.10-4
255.2
7364
7364
1.00*10-4
272.0
7364
7364
4.00*10-2
343.1
7364
7364
1.40*10-4
301.3
7364
7364
1.40*10-4
301.3
7364
73G4
2.00
401.7
7364
7364
2.80. lO-4
297.1
7364
7304
2.60. lO-4
297.1
7364
7364
7.20. IO+
253.1
7364
Ref.
Ref.
Fe-7 Cr-2 Ni-x-C (wt.%) PC
Fe-16 Cr-14 Ni-x (wt.%) PC
59Fe
C
AK
W
51Cr
59Fe
63Ni
B-G
S(R)
S(R)
W
W
1273...1173
1323...1073
1323.e. 1073
1323... 1073
2.66.10-I4
138.1
2.38 . IO- l4 5.38. IO-l4
139.2 144.3
2.74.10-l3 1.35.10-13
159.8 154.8
3.69. IO-l3 4.90.10-13
163.7 167.4
7.97-10-13 1.15.10-‘3
171.3 175.7
1.21 4.10 4.05 1.12 1.39 2.90 2.89 3.50 4.19 4.40 5.01 1.80
;;I:: ;;I::
10-13 10-13 10-14
174.0 192.5 190.8 188.3 188.6 205.0 204.4 213.4 213.7 202.9 202.6 157.7
2.73. IO- l4 2.80’. IO-l4 3.29.10-14 8.40. lo-l5 1.01~10-14
160.3 167.4 167.6 161.1 160.8
10-13 10-12 10-12 ;;I::
x = 0.003, reported b Real x = 0.006, reported bReal x = 0.021, reported b Real x = 0.045, reported b Real x = 0.03, reported b Real x = 0.1, reported b Real x = 0.2, reported bReal x = 0.03, reported b Real x = 0.1, reported b Real x = 0.2, reported bReal x = 0.03, reported b Real x = 0.1, reported b Real x = 0.2, reported b Real
-
79Gl
-
-
-
75 -
79Gl
-
-
-
75 -
79Gl
-
-
-
75 -
79Gl
-
-’
-
75 -
77A2
6.00. 1O-6
255.2
77A2
77A2
7.50.10-6
255.2
77A2
77A2
9.50-10-6
255.2
77A2
77A2
1.10~10-~
263.6
77A2
77A2
1.30*10-5
263.6
77A2
77A2
1.50~10-5
263.6
77A2
77A2
1.80. 1O-5
278.2
77A2
77A2
2.30. 1O-5
278.2
77A2
77A2
2.60. 1O-5
278.2
77A2
75 75 75 75 75 75 1 75 75 75
Matrix
Tracer
Fe-17.2 0-13.5 Ni0.001 C (wt.%) BC
Fe-18 Cr-9.5 Ni-
59Fe
Method
S(R)
Eq.
W
T
WW"
Q,,
K
m3s-1
1323...1073
-
z 238
-
x264
Remarks
Fig.
Ref.
kJmof-’ I()”
. . . 83°(OOl) TiGB, Diffusion 11 Diffusion I (001) -
lt3Sn
S(R)
W
1203...1073
3.50*10-14
136.0
51Cr
WV
W
1323.e.1073
2.50.10-13 5.30.10-‘3 5.70. lo- l4 6.74. IO-l4 1.40.10-9 2.18.10-9 1.30.10-14 2.98.10-l’ 3.00. lo- l4 3.75.lo-l3 3.20. lo- l4 5.18.10-14
193.0 198.0 172.0 170.8 276.0 278.6 244.8 235.6 194.6 185.2 313.8 315.0 174.0
2.66. IO-l4 1.21 .10-‘4 7.22. lo- l5 2.00~10-‘0 3.62. IO-lo 4.28.10-13 1.27.10-lo
170.3 159.0 152.9 257.0 260.5 41.49 38.96
x = 0.07, reported b Real x = 1, reported b Real x = 4, reported b Real x = 0.1, reported bReal x = 1.3, reported b Real x = 4.2, reported b Real x = 0.07, reported b Real x = 1, reported b Real x = 4, reported b Real Reported “Real
1.20.10-r2 1.15.10-‘2
181.6 180.0
Reported b Real
DO
Q
m2s-’
kJmof-’
6.00. IO+
259.4
75Al
Ref.
-
75Al
-
75Al
75
75M2
1.00~10-8
198.7
75M2
78 78 78 78 78 78 -
78A2
6.80.10-6
251.0
78A2
78142
8.60. 1O-6
251.0
78A2
78A2
1.20.10-’
251.0
78A2
69Dl
l.00~10-5
259.4
69Dl
69Dl
1.50.10-5
259.4
69Dl
69Dl
3.50*10-5
259.4
69Dl
78A2
1.70.10-’
272.0
78A2
78A2
2.30. IO-’
272.0
78A2
78A2
3.40.10-S
272.0
78A2
73C2
1.80.10-6
58.86
72Al
77
79Gl
-
-
-
0.027 C (wt.%) PC
Fe-16 0-14 Ni0.009 C-x Si (wt.%) PC
59Fe
S(R)
W
1373.e.1223
5.11 * 10-8 63Ni
‘Fe-19 0-9.25 Ni2 Mn-0.08 C
S(R)
W
1323...1121
3H
ss
S
458-e. 195
59Fe
AK
B-G 1273...1113
78 78 78 76
(wt.%) PC
Fe-6.91 Cr-2.08 Ni0.82 MO-0.042 (wt.%) PC
C
ss
S
458...195
4.28. IO-l3 1.27.10-lo
41.49 38.96
Reported aReal
76
73C2
1.80.10-6
58.86
72Al
ss
W
1285...923
1.50. lo-l2 2.66. IO-”
191.0 195.5
Reported b Real
77
75Sl
6.3O.lO-‘j
243.0
75Sl
ss
S
1478 ... 1178
3.05. lo-I3 3.60.10-”
177.2 219.6
Reported, UR RLSF
77
82Pl
1.18. IO-
228.5
82Pl
S(R)
BV
1134...980
7OLl
622...473
7611
Not required
Fe- 1 at. % MO PC
64Cu
S(R)
BV
1299 ... 1230 1104...980
79 -
246.9
V
Reported b Real No APs DFP No APs No APs
3.90. 1O-4
AES
159.0 157.0 68.68* -
7OLl
Sn
1.30. lo-” 6.34. lo-l3 c1.52~10-‘6 -
7OLl 7OLl
1.38.10-2 1.20.10~4
305.4 255.2
7OLl 7OLl
Fe-400 ppm N PC Fe-x wt.% Ni PC
5gFe 63Ni
S(R) S(R)
S S
973, 913 1373 ... 1083
-
ss
V
1223...1023
79 79 79 79 79 79 .79 79 -
85Hl 7621 7621 7621 7621 7621 7621 7621 7621 77D2
2.86. 1O-2 8.20.10+ 9.66. IO-’ 7.68. IO-’ 5.90. IO-’ 4.37.10-7 3.16. IO-’ 2.50. 1O-6 1.13.10-5 Not required
85Hl 7621 7621 7621 7621 7621 7621 7621 7621
14C
x=S,NTAP x = 10, NTAP x = 20, NTAP x = 30, NTAP x = 45, NTAP x = 60, NTAP x = 75, NTAP x = 90, NTAP “Unreliable
292.0 251.9 234.3 207.1 204.6 198.7 200.8 226.8 238.5
Cr
180.0 102.9 98.74 114.6 123.0 116.7 108.8 115.5 99.16 152.0
-
Fe-35 Ni-15 (wt.%) PC Fe-50 Ni-15 (wt.%) PC Fe-70 Ni-15 (wt.%) PC Fe-25 Ni-20 (wt.%) PC, Nb-stabilized
7.95. lo-I2 4.48. IO-l5 1.73 . IO- l4 1.59. IO- I4 2.18. lo-l4 3.24. lo-l4 2.34. IO-l4 1.52. lo-I4 1.59. IO-l4 c4.50.10-15
Cr
14C
ss
V
1223 ... 1023
“5.00. IO-”
252.0
“Unreliable
-
77D2
Not required
Cr
14C
ss
V
1223 ... 1023
“1.50~10-”
236.0
“Unreliable
-
77D2
Not required
Cr
51Cr 59Fe 54Mn 63Ni
ss ss ss S(R)
W w W W
1038 ... 824 1171...873 1117...875 1174***974
2.50. lo-I2 8.30. lo-I3 1.10~10-‘2 1.00. IO-”
187.0 179.9 192.9 200.4
-
80 80 80 80
6982 6833 75S2 6982
1.90.10-5 1.74. 1O-4 2.10.10-5 4.06. 1O-4
246.0 284.1 247.7 282.4
6982 6883 7582 6982
gFe-17 Cr-12 Ni3H 2.5 MO-~ Mn-0.08 C (wt.%) PC gFe-16.8 Cr-11.6 Ni- “Cr 2.55 MO-1.64 Mn0.50 Si-0.04 C (wt.%) PC gFe- 16.95 Cr5gFe 11.21 Ni-2.29 Mo0.81 MI-0.53 Si0.05 c (wt.%) PC Fe-O.2 at.% Cu PC 64Cu Fe-3.39 wt.% Mu PC
-
Tracer
Matrix
Method
Fe,O,-26% MnO19% ZnO PC
45Ca2+ SS
Fe-P PC
‘9Fe
SW
Eq.
F
S
T
(s~QJ"
Q,,
K
m3s-l
kJmol-’
2.44*10-4 1.30*10-4 2.64. lo-’ 5.02. IO-l3 2.47.10-” 2.57.10-” 2.30.10-10 4.30*10-‘2 3.36.10-” 2.31 . IO- lo 1.09.10-‘1
x 261 285.1 285.1 275.0 168.0 200.0 201 .o 223.0 153.0 168.0 192.0 162.0
Reported EU, ASS EU, OSS EU, NSS 100 ppm P 750 ppm P 1700 ppm P 3300 ppm P x = 0.16 x = 0.18 x = 0.38 -
81 81 81 82 82 82 82 82 82 82 82
85Hl 85Hl 85Hl 85Hl 83Ml 83Ml 83Ml 83Ml
6.58. lo- l2
152.0
-
82
192.0
-
1473...1123 1273, 1173 1473...1123 1373s.. 1173 1023 ~1.873
Remarks
Fig.
Ref.
DO
Q
m2s-’
kJ mol-*
Ref.
-
-
4.58. IO+ 8.78.1O-‘j 1.06. IO+ 2.86. 1O-2
185.9 197.5 215.1 292.0
6701 6701 6701 85Hl
3.76. lo-’ 2.55. 1O-3 8.87. IO-’ 1.07.10-2
275.0 247.0 259.0 265.0
83Ml 83Ml 83Ml 83Ml
83Ml
6.56. IO-’
211.0
83Ml
82
83Ml
7.93-10-s
159.0
83Ml
-
6701
32P
SW
w
Cr
32P
S(R)
W
1023 ... 823 973.e.873 1155...974 1153...974 1153...932 1155.e.974
Mn
J2P
S(R)
W
1077*..974
Mn
32P
SW
W
1077+..983
MO
J2P
S(R)
W
MO
32P
S(R)
W
Ni
32P
S(R)
W
Si
32P
S(R)
W
1155*.*1055 1018...932 1155***1055 1018...932 1077*** 1014 1018...932 1155...983
2.06.10-12 42.6 2.42.10-9 7.74 * 105 1.83.10-” 3.79.10-S 3.29.10-14
151.0 415.0 218.0 505.0 125.0 229.0 109.0
-
82 82 82 82 82 82 82
83Ml 83Ml 83Ml 83Ml 83Ml 83Ml 83Ml
4.16. lo-’ 3.23. IO6 1.30. 1O-2 6.00. IO9 5.98.10-2 43.9 8.48. 1O-4
215.0 434.0 267.0 496.0 277.0 336.0 241.0
83Ml 83Ml 83Ml 83Ml 83Ml 83Ml 83Ml
S PC
59Fe
S(R)
S
1123...1079
82Tl
S
1123...1079
82Tl
2.10.10-s
221 .o
82Tl
Fe-51 wt.ppm S PC
59Fe
S(R)
S
1123...1079
82Tl
3.00.10-5
224.0
82Tl
Fe- 120 wt.ppm S PC
‘9Fe
S(R)
S
1123.**1079
83 83 83 83 83
233.0
SW
Reported b Real Reported b Real Reported b Real Reported b Real -
1.05. 1O-4
59Fe
245.7 237.4 266.6 251.8 314.0 308.6 289.3 287.1 177.0
82Tl
Fe-35.5 wt.ppm S PC
1.20*10-8 1.55.10-8 1.20~10-’ 2.04. IO-* 7.00~10-6 3.41.10-6 1.63.10+ 1.06. IO+ 3.56.10-12
82Tl
1.50.10-5
219.0
82Tl
85Hl
2.86. 1O-2
292.0
85Hl
Fe-x at.% P PC
Fe-O.15 P-O.10 (at.%) PC Fe-O.11 P-2.11 (at.%) PC Fe-O.17 P-O.38 (at.%) PC Fe-O.14 P-O.29 (at.%) PC Fe-O.17 P-O.98 (at.%) PC Fe-O.14 P-1.03 (at.%) PC Fe-O.13 P-O.96 (at.%) PC Fe- 10.5 wt.ppm
1023 ... 883
Fe-l.48 at.% Si PC hFe-2.95% Si PC Fe-3% Si PC
“Fe 5gFe 5gFe
S(R) S(R) AK
F 1160...1088 S 1323...1173 B-G 1173...973
Fe-6.55 at.% Si PC
35s “Fe
S(R) SW
W F
1123*..973 1279... 1082
Fe-8.64 at.% Si PC
“Fe
SW
F
1183~~~1030
Fe-12.1 at.% Si PC
5gFe
W-9
F
1178...1029
185W Fe-8.5 W-4.0 Cr2.1 V-O.89 C (%) PC
S(R)
-
1052...957
Ni-0.01
AR
B
1373...973
55*5gFe S(R)
F
1255...1196
63Ni
AR
W
1363...1110
51Cr
S(R)
S
1433 ... 1323 1273...1133 1413 ... 1075 1329... 1141 1515 ... 1363 1319~~~1111
Ni-0.15%
% B PC Co PC
Ni-10 Co-10 Cr10 w-5 Al-4.7 Nl0.5 C (wt.%) DSE Ni-20 wt.% Cr PC
dSn
SS’
63Ni
S(R)
SS’ 1373~~~1111 1565.e. 1319
-
6.00.10-12 2.70. IO-l3 3.04. IO- l4 4.28. IO-l3 8.32. IO-” 2.79. 1O-4 1.43.10-4 11.0 2.66 7.30 10.1 7.15.10-‘5 5.54. IO-l4 1.02~10-‘4 1.74. IO-l1 2.76. IO-” 3.80. IO-l6 4.30.10-‘3
193.0 126.4 98.32 120.5 149.4 334.0 332.9 422.0 413.7 413.0 420.9 174.9 194.2
Reported b Real Reported bReal Reported b Real Reported b Real Reported b Real
83 83 83 83 83 83 83 84
w 146 173.5 217.6 221.1 140.2 197.9
Reported RLSF Reported b Real LPB HPB
84 84 84 84
5.10. lo-l3 8.50.10-* 7.60. IO-l4 3.60. IO-l4 1.30. lo-l3 2.30. IO-” 3.60. IO- l4 R3.00. IO-l2 3.29. IO-l2 R3.00. IO-l2 3.29. IO-l2 R1.50.10-’ 2.61. IO-’ R3.00. IO-l2 3.29. IO-l2
180.0 320.0 155.0 155.0 150.0 250.0 155.0 R209.0 200.6 R209.0 200.6 R317.0 326.3 R209.0 200.6
-
85 85 85 85 85 85 85 85 85 85
15 ppm C 100 ppm C 600 ppm C 600 ppm C 600 ppm C, HT 15andlOOppmC b Real 600 ppm C b Real 600 ppm C b Real 600 ppm C, HT b Real
81T2 7021 58B2
1.03.10-4 6.32. 1O-3 6.20. 1O-5
276.0 282.4 215.5
81T2 7021 58B2
71Gl 81T2
1.70.10-2 5.20. 1O-4
256.1 242.0
71Gl 81T2
81T2
4.93.10-4
236.0
81T2
81T2
8.00. lo- 5
213.0
81T2
6922
1.50.10-8
197.9
6922
59B2
1.41. 1O-4
252.2
59B2
60G2
1.60.10-5
246.9
60G2
81B5 81B5
5.80. 1O-4
334.7
81B5
79Dl 79Dl 79Ml 79Ml 79Ml 79Ml 79Ml 79Mi
2.20.10-3
310.0
79Dl
6.10. 1O-5
263.0
79Ml
1.50*10-5
259.0
79Ml
79Ml 79Ml 79Ml -
Tracer Method
Matrix ‘Ni-14.9
Fe
0-6.1
51Cr
S(R)
Eq. S
T
Cr-2.5 Ti0.75 Al (wt.%) PC
x 128
dSn
AR
B
1273 ... 1073 5.29.10-l’ 8.44. lo-l4
x 170 169.7 x 203R 203.8
See Fig. 86 960...905 1353a.e1083 3.46. lo- l3 1353-e. 1083 2.76. IO- ‘* 1353 ... 1068 1.61 . IO-” 1132.a.723 8.10*10-‘4 5.00~10-‘5 x9.4.10-” 454*.. 334 x I.I.IO-‘3 x 1.9. IO-‘* x 1.7.10-16 454*** 334 x 3.5.10-14 ~2.9-10-‘~ 493 ***393 4.00.10-‘6 473s.. 334 1.50. IO-l6 5.10*10-‘5
x 184 184.1 x 201 205.9 x 251 248.7 175.7 184.1 x42 ~448 x 56 z 32 z 43 ~44 z 19 z 21 z 21 33.77 29.91 41.49
Ni-Fe
63Ni
S(R)
W
Ni-4 wt.% Si PC
63Ni
SW
W
(Ni-0.1 wt.% Y)O PC 63Ni2+ SS
W
114mIn SS
W
*03Pb
W
Pb-x at.% In PC
SS
Pb-x wt.% Sn BC
*‘OPb
AR
F PD
PC
*03Pb
SS
W
65G2
Not required
84 84
59B2
=I.82.10-4
‘260.8
59B2
59B3
“5.52. IO-4
‘273.0
59B3
89NI 74AI
1.10. 1O-4 1.60. IO-4
250.0 259.4
81G2 74AI
74AI
1.60. IO-4
259.4
74AI
74AI
1.60. 1O-4
259.4
74Al
213.4
85Pl
-
4.00*10-6 7.70.10-a 2.80. IO-’ 1.50.10-6 6.40. IO-’ 2.70.10-* k6.26.10-’
86.84 75.26
x = 0.01 x= 0.1 x = 0.9
70.43 k103.2
8662 8662 8662 8662 8662 8662 60Hl
x = 2.0 x = 3.5 x = 8.3
89 89 89
85Ml 85Ml 8662 8602 86G2 8662 8662 8662 6633 6683 6683 8201 8201 8201
3.10.10-s
x = 43.6
86 85 85 85 87 87 88 88 88 88 88 88
2.60. IO+ 2.20.10-7 2.70. IO-’
94.55 83.94 81.04
8201 8201 8201
See also Fe-200-x Ni and Fe-Ni-Cr above ([7364, 77D2, 84JI]) Reported -
1473a.e1073 -
Ni-2 wt.% Si PC
77PI
-
V
S W
277.7
179.6
AR
114mIn SS 63Ni S(R)
1.60. IO-4
4.23. IO- l4
63Ni
Ni-1.4 at.% In Ni-1 wt.% Si PC
77Pl
1073 a+.673
(wt.%) PC Ni-Cr-Fe
JNi-21
Q
Ref.
kJmol-’
kJ mol-’
hW"
DO m*s-1
m3s-’
Q,,
Remarks
K
Reported RLSF 0.01% B-doped RLSF SeeFe-x Ni above [76ZI] Reported bReal Reported bReal Reported bReal LAGB SGB x = 8.7 x = 19.8 x = 43.6 x = 8.7 x = 19.8
Fig. 84
Ref.
81.05
85.87 82.01
Pb-3.5 Pb-8.3
at.% Sn PC at.% Sn PC
Pb-5 Sn-1 Au (wt.%) PC Pb-3.5 Sn-2.7 In (wt.%) PC Pb-x wt.% Tl PC
119mSn SS llgmSn SS
W W
473...322 473...322
‘03Pb
SS
W
453*..334
203Pb
SS
W
459...334
210Pb
AR
F PD 493.s.393
113,123~~ss
Sn-x wt.% Zn PC
F
455.e.313
F
463...303
233Pa4+ S(R)
S
2273 ... 2073
237u4+
S
2573 -.+ 2073
dZn
Tbo, - 50 % uo,
SP
ss
ss
Reported b Real -
89 89 89
8201 8201
2.10.10-5 1.8O.1O-5
98.41 93.59
8201 8201
8562
7.10.10-7
84.80
8502
31.80
-
89
8562
1.50*10-8
69.40
8562
x 21 x 19 z 19
x = 0.05 x = 0.3 x = 1.5
-
6683 6683 6683
k6.26. IO-’
k103.2
60Hl
2.40. IO- l4 6.00.10-15 1.80~10-‘5 9.50.10-I4 9.50.10-‘4 2.50.10-I3 5.20.10-l3 8.10~10-‘3 4.00.10-‘4 4.00.10-‘3 2.75. lo- l3
48.12 46.86 43.93 49.79 51.46 62.76 66.11 53.97 47.28 57.95 62.76
x = x = x= x = x = x = x = x = x = x = x =
0.5 4.9 10.8 15.0 26.4 54.8 7713 4.9 10.8 26.4 77.3
90 90 90 90 90 90 90 90 90 90 90
66B1,3 66B1,3 66B1,3 66B1,3 66B1,3 66B1,3 66B1,3 66B1,3 66B1,3 66B1,3 66B1,3
8.90. 1O-4
104.6
66B1,3
3.40.10-5 1.6O.1O-5 1.30.10-5 1.50.10-5
69.45 76.57 80.33 86.19
66B1,3 66B1,3 66B1,3 66B1,3
5.64. IO- l4 1.40.10-13 5.07.10-14 1.04.10-‘3 1.17~10-‘2
249.8 264.8 246.4 268.6 310.1
Reported b Real RLSF Reported, UR bReal, UR
-
68F2
1.88.10-7
384.1
68F2
68F3
7.59.10-s
359.4
68F3
See Al-Zn [69H2]
Zn-Al Zr-0.5 Cu-0.5 MO (%) PC ‘Zr-1.42 Sn-0.14 Fe0.10 Cr-0.05 Ni (%) PC
-
37.63 52.10 52.54 43.40
3.30*10-‘5 2.10.10-‘3 2.63*10-‘3 2.30.10-15
above
Zr
ssc
C
893...793
w 6.10-13
w 164
NTAP
-
67Bl
Not required
Zr
ssc
C
893...793
x 1.1. lo-l2
x 178
NTAP
-
67Bl
Not required
. AK AR ASS b
B BC B-G BV c d DFP DSE Do, Q c EU I F F F?M s h .HP HPB HT i J
For reasons discussed in detail in [89K2], these data are considered incorrect, unreliable or questionable. Absorption kinetics. Autoradiography. Air-sintered specimens. These Arrhenius parameters derived by us from the original Arrhenius plot correspond to the actual Arrhenius line drawn there; the reported ones yield a much different line lying away from the experimental data points. Bokshtein’s equation. Bicrystal. Borisov-Golikov analysis for absorption kinetics. Borisov’s equation (very similar to Fisher’s equation). From the reported, recalculated or derived (from the Arrhenius plot) value of DE assuming a value of 6 = 0.5 nm for the grain boundary width and s = 1 for the segregation factor. Radioactive, but the particular isotope used is not specified. Arrhenius parameters derived by us from the original Arrhenius plot. Directionally solidified eutectic. Volume diffusion data used for the evaluation of grain boundary diffusion data. Evaluated by us from the reported D values or from the corresponding Arrhenius plot. Evaluated by us (for details see [89K2]). Type-304 stainless steel. Fisher’s equation. Fisher’s solution for application to penetration-depth measurements. First appearance measurements. Type-31 6 stainless steel. Transformer steel containing 0.15% impurities. High purity. High-permeability boundaries. Heat treated in order to dissolve the carbide precipitates present at the grain boundaries. Inconel-600 alloy. E1437 alloy.
k
I LAGB LPB No APs NPTAP NSS NTAP oss PC R RLSF (sSDJ”.
S P’ SGB SSPR) ss ssc T
TiGB UR V W aPR ; tt
Data for self-diffusion in Pb. Zircaloy-2. Large-angle grain boundary. Low-permeability boundaries. No Arrhenius parameters were evaluated. No concentration profiles, no tabular data and no Arrhenius plot given in the original work. Nitrogen-sintered specimens. No tabular data and no Arthenius plot given in the original work. 1% O,-sintered specimens. Polycrystal. Reported. Recalculated least-squares fit. Q!,Arrhenius parameters for grain boundary diffusion in alloys. -“Suzuoka’s equation. Suzuoka’s equation; stated incorrectly in the original work. Subgrain boundaries. Sintered polycrystal. Sectioning combined with residual-activity measurements. Serial sectioning. Steady-state creep. Absolute temperature. Tilt grain boundary. Unreliable; for reasons discussed in detail in [89K2]. Analogous to volume diffusion. Whipple-Le Claire equation. a-phase, reported. Misprinted in [89K2] as 68.88. Misprinted in [89K2] as 115.5. The corresponding value in eV is misprinted in [89K2] as 2.465 in place of
Figs. 61 * a+90, see p. 691 ff.
2.645.
Matrix (cont. in wt. %)
Tracer
Method
Eq.
T
WDJ"
K
m’s11
Qb
Remarks
Fig.
Ref.
kJmol-l
DO
Q
Ref.
m2sW1
kJmol-’
b1.95. IO-’ “8.95. 1O-5 b2.00. 1O-4 “4.00. 1O-5 bl.ll .10-l “2.34. 1O-5
b288.7 “207.1* b251.0 “184.5 b278.7 “163.5
71B3 51Hl 61Ml 61B2 68Bl 67K4
12.2.4 Data for interphase boundary tracer diffusion Abbreviations
A&Fe
“‘Ag
SS
Fi
1123...918
59Fe
S(R)
Fi
925...765
124Sb
SS
Fi
1091...913
“OrnAg SS 65Zn ss
V V
893...523
co/Nbc
63Ni
S(R)
Fi
(001) Cu/Mo (011)
Ni
EPMA
Fe/Fe-C
63Ni
used are explained at the end of the table 9.00.10-9 1 36.1O-8** 2:37. IO-” 2.85. IO- lo 9.00.10-6 2.19.10-4
188.3 194.3** 172.4 167.3 246.9 274.7
d1.25.10-8 d4.00. 10-l’
177.2 156.1
1273..-973
3.54. IO-l4
Fi
1073...923
AR
-
Fe-18 Cr-10 Ni HP/59Fe Fe-22 Cr-8 Ni2.8 Al 59Fe Fe-19.4 Cr-9.3 Ni LP/Fe-22 Cr8 Ni-2.8 Al
S(R)
Fe-16 Cr-14 0.2 C/M&,
Reported “Real Reported aReal Reported aReal -
91 91 91
71B3
92 92
69Hl 69Hl
Not required Not required
w 188 199.6
Reported RLSF
93
83B2
‘4.00. 1O-5
“282.4
7982
4.00.10-‘5 4.00. IO-l5
100.4 230.1
0” (001) TiIB 15”
93 93
82B3 82B3
2.70. 1O-4
234.4
82B3
973..-823
d2.57. IO-‘*
z 121 121.4
Reported “Real, UR
-
66B4
Fi
1173...1028.
1.75.10-14 9.78. lo-I5
155.0 153.0
Reported, u/yIB aReal
94
8OJl
‘4.00. 1O-4
f245.0
8051
S(R)
Fi
1173...923
1.53.10-5
305.0
ulr IB
94
8OJl
‘4.00. 1O-4
‘245.0
8051
59Fe
SW
F
1323 ... 1073
1.47. lo-l4 2.00. lo-l4
167.4 169.5
Reported aReal
94
77A2
1.50.10-5
263.6
77A2
Ge/Sn TwIB
In
EPMA
-
434...313
See Figs. 95 . . .99
APDMP
950.. 81B6, 99 81S2, 82K2, 83Sl
Ni/NbC
‘j3Ni
S(R)
Fi
1273.e.973
-
Reported RLSF
93
AI/AI,O,
Nig
873...379
6.46. IO-l6
L
z 147 147.4
74Jl 71B3
83B2
r
.
APDMP AR b e d
Do, Q e EPMA I F 5 8 h
These Arrhenius parameters derived by us from the original Arrhenius plot correspond to the actual Arrhenius line drawn there; the reported ones yield a much different line lying away from the data points. Arrhenius parameters dependence on misorientation angle and pressure. Autoradiography. For volume diffusion on the Fe-side of the interphase boundary. For volume diffusion on the Ag-side of the interphase boundary. From the reported, recalculated or derived (from the Arrhenius plot) value of Do assuming a value of 6 = 0.5 nm for the grain boundary width and s = 1 for the segregation factor. Volume diffusion data used for the evaluation of grain boundary diffusion data. For volume diffusion on the Co-side; diffusion on the other side was assumed to be negligible. Electron probe microanalysis. For volume diffusion in the o-phase; diffusion in the y-phase was assumed to be negligible. Fisher’s equation. Fisher’s equation for application to interphase boundary diffusion. Precipitated metal carbide phase. For volume diffusion on the Ni-side; diffusion on the other side was assumed to be negligible.
High purity. Interphase boundary. Low purity. Recalculated least-squares tit. (s6DJ",Q, Arrhenius parameters for interphase boundary diffusion. Sectioning combined with residual-activity measurements. SW) Serial sectioning. ss Absolute temperature. T Tilt interphase boundary. TiIB Twist interphase boundary. TwIB Unreliable; for reasons discussed in detail in [89K2]. UR V Analogous to volume diffusion. * This value of Q. equivalent to 49.5 kcal/mol, used from the abstract of [51Hl] is not correct. The main text of this reference shows that the correct value is instead 45.95 kcal/mol = 192.3 kJ/mol. ** Taking into consideration the error in Q mentioned above, these values (~6D,)' and Q, are expected to get significantly modified. HP IB LP RLSF
Figs. 91 *a- 99, see p. 7OOff.
System
Matrix (cont. in at.%)
Method
Eq.
T
wdb)"
Q"b
K
m3 s-l
kJ mol-’
Remarks
Fig.
Ref.
DO m2 s-l
& kJmol-1
Ref.
81Sl 83B3 83B4
Not required 5.83. lo-’ 5.83. IO-’
143.8 143.8
83B3 83B3
-
-
12.2.5 Data for grain boundary chemical diffusion Abbreviations
Ag- Au Ag/Au (TF)
ECR AES
used are explained at the end of the table
W
699...384 598...523 648...523
3.80.10-14
EC
FS
348, 323
NTAP -
3.74.10-l4 -
112.6
RLSF
100
x 54.4
-
-
7583, 7682
-
-
101
80Ml
Not required
69B2 70Gl
2.90. lo- 5 -
130.2
61M2
Reported aReal -
101 101 101
77Cl
6.50. 1O-6
122.0
77Cl
-
77H4
74.10 x 60 59.46 w 60 l:85. IO- l4 61.79 1.20. lo- l4 57.00 7.40. lo- l4 62.10 3.50. lo-l4 65.00 1.80. IO-l4 60.00 See Figs. 27 ... 38 and Table 12.2.2
102 102 102 102 102 102 102
8462 86S3
Not required Not required
8683
Not required
88Sl 8551 88Sl 85Jl
Not required Not required Not required Not required 1.40.10-4
128.9
6001
170.8
75D3
blo-‘9
Ag-Cd
Ag-75.9
Al-Cr Al-Cu
Al/Cr (TF)
ESR
V
673...373
b3.80. IO-=
59.82
Al-l.71
GBP
BA
598.e.473 723...473
77.32 83.68 81.84 97.40 264.0
Al-O Al-Zn
Cd (PC)
Cu (PC)
Al/Cu (TF)
AES
W
456...405
4.00. IO- l5 1.46. lo- l4 1.11. IO-l4 4.50~10-‘5
Al,O,
EPMA
F
1643 ... 1483
2.14. IO-l4
DP DP
PH PH
465.e.270 49o.e.330
8.26. lo- l2 3.38. IO-l4
DC
PH
490...330
DP
PH
523...323
DC
PH
523 ... 323
(BC)/NiO
Al-28.4 Zn (PC) Al-20 Zn (PC)
Al-29
Zn (PC)
-
w 48 116 -
w
-
cUnreliable Reported aReal Reported ’ Real .’
-
Al (BC)/Zn
EPMA
W,F 613...523
Au-Pd
Au/Pd (TF)
RBS
W
662...473
6.85. IO-”
x 87 97.58
Pd-rich; reported aReal
103
75D3
1.38.10-8
Cu-Ag Cu-Be
Cu-3.8 Ag(PC) Cu-6.2 Be (PC)
DP
PH
893 ... 561
3.11.10-s
162.5
-
104
8664
Not required
DP DP DP
TB TB TB
823...473 823...473 823...473
3.30.10-12 3.30.10-‘2 3.30.10-‘2
130.0 130.0 130.0
-
105 105 105
79Tl 79Tl 79Tl
Not required
Cu-9.3 Be (PC) Cu-13.4 Be (PC)
System Matrix (cont. in at.%) Cu-In
Cu-Mg
Cu-Ni
Cu-Sb
Cu-Zn Fe-Ni Fe-Zn
Method
Eq. T K
(.v6m”
e, kJmol-’
Remarks
m3s-1
1.49.1o-8 l.70.10-9 7.63. IO-* 9.54.10-9 4.45. IO-” 4.45.10-” 4.45.10-” 5.25.10-16 7.60.10-‘a
x 170 168.3 162.6 c 160 171.0 w 160 167.3 163.0 163.0 163.0 9.6T,,, 141.0
4.06.10-” 4.20. IO-”
140.9 125.9
Reported RLSF RLSF Reported aReal Reported aReal Cu side, reported “Real Ni side, reported aReal Cu side
In (BC’)
DP
PH
625... 550
Cu-4.6 In (BC”) Cu-8.9 In (PC)
DP DP
PH PH
625... 550 731... 573
DC
PH
731... 573
DP DP DP XRD AES
TB TB TB W
873.a.573 873 a.. 573 873 ~1.573 1173 678 ... 553
Cu-4.6
Cu-5.1 Mg (PC) Cu-6.5 Mg (PC) Cu-8.0 Mg (PC) Cu/Ni (TF)
Cu(BC)/Ni Cu-4.0 Sb (PC) Cu-4.5 Sb (PC) Cu-5.0 Sb (PC) Cu (5N, PC foil)/ Zn vapour Fe/Ni (TF)
EPMA DP DP DP DTGM
W PH PH PH CN
773...623 1048 ... 948 523, 503 523, 503 523, 503 673...573
AES
W
773... 526
Fe-9.7 to 30.5 Zn PC) Fe-30 Zn (PC)
DP
CN
873.a.673
DC
PH
718...623
Fe-10 Zn (PC)
DP
TB
73O.a.666
Fe-20 Zn (PC)
DP
TB
689.e. 571
Fe-30 Zn (PC)
DP
TB
666.a. 571
7.71 . IO-‘* 126.0 4.10.10-14 142.8 See Table 12.2.2 zz 153 x 147 x 155 2.00*10-‘2 100.0 1.66*10-‘2 100.0 1.30. IO- l4 142.3 9.72. IO-l5 142.3 9.20.10-” 135.1 3.63. IO- l2 144.0 174.5 2.29. lO-9 174.5 177.0 1.29.10-* 177.0 183.7 3.08*10-* 183.7 195.0 1.38.10-’ 195.0
Fig.
Ref.
60 m2 s-r
Reported aReal Reported aReal Reported aReal Reported ’ Real Reported aReal Reported aReal Reported aReal
106 106 106 106 100 100 100 107 107 107 45 104 108 109 109 109 109 109
Q
Ref.
kJ mol- ’
80G5
Not required
8504 8663
Not required Not required
86G3
Not required
84Tl 84Tl 84Tl 77H5 83L2
Not required Not required Not required 2.70. lO-4 236.4
7683
83L2
5.70-10-5
258.2
7683
86Jl 86Al 75Pl 75P1 75Pl 82Cl
5.00. lo-” 130.3 1.70.10-J 231.5 Not required Not required Not required Not required
8651 7921
79Wl
4.00.10-s
79Wl
6884
Not required
72Pl
Not required
72P2 72P2
Not required
72P2
Not required
Not required
192.5
Fe-Zn
Na-Cl Ni-In
Fe-18.9, 23.7 Zn (PC) DP Fe (5N8, PC foil)/ DIGM Zn vapour Fe-17.6, 22.2 Zn (PC) DP DC Fe-13.5 Zn (PC) DP, DC DP DC
CN CN
834... 672 853...753
8.95. lo-l3 3.40.10-7
135.6 187.0
PH PH PH PH* PH*
793...673 793 ... 673 790 ... 623 830... 623 790 . . .623
6.00.10-* 3.65.10-* 6.46.10-* 8.41. 1O-7 2.19.10-’
177.5 177.8 188.4 186.0 184.7
NaCl (BC)/KCI
F
923...673
EPMA
-
109 109
73Bl 78Cl
Not required Not required
-
109 109 109 109
8563 8563 86Cl 86Cl 86Cl
required required required required required
See Table 12.2.2
-
6762
Not Not Not Not Not -
1.10.10-4 5.22. 1O-4 3.30.10-S 2.70. 1O-7
266.0 274.4 233.0 252.0
Reported Recalculated -
86C2 86C2 88Cl 88Cl
Not Not Not Not
required required required required
-
% 113 111.1
Reported aReal
71B2
1.20.10-7
48
6762
1.34.10-4
527.0
71B2
69Sl
1.40.10-10
125.5
69Sl
Zr-C
Zr (SP)/C
EPMA
F
1973 ... 1373
3.76. lo-l3 5.01f10-13
100.8 107.1
‘Reported aV’ Real
110 110 110 59 -
Zr-Ca
ZrO,-x
EPMA
0
1923 ... 1648
R2.90. lo-’ 2.72. 1O-7
R414.2 412.1
x = 0.13, x = 0.19 aReal
111
7901
1.98. 1O-4
422.6
7901
Zr-Hf
(Zr, -,Hf,)O,16 CaO (SP)
EPMA
0
2356... 1775
9.80. lo-l4
255.0
-
8101
2.30. 1O-6
377.0
8101
(Zr,-XHfJO,14 MgO (SP) (Zrl-,WXk 16 Y,O, (SP)‘
EPMA
0
2356... 1775
8.79. IO- l4 1.20. IO-l3
251.6 255.0
x = 0.02/0.1*, reported RLSF x = 0.02/0.1*
111 111
8101
3.30.10-6
381.0
8101
EPMA
0
2389... 1857 2389... 1857
1.50~10-‘2 8.61.10-12
309.0 330.9
x = 0.02/0.1* x = 0.02/0.1*
111 -
82S2 8232
2.30. 1O-6 2.30.10+
377.0 377.0
8282 8282
W-MO
a
AES b
BA
Ni-1.4
In (PC)
DP
PH’
877 ... 703
Ni-7.5
In (PC)
DP DC
PH PH
1000...667 1000...667
EPMA
S
2363...2113
W (BC)/Mo
CaO (SP)
F
These Arrhenius parameters derived by us from the original Arrhenius plot correspond to the actual Arrhenius line drawn there; the reported ones yield a much different line lying away from the experimental data points. Auger electron spectroscopy for first appearance, accumulation or sectioning measurements. From the reported, recalculated or derived (from the Arrhenius plot) value of 0”: assuming a value of 6 = 0.5 mn for the grain boundary width and s = 1 for the segregation factor. Braislford- Aaron analysis [69B2].
BC._ _. Bicrystal. BC’, BC” Bicrystals having a random grain boundary with a misorientation composed of the following tilt (6) and twist (4) components: (I) 0 = 30” (001) and 4 = 12”(001) + ll”(Oll) +Y(lll), + 32”(011) + 32”(111) and (II) 8 = 52”(001) + 29”(011) + 34”(111) and 4 = 25”<001> +61”(011) +44”<111>. E For reasons descussed in detail in [89K2], these data are considered unreliable. CN Cahn’s equation. (continued)
Footnotes for 12.2.5, continued
P, & DC DlGM DP EC
ECR EPMA ESR F F, GBP NTAP
Volume interdiffusion data used for the evaluation of grain boundary chemical diffusion data. Indirect estimation from discontinuous coarsening kinetics. Indirect estimation from investigations of diffusion-induced grain boundary migration. Indirect estimation from discontinuous precipitation kinetics. Electrochemical (involving measurement of the time dependence of the electric current flowing through the electrochemical cell (due to anodic dissolution of the specimen) and the reverse electrode potential with respect to a Cd reference electrode. Indirect estimation from time evolution of the electrical contact resistance. Electron probe microanalysis. Indirect estimation from electrical sheet resistance measurements. Fisher’s equation. Equation based on Fisher’s solution. Indirect estimation from the kinetics of growth of grain boundary precipitates. No tabular data and no Arrhenius plot given in the original work.
Figs. 1OO.e. ill,
0
Oishi’s equation. Polycrystal. PC Petermann-Hombogen equation. PH Modified Petermann-Hombogen equation. PH’ R Reported. Rutherford backscattering spectroscopy. RBS Recalculated least-squares fit. RLSF (.~6&)~, ot, Arrhenius parameters for grain boundary chemical diffusion, Sintered polycrystal. SP Absolute temperature. T Average of the absolute solidus and liquidus temperature. T, Turnbull’s equation. TB Thin-film diffusion couple. TF V Analogous to volume diffusion. W Whipple-Le Claire equation. Mole fraction. X-ray diffraction. ~RD * The notation x = 0.02/0.1 indicates that the initial composition on the two sides of the diffusion couple was x = 0.02 and x = 0.1
see p. 703ff.
System
Matrix (cont. in at.%)
Method
Eq.
T
(SSDJO
Qi
K
m3s-l
kJmol-’
Remarks
Fig.
Ref.
BO m2 s-l
Q” kJ mol-’
Ref.
68A2 69B2 70Gl
2.90. IO-’ 2.90. IO-’
130.2 130.2
61M2 61M2
12.2.6 Data for interphase boundary chemical diffusion Abbreviations AI-&
Al-l.71
Cu/CuAl,
Al/CuAl, Cu-MO
&/MO
Ge-Sn
Ge/Sn : In
a
: Ni
used are explained at the end of the table 1.15-10-‘4 4.40. lo-l4 4.60. lo-l3 5.24. IO-l3 b5.50.10-11
53.56 95.60. 100.4 100.4 97.50
Reported aReal -
112 112 112 112
75Hl
-
-
-
1073...923
4.00.10-‘5 4.00. IO-”
100.4 230.1
0’ (001) TiIB 15’ (001) TiIB
93 93
82B3 82B3
2.70. 1O-4
234.4
82B3
434*., 313
See Figs. 95 . . .99
TwIB
95... 99
81B6, 81S2, 82K2, 83Sl
-
-
-
GBP
AA BA
598... 473 598...473 723...473
MT3
-
773...623
EPMA
Fi
EPMA
-
These Arrhenius parameters (derived by us) are the ones truly corresponding to the original Arrhenius experimental data points. AA Aaron- Aaronson analysis [68A2]. b From the reported Do value assuming s = 1 and 6 = 0.5 nm. BA Brailsford-Aaron analysis [69B2]. F. Fisher’s equation for application to interphase boundary diffusion. 3, e” Volume interdiffusion data used for the evaluation of interphase boundary chemical diffusion data. EPMA Electron probe microanalysis. GBP Growth kinetics of grain boundary precipitates. MTJ Migration of triple junction. (sSfi$‘, oi Arrhenius parameters for interphase boundary chemical diffusion. T Absolute temperature. TiIB Tilt interphase boundary. TwIB Twist interphase boundary.
line; the reported ones yield a different
Fig. 93, ,95 . . .99, see p. 700 ff.; Fig. 112, see p. 707 ..
line lying away from the
[Ref. p. 708
12 Grain and interphase boundary diffusion (Figures)
676
Figures for 12 , 10-1’8, 1800 , “C mJ/s
\
1600 4,
I 1400 1 I
!
1
I 1200 ’ I
Al;O, : i
178611
Ag : Ag I I 0<00l>TiGB
10-4 0.46
0.50
0.54
0.62 .10-3K-
0.58 l/l-
I 0.70
Fig. 7. AJ0,:X.X = 02-, A13+. Grain boundary diffusivity 60, of oxygen and aluminum ions in pure and Fe-doped AI,O, vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
-T
l/l?g. 6. Ag:Ag. Grain boundary diffusivity 6D, of silver in silver vs. reciprocal temperature l/T. The temperature Tin ‘C is given at the top. TiGB: tilt grain boundary, 0: tilt angle, ‘C: polycrystal.
4 ,o-22
450’
m3/s
Ti 4
h-9
300 I
Au : Au
10-22JJ
2 \%, I7&21 lo-'3--
I,10-2' 2
o-25
n3/s
\--
\
10-25-
10-26 I s 10-2’
10-26-
\ Fig. 8. Au:Au. Grain boundary diffusivity 60, of gold in gold vs. reciprocal tempcraturc l/T. The temperature Tin “C is given at the top. TFPC: thin film polycrystal, TFSC: thin film single crystal.
lo-“-.1.3
Kaur, Gust
1.5
1.7
17LGll 1736’31 I 1.9 2.1 2.3 40-3K-’
10-28
l/TLandoh-B6rmtein New Series Ill/26
3°C
Ref. p. 7081
12 Grain and interphase boundary diffusion (Figures)
-T
loqg
151 :
m3/s
125
100
c
75
677
-T 100
4.10A7 m3/s
-
CH: 10-17
2.3
1 2.~
2.5
2.6
2.7 l/T-
2.8
2.9 .lO"K-'
3.1
Fig. 9. Cd:Cd. Grain boundary diffusivity 6D, of cadmium in cadmium vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
10-2' i+.@ 3.2
i
3.6 40" K'
l/T-
Fig. 10. C,,H,,:C, CH,C-COOH: C and CN-C,H, -CN:C. Grain boundary diffusivity 6D, of carbon in adamantane, pivalic acid and succinonitrile vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
700°C
4.T2[ m /s \
-T
10-22' 1200°C
IO-17
900
600 -
m3Ys 10‘2'
Cr : Cr IO-18 _
% 2,
i
I
10.2;
ST
t
icc-phase
c-phase
1
1 &IO Lo
-19 -
10-2:
..-
IO-20 _ 1o-2"
10-2;
$ 1.0
10-21 0.6
1
I.1 l/T-
Fig. 11. Co: Co. Grain boundary diffusivity 6D, of cobalt in cobalt vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. Land&-Biirnstein New Series III/26
0.7
0.8
0.9 1.0 l/T -
1.1 .I0
Fig. 12. Cr :Cr and Cu : Cu. Grain boundary diffusivity 6D, of chromium in chromium and copper in copper vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
Kaur, Gust
678
12 Grain and interphase boundary diffusion (Figures) -I
4.10 300”c 1 rnJ[
10100
[Ref. p. 708
--I
800
600
4.10-‘t
800 I
1000"
600 I
400 I
m3/s lo-l6
10”
Ni : Ni
i 75Dll
\ :
lo-l9
4 %
lo-,
% 10-2[ 75011 y
I ,&II-’ co
+ klLl1 10-n \ 69Cll I
$104
lo-
t
[74A11 \ \
10.2:
lo-’ y-Fe lo-IL
10-l J-
0.7
1.0 1.1 .10-sK-' 1.3 l/f Fig. 13. Fe:Fe. Grain boundary diffusivity dD, of iron in iron vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. Tc: Curie temperature, TE: theoretical estimation. 0.8
0.9
10-25
10-26
0.70
0.85
1.00
1.15 l/l-
1.30
.lO-?K-'
1.60
Fig. 15. Ni:Ni. Grain boundary diffusivity 6D, of nickel in nickel vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. See remarks in Table 1 for [88Nl]. TiGB: tilt grain boundary, TwGB: twist grain boundary.
&lo-” m3/s 10-1’8
I $0-1’9 b
!
.10-+-l
2
4 Fig. 14. KI:I-. Grain boundary diffusivity SD, of iodine ions in potassium iodide vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [62Cl]. PC: polycrystal, BC: bicrystal.
Kaur, Gust
Landolf-BGmstein New Series III,!26
Ref. p. 7081
12 Grain and interphase boundary diffusion (Figures)
679
-T 4.10-IO-m3/s
300 6N
10-20~
I 9 2
\\
10-Z' __
3N4
10-22+10-231.1
\
1.2
1.3
1.4 1.5 1/T -?
\ i-’
1.8
‘I’-
Fig. 17. Sb:Sb. Grain boundary diffusivity 60, of antimony in antimony of different purity vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [68Hl]. 0.90 0.95
1.00
1.05
1.10 1/T-
1.15
1.20 .@K-'
1.
Fig. 16. NiO:Ni ‘+. Grain boundary diffusivity 6D, of nickel ions in nickel oxide vs. reciprocal temperature l/T. The temperature T in “C is given at the top. LAGB: large-angle grain boundary, SGB : subgrain boundary. -T 1800
200°C 10-l82 m3h;
10-l9
10-i!OI s 10-l'1 .
10-i'2 _
Fig. 18. SiC:C4+, Th0,:Th4+ and W,C:C. Gra: boundary diffusivity 6D, of carbon ions in silicon carbide, thorium ions in thorium dioxide and carbon in tungsten hemicarbide vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. Land&-Biirnstein New Series III/26
1o-2'3 [1.40
Kaur, Gust
Th02: Th4+ \ 0.45
0.50
0.55 l/T-
. 1 _' 0.60WK-' 0.65
[Ref. p. 708
12 Grain and interphase boundary diffusion (Figures)
680
2.10”9 r
-1
-1 150 I I
200°C 1 I
I
100 I
I
I
m”s I\ I I I I I
-17 _1
600
10
51:
10-21
m31s
m3/s
-18 _
10
4 I &lo 'Q
I 2 cs” IQ 10-20 8
-19 -
10-20
-
6 4 10-21
0.7
1
10-n 2.0
2.6
2.1
2.2
2.8 4T3K' 3.0
0.8
0.9
1.0 l/T-
1.1
.lO-'K-'
1.3
Fig. 20. U:U. Grain boundary diffusivity 60, of uranium in uranium of different crystal structures vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
l/TFig. 19. Pb:Pb and Sn:Sn. Grain boundary diffusivity 6D, of lead in lead and tin in tin vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. -1
-1
1200
1600
104* m3/5
900
to-'* m3/s
4.10-'9 m3/s 10-19
lo-'9
10-20
10-Z'I_
I
10-2’Lo G I 10-24
I I
I I
I \lx=o.931 N-1 I
I
10-22
I D 2 10-2'
10-22-
10“
4.10-24 0.1
1.10-26
a40
0.~5
0.50
0.55 l/l -
a60
3-
.10-3K-' 0.70
I
I
I
0.5
0.6
0.7
I
0.840-~K-'a9
l/l-
Fig. 21. UC,:U’+. Grain boundary diffusivity 6D, of uranium in uranium carbide vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [75Rl].
Fig. 22. UO,:U 4+. Grain boundary diffusivity 6 D, of uranium ions in uranium dioxide vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
Kaur, Gust
Land&BCmstein New Series III,!26
681
12 Grain and interphase boundary diffusion (Figures)
Ref. p. 7081 -T 1800 I
2.10. m31 lo-
4
1400
200°C
-19
10
100 I
150 I
m3/s
w
-20
IO
loI g10 Lo
\
-21 -
loIO-22
tn 2
-
t 10-23 2.0
lo-
2.2
2.L
2.8 .IO" K-'
2.6 l/T-
Fig. 24. Zn:Zn. Grain boundary diffusivity SD, of zinc in zinc vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. lolo-l7 m3/s
-T 400
700 "C
I
Ag : X
=Te lo-
\ [87Gl I
1.60XF3K-' [ 10-“'1
l/T-
Fig. 23. W: W. Grain boundary diffusivity 6D, of tungsten in tungsten vs. reciprocal temperature l/T. The temperature T in “C is given at the top. SGB: subgrain boundary, LAGB: large-angle grain boundary.
200 T
,
-
t-
-
,o-l"
I $10-2' w
For Figs. 26,27 see next page.
1o-2' :69K;
671(31
10-2
+ \ [67K21 10-2:
10"
20"
30"
e-
LO"
50"
Fig. 28. Al: Zn. Activation energy Qb of the grain boundary impurity diffusion of Zn in aluminum bicrystals vs. tilt angle 0 [76Al, 78Al]. Land&-BBmstein New Series III/26
0.8
60"
1.0
1.2
I.4
I.6 l/T-
Fig. 25. Ag:X. Grain boundary diffusivity s6D, of impurity elements X in silver vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
Kaur, Gust
[Ref. p. 708
12 Grain and interphase boundary diffusion (Figures)
682
3x-"
m3/: 10-J
i
lo-”
Y 4 \ -
HI-’ I s v, 10“
-
20" -
10-2
30" O-
40"
50"
60"
Fig. 27. Al:Zn. Grain boundary diffusivity&D, ofimpurity diffusion of Zn in aluminum bicrystals vs. tilt angle 0 [76Al, 78Al]. -
10-2
-
lo-’
1.2
-
16
1.6
1.8
2.0 1/r -
2.2
2.4 .@K-'
2.8
Fig. 26. AI:X. Grain boundary diffusivity s6D, of impurity elements X in aluminum vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. LAGB: large-angle grain boundary, SGB: subgrainboundary. -1 350°C I&/-1oe,BI Al
300
:Zn
I
10.6 1,
250 I '
0
0.2
0.4
0.6
0.8
LO
Fig. 30. Al:Zn. Activation energy Qb of impurity diffusion of Zn in aluminum bicrystals vs. H-l/*, where I is the reciprocal of the density of coincident sites.The direction of diffusion is indicated by (001) and (11 l), respectively [77Al]. Q: activation energy of volume diffusion.
--t
10-20 1.6
1.8
1.7 l/l-
55"
1.9 @K-l
Fig. 29. Al:Zn. Grain boundary dif’fusivitysaD, of impurity diffusion of Zn in aluminum bicrystals vs. reciprocal temper2.0 ature l/T. The temperature Tin “C is given at the top [76Al, 78Al]. 8: tilt angle, T,: melting point of Al.
Kaur, Gust
Land&BBmstein New Series III!26
12 Grain and interphase boundary diffusion (Figures)
Ref. p. 7081 IO-'*
683
I
m’/s - Al : Zn 6 - diff. II< OOl>
T=613K.
Fig. 31. Al: Zn. Grain boundary diffusivity s6 D, of impurity diffusion of Zn in aluminum bicrystals vs. tilt angle 0 [77Al].
k-i0 -mol
Fig. 32. Al:Zn. Pre-exponential factor (sSD,)' of the grain boundary impurity diffusion of Zn in aluminum bicrystals vs. tilt angle 8 [77Al]. 10-g mVs
60
IO-lo 50 I P .a 40
10-l’ lo-‘? _I lo-‘3 .D 2 v) 10-l”
BFig. 33. Al: Zn. Activation energy Qs of grain boundary impurity diffusion of Zn in aluminum bicrystals vs. tilt angle @ [77Al].
,0-t I_ IO-‘!,,0-l;
lo-”
100 kJ/mol 75 QbFig. 34. Al:Zn. Pre-exponential factor (sSD,J"of the grain boundary impurity diffusion of Zn in aluminum bicrystals vs. activation energy Q,, [80Al]. TiGB: tilt grain boundary, TwGB: twist grain boundary. 25
50
l Fig. 35. Al: Zn. Grain boundary diffusivity s6D, of impurity diffusion of Zn in aluminum bicrystals vs. twist angle 4 [80Al]. TwGB: twist grain boundary. Landolt-Biirnstein New Series III/26
Kaur, Gust
[Ref. p. 708
12 Grain and interphase boundary diffusion (Figures)
684 IO-“‘9 m’/s
10-l’” mJ/s
1500“C I \I
1200 I
1000 I
800 I
55” 60” 45” 50” 4Fig. 36. Al: Zn. Grain boundary diffusivity sSD, of impurity Mfusion of Zn in aluminum bicrystals vs. twist angle r#~ 80Al]. TwGB: twist grain boundary. I0
35”
40”
I I I I 0.9 .10-jK-’1.0 Ct8 0.7 l/l Fig 39. AI,O,:X. Grain boundary diffusivity s6D, of impurity elementsX in aluminum oxide vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. I 0.6
10-2cI 05
-T _ TT ,u-:,
400 “C I
200
100
20
I
I,
I
ma/s
Au : X
10-24
Fig. 37. Al:Zn. Activation energy Qr,of grain boundary impurity diffusion of Zn in aluminum bicrystals vs. twist angle $I [SOAl]. TwGB: twist grain boundary.
%I Al:Zn 1
10-2s gI IO.26 Lo w 10-2’ 10-28 10-29 I lo-301 1.5
I
I
I
1
3.1 .10-3K-’ 2.7 l/lFig. 40. Au:X. Grain boundary diffusivity sSD, of impurity elements X in gold vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. 30”
35”
40”
45”
50”
55”
1.9
2.3
60”
dFig. 38. Al:Zn. Activation energy Qb of grain boundary impurity diffusion of Zn in aluminum bicrystals vs. twist angle I#J[80Al]. TwGB: twist grain boundary.
Kaur, Gust
I
685
12 Grain and interphase boundary diffusion (Figures)
Ref. p. 7081
-1
-I ,o-,* ~200"C I ,
180 I
160 I
,o-,g1m “C
140 I
-II IT
m3/s
m3’s Cd : Ag
X=k %-
I p-'g
10-20
y
v)
. 10-20 2.10
2.15
2.20
2.25 2.30 2.35 W3K-’ 2. l/T Fig. 41. Cd:Ag. Grain boundary diffusivity s6 D, of silver in cadmium vs. reciprocal temperature l/T. The temperature T in “C is given at the top [72Sl].
- II
%
I &1O-2' co v,
- II \_ - II
10-22 t--t 3
1.0
-II 1.140‘3K-’1.2
l/TFig. 42. Co:X. Grain boundary diffusivitys6Ds of impurity elements X in cobalt vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
For Fig. 43 see next page.
-T 800°C I
4.10-20 m3/s
\
\N
’
600
700 ’ 10.7T,
3k450 ii3
Cu:Ni
250
1:-20 6 4
t 200 0” 150
2
100 0”
15”
30”
45” 8-
I/
I
b
2
2
10-4 0.85 a
I
I
I
I
\
I
\'I00 0.90
0.95
1.00 l/T -
1.05
I
I
I
0”
15”
A
I
Y
75”
90”
I
I
1 \T=923K
’
i
1
.W3K-’ 1.15
Figs. 44a-c. Cu:Ni. Impurity diffusion of nickel in copper bicrystals of (001) type. (a) Grain boundary diffusivity s6D, vs. reciprocal temperature l/T (original plot from [55Yl]). The temperature Tin “C is given at the top T,: melting point of copper. (b, c) Activation energy Qb and the ratio D,,/D vs. tilt angle 8. Land&-Biimstein New Series III/26
1
60”
c
Kaur, Gust
30”
45” 8-
60”
75”
90”
.
12 Grain and interphase boundary diffusion (Figures)
686
[Ref. p. 708
-1 4.,o.,6 800 “C 600 1 ,
mlI
300 I
750 “C
2.1049r
m3/s 5
’ ’ lo.75 lm
mVs
10-EQ+.
10-23 m3/s
10-17
1o-24
10-n
1 lo-‘* 1
Cu : Ni
Ii
8 6 -
I0 54 -
&
2 w 10-‘9
,y2’1 2
10-m
-
I
lo-T7
lo-20L 0.950
)(10-29
4.‘o-“[_.
2.1 l/T Fig. 43. Cu:X. Grain boundary diffusivity s6D, of impurity elements X in copper vs. reciprocal temperature l/T. The temperature T in “C is given at the top. TiGB: tilt grain boundary.
J
0.975
I
36.68” 1
1.000 1.025 .W3 K-’ 1.075 l/TFig. 45. Cu:Ni. Grain boundary diffusivity s6D, of impurity diffusion of nickel in copper bicrystals of (001) (013) type vs. reciprocal temperature l/T. The temperature T in “C is given at the top [86Al]. 0: tilt angle, T’,: melting point of copper.
-1
lo-l7
-1 ' 3
1200°C I
600 I
700 1
m3/s
Fe :
X
lo-l8
lo-“9 , 10-2’
I
I
I
I
I
I
,
\ 10‘21 ID 2 bl
Ni
'Sn
10-Z’
10-2:
\ i
10-2:
1.2
1.3
1X
1.5
1.6 l/l
1.7
1.8 .lO"K-'
10-2; 2.0
I
0.7
0.8
Cd-Fe I-A0.9
1.0
\
r'
1
l/T -
-
Fig. 46. CdInSe,:Cd. Grain boundary diffusivity s6D, of cadmium in copper indium selcnide vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
Fig. 47. Fe:X. Grain boundary diffusivity s6D, of impurity elements X in alpha and gamma iron vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
Kaur, Gust
12 Grain and interphase boundary diffusion (Figures)
Ref. p. 7081
687
-T
-20 I'
-10 "C
I
2~lOP m3/s
-30 I
mJ'S/-'MqO. .
H-0 : Cs+.Na+
. Co2:Ni2+li
2
10-26 E
6 I
4
s v,
2 I;-27 I
6 4
0.70
I
I
0.75
0.80
I \
I
I
0.85
0.90
I
’
Ni2’
.10-3K-’
1.00
l/T -
-16
10
,
Fig. 49. MgO:Co’+ or Ni “. Grain boundary diffusivity s 6D, of impurity diffusion of cobalt and nickel ions in mag3.70 3.75 3.80 3.85 3.90 3.95 4.00 .W3K= 4.10 nesium oxide vs. reciprocal temperature l/T. The temperature T in “C is given at the top [85B3]. l/T-
6.1; -17
Fig. 48. H,O:Cs+ or Na+. Grain boundary diffusivity s6D, of impurity diffusion of cesium and sodium ions in pure and doped ice vs. reciprocal temperature l/T. The temperature T in “C is given at the top.
For Fig. 51 see next page.
-7
1o-l9 10-20 10-2' t 10-22 ~~ CD w 10-23
5". 10-20
\1<001> 1o-2’
0.56
0.58
0.60
0.62
0.64
0.66 .lO+K’ 0.70
l/T-
Fig. 50. MgO:Cr 3+. Grain boundary diffusivity s 6D, of impurity diffusion of chromium ions in magnesium oxide vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [8301]. TiGB: tilt grain boundary, 0: tilt angle.
10-28 0.4
0.5
0.6
0.7
0.8 -W3 K-’ 0.9
l/T-
Fig. 52. Nb:X. Grain boundary diffusivity ~6D, of impurity elements X in niobium vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
[Ref. p. 708
12 Grain and interphase boundary diffusion (Figures)
688
,”
10-23
I
. I
.._ h
\
1o-24 10-2'
w
10-25 10-26
In
10“'
10-29 10-29 0.7
0.9
1.1
1.3
1.5 40-IK-' 1.7
l/110-28 a4
0.5
0.6 l/T-
0.7
0.8 .10‘3K-' 0.9
Fig. 53. Ni:X. Grain boundary diffusivity s6D, of impurity elementsX in nickel vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. The Arrhenius straight line of self-diffusion in nickel is shown for comparison.
Fig. 51. Mo:X. Grain boundary diffusivity sSD, of impurity elementsX in molybdenum vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
-T LlO-”
200°C
150
100
m3/s 10-l'
1.10-2' 2.0
2.2
2.6
2.6 l/T -
2.8 40-j K-' 3.0
Fig. 54. Pb:Sn, Sn:Ag and Sn:TI. Grain boundary diffusivity sdD, of tin in lead, silver in tin and thallium in tin vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
Kaur, Gust
Landoh-BCmstein New Series III,/26
Ref. p. 7081
12 Grain and interphase boundary diffusion (Figures) -T
10-25
600 "C
5uu
4UI -1
IO-21 m3/s
m3/s I
4
\I
I
I
300°C 1000
-7 800
600
400
I 10-22
2
Ii-26 t
,o-2'
6
1o-2c I n 2 w
10-25
10-4 1.10
1.15
1.20
1.25
1.30 l/T-
1.35 1.40 .105K4 1.50
Fig. 55. Pt:Cr. Grain boundary diffusivity sSD, of chromium in platinum vs. reciprocal temperature l/T. The tempera:ure Tin “C is given at the top [75D2].
X=AI
10-Z" s * 5
10-21 h
lo-l6 m3/s
800°C I
-T 600 I
1o-28L
400 I
0.6
10-11
1.0
1.2
1.4 .10-j K-' 1.6
Fig. 56. Si:X. Grain boundary diffusivity sSD, of impurity elements X in silicon vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
10-l@ 10‘19 In 1o-20 : 4 10-21
Zr : Cr\ ,
0.80
0.8
l/T-
\
0.95
1.10
1.25 l/T-
‘6~~~~\ \
1.40
40-3 K-1
1.70
Tig. 57. TaSi, :P, Y: C and Zr: Cr. Grain boundary diffusiviy sSD, of phosphorus in tantalum silicide, carbon in yttrium md chromium in zirconium vs. reciprocal temperature l/T. Thetemperature Tin “C is given at the top. TF: thin film of TaSi,.
Kaur, Gust
690
12 Grain and interphase boundary diffusion (Figures) 10“s m3/s
10-2’ m3/s
10-*t
to-24
1CP
V
I G ‘Q VI
[Ref. p. 708
Th
1\
,o‘2’
lO-‘6
10-2:
,0-2’
10-z
10-28 I
0.55
0.60 .W3 K-’ 0.
*<~
l/1 Fig. 59. W:X. Grain boundary diffusivity s6D, of impurity elements X in tungsten vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
l/1 \ I
2
‘i-2:
I
I
I
I
I
I
I \
R
I
Fig. 58. UC:X”+. Grain boundary diffusivity s6D, of molybdenum, niobium and zirconium ions (X”‘) in uranium carbide vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [6632].
6 4
2
18-2 6 ‘
I
\
1
I’
\
‘W
10-m 0.4
0.5
0.6
0.7 l/T -
0.8 40°K.’ 0.9
4 Fig. 60. X:Cs. Grain boundary diffusivity sSD, of impurity diffusion of cesium in elements X vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [80G3].
Kaur, Gust
Landoh-BGmslein New Series III,‘26
Ref. p. 7081
12 Grain and interphase boundary diffusion (Figures)
(I
10-li
691
IE
m3/s
lo-: !O 1P 2 w 10.;
1.00
1.05
1.10
1.20
1.15 l/T-
1.25 .lO"K-'
1.35
Fig. 61. Ag-0.007 at.% S:S. Grain boundary diffusivity s6D, of sulphur in a dilute silver-sulphur alloy vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [79A2, 80A2].
lo- 22_ 4-lo- 23 0.56
I
I
I
I
I
0.58
0.60
0.62 l/T -
0.64
.105K-'
0
Fig. 62. (Al-O.1 wt.% Y),O,:X”+. Grain boundary diffusivity s6D, of chromium and iron ions (X”‘) in an aluminum-based oxide vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [84Ll]. 1o-'7
I
m3/s
I
I
Al-xot.xZn : Zn 10-2' m3/s
10-1'8
*
In 2 v,
16.7
,o‘2;
4.33,'-,
2\
.
1.6
1.7 l/l-
1.8
1.9
,
I’
I
h
10-24
m3’s 1o-25
\
,o-2: I ,3
\ 1.5
I
Au -1.2at.xTa : Au
-
10-1'9
10-20 1.4
I
-10 I-1 i
:
Fig. 63. Al-x at.% Zn:Zn. Grain boundary diffusivity s8D, of zinc in aluminum-zinc alloys vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [69H2].
5
10-21
,o-2!
1o-2' 1
1.6
1.7
1.8
1.9.
.lO"K-'
2.1
l/l Fig. 64. Au-l.2 at.% Ta:Au. Grain boundary diffusivity sSD, of gold in a dilute gold-tantalum alloy vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [75Gl]. LAGB: large-angle grain boundaries, SGB: subgrain boundaries. Land&-Biirnstein New Series III/26
Kaur, Gust
[Ref. p. 708
12 Grain and interphase boundary diffusion (Figures)
692 -1 10-20
1000“C
-1
c,nn ““-
600
800
-r
400 I
6.lOO"C 500
.-.,I
llr”
,
I
300 I
m3/s
m3/s
lo-”
I $lo-” u) 31.89 Y\
19.6
10-2L
\ \
10-2s-
(-1
2.
t 1o-26 0.7
0.8
0.9
1.0 l/l-
1.2‘.@K-’
1.1
Fig. 66. Cu-X:Ag. Grain boundary diffusivity sSD, of silver in dilute copper-based alloys vs. reciprocal temperature l/T. The temperature Tin "C is given at the top.
Fig. 65. Co-x% W:W. Grain boundary diffusivity sSD, of tungsten in cobalt-tungsten alloys vs. reciprocal temperature IIT. The temperature Tin “C is given at the top [69Ll]. -1 700°C
lo-"
600
-1
/Jo-” m’/s
\
l-
500°C I, I Cu-3od.x
I
10-19
I
I
Zn : Zn
m3/s 6
400 'I
4
I
I I
\
2
c$ 10-25 2i8 6
I0
,zv)
’
\
lo-”
1
Fe-xwt.XAl:Fe
1.10-2’
1.50 1.15 1.50.10-3K-' 1.f l/T Fig. 67. Cu-30 at.% Zn:Zn. Grain boundary diffusivity s6D, of zinc in a copper-zinc alloy vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [77H2]. 1.20
1.25
1.30 1.35
0.95
1.00
1.05
1.10 l/l-
1.15
40-3 K-’
1.25
Fig. 68. Fe-x wt.% AI:Fe. Grain boundary diffusivity s6D, of iron in dilute iron-aluminum alloys vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
Kaur, Gust
Land&BBmsfein New Series III!26
Ref. p. 7081
12 Grain and interphase boundary diffusion (Figures)
693
-T 11oo"c 4.10.'9 , m3/s
Fe -
700 I
900
I
I
600 I
16
4.10. m3,'S
X : Fe
lo-
16 _
lo- 17 _
6 v)
y-phase
u-phase
\
IO' I8
10-2'
I
10-22 4.10-231
0.7
_
I 5 IO' 19 Y, v,
\
691-131
I
0.8
0.9
1.0
1.1 .10-3K-'1.2
l/T-
lo-
20-
Fig. 69. Fe-X:Fe. Grain boundary diffusivity s6D, of iron in ‘dilute iron-based alloys vs. reciprocal temperature l/T. The temperature T in “C is given at the top. IO-; -T 1100 "C 4.10-'9 , mVs
I
900
I
I
700 I
600 I
IO'
Fe-xwtx Cr : Cr
lo-:
I Fig. 71. Fe-x wt.% Cr: Fe. Grain boundary diffusivity sSD, of iron in dilute iron-chromium alloys vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
Tig. 70. Fe-x wt.% Cr:Cr. Grain boundary diffusivity :SD, of chromium in dilute iron-chromium alloys vs. recip,ocal temperature l/T. The temperature Tin “C is given at he top [69H3]. Land&-Bknstein New Series III/26
Kaur, Gust
694
12 Grain and interphase boundary diffusion (Figures)
[Ref. p. 708
-T
2.10
,o-,g 1100 "C I
-
l”d
I0
-T
1100 -r
800 I
m3/s
600 '
I
Fe-XCr-yNi : Fe (wt.%)
10
5
-
10
2.10 --I
j
0.80 0.85 0.90 0.95 1.00 .lO
4
,'
l/T-
Fig. 72. Fe-x Cr-y Ni:Cr (wt.%). Grain boundary diffusivity s6D, of chromium in iron-chromium-nickel alloys vs. reciprocal temperature l/T. The temperature T in “C is given at the top. HP: high purity. MT
2.10 m: 10
11oo”c 1000 I , I x=7.y=2 - 179611 -
9bo I,
800 ,,
I
Fe-xCr-yNi-ZC
0.7
0.8
1.0
0.9
1.1.lO-jK-’
l/T-
Fig. 73. Fe-x Cr-y Ni:Fe (wt.%). Grain boundary diffusivity s6D, of iron in iron-chromium-nickel alloys vs. reciprocal temperature l/7’. The temperature Tin “C is given at the top. HP: high purity.
x (wt.%) -T
IO“8 m3/s
Fe(z=0.03)
1Q&&
800 I 1
1
I
600 1 I
Fe-XCrfyNi : Id (wtml
lo-l9
X= ‘Fe
10
1200“C 1000 I, II
----x:y=
20:75 I73641
Sn I 6 co v)
t
10
I
10
,o-2'
1o-2:
6.10-4
4.10 0.70
0.75
0.
1.00
l/TFig. 75. Fe-x Cr-y Ni-z C:X (wt.%). Grain boundary diffusivity s6D, of chromium, iron, nickel and tin (X) in ironchromium-nickel-carbon alloys vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
0.7
0.8
0.9
1.0
W3 K-’ 1.2
l/T -
Fig. 74. Fe-x Cr-y Ni:Ni (wt.%). Grain boundary diffusivity s6D, of nickel in iron-chromium-nickel alloys vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
Kaur, Gust
Landoh-BCmstein
New Series III!26
Ref. p. 7081
12 Grain and interphase boundary diffusion (Figures) -T 0
00“C
lo-l4
I
m3/s
,
I'
I
-80 I '
I
Fe-Cr-Ni-&l;-Mn-C Fe-Cr-Ni-Mn-C
-
“r
10-l m3,
:H : H
-T 1000 I
11oo"c
695
900 I
\a\
Fe-isCr-v+Ni-o.09C-xSi : X
Cr
-
lo-'
-
-
800 I
X =Cr,Ni [78A21 Fe L69011
:r< \ X =Ni I c.4
I G 2
10-2
10-2
-Tc
lo-'1
-1
6.0
and Fe-Cr-NiFig. 16. Fe-Cr-Ni-Mo-Mn-C:H Mn - C: H. Grain boundary diffusivity s 6D, of hydrogen in 304 and 316 austenitic stainless steelsvs. reciprocal temperature l/T. The temperature Tin “C is given at the top [73C2]. -T .,.-IR 12oo"c
1000
4.10-T 0.70
0.75 -
0.85
0.90W3K-' I
l/T -
Fig. 78. Fe-16 Cr-14 Ni-0.09 C-x Si:X (wt.%). Grain boundary diffusivity SSD, of chromium, iron, and nickel (X) in an iron-chromium-nickel-carbon-silicon allov vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. I
900
800
700
I
1o-2o
=? Q Y
10-2'
IO
-22
‘0 11
._
10-233 0.650
Land&-Bknstein New Series III/26
0.725
0.800
0.875 l/T -
v I r, ++ -I 0.950 4O-3K , ,OO
4
Fig. 77. Fe-Cr-Ni-Mo-Mn-Si-C:X. Grain boundary diffusivity s6D, of chromium and iron (X) in an ironchromium-nickel-molybdenum-manganese-silicon-carbon alloy vs. reciprocal temperature l/T. The temperature T in “C is given at the top.
Kaur, Gust
[Ref. p. 708
12 Grain and interphase boundary diffusion (Figures)
696
-T
-1 3
700 I
800
900
I
II
'
0°C 800 4*10-2 d m3/ s
Fe-xX : X .
Nb -stabilized
: X ~
( wt.% 1
!I _ 1(=t-
lo-'
. P *
Fe-xNi-2oCr
‘0 \ bIi\ F&
IO“
700
I !2 -
I
10-i
x = 0.2 ot.%Cu 2
\ \ 10-j
0.75
l-L Cl85 0.90 l/T-
0.80
‘4
-
0.85
I
0.70
‘3
0.95
0.90
0.95
1.00
1.05 l/l
a10-3
3g. 79. Fe-xX:X. Grain boundary diffusivitys6D, ofcopor and nickel (X) in iron-based alloys vs. reciprocal temperrture l/T. The temperature Tin “C is given at the top.
1.10
1
-7
-
Fig. 80. Fe-25 Ni-20 Cr:X (wt.%). Grain boundary diffusivity s6D, of chromium, iron, manganeseand nickel (X) in a Nb-stabilized iron-nickel-chromium alloy vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
-1 1200°C
lo-'L m3/s
850
1000
-zs%MnO-ig%ZnO,
lo-'5
lo-'6 I m 2 .I 10-l'
r’
‘8. Q+ %-
10“ 4 10-l l
& 3
i
0.70
0.75
l/l -
0.80
-@K-’
0.90
Fig. 81. Fe,O,-26% MnO-19% ZnO:Ca**. Grain boundary diffusivity s6D, of calcium ions in an Fe-Mn-Zn oxide alloy vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [6701].
Kaur, Gust
LandolbB6mstein New Series 111,l26
Ref. p. 7081
12 Grain and interphase boundary diffusion (Figures)
Fig. 82. Fe-yat.% P-xat.% X:P and Fe-nppm P:Fe. Grain boundary diffusivity s6Q of phosphorus and iron in Fe-based alloys vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. b
10-l m3/
00 “C
-T 800
500
-T-r-l-
PC
800
697
700
600
m3/s
1o-l9 k&L/
IO-** m3/s
,;=0.11,'x=2.11:
X=M;
lo-*( IO“
.y=O.l4,x=l.O3,X=Ni
1o-23 I s
1
I\ \v=O.l4P,x=O.29,
X=M 0
,o-2’
v,
lo-24
10-j
10.2;
I 10-25rf co v)
I 5 lo‘* v,
10-z:
;;+4h;-xfo";;4[8;1
1
'
boo
IO.26
10-j
0.90
‘O-5
0.95
7 1 100°C
10-I
Fe-9.7Co/-9.5W-4.1Cr-2.iV-0.94C: Wm
m3/r
169Zll IO-*
1.05 l/T-
-T 900 I
lo-27
10-j
1.00
I
1.10
I
6.55at.%Si [81T21
1.15 .lO-
700 '
Fe-X
-’ 1.;
600 I : Fe
/O-*8 0.9
1.1 l/T -
1.3 e10-3K-' 10-l
Fig. 84. Grain boundary diffusivity sSD, of chromium, iron, nickel, tin and tungsten in iron- and nickel-based alloys vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
10-l I n 2 v, 1o-2
lo-'
Fig. 83. Fe-X:Fe and Fe-3 wt.% Si:S. Grain boundary diffusivity s6D, of iron and sulphur in iron-based alloys vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
10-j 3.8
0.9 l/T-
Land&-Biimstein New Series III/26
Kaur, Gust
1.0
1.1 .lO" K' 1.2
12 Grain and interphase boundary diffusion (Figures)
698
?ig. 86. Ni-1.4 at.% 1n:In. Grain boundary diffusivity ;6D, of indium in a nickel-indium alloy vs. reciprocal temxrature I/T. The temperature Tin “C is given at the top. The ,alucs reported are not the original ones [89Nl], but the talues corrected by Neuhaus and Herzig (1990). M, S: miyating and stationary grain boundaries, respectively. The 4rrhenius straight line for the diffusion of indium in nickel b 89Nl] is shown for comparison.
[Ref. p. 708
-1 687°C II \
2.10-'0,
m3's
639 632
I
~j-zq
-1 -10
1s
1200°C I ' A%!!
I
'I
I
I
'
I
Ni -1.4ot.xIn : In 1
y-2' -..- [ 79 0 11 -179M11 ---174Al1
-*S+M
8 64;‘221 1.02
1.04
1.06
1.08
40.3K-’
-
1.12
l/l-
4.10-Z’ 900“C m3/s _
-1 700 I,
I
I
500 I
, (Ni -o.lwt.xY10 : Ni2’
4.10-23 m3/s ..
lo-II;ll’“:;
-?I
I
I I
\ I \\\I
I
I10125
I
I G
, -22
OHI
0.65
0.70
0.75
0.80
0.85 .10-3K-' 0.95
1o-26’
l/TFig. 85. Ni-20 Cr:X and Ni-x Si:Ni (wt.%). Grain boundary diffusivity s6D, of chromium and nickel in nickelbased alloys vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
1o-27
0.8
0.9
1.0
1.1 l/l-
1.2
W3K-'
-IO 10 1.5
Fig. 87. (Ni-0.1 wt.% Y)O:Ni*+. Grain boundarydiffusivity s6D, of nickel ions in a nickel-based oxide vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [85Ml]. SGB: subgrain boundary, LAGB: large-angle grain boundary.
Kaur, Gust
12 Grain and interphase boundary diffusion (Figures)
Ref. p. 7081
-T
-T 70
120
10-l
699
IO-" m3/:
m31S’
200 "C
100
50
Zn
\ \ \ I
,o-l!
9’
!n Sn
.
3 Zn
Sn
lo-*
!l
"
2.2
2.3
2.4
2.5
2.6 l/T -
2.7
I t . _ I,1o-1
2.8 .lO-'K-' 3.0
Fig. 88. Pb-x at.% 1n:In or Pb. Grain boundary diffusivity sSD, of indium and lead in lead-indium alloys vs. reciprocal temperature l/T. The temperature Tin “C is given at the top
3
X =Sn
5
IO“
[8662].
! P
1OP m3/s
200°C
ln
100
150
&
1.4
2.6 l/T-
2.8
3.0 .10-j K-'
3.4
Fig. 90. Sn-x wt.% Zn:X. Grain boundarydiffusivitysSD, of tin and zinc o() in Sn-Zn alloys vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [66Bl, 31. Pt
2.2
2.4
2.6 l/T-
2.8
.10-IK-1
Fig. 89. Pb-x Sn:Pb or Sn and Pb-x Sn-y X:Pb (wt.%). Grain boundary diffusivity s6D, of lead and tin in leadbased alloys vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. Land&-Biimstein New Series III/26
Kaur, Gust
12 Grain and interphase boundary diffusion (Figures)
700
500
600
. ..JP
IU ‘”
400 I
600°C
[Ref. p. 708
100
200 I
300 I
m3h 10-20
lo-j2 1.1
1
1.3
1.5
1.7
2.1
1.9
2.3 ~10‘~K-’2.7
Fig 92. AI/AI,O,:X. Diffusivity sSD, of silver and zinc along an aluminum-aluminum oxide interphase boundary vs. reciprocal temperature l/T. The temperature T in “C is given at the top [69Hl]. l.25.10’3 K-’1.35 1.05 1.15 l/TFig. 91. AgfFe:X. Diffusivity s6 Di of silver, iron and antimany along a silver-iron interphase boundary vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. I.95
lo-l9 1000“C ( , lo-l91 m3/s
800
,
I
700
10-22
I
I
I
m3k
Fe-Cr-Ni/Fe-Cr-Ni- Ai : Fe
I I
b
Y
800 I,
700
I ,
I
1o-‘O lo-” I
lo-‘*
-1 1000“C 900
I
I
IO-20
.2 Irr IO‘”
10-23
t.2v) 10-2
1o-22 10-2s lo-23 0.70 0.75 0.80 0.85 0.90 0.95 1.00 40-3K-’ 1.10 l/l-
Fig 94. Fe-Cr-Ni/Fe-Cr-Ni-AI:Feand Fe-Cr-Ni-C/ M,,C:Fe. Diffusivity s6D, of iron along interphase boundaries in iron-nickel-chromium-based alloys vs. recip0.75 0.80 0.85 0.90 0.95 1.00 .10-3K” 1.10 rocal temperature l/T. The temperature Tin “C is given at l/Tthe top. Fig. 93. X/Y:Ni. Diffusivity s6D, of nickel along coppermolybdenum. cobalt-niobium carbide and nickel-niobium carbide interphase boundaries vs. reciprocal tempcraturc l/T. The temperature Tin “C is given at the top. TiIB: tilt interphase boundary, TwIB: twist interphase boundary.
Kaur, Gust
Land&-BBmslein New Series Ill,/26
12 Grain and interphase boundary diffusion (Figures)
Ref. p. 7081 KY"1 m%
I
Ge-Sn :
701
10-1'1 m%
I In
p = 0.1MPa lo-l6
lOA9 I.2 Y,
1OP
10-n
1o-22 25 w6 m3 mol 20
10-7 mV 10-c 10-g lo-'1 I 10-l' L 2 'O-l; 2 10.1:
10-l' 10-l!
10-l' ,p;
kY iid H
Fig. 97. Ge-Sn:In. Diffusion of indium in germanium-tin bicrystals: Interphase boundary diffusivitysdD, (a) and activation volume y (b) vs. twist angle C$[83Sl].
70
I 5
60
For Fig. 96 see next page.
4 Fig. 95. Ge-Sn:In. Interphase boundary diffusivity s6D, (a), pre-exponential factor (s6DJ” (b) and activation energy Qi (c) of diffusion of indium in tin-germanium bicrystals vs. twist angle 4 [81S2]. Land&-Biimstein New Series III/%
Kaur, Gust
32 Grain and interphase boundary diffusion (Figures)
702
Qi 0.5 I
0.7
I
10-l' lo-", mVs
ev 0.9 ,
10.‘3 0, $-lo-” 2 lo-”
1
1o-*O 0
1 lo-” -
[Ref. p. 708
5
15 40-f m3/mol 25
10
a
Vi90
10-s 10-s m3/s 10-7 20
kJ iii 80 30
40
I
70 kJ/mol 90
50 60 Qi -
Fig. 96. Ge-Sn:In. Pm-exponential factor (s6DJ” vs. activation energy Qi of interphase boundary diffusion of indium in germanium-tin bicrystals [81S2].
b
6
70 c;-
5
60 I
I -\I
1
5
:I:
1 I
10
17
X-
Fig. 99. Ge-Sn:In. Diffusion of indium in germanium-tin bicrystals: Interphase boundary diffusivity (s6DJsi0 vs. activation volume V, (a) and ratio of the activation volume for interphase boundary diffusion (VJ to that for volume diffusion (I’) and activation energy Qi vs. reciprocal density of coincidence lattice sites C (b) [83Sl]. p: pressure.
104 lo-” 0
250
500
I
750
I 1000 MPo1250
PFig. 98. Ge-Sn:In. Interphase boundary diffusivitys6Dr of diffusion of indium in germanium-tin bicrystals at 433.5 K vs. pressurep for a twist angle of 4” [83Sl].
Kaur, Gust
12 Grain and interphase boundary diffusion (Figures)
Ref. p. 7081 -T
IO“C IO 7c m.31s \
300
500 I
-21
10-l m3/
-22
10.
200
-
,AI-Cr : AI+Cr
10-25
1
m3/s
1
IL
AS-Au : AgI+ Au
lO-26
lo-:
1 \
lo- -23i '5 m
-T 300
703
I to" 10-l % v,
IO.-24 _
\ IO.-25 _ 10.; IO'-26 _ It-lo- -21 1.0
1.4
1.2
1.8 .lO-j K-' 2.0
1.6 l/T-
10-i
Fig. 100. Ag-Au:Ag + Au and Cu-Mg:Cu + Mg. Grain boundary chemical diffusivity ~66~ in the silver-gold and :opper-magnesium systems vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
1.5
1.7
1.9 2.1 l/T -
2.3 .@K-'
:
Fig. 101. Al-Cu:Al+ Cu and Al-Cr:Al + Cr. Grain boundary chemical diffusivity s6B, in the aluminum-copper and aluminum-chromium systemsvs. reciprocal temperature l/T. The temperature T in “C is given at the top.
-7 4.10-27,
350 "C I
m3/s
200 I
250
I
I
Au - Pd : Au : Pd
1o-27-'
I
\
For Fig. 102 seenext page.
\
\
t
I.6
Land&-BBmstein New Series III/26
1.7
1.8 I.5 l/T -
\
2sI
\ .W3K-'
Fig. 103. Au-Pd: Au + Pd. Grain boundary chemical diffusivity ~66, in the gold-palladium system vs. reciprocal tem2.2 perature l/T. The temperature T in “C is given at the top [75D3].
Kaur, Gust
12 Grain and interphase boundary diffusion (Figures)
704
10-l’ m3P
250 x=
!g\
\
-Fll+
[Ref. p. 708
-
Al-xat.“/.Zn : AI+Zn
%
lo-’ 21
4 \: \ \
HI-
10-: I its” B lo-:
lo-;
\ 10-i
10“
.l
Fig. 102. Al-x at.% Zn:Al + Zn. Grain boundary chemical diffusivity s6& in aluminum-zinc alloys vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. DC: discontinuous coarsening, DP: discontinuous precipitation.
Kaur, Gust
Landolt-BSmstein New Series III/26
Ref. p. 7081
705
12 Grain and interphase boundary diffusion (Figures)
Fig. 105. &-Be: Cu + Be. Grain boundary chemical diffusivity sSI)“, in the copper-beryllium system vs. reciprocal temperature l/T. The temperature Tin “C is given at the top b [79Tl].
c-T 500°C I I
-20 _
4.10
m3/S \
Klo ,
200 I
300 I
I
Cu-Be : Cut Be
IO‘-20
-T
._ -21 _
1CP m31s -22 _ -19
IO
-23 _
IP
-24 _
IO I 1g 10-2' Lc v)
IO-25,o-2;
\
IO-26 1.2
4-3
1.6 l/T-
1.4
K-’
,o-2:
500°C I \
24-
4.10. m3,‘S
lo- -21 _
10‘2'
Fig. 104. Cu-Ag:Cu + Ag and Cu-Zn:Cu + Zn. Grain boundary chemical diffusivity sdD”, in the copper-silver and copper-zinc systems vs. reciprocal temperature l/T. The temperature 7’ in “C is given at the top.
r
-T 400 II
I
I
300 I I
Fe-Ni : Fet Ni L
-25
IO-
f
\
I D
'2 lo- -26 VI
For Figs. 106, 107 seenext page. IO-*I-
b
Fig. 108. Fe-Ni: Fe + Ni. Grain boundary chemical diffusivity sSb, in the iron-nickel system vs. reciprocal temperature l/T. The temperature Tin “C is given at the top [79Wl]. Land&-BBmstein New Series III/26
IO-20
-
4.10-29 1.2
Kaur, Gust
1.3
1.4
1.6 l/T-
1.7
1.8 .W3K'
;
12 Grain and interphase boundary diffusion (Figures)
706
[Ref. p. 708
Fig. 106. Cu-x at.% In:Cu + In. Grain boundary chemical diffusivity sad, in the copper-indium system vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. DC: discontinuous coarsening, DP: discontinuous precipitation, BC’, BC”: bicrystals of type I and II. 4
10-l m3/
1 -I lo-'3 10 -2L
500°C
LOO
300
m3/s
1.5
1.7
1.6 l/T-
.lo-)K-'
1.9
1o-25
I rc$0-26
-1 -,o-20
lx7
m3/s 10-2' -lo-" 1o-28 - 1o-22 t
I
I
231cf
lo- :
10-29 1.2
1.2
1.3
1.4
1.5 l/l-
1.6
.lO"K-'
1.4
1.5
1.6
1.7
-101-31 c’
19
l/l-
Fig. 107. Cu-Ni:Cu + Ni. Grain boundary chemical diffusivity sSb, in the copper-nickel system vs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
Fig.109.
1.1
1.3
Fe-xat.%
Zn:Fe
+ Zn. Grain
boundary
chemi-
cal diffusivity ~66, in iron -zinc alloys vs. reciprocal temperaturc l/T. The temperature Tin “C is given at the top. DC: discontinuous coarsening, DP: discontinuous precipitation, DIGM: diffusion-induced grain boundary migration.
Kaur, Gust
Land&-BBmstein New Series III,/26
Ref. p. 7081
12 Grain and interphase boundary diffusion (Figures) -1 600
700°C
,p
m3/s
I'
-2f
I"
500 1,
I
-1 1800
2.10-l* - 2100°C
400 I
707
1500
m3/s 10-18-
. Ni-xot.%In : Ni+In
IO
1iFx?-Gl t 77
10-2'
Zr-Hf : Zr+Hf I
,o-2;
I 10-19 ,gI
I&
10-2:
2
Lo v) lF21 10-25 10-26
I
10-2' [
\
1.0
1.1
1.2 l/l-
1.3
1.4 .W3K-'
2.10-2' 0.41
1.6
Fig. 110. Ni-x at.% 1n:Ni + In. Grain boundary chemical diffusivity sSD”, in nickel-indium alloys vs. reciprocal temperature l/T. The temperature Tin “C is given at the top. DC: discontinuous coarsening, DP: discontinuous precipitation.
I 0.45
I 0.49 l/T-
0.53
.10-3K-'
0.
Fig. 111. Zr-Ca:Zr + Ca and Zr-Hf:Zr + Hf. Grain boundary chemical diffusivity sSD”, in the zirconium-calciurn and zirconium-hafnium systemsvs. reciprocal temperature l/T. The temperature Tin “C is given at the top.
-1 300 I ,
4.10-2[ m3/s lo-21
I
200 '
AL-CU : Al + Cu ---t
10-T'
m3/s IO“'
1o“8
I
,o-2i
‘2
4.w
I O-l9
I '$7 *
v) ,o-2'
o-20
lo-24
o-21
Fig. 112. Al-Cu:Al + Cu. Interphase boundary chemical diffusivity ~66~ in the aluminum-copper system vs. recipro:a1temperature l/T. The temperature Tin “C is given at the :op. Land&-Biirnstein New Series III/26
Kaur, Gust
o-22
1.2
1.4
1.6 l/T-
1.8
.,o-JjK-1
2.2
708
12.3 References for 12
12.3 References for 12 34Ll 45Ll 5lFl 5lHl 53Sl 54Hl 54K1 5401 54Tl 54Wl 54W2 55Kl 55Tl 55Wl 55Yl 56Hl 57Bl
57B2
57Hl 57Ml 58Bl 58B2 58Tl 58Ul 59Bl 59B2 59B3 59Cl 59Dl 59Gl 5962 59Hl 59Ll 59L2
Lan_mnuir,I.: J. Franklin Inst. 217 (1934) 543. van Liempt, A.M.: Rec. Trav. Chim. Pays-Bas 64 (1945) 239 (subsidiary reference cited after [71Tl]). Fisher, J.C.: J. Appl. Phys. 22 (1951) 74. Hoffman, R.E., Turnbull, D.: J. Appl. Phys. 22 (1951) 634. Shim, G.A., Wajda, ES., Huntington, H.B.: Acta Metall. 1 (1953) 513 (subsidiary reference cited after [54W2]). Hendrickson, A.A., Machlin, ES.: Trans. AIME 200 (1954) 1035. Kuper, A., Letaw, Jr., H., Slifkin, L., Sonder, E., Tomizuka, C.T.: Phys. Rev. % (1954) 1224 (subsidiary reference). Okkerse, B.: Acta Metall. 2 (1954) 551. Turnbull, D., Hoffman, R.E.: Acta Metall. 2 (1954) 419. Whipple, R.T.P.: Philos. Mag. 45 (1954) 1225. Wajda, E.S.: Acta Metall. 2 (1954) 184. Kuper, A., Letaw, Jr., H., Slifkin, L., Sonder, E., Tomizuka, C.T.: Phys. Rev. 98 (1955) 1870 (subsidiary reference). Turnbull, D.: Acta Metall. 3 (1955) 55. Wajda, E.S., Shirn, G.A., Huntington, H.B.: Acta Metall. 3 (1955) 39. Yukawa, S., Sinnot, M.J.: Trans. AIME 203 (1955) 996. Hoffman, R.E., Pikus, R.F., Ward, R.A.: Trans. AIME 206 (1956) 483 (subsidiary reference cited after [58Ul]). Bokshtein, S.Z., Kishkin, ST., Moroz, L.M.: Radioisotopes in Scientific Research, Proc. Int. Conf., Paris 1957, Vol. I, R.C. Extermann (ed.), London: Pergamon Press 1958, p. 232; Study of the Structure of Metals by the Method of Radioactive Isotopes, Moscow: State Publishers for Defence Industry 1959, p. 181. Bokshtein, S.Z., Kishkin, S.T., Moroz, L.M.: Zavod. Lab. 23 (1957) 316; Radioisotopes in Sci. Res., Proc. Int. UNESCO Conf., Vol. I, R.C. Extermann (ed.), London: Pergamon Press 1958, p. 232; Study of the Structure of Metals by the Method of Radioactive Isotopes, Moscow: State Publishers for Defence Industry 1959, p. 184. Hino, J., Tomizuka, C., Wert, C.: Acta Metall. 5 (1957) 41 (subsidiary reference cited after [7782]). Makin, S.M., Rowe, A.H., Le Claire, A.D.: Proc. Phys. Sot. London 70 (1957) 545 (subsidiary reference). Bokshtein, B.S., Magidson, I.A., Svetlov, 1.1.:Phys. Met. Metallogr. (English Transl.) 6 (6) (1958) 81. Borisov, V.T., Golikov, V.M., Ljubov, B.Y., Shcherbedinsky, G.V.: Research with Radioisotopes in Physics and Industry, Proc. UNESCO Int. Conf. on Radioisotopes in Scientific Research, Vol. I, R.C. Extermann (ed.), London: Pergamon Press 1958, p. 212. Turnbull, D., Treaftis, H.N.: Trans. AIME 212 (1958) 33. Upthegrove, W.R., Sinnot, M.J.: Trans. ASM 50 (1958) 1031. Bokshtein, B.S., Kishkin, S.T., Moroz, L.M.: Study of the Structure of Metals by the Method of Radioactive Isotopes, Moscow: State Publishers for Defense Industry 1959, p. 181 and 186. Bokshtein, B.S., Kishkin, S.T., Moroz, L.M.: Study of the Structure of Metals by the Method of Radioactive Isotopes, Moscow: State Publishers for Defence Industry 1959, p. 187. Bokshtein, B.S., Kishkin, ST., Moroz, L.M.: Study of the Structure of Metals by the Method of Radioactive Isotopes, Moscow: State Publishers for Defence Industry 1959, p. 198. Cahn. J.W.: Acta Metall. 7 (1959) 18. Dubovtsev, R.M., Zotov, VS.: Tsvetn. Met. 1959, p. 67. Gertsriken, S.D., Pryanishnikov, M.R.: Issled. Zharoprochn. Splav. 4 (1959) 123. Gertsriken, S.D., Yatsenko, T.K., Slastnikova, L.F.: Probl. Metalloved. Fiz. Met. (Vopr. Fiz. Metalf. Metalloved.), Akad. Nauk Ukr. SSR 9 (1959) 154. Hilliard, J.E., Averbach, B.L., Cohen, M.: Acta Metall. 7 (1959) 86 (subsidiary reference cited after [74Hl]). Leymonie, C., Adda, Y., Kirianenko, A., Lacombe, P.: C.R. Acad. Sci. Paris 248 (1959) 1512; Leymonie, C., Lacombe, P.: Mem. Sci. Rev. Met. 57 (1960) 285. Leymonie, C., Lacombc, P.: Mem. Sci. Rev. Met. 56 (1959) 74; Guiraldenq, P., Lacombe, P.: 4th Colloque de Metalurgie, Saclay 1960, Properties of Grain Boundaries, PressesUniversitaire de France 1961, p. 105; Acta Metall. 13 (1965) 51; Lacombe, P., Guiraldenq, P., Leymonie, C.: RaKaur, Gust
Land&-BBmstein New Series 111126
12.3 References for 12
60Al 60Gl 60G2 60Hl 6OLl 6OL2 60Ml 6001 6lBl 6lB2 61Gl 61Hl 61Ll 61Ml 61M2 61Rl 61Sl 61S2 61S3 61S4 62Bl 62Cl 62Hl 62Ll 63Cl 63Dl 63Gl 63Jl 63Ll 63L2 63Sl 64Bl 64Jl 64Ll 65Al 65A2 65A3 65Bl 65Cl 65Gl
709
dioisotopes in the Physical Sciencesand Industry, Proc. IAEA and UNESCO Conf., Copenhagen 1960, Vol. I, Vienna: IAEA 1962, p. 179. Ainslie, N.G., Seybolt, A.U.: J. Iron Steel Inst. 194 (1960) 341; Seibel, G.: Mem. Sci. Rev. Met. 61 (1964) 413 (subsidiary references cited after [68Rl, 68Al]). Gertsriken, S.D., Revo, A.L.: Phys. Met. Metallogr. (English Transl.) 9 (4) (1960) 92. Guiradenq, P., Lacombe, P. : Properties of Grain Boundaries, 4th Colloque de Metallurgie, Saclay 1960, Paris: PressesUniversitaires de France 1961, p. 14. Hudson, J.B. et al. : Aeronautical Research Laboratory Technical Report 60-321 (Contract No. AF 33 (616)-5951), Whright Air Development Centre, Deyton, Ohio (subsidiary reference cited after [6682]). Levine, H.S., MacCallum, C.J.: J. Appl. Phys. 31 (1960) 595. Lazarus, D.: Solid State Physics, Vol. 10, New York: Academic Press 1960, p. 117 (subsidiary reference cited after [69Ll]). Mortlock, A.J., Rowe, A.H., Le Claire, A.D.: Philos. Mag. 5 (1960) 803 (subsidiary reference cited after [78Ml]). Ovsienko, D.Y., Zasimuk, I.K.: ,Phys. Met. Metallogr. (English Transl.) 10 (5) (1960) 743. Bolk, A.: Acta Metall. 9 (1961) 643 (subsidiary reference cited after [78Ml]). Buffington, ES., Hirano, K., Cohen, M.: Acta Metall. 9 (1961) 434 (subsidiary reference cited after [74Jl]). Gertsriken, S.D., Yatsenko, T.K.: Sb. Nauchn. Rabot Inst. Metallofiz., Akad. Nauk Ukr. SSR 12 (1961) 135. Harrison, L.G.: Trans. Faraday Sot. 57 (1961) 1191. Lange, W., HilJner, A., Berthold, I.: Phys. Status Solidi l(l961) 50 (subsidiary reference cited after [62Ll]). Mullen, J.G.: Phys. Rev. 121 (1961) 1649 (subsidiary reference cited after [74Jl]). Murphy, J.B.: Acta Metall. 9 (1961) 563 (subsidiary reference cited after [69B2] and [70Gl]). Revo, A.L.: Phys. Met. Metallogr. (English Transl.) 11 (5) (1961) 77. Suzuoka, T.: Trans. Jpn. Inst. Met. 2 (1961) 25. Sobaszek,A.: Zesz. Nauk. Polit. Warsz., Elektryka 23 (1961) 17 (for Q); Zimija, J.: II Krajowe Symp. Zast. Izot, Techn. Spala 1963 (for 0’) (subsidiary reference cited after [68Sl]). Suzuoka, T.: Jpn. Inst. Met. 2 (1961) 176. Sze, S.M., Wei, L.Y: Phys. Rev. 124 (1961) 84. Blackburn, D.A., Brown, A.F.: J. Inst. Met. 91 (1962/63) 106. Cabone, J.: J. Chem. Phys. 59 (1962) 1135. HBBner, A.: Ph.D. Thesis Technical Univ. Dresden, DDR 1962 (subsidiary reference cited after [66Bl]). Lange, W., Bergner, D.: Phys. Status Solidi 2 (1962) 1410: Bergner, D., Lange, W.: Phys. Status Solidi 18 (1966) 67. Coble, R.L.: J. Appl. Phys. 34 (1963) 1679. Dengel, O., Riehl, N.: Phys. Condens. Mater. 1 (1963) 191 (subsidiary reference cited after [7OJl]). Gruzin, P.L., Mural, V.V.: Fiz. Met. Metalloved. 16 (1963) 551 (subsidiary reference cited after [72R2, 72R3]). Johnson, D.L., Cutler, LB.: J. Am. Ceram. Sot. 46 (1963) 541, 545. Le Claire, A.D.: Brit. J. Appl. Phys. 14 (1963) 351. Love, G., Shewmon, P.G.: Acta Metall. 11 (1963) 899. Shinyayev, A.Y: Phys. Met. Metallogr. (English Transl.) 15 (1) (1963) 93. Borisov, V.T., Golikov, V.M., Shcherbedinsky, G.V.: Phys. Met. Metallogr. (English Transl.) 17 (6) (1964) 80. Johnson, D.L., Clarke, T.M. : Acta Metall. 12 (1964) 1173. Lange, W., HBBner, A., Mischer, G.: Phys. Status Solidi 5 (1964) 63. Andelin, A.L., Knight, J.D., Cahn, M.: Trans. AIME 233 (1965) 19; Danneberg, W.: Metal1 15 (1961) 977 (subsidiary reference cited after [67Kl]). Agarwala, R.P., Murarka, S.P., Anand, M.S.: Trans. AIME 233 (1965) 986. Aucouturier, M., Lacombe, P. : Kobalt 28 (1965) 111. Bokshtein, S.Z., Bronfin, M.B., Kishkin, S.T.: Diffusion Processes, Structure and Properties of Metals, S.Z. Bokshtein (ed.) New York: Consultants Bureau 1965, p. 16. Cordes, H., Kim, K.: Z. Naturforsch. 20 a (1965) 1197 (subsidiary reference cited after [68Hl]). Gibbs, G.B. : Mem. Sci. Rev. Met. 62 (1965) 941 (subsidiary reference cited after [74H2]).
Land&BBmstein New Series III/26
Katir, Gust
710 j5G2 SC3 SC4 55Jl 55Sl 55Wl 56Al 56Bl 56B2 56B3 56B4 56Dl 56Fl 56F2 56Sl 56S2 66S3 56Yl 67Bl 67Fl 67Gl 6762 67Hl 67Kl 67K2 67K3 67K4 6701 67Vl 68Al 68A2 68Bl 68Cl 68Fl 68F2 68F3 68Gl 68Hl 68Kl 68P1 68Rl 68Sl 68S2 68S3 6834 69Bl
12.3 References for 12 Gubareva, M.A., Moroz, L.M.: Diffusion Processes,Structure and Properties of Metals, S.Z.Bokshtein (ed.), New York: Consultants Bureau 1965, p. 9. Guiraldenq, P., Lacombe, P. : Acta Metall. 13 (1965) 51. Geguzin, YE., Dobrovinskaya, E.R.: Sov. Phys. Solid State (English Transl.) 7 (1965) 1660 (subsidiary reference cited after [6762]). James,D.W., Leak, G.M.: Philos. Mag. 12 (1965) 491. Sparke, B., James,D.W., Leak, G.M.: J. Iron Steel Inst. 203 (1965) 152 (subsidiary reference cited after [65Jl]). Wazzan, A.R. : J. Appl. Phys. 36 (1965) 3596. Alcock, C.B., Hawkins, R.J., Hills, A.W.D., McNamara, P.: Thermodynamics, Proc. Symp. Thermodynamics with Emphasis on Nuclear Materials and Atomic Transport in Solids, Vol. 2, Vienna: IAEA 1966, p. 57. Bergner, D., Lange, W.: Physl Status Solidi 18 (1966) 75. Bartha, L.: Z. Metallkde. 6 (1966) 482. Bergner, D., Lange, W.: Phys. Status Solidi 18 (1966) 67. Bokshtein, S. Z., Zhukhovitskiy, A.A., Kishkin, S.T., Moroz, L.M., Chaplygina, V.S.: Russ. Metall. (English Transl.) 6 (1966) 42. Dobrovinskaya, E.R., Podorozhanskaya, N.M.: Ukr. Fiz. Zh. 11 (1966) 227 (subsidiary reference cited after [6762]). Farnsworth, P.L., Coble, R.L.: J. Am. Ceram. Sot. 49 (1966) 264. Fedorov, G.B., Smirnov, Y.A., Zshomov, F.I.: Metall. Metalloved. Chist. Met. 5 (1966) 92. Stark. J.P., Upthegrove, W.R.: Trans. ASM 59 (1966) 479. Schroerschwarz, R., Lindner, R.: Radiochim. Acta 6 (1966) 190. Stark, J.P., Upthegrove, W.R.: Trans. ASM 59 (1966) 486. Yajima, S., Furuya, H., Hirani, T.: J. Nucl. Mater. 20 (1966) 162. Bernstein, I.M.: Trans. AIME 239 (1967) 1518. Fedorov, G.B., Smirnov, YA.: Metall. Metalloved. Chist. Met. 6 (1967) 181. Ghoshtagore, R.N.: Phys. Rev. 155 (1967) 603. Geguzin, Y.E., Dobrovinskaya, E.R., Lev, I.E., Mozharov, M.V.: Sov. Phys. Solid State (English Transl.) 8 (1967) 2599. Huntz, A.M., Aucouturier, M., Lacombe, P.: C.R. Acad. Sci. Paris 265 (1967) 554. Kreider, K.G., Bruggeman, G.: Trans. AIME 239 (1967) 1222. Kaygorodov, V.N., Rabovskiy, Y.A., Talinskiy, V.K.: Phys. Met. Metallogr. (English Transl.) 24 (1) (1967) 114. Kaygorodov, V.N., Rabovskiy, Y.A., Talinskiy, V.K.: Phys. Met. Metallogr. (English Transl.) 24 (4) (1967) 68. Kaygorodov, V.N., Rabovskiy, Y.A., Talinskiy, V.K.: Phys. Met. Metallogr. (English Transl.) 24 (4) (1967) 661 (subsidiary reference cited after [7lB3]). Ogawa. S., Nakagawa, Y.: J. Phys. Sot. Jpn. 23 (1967) 179. Villaine, R. : Ph.D. Thesis, Univ. Grenoble, France 1967 (subsidiary reference cited after [75Rl I). Aucouturier, M., Araki, T., Rosso, T., Lacombe, P.: Mem. Sci. Rev. Met. 65 (1968) 255. Aaron. H.B., Aaronson, H.I.: Acta Metall. 16 (1968) 789. Bruggeman, G., Roberts, J.: J. Met. 20 (1968) 54 (subsidiary reference cited after [7lB3]). Chatterjee, A., Fabian, D.J.: J. Inst. Met. 96 (1968) 186. Fedorov, G.B., Smirnov, YA., Moiseenko, S.S.: Metall. Metalloved. Chist. Met. 7 (1968) 124. Furuya, H., Yajima, S.: J. Nucl. Mater. 25 (1968) 38. Furuya, H.: J. Nucl. Mater. 26 (1968) 123. Geguzin, YE., Dobrovinskaya, E.R., Lev, I.E., Melamud, M.D.: Ukr. Fiz. Zh. 13 (1968) 1972. HlOner, A., Voigt, G.: Z. Metallkde. 59 (1968) 559; Hafiner, A.: Isotopenpraxis 5 (1969) 143. Kaygorodov, V.N., Klotsman, S.M., Timofeyev, A.N., Trakhtenberg, I.S.: Phys. Met. Metallogr. (English Transl.) 25 (5) (1968) 910. Petermann, J., Hornbogen, E.: Z. Metallkde. 59 (1968) 814. Rosso, T., Aucouturier, M., Lacombe, P.: Ser. Metall. 2 (1968) 393. Sobaszek,A.: Nukleonika 13 (1968) 279. Sobaszek,A.: Phys. Status Solidi 26 (1968) K59. Smith, A.F., Gibbs, G.B.: Met. Sci. J. 2 (1968) 47. Speich. G.R.: Trans. AIME 242 (1968) 1359. Bartha, L., Szalay, T.: J. Appl. Rad. Isotop. 20 (1969) 825. Kaur, Gust
Land&B6mstein New Series III!26
12.3 References for 12 69B2 69Cl 69C2 69Dl 69Gl 69Hl 69H2 69H3 69Kl 69K2 69K3 69Ll 69Ml 69M2 69Rl 69Sl 6982 6921 6922 70Bl 70B2 70Gl 7OJl 70Kl 70K2 7OLl 70Ml 7OPl 70Rl 7OSl 7021 71Bl 71B2 71B3 71Cl 71Gl 71Hl 71Jl 71Kl 71Ll 71Ml 71Pl 71Tl 72Al 72Bl 72Cl 72Gl
711
Brailsford, A.D., Aaron, H.B.: J. Appl. Phys. 40 (1969) 1702. Cannon, R.F., Stark, J.P.: J. Appl. Phys. 40 (1969) 4366. Chatterjee, A., Fabian, D.J.: Acta Metall. 17 (1969) 1141. Desestret, A., Froment, M., Guiraldenq, P. : C.R. Acad. Sci. Paris C 269 (1969) 1505; seealso [78A2]. Gunther, F., HBBner, A., Oppermann, L. : Isotopenpraxis 5 (1969) 461. HSiBner,A., Jurisch, M., Lange, W.: Z. Metallkde. 60 (1969) 219. HSiBner,A.: Isotopenpraxis 5 (1969) 143; Krist. Tech. 8 (1973) Kl, 9 (1974) 1371. Huntz, A.M., Guiraldenq, P., Aucouturier, M., Lacombe, P. : Mem. Sci. Rev. Met. 66 (1969) 86. Kaygorodov, V.N., Klotsman, SM., Timofeyev, A.N., Trakhtenberg, I.S. : Phys. Met. Metallogr. (English Transl.) 27 (6) (1969) 91. Kaygorodov, V.N., Klotsman, S.M., Timofeyev, A.N., Trakhtenberg, I.S. : Phys. Met. Metallogr. (English Transl.) 28 (6) (1969) 128. Klotsman, S.M., Rabovskiy, Y.A., Talinskiy, V.K., Timofeyev, A.N.: Phys. Met. Metallogr. (English Transl.) 28 (6) (1969) 66. Larikov, L.N., Chernaya, L.F., Shmatko, O.A.: Metallofizika 28 (1969) 85. Marin, J.F., Contamin, P.: J. Nucl. Mater. 30 (1969) 16 (subsidiary reference). Mehrer, H., Seeger,A.: Phys. Status Solidi 35 (1969) 313 (subsidiary reference cited after [74H2]). Rothman, S.J., Peterson, N.L., Robinson, J.T.: Phys. Status Solidi 35 (1969) 305 (subsidiary reference). Suzuki, H., Kimura, S., Hase, T., Tsuchie, Y.: Bull. Tokyo Inst. Technol. 90 (1969) 105. Smith, A.F., Gibbs, G.B.: Met. Sci. J. 3 (1969) 93. Zemskiy, S.V., Kupalova, I.K.: Phys. Met. Metallogr. (English Transl.) 27 (2) (1969) 119. Zemskiy, S.V., Kupalova, I.K.: Phys. Met. Metallogr. (English Transl.) 27 (2) (1969) 315. Burton, B., Greenwood, G.W.: Met. Sci. J. 4 (1970) 215. Barreau, G., Brunel, G., Cizeron, G., Lacombe, P.: CR. Acad. Sci. Paris C 270 (1970) 516; Mem. Sci. Rev. Metall. 68 (1971) 357. Goldman, J., Aaronson, H.I., Aaron, H.B.: Metall. Trans. 1 (1970) 1805. Jellinek, H.H.G., Juznic, K.: Phys. Status Solidi (a) 2 (1970) 837. Klotsman, S.M., Rabovskiy, Y.A., Talinskiy, V.K., Timofeyev, A.N.: Phys. Met. Metallogr. (English Transl.) 29 (4) (1970) 127. Krishtal, M.A., Mokrov, A.P., Stepanova, O.V., Goncharenko, LA.: Prot. Coat. Met. 2 (1970) 169. Lazarev, V.A., Golikov, V.M.: Phys. Met. Metallogr. (English Transl.) 29 (3) (1970) 154; 31(4) (1971) 213. Marin, J.F.: J. Nucl. Mater. 34 (1970) 348. Peterson, N.L., Rothman, S.J.: Phys. Rev. 18 (1970) 3624 (subsidiary reference). Renouf, T.J.: Philos. Mag. 22 (1970) 359. Sandadze, V.V., Tatrishvili, K.G. : Tr. Nauchn. Tekhn. Konf. Prof.-Preprodavat Nauch. Rabotn. Probl. Otrasl. Labor. Gruz. Politehn. Inst. 15 (1970) 107; cited from Defect and Diffusion Data 6 (1972) 563. Zemskiy, S.V., Grigorkin, V.I., Moskaleva, L.N.: Izv. Vyshch. Ucheb. Zaved. Chern. Metall. 13 (1970) 86. Buhsmer, C.P., Crayton, P.H.: J. Mater Sci. 6 (1971) 981. Butz, R., Erley, W., Wagner, H.: Phys. Status Solidi (a) 7 (1971) K5. Bondy, A., Regnier, P., Levy, V.: Ser. Metall. 5 (1971) 345. Cheetham, D., Ridley, N.: J. Inst. Met. 99 (1971) 371, Gruzin, P.L., Mural, VV., Fokin, A.P.: Phys. Met. Metallogr. (English Transl.) 32 (1) (1971) 226. Hoshino, Y, Araki, T.: Trans. Natl. Res. Inst. Met. 13 (1971) 99. Jellinek, H.H.G., Chatterjee, A.K.: Phys. Status Solidi (a) 4 (1971) 173. King, A.D.: J. Nucl. Mater. 38 (1971) 347. Lazarev, VA., Golikov, V.M.: Phys. Met. Metallogr. (English Transl.) 31 (4) (1971) 213. Mulyakaev, L.M., Shcherbedinskii, G.V., Dubinin, G.N. : Metalloved. Term. Obrab. Met. 8 (1971) 45. Paul, A.R., Agarwala, R.P.: Metall. Trans. 2 (1971) 2691. Tyshkevich, V.M.: Mttallofizika 37 (1971) 58. Austin, J.S., Elleman, T.S. : J. Nucl. Mater 43 (1972) 119 (subsidiary reference cited after [73C2]). Burton, B., Reynolds, G.L.: J. Nucl. Mater. 45 (1972/73) 10. Chen, W.K., Peterson, N.L.: J. Phys. Chem. Solids 33 (1972) 881 (subsidiary reference). Gorbachev, V.A., Klotsman, S.M., Rabovskiy, Y.A., Talinskiy, V.K., Timofeyev, A.N.: Phys. Met. Metallogr. (English Transl.) 34 (4) (1972) 202 (subsidiary reference).
Land&Biimstein New Series III/26
Kaur, Gust
712 7262 72M1 72Pl 72P2 72Rl 72R2 72R3 72Sl 72Wl 73Bl 73Cl 73C2 73Gl 7362 7363 7364 73Hl 73Ml 73Pl 73P2 73Sl 74Al 74Gl 74Hl 74H2 74H3 74Jl 74Kl 74Ll 74Sl 74Vl 75Al 75Bl 75c1 75Dl 75D2 75D3 75Gl 75Hl 75Kl 75Ml 75M2 75Pl 75Rl 75Sl 75S2 75s3 75Tl 75Vl 76Al
12.3 References for 12
1
Gruzin, P.L., Mural, V.V., Fokin, A.P.: Phys. Met. Metallogr. (English Transl.) 34 (6) 1972) 209. Mehrer, H., Seeger,A. : Cryst. Lattice Defects 3 (1972) 1 (subsidiary reference cited after [SOGII). Predel, B., Frebel, M.: Acta Metall. 20 (1972) 1259. Predel, B., Frebel, M.: Arch. Eisenhiittenwesen 43 (1972) 839; Metal1 27 (1973) 460. Robinson, J.T., Peterson, N.L.: Surf. Sci. 31 (1972) 586. Rosso, T., Sabatini, C.: Ser. Metall. 6 (1972) 51. Rosso, T., Torti, G., Colombo, R.L.: Mem. Sci. Rev. Met. 69 (1972) 875. Sinha, A.K., Sinha, U.P., Godkhindi, M.M., Balasubramanian, V.: Ser. Metall. 6 (1972) 495. Woolfrey, J.L.: J. Am. Ceram. Sot. 55 (1972) 383. Budurov, S., Russev, K., Zlateva, G., Petrov, R.: Z. Metallkde. 64 (1973) 372. Chen, W.K., Peterson, N.L., Robinson, L.C.: J. Phys. Chem. Solids 34 (1973) 705 (subsidiary reference cited after [8OCl, 86A2]). Calder, R.D., Elleman, T.S., Verghese,K.: J. Nucl. Mater. 46 (1973) 46. Gordon, R.S.: J. Am. Ceram. Sot. 56 (1973) 147. Gupta, D.: J. Appl. Phys. 44 (1973) 4455. Gupta, D.: Phys. Rev. B 7 (1973) 586. Guiraldenq, P., Poyet, P.: Mem. Sci. Rev. Met. 79 (1973) 715. Huntz, A.M.: Mem. Sci. Rev. Met. 70 (1973) 81; Chaix, F., Huntz, A.M.: Mem. Sci. Rev. Met. 71 (1974) 115. Moya-Gontier, G.E., Moya, F.: Acta Metall. 21 (1973) 701. Perkins, R.A., Metall. Trans. 4 (1973) 1665. Perkins, R.A., Padgett jr., R.A., Tunali, N.K.: Metall. Trans. 4 (1973) 2535. Sidorenko, V.M., Sidorak, 1.1.: Fiz. Khim. Mekh. Mater. 9 (1) (1973) 52. Assassa,W., Guiraldenq, P., C.R. Acad. Sci. Paris C 279 (1974) 59. Gupta, D., Asai, K.W.: Thin Solid Films 22 (1974) 121. HBgner, A.: Krist. Tech. 9 (1974) 1371. HBBner, A.: Krist. Tech. 9 (1974) 1374. Huntz, A.M., Lacombe, P.: Can. Met. Quart. 13 (1974) 155; seealso: Huntz, A.M. [73Hl]. Job, B., Mathie, J., Regnier, P.: Acta Metall. 22 (1974) 1197. Kozma, L., Riedel, M.M., Bartha, L.: Phys. Status Solidi (a) 26 (1974) 711. Lesage, B., Huntz, A.M.: J. Less-Common Met. 38 (1974) 149. Sidorak, II., Sidorenko, V.M., Fiz. Khim. Mekh. Mater. 10 (1) (1974) 34. Vishnevskii, II., Aksel’rod, E.I., Tal’yanskaya, N.D.: Izv. Akad. Nauk SSSR, Neorg. Mater. 10 (1974) 1094. Assassa,W., Guiraldenq, P., Beaunier, L., Froment, M.: J. Phys. (Paris) C4 3 (1975) 225. Brik, V.B., Larikov, L.N., Fal’chenko, V.M.: Ukr. Fiz. Zh. 20 (1975) 397. Campbell, D.R., Tu, K.T., Schwenker, R.O.: Thin Solid Films 25 (1975) 213. de Reca, N.W., Pampillo, C.A.: Ser. Metall. 9 (1975) 1355. Danyluk, S., McGuire, G.E., Koliwad, K.M., Yang, M.G.: Thin Solid Films 25 (1975) 483. DeBonte, WJ., Poate, J.M.: Thin Solid Films 25 (1975) 441; Poate, J.M., Turner, P.A., DeBonte, W.J., Yahalom, J.: J. Appl. Phys. 46 (1975) 4275. Gupta, D., Rosenberg, R.: Thin Solid Films 25 (1975) 171. Ho, E., Weatherly, G.C.: Acta Metal]. 23 (1975) 1451. Klotsman, S.M., Arkhipova, N.K., Timofeyev, A.N., Trakhtenberg, IS. : Phys. Met. Metallogr. (English Transl.) 20 (1975) 70. Mody, M.N., Balasubramanian, V., Tendolkar, G.S.: Sci. Sintering 7 (1975) 221. Marchive, D., Juve-Due, D., Treheux, D., Guiraldenq, P.: C.R. Acad. Sci. Paris C 280 (1975) 25. Predel, B., Gust, W.: Metall. Trans. A 6 (1975) 1237. Routbort, J.L., Matzke, H.: J. Am Ceram. Sot. 58 (1975) 81. Smith, A.F.: Met. Sci. J 9 (1975) 375. Smith, A.F.: Z. Metallkde. 66 (1975) 692. Schwitzgebel, G., Michael, P., Zohdi, Y: Acta Metall. 23 (1975) 1551. Treheux, D., Heurtel, A., Guiraldenq, P.: C.R. Acad. Sci. Paris C 280 (1975) 1192; Acta Metall. 24 (1976) 503. Vladimirov, A.B., Kaygorodov, V.N., Klotsman, S.M., Symbelov, V.D., Trakhtenberg, I.S.: Phys. Met. Metallogr. (English Transl.) 39 (1) (1975) 78. Aleshin, A.N., Bokshtein, B.S., Shvindlerman, L.S.: Izv. Vyshch. Uchebn. Zaved. Chern. Metall. 9 (1976) 138.
Kaur, Gust
Land&BGmstein New Series III/26
12.3 References for 12 76Cl 76Hl 76H2 76H3 7611 76Ll 76Ml 76M2 7601 76Sl 7682 7683 76Tl 7621 77Al 77A2 77Bl 77Cl 77Dl 77D2 77Hl 77H2 77H3 77H4 77H5 77Kl 77Ll 77Ml 77Pl 78Al 78A2 78Cl 78Gl 78Hl 78Jl 78Ml 78Sl 78S2 79Al 79A2 79Dl 79Fl 79Gl
713
Chang, C.C., Quintana, G.: Thin Solid Films 31 (1976) 265. Hall, P.M., Morabito, J.M.: Surf. Sci. 59 (1976) 624. Harris, L.B., Fiasson, J.: Phys. Status Solidi 37 (1976) 697; Harris, L.B.: J. Phys. (Paris) C7 37 (1976) 365. Holloway, P.H., Amos, D.E., Nelson, G.C. : J. Appl. Phys. 47 (1976) 3769. Ishida, Y, Iida, F., Koyama, N., Shimizu, H.: Ser. Metall. 10 (1976) 1021; Seisan Kenkyu 28 (1976) 31. Lesage, B., Huntz, A.M.: Mem. Sci. Rev. Met. 73 (1976) 19. Maier, K., Mehrer, H., Lessman, E., Schiile, W: Phys. Status Solidi (b) 78 (1976) 689 (subsidiary reference cited after [88Nl]). Majni, G., Ottaviani, G., Prudenziati, M.: Thin Solid Films 38 (1976) 15. Okabe, T., Hines, A.L., Hochman, R.F.: J. Appl. Phys. 47 (1976) 49. Sun, P.H., Ohring, M. : J. Appl. Phys. 47 (1976) 478. Schwitzgebel, G.: Z. Phys. Chem. NF 99 (1976) 217. Smithells, C.J.: Metals Reference Book, London: Butterworths 1976 (subsidiary referencecited after [83L2]). Treheux, D., Heurtel, A., Guiraldenq, P.: Acta Metall. 24 (1976) 503. Zemskiy, S.V., L’vov, VS., Makashova, L.S.: Phys. Met. Metallogr. (English Transl.) 41 (4) (1976) 85. Aleshin, A.N., Bokshtein, B.S., Shvindlerman, L.S.: Sov. Phys. Solid State (English Transl.) 19 (1977) 2051. Assassa,W., Guiraldenq, P.: Met. Corros. Ind. 621 (1977) 170. Bleay, J., Salthouse, P.W, Sherwood, J.N.: Philos. Mag. 36 (1977) 885. Chamberlain, M.B., Lehozky, S.L.: Thin Solid Films 45 (1977) 189. Decker, D.L., Weiss,J.D., Yanfleet, H.B.: Phys. Rev. B 16 (1977) 2392 (subsidiary reference cited after [82Kl]). Demel, 0.: Radex-Rundschau 2 (1977) 201. Hettich, G., Mehrer, H., Maier, K.: Ser. Metall. 11 (1977) 795 (subsidiary reference). HilJner, A. : Wiss. Z. Techn. Hochschule Karl-Marx-Stadt, DDR 19 (1977) 619. Hanatate, Y, Majima, K., Mitani, H. : J. Jpn. Inst. Met. 41 (1977) 1211; Hanatate, H., Majima, K., Mitani, H.: Trans. Jpn. Inst. Met. 19 (1978) 669. Hirota, K., Komatzu, W.: J. Am. Ceram. Sot. 60 (1977) 105. Houska, C.R., Dietrich, F., Subbaraman, G.: Thin Solid Films 44 (1977) 217. Kazmerski, L.L., Cooper, R.B., White, F.R., Merrill, A.J.: IEEE Trans. Electron Devices 24 (1977) 496. Lessing, P.A., Gordon, R.S. : J. Mater. Sci. 12 (1977) 2291. Majima, K., Orito, S., Mitani, H.: J. Jpn. Inst. Met. 41 (1977) 1207; Majima, K., Mitani, H.: Trans. Jpn. Inst. Met. 19 (1978) 663. Pruthi, D.D., Anand, M.S., Agarwala, R.P. : J. Nucl. Mater. 64 (1977) 206. Aleshin, A.N., Aristov, V.Y., Bokshtein, B.S., Shvindlerman, L.S.: Phys. Status Solidi (a) 45 (1978) 359. Assassa,W, Guiraldenq, P.: Met. Sci. 12 (1978) 123. Chongmo, L., Hillert, M.: Acta Metall. 26 (1978) 333. Gas, P., Bernardini, J.: Surf. Sci. 72 (1978) 365. Holloway, P.H., McGuire, G.E.: J. Electrochem. Sot. 125 (1978) 2070. Juve-Due, D., Treheux, D., Guiraldenq, P.: Ser. Metall. 12 (1978) 1107; Mater. Sci. Eng. 42 (1980) 281. McGuire, G.E., Wisseman, W.R., Holloway, P.H. : J. Vat. Sci. Technol. 15 (1978) 1701. Scheidecker, R.W., Berard, M.F. : J. Am. Ceram. Sot. 61 (1978) 399. Spindler, P., Nachtrieb, K.N.: Metall. Trans. A 9 (1978) 763. Atkinson, A., Taylor, R.I.: Philos. Mag. A 39 (1979) 581. Aufray, B., Cabane-Brouty, F., Cabane, J.: Acta Metall. 27 (1979) 1849; Aufray, B., Gas, P., Bernardini, J., Cabane-Brouty, F.: Ser. Metall. 14 (1980) 1279. Delaunay, D., Huntz, A.M., Lacombe, P.: Ser. Metall. 13 (1979) 419. Fedorov, G.B., Zhomov, F.I., Smirnov, YA., Sokolov, N.A., Ediberidze, G.I.: Metall. Metalloved. Chist. Met. 13 (1979) 133. Golikov, V.M., Kogan, L.I., Novikov, B.A., Entin, R.I. : Phys. Met. Metallogr. (English Transl.) 45 (5) (1979) 141.
Land&-Bihstein New Series III/26
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714 79Hl 79H2 79Kl 79Ml 7901 79Rl 79Sl 79s2 79Tl 79Vl 79V2 79Wl 7921 80Al 80A2 8OC1 8OC2 80Gl 80G3 80G4 80G5 80Hl 8OJl 80Ml 8OWl 81Al 81Bl 81B2 81B3 81B4 81B5 81B6 81Gl 81G2 8101 81Rl 81Sl 81S2 81Tl 81T2 81Vl 82Al 82Bl 82B2
12.3 References for 12 Hong. J.D., Hon, M.H., Davis, R.F.: Ceramurgia Int. 5 (4) (1979) 155; Hon, M.H., Davis, R.F.: J. Mater. Sci. 14 (1979) 2411. Hwang. J.C.M., Balluff, R.W.: J. Appl. Phys. SO(1979) 1349. Kazmerski, L.L.: Thin Solid Films 57 (1979) 99. Moulin, P., Huntz, A.M., Lacombe, P.: Acta Metall. 27 (1979) 1431. Oishi, Y., Ichimura, H.: J. Chem. Phys. 71 (1979) 5134. Reynolds, G.L., Burton, B.: J. Nucl. Mater. 82 (1979) 22. Schoen, J.M., Poate, J.M., Doherty, C.J., Melliar-Smith, CM.: J. Appl. Phys. 50 (1979) 6910. Smithells, C.J. (ed.): Metals Reference Book, London: Butterworths 1979, p. 937 (subsidiary reference cited after [83B3]). Tsubakino, H., Nozato, R.: J. Jpn. Inst. Met. 43 (1979) 42. Vladimirov, A.B., Kaygorodov, V.N., Klotsman, S.M., Trakhtenberg, I.S.: Phys. Met. Metallogr. (English Transl.) 45 (5) (1979) 100. Vladimirov, A.B., Kaygorodov, V.N., Klotsman, SM., Trakhtenberg, IS.: Fiz. Met. Metalloved. 48 (1979) 352 (subsidiary reference cited after [87Nl]). Wandelt, K., Chuang. T.J.: Proc. 7th Int. Vat. Congr. and 3rd Int. Conf. Solid Surfaces,Vienna 1977, p. 2091; Chuang, T.H., Wandelt, K.: Surf. Sci. 81 (1979) 355. Zshuravskaja, V.Y., Ugaste, YE.: Diffuzionnyje prozessy v metallah (Tula Polytechn. Inst., Tula, USSR) 1979 (subsidiary reference cited after [86Al]). Aleshin, A.N., Bokshtein, B.S., Petelin, A.L., Shvindlerman, L.S.: Metallotizika 2 (1980) 83. Aufray, B., Gas, P., Bernardini, J., Cabane-Brouty: Ser. Metall. 14 (1980) 1279. Chen, W.K., Peterson, N.L. : J. Am. Ceram. Sot. 63 (1980) 566. Cannon, R.M., Rhodes, W.H., Heuer, A.H.: J. Am. Ceram. Sot. 63 (1980) 46. Gupta, D., Kim, K.K.: J. Appl. Phys. 51 (1980) 2066. Gedgovd, K.N., Krasovskiy, A.I., Novikov, S.M.: Phys. Met. Metallogr. (English Transl.) SO (2) (1980) 185. Gupta, D., Campbell, D.R.: Philos. Mag. A 42 (1980) 513. Gust, W., Predel, B., Roll, U.: Acta Metall. 28 (1980) 1395. Hwang. J.C.M., Ho, P.S., Campbell, D.R.: J. Appl. Phys. 51 (1980) 1576. Juve-Due. D., Treheux, D., Guiraldenq, P.: Mater. Sci. Eng. 42 (1980) 281. Mgbcnu, E.N.: Vacuum 30 (3) (1980) 129. Wang. H.A., Kriiger, EA. : J. Am. Ceram. Sot. 63 (1980) 614. Atkinson, A., Taylor, R.I.: Philos. Mag. A 43 (1981) 979. Ballufti, R.W., Kwok, T., Bristowe, P.D., Brokman, A., Ho, P.S., Yip, S.: Ser. Metall. 15 (1981) 951. Brissaud-Lancin, M., Marphic, C., Riviere, A., Philibert, J.: Philos. Mag. A 44 (1981) 815. Baumgart, H., Leamy, H.J., Trimble, L.E., Doherty, C.J., Celler, G.K.: Grain Boundaries in Semiconductors, Proc. Mater. Res. Sot. Ann. Meeting Boston 1981, H.J.Leamy, G.E.Pike, C.H.Seager (eds.), New York: North-Holland, 1982, p. 311. Borisov, E.V., Senchukov, A.D., Shlykov, V.I.: Izv. Akad. Nauk SSSR,Neorg. Mater. 17 (1981) 277. Bokshtein, S.Z., Bolberova, YV., Kishkin, S.T., Razumovskiy, I.M.: Phys. Met. Metallogr. (English Transl.) 51 (1) (1981) 84; Bokshtein, S.Z., Bolberova, Y.V., Kishkin, S.T., Kostyukova, Y.P., Mishin, Y.M., Razumovskiy, I.M.: Phys. Met. Metallogr. (English Transl.) 58 (1) (1984) 172. Bokshtein, B.S., Klinger, L.M., Straumal, B.B., Shvindlerman, LX: Acta Cryst. A 37 (1981) C 147. Gust, W., Hintz, M.B., Lodding, A., Lucic, R., Odelius, H., Roll, U.: Microchim. Acta, Suppl. 9 (1981) 307. Gust, W., Hintz, M.B., Lodding, A., Odelius, H.: Philos. Mag. A 43 (1981) 1205. Oishi, Y., Sakka, Y., Ando, K.: J. Nucl. Mater. 96 (1981) 23. Richter, I., Feller-Kniepmeier, M.: Phys. Status Solidi (a) 68 (1981) 289 (subsidiary reference cited after [8582]). Sen, SK., Kluge-Weiss, P.M., Bauer, CL.: Thin Solid Films 82 (1981) 299. Straumal, B.B., Bokshtein, B.S., Klinger, L.M., Shvindlerman, L.S.: Ser. Metall. 15 (1981) 1197. Treheux, D., Dubois, J., Fantozzi, G.: Ceramurgia Int. 7 (1981) 142. Treheux, D., Vincent, L., Guiraldenq, P.: Acta Metall. 29 (1981) 931. Volkova, R.P., Palatnik, L.S., Pugachev, A.T.: Dokl. Akad. Nauk SSSR 259 (1981) 351. Atkinson, A., Taylor, R.I.: Philos. Mag. A 45 (1982) 583. Bernardini, J., Gas, P., Hondros, E.D., Seah, M.P.: Proc. Royal Sot. London A 379 (1982) 159. Baumgart, H., Leamy, H.J., Celler, G.K., Trimble, L.E.: J. Phys. (Paris) Cl (Suppl. No.10) 43 (1982) 363.
Kaur, Gust
Landolt-BBmstein New Series III/26
12.3 References for 12 82B3 82Cl 82Kl 82K2 82Ll 8201 82Pl 82Sl 8232 82Tl 83Bl 83B2 83B3 83B4 83Gl 83Ll 83L2 83Ml 8301 83Pl 83Sl 84Gl
84G2 84Jl 84Ll 84Nl 84Sl 8482 84Tl 85Bl 85B2 85B3 85Gl 8502 85G3 8564 85Hl 85H2 85Jl 85Ml 85Pl 85Sl 86Al 86A2 86Bl
715
Bokshtein, B.S., Videnskii, I.V., Klinger, L.M.: Metallofizika 4 (1982) 109. Chongmo, L., Hillert, M.: Acta Metall. 30 (1982) 1133. Kim, K.K., Gupta, D., Ho, P.S.: J. Appl. Phys. 53 (1982) 3620. Klinger, L.M., Kogay, I.R., Straumal, B.B.: Phys. Met. Metallogr. 53 (4) (1982) 142. Liofard, J.J.,Biberian, R., Cabane, J.: J. Phys. (Paris) Cl (Suppl. No.10) 43 (1982) 213. Oberschmidt, J., Kim, K.K., Gupta, D.: J. Appl. Phys. 53 (1982) 5672. Patil, R.V., Sharma, B.D.: Met. Sci. 16 (1982) 389. Swaminathan, B., Saraswat, K.C., Dutton, R.W, Kamins, T.I.: Appl. Phys. Lett. 40 (1982) 795. Sakka, Y, Oishi, Y, Ando, K.: J. Mater. Sci. 17 (1982) 3101. Treheux, D.: Acta Metall. 30 (1982) 563. Beke, D.L., Giideny, I., Kedves, F.J.: Philos. Mag. A 47 (1983) 281 (subsidiary reference). Bokshtein, B.S., Bolberova, YV., Kishkin, S.T., Razumovskii, I.M.: Metallofizika 5 (1983) 69. Bukaluk, A.: Surf. Interf. Anal. 5 (1983) 20. Bukaluk, A.: Stud. Surf. Sci. Catal. 23 (Phys. Solid Surf.) (1983) 170. Gust, W., Ostertag, C., Predel, B., Roll, U., Lodding, A., Odelius, H.: Philos. Mag. A 47 (1983) 395 (subsidiary reference). Lesage, B., Huntz, A.M.: J. Mater. Sci. 18 (1983) 189 (subsidiary reference cited after [84Ll]). Lefakis, H., Cain, J.F., Ho, P.S.: Thin Solid Films 101 (1983) 207. Matsuyama, T., Hosokawa, H., Suto, H.: Trans. Jpn. Inst. Met. 24 (1983) 589. Osenbach, J.W, Stubican, VS.: J. Am. Ceram. Sot. 66 (1983) 191; Stubican, VS., Osenbach, J.W.: Solid State Ionics 12 (1984) 375. Pelleg, J.: Thin Solid Films 110 (1983) 115, 129. Straumal, B.B., Klinger, L.M., Shvindlerman, L.S.: Ser. Metall. 17 (1983) 275. Gust, W!, Lodding, A., Odelius, H., Predel, B., Roll, U.: Ser. Metall. 18 (1984) 1149; DIMETA-82, Diffusion in Metals and Alloys, Proc. Int. Conf., Tihany, Hungary 1982, Diffusion and Defect Monograph Series No.7, F.J. Kedves, D.L. Beke (eds.), Aedermannsdorf: Trans. Tech. Publications 1983, p. 418; See also: Gust, W., Hintz, M.B., Lodding, A., Lucic, R., Odelius, H., Predel, B., Roll, U.: J. Phys. (Paris) C4 46 (1985) 475. Gust, W., Hintz, M.B., Lucic, R., Predel, B., in: Phase Transformations in Solids, Mater. Res. Sot. Symp. Proc., T. Tsakalakos (ed.), New York: North Holland, Vol. 21, 1984, p. 513. Juve-Due, D., Treheux, D.: Acta Metall. 32 (1984) 2063. Lagrange, M.H., Huntz, A.M., Davidson, J.H., Corros. Sci. 24 (1984) 613. Noda, T., Kainuma, T., Okada, M.: J. Jpn. Inst. Met. 48 (1984) 30. Singh, P., Ohring, M.: J. Appl. Phys. 56 (1984) 899. Stubican, V.S., Osenbach, J.W.: Solid State Ionics 12 (1984) 375. Tsubakino, H., Nozato, R.: J. Mater. Sci. 19 (1984) 3013. Bokshtein, S.Z., Kishkin, S.T., Mishin, YM., Razumovskii, I.M.: Dokl. Akad. Nauk SSSR 280 (1985) 1125. Beke, D.L., Kedves, F.J.: Cryst. Res. Technol. 20 (1985) 73 (subsidiary reference cited after [86B2]). Bunch, R.M., Unruh, W.P., Iverson, M.V.: J. Appl. Phys. 58 (1985) 1474. Geise, J., Herzig, C.: Z. Metallkde. 76 (1985) 622. Gupta, D., Oberschmidt, J.: Proc. Conf. Diffusion in Solids: Recent Developments, Metallurgical Society, Warrendale, Pennsylvania 1985, p. 121. Gupta, S.P., Parthiban, G.T.: Z. Metallkde. 76 (1985) 505. Gust, W., Hintz, M.B., Predel, B.: J. Phys. (Paris) C4 46 (1985) 529. Hansel, H., Stratmann, L., Keller, H., Grabke, E.J.: Acta Metall. 33 (1985) 659. Herzig, C., Neuhaus, P., Geise, J.: Solute-Defect Interaction: Theory and Experiment, Proc. Int. Sem., Kingston, Canada 1985, S. Saimoto, G.R. Purdy, G.V. Kidson (eds.), Toronto: Pergamon Press 1986, p. 271. Ju, C.P., Fournelle, R.A.: Acta Metall. 33 (1985) 71. Moosa, A.A., Rothman, S.J.,Nowicki, L.J.: Oxid. Met. 24 (1985) 115. Peterson, N.L., Wiley, CL.: J. Phys. Chem. Solids 46 (1985) 43 (subsidiary reference cited after [85Ml]). Spit, F.H.M., Albers, A., Lubbes, A., Rijke, Q.J.A, v. Ruijven, L.J., Westerveld, J.P.A., Bakker, H., Radelaar, S.: Phys. Status Solidi (a) 89 (1985) 105. Aleshin, A.N., Prokofjev, S.I.: Poverkhn. Fiz. Khim. Mekh. 9 (1986) 131. Atkinson, A., Taylor, R.I.: J. Phys. Chem. Solids 47 (1986) 315. Brissaud-Lancin, M., Marphic, C., Riviere, A.: Philos. Mag. A 53 (1986) 61.
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36B2 86Cl B6C2 B6Gl B6G2 B6G3 B6G4
B6Hl B6Jl 86M1 86Sl 86S2 86S3
87B2 87Gl 87Nl 88Cl 88Ll 88Nl 88Sl 89Kl 89K2 89Nl
12.3 References for 12 Beke, D.L., Godeny, I., Kedves, F.J.: Trans. Jpn. Inst. Met., Suppl. 27 (1986) 649. Chuang. T.H., Gust, W., Predel, B., Fournelle, R.A.: Proc. 7th Brazilian Congr. Eng. Mater. Sci., A.Blass (ed.), Florianopolis, Santa Catarina 1986, p. 281; Chuang, T.H., Fournelle, R.A., Gust, W., Predel, B.: Z. Metallkde. 80 (1989) 318. Chuang. T.H., Gust, W., Fournelle, R.A.: Proc. 7th Brazilian Congr. Eng. Mater Sci., A.Blass (ed.), Florianopolis, Santa Catarina 1986, p. 7; Biigel, A., Gust, W.: Z. Metallkde. 79 (1988) 296. Godeny, I., Beke, D.L., Kedves, F.J.: Trans. Jpn. Inst. Met., Suppl. 27 (1986) 525. Gupta, D., Oberschmidt, J.: Proc. Conf. Interface Migration and Control of Microstructure, Am. Sot. for Metals, Metals Park, Ohio 1986, p. 51. Gupta, S.P.: Acta Metall. 34 (1986) 1279. Gust, W., Beuers, J., Steffen, J., Stiltz, S., Predel, B.: Acta Metall. 34 (1986) 1671. Herzig. C., Neuhaus, P., Geise, J., in: Solute-Defect Interaction: Theory and Experiment, Proc. Int. Sem., Kingston, Canada 1985, S. Saimoto, G.R. Purdy, G.V. Kidson (eds.), Toronto: Pergamon Press 1986, p. 271. Johnson, B.C., Bauer, CL., Jordan, A.G.: J. Appl. Phys. 59 (1986) 1147. Moya, E.G., Badrour, L., Bernardini, J., Moya, F.: Trans. Jpn. Inst. Met., Suppl. 27 (1986) 517. Sura, V.M., Kohlstedt, D.L.: J. Mater. Sci. 21 (1986) 2356. Spit, F.H.M., Bakker, H.: Phys. Status Solidi (a) 97 (1986) 135. Suresh, V., Gupta, S.P.: Z. Metallkde. 77 (1986) 529. Beke, D.L., Godeny, I., Erdelyi, G., Kedves, F.J.: Philos. Mag. A 56 (1987) 659. Geise, J., Mehrer, H., Herzig. C., Weyer, W.: Mater. Sci. Forum 15-18 (Part I) (1987) 443. Neuhaus, P., Herzig, C.: Acta Metall. 35 (1987) 881. Chuang. T.H., Fournelle, R.A., Gust, W., Predel, B.: Acta Metall. 36 (1988) 775. Lee, J.S., Vieregge, K., Herzig, C.: Ser. Metall. 22 (1988) 1639. Neuhaus, P., Herzig. C.: Z. Metallkde. 79 (1988) 595. Shaarbaf, M., Fournelle, R.A.: Mater. Sci. Eng. A 102 (1988) 271. Kaur, I., Gust, W.: Fundamentals of Grain and Interphase Boundary Diffusion, Second Edition, Stuttgart: Ziegler Press, 1989. Kaur, I., Gust, W., Kozma, L.: Handbook of Grain and Interphase Boundary Diffusion Data, Stuttgart: Ziegler Press 1989. Neuhaus, P., Herzig, C., Gust, W.: Acta Metall. 37 (1989) 587.
Kaur, Gust
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Ref. p. 7441
13.1 Introduction
717
13 Surface diffusion on metals 13.1 Introduction Surface diffusion is the motion of well-defined species,such as atoms or molecules, on top of the surface of a solid material, here in this chapter crystalline metals only. Such a surface has a well-defined crystallographic structure which is described in terms of low-index terraces,steps,kinks and possibly more complex defects,such as dislocation emerging points, impurity clusters, high-index facetsor hillocks. A simple caseof a crystallographic surface is illustrated in Fig. 1a [67G2]. The energetic situation of an adsorbed particle is described by a 2-dimensional potential energy surface E(x, y). A one-dimensional representation is shown in Fig. 1b. Such a potential has several types of minima corresponding to different surface sites. The largest number of sites are terrace sites (for a flat, nearly low-index surface; so called “vicinal”). Other sites of higher binding energy are step and kink sites, for example. A single atom adsorbed at a monatomic step is called a step adatom. Because of the structural and energetic non-uniformity of surfaces there are different energy barriers for diffusional motion of adsorbed species.If diffusion on an isolated terrace is considered, the activation barrier is H”, the enthalpy of migration. If diffusion over a large distance involving interaction with steps and kinks is considered, the activation energy is HM + HF, with HF as the enthalpy of formation of a single adsorbed species (enthalpy defined for moving an atom from a kink site to a terrace site) [65Gl]. Hence there are two principally different surface diffusion coefficients which can be measured depending on the scale of observation, equally valid for self- or hetero-diffusion. The first is the intrinsic surface diffusion coefficient defined by movement of particles across a surface of uniform potential (single site) [83G]. Depending on the coverage of diffusable species one can distinguish a tracer surface diffusion coefficient for very low coverage (no interaction) and a chemical surface diffusion coefficient at intermediate to high coverages(interaction between adparticles included) [83G, 81Ml]. The tracer diffusion coefficient (not equal to the diffusion coefficient measured by the use of radioactive tracers!) describes random walk diffusion and is given by Di = & (A?)
where (Ar’) is the mean square displacement of the diffusing species during the observation period t. The chemical diffusion coefficient for an average particle concentration Ni is generally defined via particle velocity correlations [81Ml, 77E]:
where K(t) is the velocity of a particle at time t, K is the 2-dimensional isothermal compressibility, k the Boltzmann constant and T absolute temperature. It can be shown that only for totally uncorrelated particle velocities a simple relationship between Di and Di, can be obtained [81Ml]:
where p is the chemical potential of the adparticles. The second principally different quantity is the mass transfer surface diffusion coefficient describing transport of material acrosslarge distances.The potential is non-uniform (multiple site) but the concentration of diffusable speciesis still low. The basis for the definition is Fick’s first law based on the chemical potential for non-interacting species: pi=po+kTlnNi (13.4) where Ni is the temperature dependent surface concentration of surface species in the intrinsically diffusable state. The diffusion flux is then
Land&Biimstein New Series III/26
Bowel
718
13.2 Mechanisms of surface diffusion
[Ref. p. 744
The mass transfer surface diffusion coefficient is defined as [65Gl, 73B] D, - ‘hDi 0
(13.6)
with N, as the number of adsorption sites per unit area. In macroscopic experiments, where (Ar’) is larger than the mean separation between steps,the result ofa surface diffusion measurementis always D, becausethe driving force is the gradient in chemical potential. For larger concentrations of diffusable speciesthe interaction between these speciesneedsto be considered. This is almost always the casefor surface diffusion of adsorbed foreign atoms or molecules, i.e., hetero surface diffusion. Particle interaction is taken into account by re-writing eq. (13.4) in terms of an activity coeflicient y for adspeciesNi. In this case the surface diffusion coefficient is defined by [81R, 85N]
J=-o,(y)(l+z)VN,. The factor in parentheses can lead to a pronounced concentration dependence of the surface diffusion coefficient at constant temperature. With the identity
lIdIny=l
d/J
d InNi
kT d In&
(13.8)
one obtains an expression for the concentration dependent masstransfer diffusivity which is also a relationship between mass transfer and intrinsic hetero diffusion coefficient (analogous to eq. (13.3)): (13.9)
13.2 Mechanisms of surface diffusion Evidence for different surface diffusion mechanismscomesfrom experiment (e.g.field-emission microscopy) and theory [68W, 81M4,82D2, SOW,83B1, 80El]. In the casesof self-diffusion and atomic hetero-diffusion on metals the fundamental diffusion step is the jump of&orbed atomsfrom one equilibrium adsorption site to the next, with the jump distance equal to the separation, a, between sites. In analogy to bulk diffusion the temperature dependence of the intrinsic surface diffusion coefficient is (13.10) where S”’ and H" are entropy and enthalpy of single adatom migration, and vo is a frequency factor. An equivalent mechanism has been postulated for strrjke vacnrtcies(“terrace vacancies”). The temperature dependenceof the corresponding diffusion coefficient is analogous to that above [68w]. If masstransfer surface diffusion occurs by an adsorbed atom (adatom) or terrace vacancy mechanism, the Arrhcnius equation would read [6362, 63B] (13.11) where SF and HF are entropy and enthalpy of formation of this particular species. Another surface diffusion mechanism prevalent at low temperature and on surfacesof some atomic roughness,e.g.a fcc(l10) orientation, involves an exchange between adatom and surface atom. As illustrated in Fig. 2, an adatom pushes a surface atom from its equilibrium site and eventually to a new position while the original adatom occupies the lattice site of the displaced atom. In this fashion an atom has jumped across the atomic row into an adjacent channel although its identity has changed [8Ow]. This atom exchange mechanism is energetically more favorable than a single atom jump across the row [79H, 82D2]. A specific low-temperature mechanism is tunneling [80D]. This has been observed for adsorbed hydrogen atoms on W(110). At high temperatures, T/Th,> 0.75 (Th,= melting point), several mechanisms have been proposed. The first concerns the non-locul swfire d$ir.sion of adsorbed atoms or complexes thereof [70B2]. This mechanism explains a non-linearity in the Arrhenius plot, i.e. an increase in activation energy and pre-exponential factor
Bonzel
Landolt-BCmstein New Series Ill.‘26
Ref. p. 7441
13.3 Anisotropy of surface diffusion
719
with rising temperature. The second mechanism is based on order-disorder transitions (below TM)at the surface which causesa non-exponential increase in the number of diffusable species.This process, also referred to as “surface melting”, leads to higher activation energies of surface diffusion at high temperatures and hence very large surface diffusion coefficients [69R, 85Bl] which are in fact observed experimentally (see 13.5).
‘13.3 Anisotropy of surface diffusion Surfaces of different crystallographic orientation exhibit different potential energy functions. Therefore the enthalpy of migration for adatoms (or terrace vacancies)depends on the orientation of the surface. For surfaces with C3”, C4”, C,, symmetry there is only one value of minimum HM per surface but for C,, symmetry there are two different enthalpies of migration Hy and Hy, representative of two orthogonal directions. Hence there are two kinds of diffusional anisotropy to distinguish: orientational and directional anisotropy of surface diffusion [6362]. Examples for anisotropic surfaces are illustrated in Fig. 3 for a fee crystal. Several low-index faces and a vicinal surface are shown in Fig. 3a where the symmetry is C3”, C,, and C,,. For all surfacesthe enthalpy of migration is expected to be different but surface diffusion is directionally isotropic for (111) and (100) orientations. Only for surfaceswith C,, symmetry, e.g.(110) and (112),a directional anisotropy is observed in addition to the orientational effect. In this case the surface diffusion coefficient is a tensor of second rank [Oij]. Due to the existence of two principal crystallographic axes in the surface the tensor may be transformed into a simpler form. If D, and D, are the maximum and minimum surface diffusion coefficients, respectively, then the diffusion coefficient in a direction @,where @is the angle relative to the direction of maximum diffusion rate, is given by D(Q) = D, cos’@ + D, sin’ @.
(13.12)
A plot of this function is presented in Fig. 3 b [78B3]. An example for the orientational anisotropy of intrinsic surface self-diffusion is shown in Fig. 4 which summarizes data obtained by FIM for Rh adatoms on five different Rh planes [74A]. The activation energies, listed in Table 1, are quite different for these surfaces resulting in several orders of magnitude difference in D, at a given temperature. On (llO), (311) and (331) surface diffusion is one-dimensional in (110) direction since these are surfaces of 2-fold symmetry. An experimental quantitative example for the directional anisotropy of Ni mass transfer diffusion on a stepped W(110) surface at 1170 K is shown in Fig. 5 [82G]. The diffusion is faster along the steps in [OOI] direction than perpendicular to the steps. Also there is a small difference in the diffusion coefficient for atoms jumping “up” compared to jumping “down”. The sameeffect is illustrated in Fig. 6 by scanning Auger patterns of Pd on a stepped W(110) surface that was allowed to diffuse for 15 and 50 minutes at 1028 K [79B]. Predominant spreading occurs parallel to the step direction. Another clear demonstration of the influence of steps on the directional anisotropy of surface diffusion is shown in Fig. 7 for Pd on a W(110) crystal with a slightly rounded surface [79B]. Becauseof this roundness there is a continuous step distribution on the surface with the center of this distribution corresponding to the actual (exact) (110) orientation. Circular Pd deposits (bright spots) were evaporated in a hexagonal array to serve as diffusion sources.The crystal was then annealed at 1050 K for 5 minutes, and the distribution of Pd was imaged by Auger electron spectroscopy.The more or lesselongated Pd distributions around each spot indicate the local step directions becausesurface diffusion occurs predominantly in directions parallel to steps [79B]. Hence this pattern illustrates the anisotropy of surface diffusion due to steps as well as the step distribution on this particular W (110) crystal. The anisotropy of surface self-diffusion is shown in Figs. 8 and 9 for Ni(ll0) and several Cu surfaces, respectively [78B3,81C]. The activation energy of surface diffusion is considerably lower for the (110) direction than for the (001) direction, Fig. 8. The data in Fig. 9 show concentration profiles of 64Cu plotted in semilog fashion. They were obtained after annealing various Cu crystals at a constant temperature of 820 K; anisotropy is observed for (llO), (331), and (511) surfaces [81C].
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13.4, 5 Cluster surface diffusion, Adsorbate-modified
surface self-diffusion
[Ref. p. 744
13.4 Cluster surface diffusion Adsorbed particles diffusing on a crystalline surface interact with each other and can occasionally form clusters. The correlated motion of such clusters, which are formed in the FIM by depositing atoms from the vapor phase (!tence: adlayer is supersaturated), has been studied in detail [SOEl, 88Tl]. Most information has been collected for surfaceswith a channel-like structure, such as W(21 I), but some data is available for W(110) [76Bl, 88w] as we!!. For channelled surfacesthe orientation of the cluster relative to the direction of the channel is important. For example, a diatomic cluster, with the two atoms in adjacent channels, diffuses with a rate that can be larger [76S] or smaller [78K] than that of a single atom. Figure 10 compares the diffusion of single adatoms and W, pairs on a W(211) surface [75G, 74E]. The activation energies are quite different such that at T-e 250 K the diffusion of W, pairs would exceed that of W monomers. For Re monomers and dimers on the same surface the activation energies of surface diffusion were found to be nearly equal, with the rate for pairs always slightly higher than for singles [76S]. The opposite is true for W self-diffusion on W(110); here the diffusion coe!!icients for single atoms are higher than for W, pairs [78K], as shown in Fig. 11.The corresponding activation energies are listed in Table 1. On surfacessuch as W(211) the orientation of the cluster is important. For dimers the two atoms can be in adjacent rows (“cross-dime?‘) or in the samerow. The examples cited above were for cross-dimers.The diffusion of in-row-dimers is usually quite slow compared to that of cross-dimers [85E]. The mobility of larger clusters is generally lower than that of dimers (pairs). Fig. 12 shows as an example the intrinsic surface diffusion coefficients of Pt clusters of various sizes on W(110) [76Bl]. The activation energies increase with increasing size of the cluster.
13.5 Adsorbate-modified surface self-diffusion The chemical composition of a metal surface, i.e. the exact knowledge of impurities on or near the surface, plays a very important role for the rate of surface self-diffusion. This has been documented in a variety of cases. Impurity effects may also occur for hetero-diffusion but these are less well studied. In al! cases one should distinguish results in which impurities have been intentionally introduced on the surface from those where unintentionally added, often unidentified impurities cause deviations from measurementson clean surfaces. Fig. 13 shows an example of intrinsic surfaceself-diffusion data from Ni(ll0) by FIM [801] where the emitter tip was annealed in either UHV or H, ambient. The result is a large increase in D, for the HZ-annealed samples. The directional anisotropy seemsto be of minor importance at theselow temperatures,perhaps becausean atom exchange mechanism [78Bl, 79H] is operative. The exact reason for the H, induced increase in !I is not known. Other drastic examples have been observed with mass transfer diffusion. Fig. 14 shows the increase in Cu self-diffusion with the sample exposed to a partial pressure of Bi [70Hl]. There are four orders of magnitude increase in D, at 1173 K. Similar increaseswere measured for other adsorbates,such as Pb, T!, and S on Cu or Ag surfaces[70Hl]. A summary Arrhenius plot is presented in Fig. 15. Very large surface diffusion coefficients above IO-’ m*/s are observed so that the authors proposed these diffusion coefftcients to be characteristic of partially molten surface layers [69R, 70Hl]. Not only metallic adsorbatescausean increase in D,. Fig. 16 shows that adsorbed Br on Cu also leads to very large surface self-diffusion coef!icients [71D]. The adsorbate effect seemsto change the activation energiesas well as the pre-exponential factors. Elements that reduce the melting point of the substrate generally cause an increase in D, and a decreasein Q. An example for the latter effect is seenin Fig. 17 for W self-diffusion in the presenceof surface Ni [73P, 76R2]. Surface impurities can also decreasethe rate of surface self-diffusion. Typical impurities of this kind are carbon: sulfur and oxygen [72P2,74B, 66A, 84Bl]. The rate of decay of a sinusoidal profile, as a measureof the rate of surface diffusion, is shown in Fig. 18 for Cu(l10) at 890 K in 0, ambient and in UHV or H, ambient [69Bl]. In UHV or H, carbon segregatesto the Cu surface and stops surface diffusion at this temperature but during 0, exposure the carbon is oxidized and removed, and surface diffusion proceeds with a normal rate. Since carbon is a frequently observed surface impurity under vacuum conditions (even in UHV) due to hydrocarbon cracking or carbon segregation from the bulk, it may often play a role as suppressor of surface diffusion. Other impurities, with melting temperatures higher than that of the substrate, may do the same.The critical concentration of theseimpurities for which a suppression setsin is not known becausesystematic studies of this effect have not been carried out. In view of these data it is understandable, however, that different samples (of
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13.6,7 Cont. dependence in surface hetero-diffusion,
Measuring techniques
721
the same material), annealing history, surface cleaning procedures, vacuum or inert gas environments, etc. can generate different impurities on the surface and thus lead to a large variability in measured surface diffusion coefficients. In all likelyhood this is one of the main reasons for an apparently poor reproducibility in surface self-diffusion measurements.
13.6 Concentration dependence in surface hetero-diffusion For surface diffusion of adsorbed hetero-species in the sub-monolayer to monolayer coverage range one observesoften a strong coverage dependenceof surface diffusion coefficients [85N]. The reason for this behavior lies in particle interactions that may even lead to various ordered phasesat certain coveragesand temperatures. In other words, adlayers of strongly interacting particles are described by a 2-dimensional phase diagram. An example of this effect is given in Fig. 19 for adsorbed oxygen on W(110) [77B]. This figure shows the measured diffusion coefficient versus oxygen coverage at two different temperatures. The variation in D, is over two orders of magnitude. The maximum in D, at 0 M 0.4 is correlated with the growth of an ordered p (2 x 1) - 0 layer up to a maximum coverage of 0.5. A corresponding jump in free energy near 0 E 0.5 is expected to influence D, at this coverage becauseof a related sudden change in chemical potential [77B]. Becauseof such a behavior, the Arrhenius plot for 0 surface diffusion on W(110) is not simple, as shown in Fig. 20 [79C]. Several lines for constant 0 coverage are seen and concomitant changes in activation energies of diffusion can be recognized. A much more elaborate example for Li surface diffusion on W(110) is illustrated in Fig. 21 [82L]. Coverages range from 0.025 to 0.95. This case is convincing in a sensethat the concept of a simple Arrhenius plot for diffusion is no longer applicable. Possible values of D,(T) are not described by a single line but rather by a data field. A similar complicated caseis Ba diffusion on W(110) [88N]. Fig. 22 summarizes D, data versus Ba coverage for several different temperatures. For example, the variation in D, at 110 K is over 3.5 orders of magnitude. Ordered layers of Ba are indicated on the abscissaat several coverages.Becauseof this complex behavior there are large variations in Q and Do with coverage, as shown in Figs. 23 a and b [88N]. Not only are these values coverage dependent but they are temperature dependent in addition. For this reason two sets- at low and high temperature - are plotted in the figures. Most chemisorbed atoms or molecules on metal surfaces exhibit more or less strong interparticle interactions. One expects therefore that the coverage dependenceof surface hetero-diffusion is a general phenomenon. In this context one should note that some diffusion data obtained with techniques that evaluate concentration profiles should be looked at with considerable caution. Although the concentration profile may cover a large range of adsorbate coverage, the resulting D is usually quoted for an average concentration only. This is most likely an oversimplification.
13.7 Measuring techniques 13.7.1 Intrinsic surface diffusion In the experiments utilizing the techniques described below the mean diffusion distance is only of the order of 10 nm or less such that steps do not interfere (except reflect) with the intrinsic diffusion process.
13.7.1.1 The field ion microscope (FIM) is an ideal technique for observing intrinsic surface diffusion of isolated adatoms on a small perfect surface [57Ml], [66E]. Single adatoms are imaged with atomic resolution. By measuring the mean square diffusion distance (Ar”) for a given time of observation, t, the intrinsic diffusion coefficient is determined via
Di = $
(Ar2)
(13.13)
where u is either 2 or 4 for one- and two-dimensional diffusion, respectively. Measuring (Ar2) and t at various temperatures yields the temperature dependenceDi(?) and the activation enthalpy of surface diffusion, H”. This technique is suited for studying self- and hetero-diffusion. Adatoms are not generated thermally but condensed on the surface from an external source. In somecasesthe migration of dimers or larger aggregatesis investigated by FIM.
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13.7.1.2 7%~field electron microscope (FEM) is a technique for measuring hetero-surface diffusion of adsorbed atoms 3r molecules when fitted with a small probe hole that allows a continuous monitoring of the emission current rrom a small area of the FEM tip, typically about 5 nm diameter [79C]. This emission current exhibits current fl~rct~rotiorlsbecauseof density fluctuations of the adsorbed species,causedby surfacediffusion in and out of this area.These fluctuations (or the electron emission flicker noise) are monitored by measuring either the spectral 3ensity [71K] or the autocorrelation function [7362]. The autocorrelation function of the probe hole emission :urrent [71K, 73621. X(t) = (6ln i(0) &In i(t))
(13.14)
is compared to the calculated density fluctuation correlation, f,(r) = (WO) W)>
(13.15)
where the changesin density, 6,1(t) depend on the surface diffusion coefficient Di. The value of Di is determined rrom a match between j.(r) and the experimental J(r). An extension of the autocorrelation measurementis the analysis of the emission statistics from two adjacent probe hole areas by applying a cross-correlation technique [82Dl, 88K]. The advantage is in information on correlations of adparticle movements in space and time. A disadvantage of these FEM current fluctuation techniques is the presenceof a high electric field during the diffusion measurement.It is not easy to prove that the diffusion process is not influenced by this field. These techniques require medium to high concentrations of adspecies.Hence the concentration dependence of Di can bc measured by evaluating the autocorrclation of the current fluctuations at various concentrations of adsorbed species(at a given temperature).
13.7.1.3 The scamir~g electron rmnelir~g microscope can in principle bc used to observe the diffusional displacement of single atoms on flat substrates [82B]. Experiments of this kind, however, have thus far not been reported, presumably becausethere are significant problems with thermal drift at elevated sample temperature. The STM can also be used as a monitor of tunneling current fluctuations across the electron tunneling region, similar to the FEM probe hole observations under 13.7.1.2.In this case current fluctuations due to diffusing foreign atoms or self-adsorbed atoms can be detected and correlated with the rate of surface diffusion. An example with oxygen on Ni(lOO) has been reported [86B, 86G]. The difficulty is here the distinction between diffusion events due to different species.
13.7.1.4 Intrinsic surface self-diffusion can also be studied by quasielastic scattering of low-energy He atom [88F]. The process is analogous to quasielastic scattering of thermal neutrons for measuring volume self-diffusion (compare section 1.6.2).When He atoms are reflected from a surface, some collisions occur with surface atoms that are in diffusive motion. These weakly inelastic collisions will cause a slight energetic broadening in the elastic peak. i.e. in the energy distribution of diffusely scattered He atoms. For random continuous surface diffusion a Lorentzian energy profile with a full width at half maximum (FWHM) is expected [88F, 89FJ: AE = 2hD(Ak)*
(13.16)
where Ak is the component of the momentum transfer parallel to the surface and D the intrinsic surface self-diffusion coefficient in the direction of the diffusion jump (momentum). The amount of broadening is small such that extremely good resolution is required. Also Ak becomes appreciable only at high temperature; therefore measurementsof D seemonly feasible at T/T, > 0.7. In this sensethey are a valuable complement to the FIM adatom technique. This technique has been applied to Pb surface self-diffusion [88F].
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13.7.1.5 Relaxation measurements for studying surfacehetero-diffusion of adsorbed speciesare possible by techniques that are capable of distinguishing these speciesin different adsorption sites.The principle of the technique works as follows: A small amount of adsorbate is initially deposited on the surface in a non-equilibrium configuration, i.e. at sufficiently low temperature such that the attainment of equilibrium via surface diffusion is slow. The initially adsorbed speciesare distributed at random in low binding energy (“terrace”) and high binding energy sites (“defects”). At some annealing condition a redistribution from terrace to defectssites towards equilibrium will occur. Techniques that can distinguish adparticles in these two kinds of sites can be utilized to follow this process as a function of time. One of these techniques is He atom scattering from surfacesfor which the scattering cross section for terrace and defect site adsorbed speciesis vastly different [82P]. First a defect-rich surface is prepared by high-energy ion bombardment. Then a low concentration of an atom or molecule is adsorbed at such a low temperature that no surface diffusion takes place. The intensity of scattered He atoms in the specular direction decreasesdue to the presence of adspecies,see Fig. 24, which act as additional diffuse scatterers. On annealing the adspecies become mobile and diffuse to the defect sites where their binding energy is higher than on the flat part of the surface. As the flat parts of the surface becomeclean the intensity of scattered He in the specular beam increases again. The temperature dependenceof this intensity increase is evaluated to yield the pre-exponential factor and activation energy of intrinsic surface diffusion of the adspecies. Another elegant relaxation experiment is carried out with the combined use of a pulsed molecular beam (PMB) and a fast scanning infrared interferometer (IRI) [88R]. The PMB source is used to deposit a small amount of adsorbate on the surface kept at a certain temperature. The IRI follows a site-specific frequency of the adsorbate in real time, e.g. the C - 0 stretch frequency of adsorbed CO. Since CO in terrace sites and in defect sites is characterized by wavenumbers of 2087.5 cm- ’ and 2057.6 cm- ’ respectively, the redistribution of CO from random to equilibrium can be followed. The evaluation of this time dependenceyields the surface hetero-diffusion coefficient. In the example of CO on Pt(ll1) at low coverage an activation enthalpy of CO migration of 18.4 kJ/mol was found [88R]. A similar but not adsorbate-specific possibility for monitoring the surface diffusion from non-equilibrium adsorption sites to an equilibrium distribution exists with measurementsof the workfunction [83S]. This can be done for self-adsorbed atoms or hetero-adsorbed species. Atoms evaporated onto a metal surface at low temperature, typically 100 K, are nearly frozen in place. During warm-up they begin to diffuse and preferentially adsorb at step and kink sites. The work function measured during this process is seen to increase becausethe negative dipole moments associatedwith single atoms or small clusters on the flat terrace of the crystal are being eliminated. Depending on the size of the initial clusters (if they are not all single atoms) the measured surface diffusion can vary between intrinsic and mass transfer diffusion [83S].
13.7.2 Mass transfer surface self-diffusion For mass transfer surface self-diffusion experiments the mean diffusion distance is generally of the order of several pm; this means a relatively high temperature (T/T, 2 0.5) and a large amount of masstransport. Under those conditions someexchange between surface and bulk as well as evaporation occurs. Both of theseprocesses have to be taken into account in the evaluation. In particular the bulk diffusion coefficient will appear explicitely in the evaluation formulas.
13.7.2.1 Radio-active tracer technique (RAT) [70G]. A locally finite or semi-infinite source of radio-active material is deposited on a flat surface, preferably under ultra-high vacuum conditions to ensure cleanliness. Different kinds of sourcescan be used, such as point, edge and half-plane sources(compare chapter 12 on grain boundary diffusion). The concentration profile of the diffused tracer material has to be determined after a given diffusion time at constant temperature. A comparison of experimental concentration profiles and theoretical solutions of Fick’s equation then yields a value of the surface diffusion coefficient together with values of either volume or grain boundary diffusion coefficients. Although the surface diffusion coefficient is basically a mass transfer quantity, a comparison with other masstransfer self-diffusion data often shows poor agreement.This can be due to insufficient surface cleanliness in the caseof radiotracer experiments becausea poisoning of step and kink sites by impurities can lead to a lower apparent activation energy of surface self-diffusion. Evaluation formulas are given in chapter 12.
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13.7.2.2 Copillnrity techiqrres. The principle of these techniques is eq. (13.3)where the chemical potential is given by the Gibbs-Thompson equation [63M]:
(13.17) P(K) = P(O)+ Y(Q QK where ~(0) is the orientation-dependent surface specific energy, Szthe atomic volume, and K the local curvature at the surface.Hence the clean surface has to be perturbed from its lowest energy contiguration in order to cause a mass flow at elevated temperatures from which a surface self-diffusion coefficient can be extracted. It is /essential to have a phenomenological solution of the diffusion equation. These solutions depend on the boundary conditions of the particular experiment that is set-up to measuresurface self-diffusion. Solutions are available for the following surface conditions and shapes: -
sinusoidal or general periodic profile (SPD) [59M] isolated ridge or groove [62K] grain boundary groove (i.e. flat surface of a polycrystalline material) (GBG) [57M2] linear surface facets [61M] conical points (field emitter tips) [65Nl, 87B3] contacting spheres (sintering) or voids inside a solid [65N2].
Most solutions are based on the assumption of a nearly isotropic (constant) surface free energy for the range of orientations present in the surface profile. However, this assumption is violated in caseswhere local minima in y(0), i.e. cusps, occur for low-index orientations. Under those conditions more involved solutions of the diffusion problem have to be used [75B2, 84B2, 84B3, 86P, 86VJ. The solution for the decay of a sinusoidal profile (SPD) by surface self-diffusion, for example, is given by [59M]: A(t) = A, exp(- Bw~I) (13.18) yD N f-2’ B= A, kT
2K WC-.1
where A is the amplitude and 1. the wavelength of the profile, N, the number of surface atoms per unit area? k the Boltzmann constant and t the diffusion time. By measuring the time dependence of the amplitude at constant temperature, the surface self-ditTusion coefficient D, can be determined. Since the profile can be prepared on any surface, the crystallographic orientation dependenceof D, can be measured by this technique. In addition the directional variation of D, on a given surface can also be studied because the profile is one-dimensional and governs the diffusion direction [78B3]. It is important for the above solution that A/i. 5 0.02 or that the slope of the profile is small compared to unity. For surface profiles with A/,? > 0.02 and in particular for orientations where y(0) is strongly anisotropic (in the vicinity of a cusp) a more complete formula for the chemical potential has to be used: m=m+Iy(O)+~}
(13.20)
QK.
Inserting eq. (13.20)into Fick’s law, eq. (13.3),and by using the continuity equation leads to the following differential equation (in one dimension) [84B2] $=g
[1 +($ry”
with
2
[y(O)+%]
(13.21)
ax [ 01
(13.22)
-2
(13.23)
& = j + !?! * “* dxK(x)=
K(x)
(1 +(gyj-3’2.
The differential equation (13.21) has been solved numerically for several functions y(0) [84B2, 84B3] and provided a basis for the evaluation of experimental results [86P]. The technique of the sinusoidal profile decay has the advantage that it is compatible with ultrahigh vacuum environment and surface cleanliness diagnostics. The amplitude can be measured via the intensity distribution of a diffraction pattern generated by the profile [68B2]. Such an in situ determination of A is important from the point of view of maintaining surface cleanliness throughout the entire experiment. Land&-BBmzbin New Series 111’26
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13.7 Measuring techniques
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The separation of contributions due to surface and volume diffusion as well as other processes,such as evaporation/condensation, viscous flow, is feasible by phenomenological equations [59M].
13.7.2.3 Scanning electron tunneling microscope (STM). This technique is not only capable of imaging single atoms or small clusters on flat surfaces but also larger irregularities, such as indentations or hills, with a lateral resolution of about 1 nm. These small irregularities change their structure due to the minimization of surface free energy, and these changes occur by surface self-diffusion. The process is mass transfer diffusion because adatoms have to be created at sourcesaway from the irregularity and adsorbed (annihilated) at the indentation, for example (or vice versa for a hillock). Such changes have been observed [88J, 88Sl]. It should be possible to generate some well-defined surface structures whose annealing can be observed by STM and evaluated by a phenomenological theory similar to those for macroscopic mass transfer studies.
13.7.3 Hetero surface diffusion - mass transfer 13.7.3.1 Radio-active tracer technique. The principle is the same as for surface self-diffusion (seesection 13.7.2.1for
further details).
13.7.3.2 Scanning techniques. These techniques apply to the typical surface diffusion geometry of an initial localized source of diffusing material A on a well-defined substrate surface B (similar to the geometry for radio-active tracers). The source can be a point or edge source. The diffusion from the source across the surface is treated by solving Fick’s equation with appropriate boundary conditions. Depending on the material A and B and also on the diffusion temperature, some loss of A into the bulk of B or into the gas phase by evaporation may occur and should be accounted for (compare chapter 12 on grain boundary diffusion). There are several scanning techniques with different surface sensitivity and lateral resolution; all of them work only under vacuum conditions: - scanning tunneling electron microscope (STM) with an intentionally degraded resolution of 1 nm, - scanning electron microscope (SEM), maximum resolution about 3 nm, - scanning Auger electron microscope (SAM) with a maximum resolution near 50 nm, - scanning secondary ion (SIMS) microprobe with a resolution of 0.1 pm, - scanning one-dimensional (wire) work function probe with a resolution of w 12 pm [77B], - local X-ray photoemission spectroscopy (XPS) with a resolution of 150 pm.
The techniques SAM, SIMS and XPS provide material-specific signals of highest surface sensitivity whereas the other techniques are indirect with regard to material specificity. In somecasesSEM or SAM is used in conjunction with the growth of thin films of material A on a substrate B [83V, 85F2]. The appearance of various growth forms of islands, depending on temperature, is linked to the energetics at the interface and to surface diffusion. The observation of particle growth or coalescenceas a function of time can be evaluated to yield surface diffusion coefficients [81D].
13.7.3.3 Laser induced thermal desorption (LITD) is suitable for relatively weakly adsorbed atoms or molecules on metal surfacessuch that they can be desorbed by a single laser pulse irradiating the surface. The experiment is carried out as follows [82V]. A clean well-defined metal surface in UHV at low temperature is exposed to a gas or atom beam to achieve a certain coverage.The temperature is then raised to the desired diffusion temperature which, however, should be well below the temperature for desorption. Then a single pulse of a focussed laser beam is aimed at the surface. The energy of this pulse has to be such that the temperature in the irradiated area increasesfar above the desorption temperature of the adsorbed speciesbut not so high that the metal surface becomesstructurally damaged.As a result of the laser pulse an area about equal to the diameter of the light spot will become (nearly) free of adsorbate. Becauseof the concentration gradient set up in this way surface diffusion of adsorbate from outside this area will begin and fill in the area cleared by the laser shot. After a certain elapsed time At a second laser pulse will desorb the amount of adsorbate that has diffused into this area. A measurement of this amount as a function of waiting time at constant temperature can then be evaluated to yield the surface diffusion coefficient.
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[Ref. p. 744
The solution of the diffusion problem based on cylindrical symmetry is [85G] S(t) = l-2
m J:(ua)
d
-
u
exp(- Dtu’) du
where S(t) is the normalized amount desorbing after time t from the circular area, a = the radius of the circular area,.I, the Besselfunction of the first kind. A typical value of a is 250...500 pm. This technique measuresa masstransfer diffusion coeficient becausethe diffusion distance is large compared to interstep distances on single crystal surfaces. Therefore diffusing atoms or molecules will sample sites of different adsorption energies. Since the initial coverage of the adsorbate can be varied, the concentration dependenceof D can in principle be determined. An important variation of the LITD technique involves the preparation of an adsorbate covered surfacewith a regular spatial modulation of the coverage. Such a square wave or sinusoidal wave modulated coverage (in one dimension) is produced by laser-induced desorption due to two laser beamsimpinging on the surface at the samelocation and interfering with each other. This optical interference causesa line pattern or grating where the adsorbed molecules are desorbed at maximum intensities and left unperturbed in the dark regions [882]. The grating is produced by a single laser shot with the sample held at temperature. The periodically modulated concentration profile wants to relax by surface diffusion towards a uniform coverage.This processis monitored by shining laser light (of lower intensity) at the grating and by measuring the diffracted intensity as a function oftime. To enhance surface sensitivity one utilizes the optical second harmonic of the incident wavelength [88ZJ. This novel technique was applied to surface diffusion of CO on Ni(l11). The arrangement of the one-dimensional grating on the surface permits the study of directional anisotropy of surface diffusion. On the other hand, reasonably large concentrations of adsorbate are needed to measure changes in the concentration profiles, just as with other relaxation techniques. Hence these techniques are not likely to be very suitable for the investigation of the coverage dependence of surface hetero-diffusion.
13.7.3.4 7%~jield electron microsrope (FEM) has been used to image the diffusion front of an adlayer of atoms or molecules advancing across a region of clean surface [58G]. In this mode of operation the whole emitter tip of the FEM is being imaged, with a resolution of about 2 ... 3 nm. The operation is similar to a scanning device except that the boundary between high and very low concentration of adsorbate can be seenmost clearly due to dilferences in local work function. There are complications with this procedure and the use of FEM tip geometries. First of all, the possibly strong concentration dependenceof surface diffusion leads to a more or less sharp boundary yielding different activation energies [58G]. In addition the surface is quite heterogeneous and curved so that curvature-related driving forces for surface diffusion should be considered. The evaluation of surface diffusion occurring with a sharp boundary is according to the observed mean square diffusion distance in one dimension, 2 = 2 fi, which is a further approximation because the tip geometry does not permit a truly one-dimensional motion of a diffusion front that has a finite width.
13.8 Systematics of surface diffusion coefficients The activation enthalpy of migration of a single adatom is defined as the enthalpy difference between the :quilibrium site and the saddle point configuration. Both of these enthalpies are related to the bond strength between two atoms of this material (energy of cohesion). This latter quantity can to a lirst approximation be derived from the enthalpy of sublimation (or evaporation at TM)of the solid, AH,,,. Therefore one expects the :nthalpy of migration to be a certain fraction of the enthalpy of sublimation. This is easy to understand for self-diffusion but for hetero-diffusion of different species on the same substrate metal one assumesa similar relationship to hold becausechanges in the adsorption enthalpy of different speciesare related to changes in their sublimation enthalpies. Therefore one compares HM of A on B to the enthalpy of sublimation of the adsorbed material.
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13.9 Commentary to tables
727
A good demonstration of the utility of such a relationship are intrinsic surface diffusion data for several adatoms on W(211) [SSW]. The Arrheniusdiagram in Fig. 25 summarizes the results and shows that D, is the larger, the smaller AH,,, of the adatom material. The average ratio between HMand AH,,, for these measurements turns out to be 0.107(3). Data for AH,,, were taken from [86K]. Such a result is useful for estimating the activation enthalpy of adatoms that have not been measured. A further remarkable feature with the data in Fig. 25 is the close similarity of the pre-exponential factors Do which are about lo-’ m2/s as expected [SSW]. The same principal approach has been applied to mass transfer surface self-diffusion data [6762] in order to derive a general material-independent expression for the temperature dependenceof D,. Although in this case the activation enthalpy is equal to the sum of migration and formation enthalpy, both of these quantities are related to the interatomic bond strength and hence AH,,, which by itself is proportional to TM.Hence an Arrheniusdiagram of log D, versus TM/Tshould concentrate the data into a “narrow” data band for different metals. Such plots have been constructed independently for fee and bee metals [67G2, 75Bl] and are illustrated in Figs. 26 and 27, respectively. The result is a data band in both casesabout one order of magnitude in D,-width. It is interesting to seethat the activation enthalpy increaseson the averagewith increasing temperature. Various speculations as to the origin of this effect have been put forward: change in diffusion mechanism [6762], non-localized surface diffusion at high temperature [70B2], surface roughening [69Bl] or surface melting [69R] at high temperature. The latter idea has received further support by recent experiments [SSF,89F] and phenomenological theory [85Bl]. The usefulness of figures, such as 26 and 27, is however very limited. Becauseof the variability of surface self-diffusion with orientation, diffusion direction, and surface cleanliness one does not seriously expect data of such different origin to fall into a narrow range when plotted in this fashion. A good correlation could only result if all data were taken under equal conditions of measurement,such as for the intrinsic surface hetereo-diffusion on W(211) in Fig. 25. Adsorbate-modified surface self-diffusion coefficients (section 13.5) have also been compared and summarized in terms of a log D, versus T,/Tplot, as shown in Fig. 28 [70Hl]. Becauseof the presenceof the adsorbate the melting point of the substrate material in the surfacelayer is lowered below TMof the pure element. The lower melting temperature can be estimated from the bulk phase diagram of the B -A binary system,where A is the adsorbate and B the substrate element. For CuPb, for example, the monotectic temperature is 1227 K (compared to TM(Cu) of 1356 K). The Pb-enhanced surface self-diffusion data of Cu were hence plotted against TM/T, with TMchosen to be 1213 K [69R]. Similarly, for Cu(T1) and Ag(S) self-diffusion coefficients “melting” temperatures of 1233 K and 1073 K were assumed, respectively, corresponding to the monotectic temperature of 1241 K in the Cu-Tl system and to 1098 K for the bulk melting point of Ag,S. Under these assumptions the rather different data can be represented by a single curve in Fig. 28 which even corresponds to the samemedium curve in Fig. 26 for “clean” fee metals [67G2]. The implication of this fit in Fig. 28 is, however, that the surface layer of adsorbate covered Cu or Ag is molten at TM/T< 1. No independent proof of surface melting in these systemshas been given. Alternate explanations for the high diffusivities in Fig. 28 were given elsewhere [69Bl, 70B2, 75Bl].
13.9 Commentary to tables Measurements of surface diffusion data can be very reproducible for identical systemsif carried out under well-defined conditions. A convincing example is presented in Fig. 29 for Re diffusion on W(211) showing two independent measurementsin 1976 and 1988 [76S, 88Wj. On the other hand, a cursory inspection of the surface diffusion data listed in the following tables will frequently show a very large variation from one set to another for the same material. Actual values of D calculated from different sets of data for a certain temperature will sometimes vary over several orders of magnitude. A good example for this kind of variation is seenin Fig. 30 for Ni surface self-diffusion data [83B3]. The reason for this variation can be poor experimentation and surface quality control of one research group against another; but more likely there are physical reasons for the observed differences. The latter may be classified into five categories: a) b) c) d) e)
different diffusion coefficients: intrinsic and mass transfer surface impurities (also effecting r(0)) crystallographic surface orientation and diffusion direction orientation dependent faceting due to y(B) anisotropy (only for mass transfer diffusion) concentration dependence (only for hetero-diffusion)
Land&-Biirnstein New Series III/26
Bonzel
13.IO Surface diffusion tables
728
[Ref. p. 744
Becauseof (a) the data are listed in different tables, but even for the intrinsic diffusion data there may be principal differencesarising from the measurementtechnique and coverage(“tracer” versus “chemical” diffusion coefficient) [Sl Ml]. When comparing intrinsic and masstransfer diffusion data one should always rememberthe principal difference in activation energies (eq. 13.4),i.e. that mass transfer diffusion is governed by the sum of energy of migration and formation. Surface impurities can crucially effect surface diffusion coefficients, as outlined in section 13.5.Therefore it is possible that some disparities in different measurements arise from this source due to insufficient surface diagnostics. In the case of mass transfer diffusion impurities can alter y(0) and hence the measured product D,y(O) which cannot be unravelled without an independent measurement of y(0) itself. The other points (c)-(d) have been sufhcicntly discussed and demonstrated in sections 13.3 and 13.6. In summary, unequal diffusion data for the samematerial may not be a sign of poor reproducibility but rather be indicative of incomplete documentation of experimental details. Since documentation, particularly of surface composition and surface orientation, has generally improved during recent years, newer data have been preferentially included in the tables compared to older diffusion data.
13.10 Surface diffusion tables Table 1. Intrinsic surface diffusion data (self-diffusion, hetero-diffusion, cluster diffusion). Metal Diffusing (Substrate) species
Do m’/s
i/m01
Temperature Technique/Remarks range [K]
Ni(311) Ni (331) NI (1lo),,
Ni Ni NI
2.10-10 2.10-7 % 10-13
29 (3) 43 (3) 22 (4)
133...175 I%...182 145...185
Ni(IlO), Ni (1IO),, Ni(IlO),
Ni Ni Ni
z 10-l’ (% 10-S) (x 10-S)
31 (5) x 29 x 25
145...185 81 . ..90 81 . ..90
Ni(II1) Ni (100) Ni(ll1) Rh(111) Rh(311) Rh (1IO),, Rh(331) Rh(lO0) Ir(3Il) Pt(311)
Ni Ni S Rh Rh Rh Rh Rh Ir Pt
(2.10-s) 2.10-E 2.10-7 3.10-s 1.10-6 1. lo-’
107...114 53 ... 63 186...208 177.e.200 202,s. 222 300...324
(i0-J)
x 32 x 61 28.5 I5 (2) 52 (5) 58 (3) 62 (4) 85 (7) 89 67 (19)
Pt (I IO),, Pt(IlO), Pt (331) Pt(311) Pt (I IO),, Pt(llO), Pt(311) PI (1IO),,
Pt Pt Pt Ir Ir Ir Au Au
8. IO-’ 1.10-7 4.10-S 3.10-S -
81 (10) 75 (10) 81 (10) 71 (14) 77 (14) 77 (14) 54 (10) 61 (14)
Ta(ll0) W(ll0) W(321) W(211) W(211)
Pd w W w w
‘3”.;;e-6’)
47 92 84 54 73 (7)
-
l.lO-’ 2.10-i’ 3.10-s
Ref.
80T FIM FIM FIM, (110) diffusion direction (seeFig. 13) FIM, (001) diffusion direction FIM, (110) diffusion, H, treated FIM, (001) diffusion direction, H, treated (seeFig. 13) FIM; estimate FIM; estimate FIM; Do assumed 85K FIM (seeFig. 4) 74A only in (110) direction FIM FIM; Q estimated by assuming Do = k Ta2/2h (110) diffusion direction (001) diffusion direction
83Bl 78Bl
Q estimated by assuming Do = k Ta*/2 h
z 180 288...337 288...337 224...288 255...300
Bonzel
Q estimated by assuming Do = kTa2J2h FIM; Do assumed FIM FIM (seeFig. 10)
8882 66E 75G (continued) Land&-BCmstein New Series Ill:26
13.10 Surface diffusion
Ref. p. 7441
tables
729
Table I, continued
Q
Temperature range [K]
Metal (Substrate)
Diffusing species
Do m”/s
kJ/mol
W(211) W(321) W(ll1) W(211) W(110) W(110) W(ll0) W(ll0) W(l10)
w W w w, w w, w, w H
7.7. 10-7 1 10-E 2.10-15 6.2. 1O-7 1.4. 10-7 7.10-B x IO3 5.10-g
79.6 (25) 260 . . ,320 286 ... 335 79 (8) z 172 260 ... 295 36 (3) 86.9 (6) 295 ..I 320 307 . .. 345 88.8 283 ... 310 78 125 (19) 1135... 1290 143 ... 200 20
W(110)
D
1.3. 10-g
W(110)
0
4.5. 10-s
101
600...720
W(110)
0
lo-*
‘92
500 ... 570
W(l10) W(ll0) W(l10)
Si Ni Ni
3.1 . 10-S
250 ... 280
(2.10-y
68 (7) 47 47
W(211) W(110) W(110) W(110) W(211) W(321) W(l10) W(l10) W(211) W(211) W(211) W(321) W(211) W(110) W(110) W(211) W(211) W(211) W(211) W(l10)
Rh Pd Ta Ta Ta Ta Re Re Re Re Re Re Re, Ir Ir Ir Ir Ir Ir, Pt
3.3 . 10-7 4.4.10-6 9.10-12 1.9. IO-’ 1.5. 10-6 1 ’ 10-6 2.2. lO-7 7.3 . 10-8 4.8. IO-’ 4.5.10-8 8.9 . lo-’ 1 .10-g 2.7. IO-’ 6.1 . IO-’ 5. lo-” 9. lo-” 3.10-7
51.9 (17) 49 68 75 47 65 100 ,97 85 83 80.4 (21) 85 75 75 68 56 64.5 (17) 51 66 65 (6)
W(ll0) W(110) W(110) W(211) W(211) W(211) W(321) W(321) W(ll0)
Pt, Pt, Pt, MO MO MO MO MO, Xe
9 ’ 10-8 1.5. ‘10-7 5.10-7 2.4. 10-l’ 9.3 . lo-” 2.0. 10-7 1.2.10-” 2.3. lo-l6 7. lo-l2
65 (6) 77 (15) 84 (15) 54 55 68.7 (21) 53 25 4.6 (13)
Land&Bhstein New Series III/26
19.7
90.‘.. 180
IgO...
290.. .350 295 . . .360
230 ... 285
220 .. .260 235...260 285 ... 320 300... 335
235 ... 285
54 ‘. ’ 72
Bonzel
Technique/Remarks
Ref.
FIM (see Fig. 25) FIM FIM FIM (see Fig. 10) FIM (see Fig. 11) FIM (see Fig. 11) FIM FEM; removal of edge atoms FEM-CF; at T-e 140 K nearly constant D due to H tunneling FEM-CF; coverage = 0.5; constant D at T< 90 K FEM-CF; coverage z 0.6; also data on directional anisotropy FEM-CF; coverage 0.56; extensive data on coverage dependence (see Fig. 20) FIM FIM FIM; Do assumed; cluster formation at higher temperature FIM (see Fig. 25) FIM FIM FIM FIM FIM FIM FIM FIM FIM (see Fig. 29) FIM (see Fig. 25; 29) FIM FIM FIM FIM FIM FIM (see Fig. 25) FIM FIM FIM (see Fig. 12)
88W 75G
FIM FIM FIM FIM FIM (see Fig. 25) FIM FIM FEM current fluctuation,
75C, 78K 75C, 78K 75Tl 8682 80D 85T
79C
82C 78B2 87Kl 88W 78B2 75T2 70Bl
70Bl 73T 70Bl 76s 88W 70Bl 76s 70Bl 75T2 79B 88W 76Rl 76B1, 70Bl
70Bl 75s 88W
0 = 0.3 8OC
730
13.10 Surface diffusion tables
[Ref. p. 744
Table 2. Mass transfer surface self-diffusion data. Metal
DO
(Substrate) m’/s
Q
Environ- Temperature Technique/Remarks ment range [K]
Ref.
kJ/mol
84C
Gd DY Nb Nb Ta Ta Ta Ta Ta(C)
4.3. 10-s 2.2 31O-3 -
160 (IO) 99 (19) 229 (9) 193 (11) 232 (19) 252 280 267 473
Vat Vat Vat Vat; Ar Vat Vat Vat Vat Vat
Cr CrRe MO Mo(ll0) Mo(lO0) Mo(ll0) Mo(lO0) MO MO (Cl MO(C) MO MO MoRe W
8.3. IO-’ 1.1 . 1O-4 3.9. lo-’ 5.5.10-3 8.9. lo-’ 4.10-2 2.9 1.6. lO-4 9 10-4 3.7.10-2 3.10-s 6.9. IO-* 1.5. lO-3 4.10-4
209 218 216 309 376 289 (42) 402 (8) 234 236 315 202 321 244 303
Ar Ar; He Ar Ar Ar Vat Vat Ar Ar Ar Vat Vat Ar; He Vat
W W W W W(lO0)
8.5. 1O-4 1.1 . IO-’ 2.10-5 8.9. lO-5 7.6
327 132 222 264 536 (33)
Vat Vat H2 Ar Vat
W W W(C) W(Si)
9.10-S -
290 299 820 676
Vat Vat Vat Vat
Re Fe Rh(ll1) Ir(ll1) Ir Ni Ni Ni (100)
5.10-6 5.10’ 4.10-6 8. IO-* 2.6. lO-4
216 250 174 222 188
Vat; Ar H2 Vat Vat Vat Vat Vat Vat
2270.. .2770
Ni (1IO) Ni(ll0) Ni(ll0)
1.3. 10-3 168 (4) 2.4. 1O-3 179 (4) 2.lO-‘j 85
Vat Vat Vat
1196... 1725 1196...1725 IOOO...1380
4.2. lo-*
Vat
1380...1522
;; (IO) 149 (7)
200
547 .+. 647 FEM 481 ‘1. 662 FEM FEM protrusion decay 1470. .. 2570 GBG (seeFig. 27) 1200... 1400 FEM protrusion decay FIM ring rate FEM ring rate 1600.** 2400 FEM tip blunting FEM; Q variable with amount of surface C 1470... 1670 GBG; near (100) (seeFig. 27) 1620...2070 GBG; 35 at % Re 1470..*2770 GBG; near (100) 1870...2670 GBG 1870...2670 GBG 2200.. .2400 SPD 1900.. .2400 SPD (seeFig. 27) 1500... 2770 GBG (seeFig. 27) 1820..*2620 GBG; 0.02 at % C 1820...2620 GBG; 0.003 at % C 1500... 1800 FEM tip blunting 1800...2380 1820...2570 GBG; 33 at % Re x 1832... FEM tip blunting (seeFig. 27) 2700 2870.9.3270 GBG 1970...2570 ‘*‘W tracer SPD, GBG 1970...2770 GBG; near (100) 2600.. *3150 SPD (seeFig. 27) 2100...2850 1900~~~2300
1200... 1500 1700~~~2100 738 ... 1000 510... 750 1070... 1470 1196... 1725
680 72A 68P 65B 74B 81H 74B 69A2 66A 69Al 69A2 70s 72A 66A 76B2 66A 60B 66A 66N 67H 69Al 69B2, 70s 74B 74P 74B
FEM FEM tip blunting FEM; Q variable with amount of surface impurities (C; Si) 72A GBG (seeFig. 27) SPD 642 FEM ring rate 68Bl FEM ring rate FIM ring rate 64B2 FEM protrusion decay 67M2 Single scratch decay (seeFig. 30) 61B SPD; (110) direction 67Ml (seeFigs. 26; 30) SPD; (001) direction SPD; (110) direction SPD; (233) direction 68B2, (seeFigs. 26; 30) 69Bl SPD; (233) direction (seeFigs. 26; 30) (continued)
Iandolt-Bkmstein New Series 111126
Ref. p. 7441
13.10 Surface diffusion tables
731
Table 2, continued Metal DO (Substrate) m2/s
Q
Environment
Temperature Technique/Remarks range [K]
Ref.
kJ/mol
Ni Ni Ni Ni (100) Ni(ll1) Ni(lOO) Ni(ll0) Ni(ll0)
10-6 2.10-2 7.5. 1O-4 8.7. IO-’ 4.101 1.1 . 101 lo2 4.7.10-2
84 199 148 251 269 (19) 270 (11) 278 (29) 188
Vat Vat Vat Vat Vat Vat Vat Vat
1225... 1380 1380... 1690 1073... 1473 1073... 1473 1400. .. 1600 1400... 1600 1400... 1600 1023... 1570
69M
Ni(ll0) Ni(ll0) Ni(ll1) Pt Pt Pt (110) cu cu cu cu
9.10-7 5.10-2 3.10-2 4.10-7 4.0 2.9. 1O-4 6.5. 1O-2 1.8 1.4 10
73 188 159 (17) 108 (10) 90 309 164 171 (8) 203 219 228
Vat Vat Vat Vat Vat Vat Vat H2 H2 H2
773 . .. 1150 1253... 1570 887...1113 1160.. .I580 510...750 1250... 1750 1200...1750 993 . . .1343 1084...1342 1084... 1342 1123... 1333
cu
10-5
cu cu Cu(ll0)
2.10-5 3.10-2 103
75 160 264
02 H2 Vat; H,
Cu(ll0) Cu(ll0) Cu(ll1) Cu(100)
2.6. 1O-5 5.10-2 2.6. 1O-4 2.5. 10-l 2.5. 1O-4
87 250 106 160 117
Vat Vat Vat Vat Vat
780... 1220 920... 1100 750.. . 1100 793... 873 793... 873
Ag
IO4
264
H2
873 ... 1173
Ag Au(110)
5.103 1 . IO2
266 227
H2 HZ2
988...1112 1138. .. 1329
Au Au
8. lo2 -
272 42 . . .84
Vat Vat
1200... 1300 545... 885
Ag
3.10-5
Vat
580...730
Land&-BBmstein New Series III/26
92
49
H2
H2
673 . . .1273 673 ... 1273 870... 1300 1220.. .1330
SPD, random (seeFig. 26; 30) SPD, GBG SPD (seeFig. 30) SPD SPD (seeFig. 30) SPD; (001) direction (seeFigs. 8; 30) SPD; (110) direction (seeFig. 8) SPD; (110) direction (seeFig. 8) 63Ni tracer (seeFig. 30) SPD (seeFig. 26) FEM protrusion decay SPD; (001) direction SPD; (110) direction GBG (seeFig. 26) GBG, near (111) GBG; near (100) Scratch smoothing; near (100); similar data for near (111) GBG; single scratch smooth; similar data for low H, pressure GBG; 5 . lo-’ torr 0, SPD; near (110) SPD (seeFig. 26) SPD SPD; (001) SPD; (110) direction 64Cu tracer; assuming 6 = 2.10-l’ m for thickness of diffusion layer GBG; also influence of S (seeFig. 15) GBG SPD; other orientations show similar activation energies (seeFig. 26) SPD 1g8Au tracer, non-linear Arrhenius-plot l1 ‘Ag tracer
8OJ 76A 78B3
69W 62B 67M2 86P 61G 62C 63s 64Bl
68B3 69B1, 73B 85Fl 72Pl 67P 70H2 65G2, 67Gl 68M 63Gl
13.10 Surface diffusion tables
732
[Ref. p. 744
Table 3a. Mass transfer surface hetero-diffusion, metallic adsorbates. Environ- Temperature Technique/Remarks Q kJ/mol ment range [K]
Diffusing Metal (Substrate) species
Do
W(II0)
Li
10-7
9.6
Vat
114.**150
W(I12)
K
3.10-s
44.4
Vat
960 ... 1300
W(I12)
K
3.10-s
73.4
Vat
850 ... 1000
W(I12)
K
1.7.10-i
53
Vat
W(I12)
K
-
40
Vat
Ni
K
-
43
Vat
W(IOO) W(IO0) W(100) W(II0)
K Rb cs Ba
83 (8)
Vat Vat Vat Vat
820 ... 1180 820 ... 1180 820 . . .1180 loo... 170
W(II1) W(IO0)
La In
Vat Vat
645 ... 862
w W(II0)
Pd Pd
w
cu
6. IO-9
71 (8) Vat
w
Pb
1.10-9
58
Vat
350...550
MO cu
cu Ag
8.7. IO-’
52
Vat
% 10-s
73 (I 5) Vat
770 ... 1070 523...713
Ni
Ag
2.2. 1O-3 67
m*/s
6 ’ 1O-4 1.6. IO-’ 6.10-4
x 10-4 6.4. IO-’
-
87 79 16.4
280
106 100 167... 188
Vat Vat
Vat
395...490
470..*545
870 ... 1I70
500...708
Bowel
Ref.
WF; data are strongly coverage dependent, here for 0 = 0.15 (seeFig. 21) Surface ionization microscope, in (1 I I) direction Surface ionization microscope; in (I 10) direction FEM current fluctuation; coverage 0 = 0.3 FEM current fluctuation in (110) direction FEM current fluctuation increasein Q due to coadsorbed sulfur thermal ion microscope thermal ion microscope thermal ion microscope WF; strong coverage dependence; here for 0 = 0.3 (seeFigs. 22; 23) FEM SAM; strong coverage dependence; here for 0 = 0.25 FEM; curved surface SAM; directional anisotropy; also Au diffusion (seeFigs. 6; 7) FEM; also data near (I IO) and (100) vicinals FEM’probehole; strong coverage dependence; here for Pb surface concentration of x 6 * lOi atoms/cm*; also data in presenceof C SIMS Vapor deposition/oxidation for (100) and (1I I) orientations; for (110) higher values (factor IO) and directional anisotropy ‘i”Ag tracer
82L 83B2
87BI 87B2 85B2 74K 88N
87K2 86M2 84R 79B 65M 8IM2, 8IM3
70A 73R
63GI
LandokBRmslein New Serk 111’26
Ref. p. 7441
13.10 Surface diffusion tables
733
Table 3 b. Mass transfer surface hetero-diffusion, non-metallic adsorbates Diffusing Metal (Substrate) species
Do m2/s
keJ/mo*
Rh(lll)
D
8 ’ 1O-8
15.5...18.0 150...280
Ni(lOO) Ni(lOO) Ni(lOO) Ru(001) Ru(001) Ru(001) Pt(ll1)
H H D H H D D
4.5. 10-7 2.5. lO-7 8.5. 1O-7 6.3 . 1O-8 7.9. 10-E 4.6. IO-* 5.10-5
17 (2) 14.7 18.4 16.8 (20) 15.5 (20) 17.2 (20) 29
W(110) W
H H
1.8. lo-’ 3.2. IO-’
25 40...67
W(ll0)
0
3.8. IO-’
113
933 ... 1153
W(110) W(411)
0 0
3.10-5 3.1b-7
101 220
917 ... 1310 1040... 1440
W(110)
0
3.10-6
104
W
0
8.2. 1O-3 126
W(110) Cu(100) Ni(lOO) Ni(ll1) Ru(001)
N co CO CO CO
1.4.10-6
Rh(lll)
CO
W(110) Pt Ru (001) Ru (001) Ru (001)
co co c-propane c-pentane c-hexane
Land&Biirnstein New Series III/26
Temperature Technique/Remarks range [K]
223...283 211...263 211...263 260...330 230...270 260...300 200...250
6.10-5 1.2.10-g 6.10+
88 8...13 21 29 26
800...900 140 211...263 219...261 210...290
10-6
29.3
240...370
-
151 44 8.4 13.8 18.8
-
256...290
LITD; coverage range 13= 0.02 ... 0.33; data also for H LITD; low coverage LITD LITD LITD LITD; coverage dependence LITD LITD; Q and Do strongly coverage dependent; here 0 = 0.33 FEM; boundary diffusion FEM; boundary free diffusion (low coverage) WF probe; Do and Q coverage dependent; here 0 w 0.4 (seeFig. 19) SEM SEM; also Q data for W (320); coverage dependence FEM; boundary diffusion; similar Q for W (100) FEM; boundary-free diffusion (low coverage) AES LITD; estimate of Q LITD Optical diffraction (grating) LITD; coverage dependence; here for 0 w 0.58 LITD; coverage dependence; here for 8 = 0.40 FEM; boundary diffusion FEM; boundary diffusion LITD; Do assumed as lOA m2/s
Ref. 88S3 85G 87M3 86Ml 87M2 87Ml 86Sl 58G 77B 80B 58G
77P, 80El 82V 86M3 882 88D 8833 58G 67L 88M
134
33 Surface diffusion on metals (Figures)
[Ref. p. 744
Figures for 13 Terrace
Kink ,/ ,/’
.-f lf3
Mo;afomicstep Step od/otom
Terrace vocincy
a -
b
Step site
Kink site
Fig. 1. (a) Terrace-ledge-kink model of the surface of a metal single crystal. (h) One-dimensional potential energy diagram for adatoms on a single crystal surface with step and kink sites.The deeper minima arc for adatoms located at a step or at a kink, respectively.
a
b
a
(1101
-20 -16 -12 -8 C
-4
0
4
8
12
16
b
Fig. 2. Model for adatom cross-channelsurface diffusion on a fee (110) surface by an atom exchange mechanism [79H, 82D23.
Fig. 3. (a) Several surface orientations of a fee metal crystal with different symmetries; (110) and (211) surfaceshave C,, symmetry and will exhibit directional anisotropy of surface diffusion. (b) Polar plot of relative anisotropy of surfacediffusion coefficients, D,/D,, for a C,, surface [78B3].
Bonzel
Land&BGmstein New Series Ill!26
Ref. p. 7441
13 Surface diffusion on metals (Figures) -T 190
180
”
”
5.3 l/T-
5.6
I
735
60 I
I
55 I
I
50
\I 5
k
1 1, “, =z z 3
3.0
(100 1 T
3.3
4.4
4.7
5.0
16
17
18
19 -1O-3K-’ :
Fig. 4. Orientational dependence of intrinsic surface self-diffusion of Rh; on (IIO), (311) and (331) the data represent onedimensional diffusion along [IIO], while diffusion perpendicular to [IIO] is too slow to be measuredat thesetemperatures [74A]. The diffusion interval is 3 min., N is the number of jumps per interval, and I the jump distance. Units and ordinate as given in the original paper.
For Fig. 6 see next page. UP 1.0 D [ -lOegm*/s
1
-Step
direction 10011 -
t
1.0 t
Ni/W (110)
Fig. 5. Polar plot of the surface diffusion coefficient of Ni on a stepped W (110) crystal at 1170 K [82G].
Land&-Biirnstein New Series III/26
Fig. 7. Pd surface diffusion pattern obtained on an ellipsoidally shaped W single crystal. Circular bright spots are the original Pd sourcesdeposited on the W surface.The diffusion zones were obtained after annealing at 1050K for 5 min. The (110)orientation of the crystal is indicated by the center ofthe circular pattern [79B].
Bonzel
13 Surface diffusion on metals (Figures)
736
loo11 50min
15min
Omin
Ill01
[ii01
fl
[Ref. p. 744
4 Fig. 6. Pd distribution measured by scanning Auger spectroscopy on a stepped W (650) crystal after diffusion at 1028 K for 15 and 50 min. The lower part shows schematically the step and terrace orientation of the crystal [79B].
W(650)
1 1300 "C 1100 1000 900 10-i m'/ 5
00 i
700 1
600 1
l-
\ ..
\.
71
\ E-
9-
IO . 0
8 0
11 _
.
\ 0 4 Fig. 8. Directional anisotropy of surface self-diflusion on Ni(ll0) measuredin [OOl]and [liO]. The temperature dependence indicates ditkrent activation energies below [liO] and [OOl], respectively (78B3J.
o 10011 -direction . [liOl - direction 12
Jr---L 0.7 0.6
Ylk
0.8
1.0
-
.l( l-3K-1
1
l/1-
Bonzel
Land&-BCmsfein New Series III:26
Ref. p. 7441
13 Surface diffusion on metals (Figures)
IO3
102
10
4 (100) p l 1 (310) I
.;7'
(511) IO 8 6
1 I
4
104 3.2
I 3.4
I 3.6
I --I 3.8 4.0 l/l -
I
I 4.4
.'0‘3K-'
Fig. 10. Temperature dependenceof the intrinsic surface selfdiffusion coefficient of single adatoms and dimers on W (211) [74E, 75G]. Note difference in activation energies. 0
0.1
0.2
0.4 pm
0.3
0.5
X-
Fig. 9. Concentration profiles of radio-active 64Cu on various Cu single crystal surfacesplotted as log (intensity) versus distance. The diffusion temperature was 993 K in all cases. Note directional anisotropy of surface diffusion for (IIO), (331)and (511) orientations [UC]. -43
-44 IO
I Y -4:
-4E I i$ 5 -45
-4E -4! -51: 3.1 2.8
2.9
3.0
3.1 l/T-
3.2
3.3
.10-3Kq 3.5
Fig. Il. Temperature dependenceof the intrinsic surfaceselfdiffusion coeftkient of single adatoms and dimers on W (110) [78K].
Land&-Bhstein New Series III/26
3.4
3.7 l/T-
4.0
.10-jK-1
4.6
Fig. 12. Temperature dependence of intrinsic surface diffusion coefficients of Pt adatoms and Pt clusters on a W (110) surface [76B11.iV1’ in m”/s.
Bonzel
[Ref. p. 744
13 Surface diffusion on metals (Figures)
738
10“’ 5.0
5.5
6.0
7.0 l/7-
6.5
11.0
12.0 .W3K-'
11.5
13.0
Fig. 13. Temperature dcpcndence of intrinsic surface self-diffusion coefficients on Ni(ll0) in [OOl](open symbols) and [liO] (tilled symbols) directions. Annealing the Ni tip in H, ambient causesa large increasein diffusion coctlicicnts [8OTJ.
10-3 m2/s 1o-c
10-1 I rnT,+5 r,, 10:\
10-5
10-s
10-6
Cu(Pb1 I\ \
F-rY+l-bli I ! LL-l I
10-s I
,-lo-'
l----&H/ICI 10-s
< 10-7
10-s
10-g
10-s
10"
,0-l!
I
10-l 0
OS
0.2
0.3 OA PIPmox-
0.5 '
0.6
0.8
0.7
Fig. 14. Enhancement of Cu surface self-ditfusion by adsorbed Bi at 1173 K. Mcasurcmcnts arc carried out in the presenceof a Bi partial pressurep(T) whcrc p(T) is mcasurcd relative to p,,, defined at T= T(sample) [70Hl].
0.9
1.0
1.1.10-3K-'
Fig. 15. Enhanced mass transfer surface self-diffusion coefficicnts of Cu, Ag and Au due to various adsorbatcs, compared to surface self-diffusion cocfiicients on clean metals [71D].
Bowel
LandolG36mskin New S&c 111’2G
Ref. p. 7441
13 Surface diffusion on metals (Figures)
Fig. 17. Activation energy of surface self-diffusion of W as a b function of the coverage 0 of adsorbed Ni [76B2, 73P].
PV atom 3.0
10-5 ml/s 10-6
1.5
1.0
0.5 10-l' 0.70
0.85
1.00
1.15 l/T-
1.30
^
.10-j K-1
1.60
0
0.2
0.4
0.6
0.8
1.0
0.6
0.8
'
eNi -
Fig. 16. Temperature dependence of surface self-diffusion of Cu. (a) Enhancement due to adsorbed Br; (b) clean Cu (110) data; (c) clean Cu(100) data [71D].
10-g ml/:
0
0.2
0.4 Qtl -
Fig. 19. Surface diffusion coefficient of adsorbed oxygen on W (110) as a function of oxygen coverage at two different temperatures [77B]. 0
4
t-
8
12
h
16
Fig. 18. Plot of the depth of a periodic profile on Cu(110) versusannealing time at 890 K. The crystal is annealed either in vacuum or in a low partial pressure of H, or 0, gas. The surface diffusion coefficient is proportional to the slope [69Bl].
Fig. 20. Surface diffusion coefficient of adsorbed oxygen on b W (110)versusreciprocal temperature for several oxygen coverages[79C]. Landolt-BGmstein New Series III/26
Bonzel
1o-l4 m2/s
7
\
‘O-l7 1.0
l.2
1.4
1.6 1.8 l/T -
2.0 .10-3K-'
13 Surface diffusion on metals (Figures)
ld 3
1
8 .10-jK-1
I
6
5
4 Fig. 21. Temperature dependence of surface diffusion coeffkient of Li on W (110) for various coverages: (curve 1)0.025;(2)0.09;(3)0.13;(4)0.15;(5) 0.19; (6) 0.22; (7) 0.23; (8) 0.27; (9) 0.30; (10) 0.32; (If) 0.42; (f2) 0.52; (13) 0.65; (14) 0.75; (Is) 0.88; (16) 0.95 [82L]. C
10-l
10-l
I p-
lo-
10'
10 0
0.2
0.4
0.6
[Ref. p. 744
0.8
Fig. 22. Dependence of surface diffusion coellicient of Ba on W(110) on the coverage of Ba at several temperatures. Ordered Ba layers as detected by LEED are indicated on the abscissa [88N].
13 Surface diffusion on metals (Figures)
Ref. p. 7441
0.5
kJ Bo/W(llO) i~+t+++
I
He-CO/Pt(lll) I
A
/;'
300
400
K
500
TFig. 24. Relative intensity of specularly scattered He beam versus temperature for a Pt (111)crystal as target. The initial decreasein I/I0 is obtained after CO adsorption. The increase at T> 150 K is due to surface diffusion of CO from terrace sites to defect sites [82P].
IO-'* m*/s
IO-'
360 K 3i
10.* -19
IO 1o-3 I 1 10-4 ~
10-20
1o-5
I 0" lo-*'
10-b
10-q b 0
, I I I 0.2
I c
1h
0.4
1x1 0.6
0.8
1
4.u l/T-
ho Fig. 23. Coverage dependence of surface diffusion parameters for Ba on W (110).(a) Activation energy at low (full circles) and high (open circles) temperature; (b) pre-exponential factor at low (full circles) and high (open circles) temperature Wm.
Land&-Biirnstein New Series III/26
4.8W%'
Fig. 25. Temperature dependence of intrinsic surface diffusion of several adspecieson W (211).The activation energies are proportional to the heat of sublimation of the solid adspeties material [88w].
Bowel
13 Surface diffusion on metals (Figures) 10.’ m’h :u-2
[Ref. p. 744
7-
I
1o-7 m7/s
fee metals
lU8
I
I
bee metals
10-s
10-s
10-s
I s
\
I d
\\Vi-3
10-‘”
1o-1’ ‘\-Ni.1 \I-l
lo-”
4-
10-l
:Nb
\ ' ?
cu.1 0 10-11 1
,o-l;
1.8
2.0
IN ll-
Fig. 26. Comparative temperature dependence of mass transfer surface self-diffusion coefkicnts of fee metals; Th is the absolute melting temperature of a metal. Cu-1 [61G], Cu-2 [69Bl], Ni-1 [67Ml], Ni-2 [69Bl], Ni-3 [69M], Au-l [6762], Au-2 [72H], Pt [62B]. Fig. from [75Bl].
I
I 1.0
1.2
k
1.4
1 1.6 1.8 1,/r Fig. 27. Comparative temperature dependence of mass transfer surface self-diffusion coefficients of bee metals. MO [72A],Mo(100)[70S],Nb[72A], W(lOO)[69B2], Re[72A], W [60B], Cr [69A2]. Fig. from [75Bl]. For q, see Fig. 26.
10-l m’/s
lo-‘* ml/s
10-s lo-l9
10-s
I a”
1o-7
I s lo-‘t
10-s 10-s
10-n
lo-” lo-” [
,o-2:
0.9
1.0
1.1
1.2 1,/r---
1.3
1.6
1.5
Fig. 28. Comparative temperature dependence of mass transfer surface self-diffusion coetlicicnts of metals with adsorbates and clean metals. Th,is the absolute melting temperature of a clean metal or in the caseof adsorbates, the monotectic temperature of a surface phase between substrate and adsorbate [70Hl].
4 1765) f l88Wl I 2.8
3.0 l/f-
I\\ k 1 3.2
\ 40-sK-’ 3.6
Fig. 29. Reproducibility of surface diffusion data: temperature dependenceof Re surfacediffusion on W (211)measured in 1976 [76S] and 1988 [88w].
Bonzel
Land&-B6mstein New Series Ill/26
13.11 Special references : review articles
Ref. p. 7441
IF7 ml/s
1200
600 K 1LOO
1100
800
900
1000
I 167Mll 169Ml ------[76Al I2 I 10-l 0.7 0.E,
~~,00)l001
0.8
\ 0.9
1.0
1.1
1.2 .lO" K-'
Fig. 30. Comparison of mass transfer surface diffusion data for Ni. Spread in data may be due to different surface orientations and/or different degree of surface cleanliness [83B3]. Original data of [69Bl] were multiplied by the factor 2.18 for easier comparison with the data of [78B3].
13.11 Special references: review articles Gomer, R. : Surface structure and diffusion. Discuss. Faraday Sot. 28 (1959) 23. Sjostein, N.A. : Surface self-diffusion, in: Metal Surfaces, Structure, Energetics and Kinetics, Gjostein, N.A., lnd Robertson, W.D. (eds.), Metals Park, Ohio: Am. Sot. for Metals, 1963. Blakely, J.M.: Surface diffusion. Progr. Mater. Sci. 10 (1963) 395. Geguzin, Ya.E. : Diffusion along a real crystal surface, in: “Poverkhnostnayi Diffuziya i Rastekaniye,” p. 11. =ieguzin, Ya.E. (ed.), Moscow: Izd. Nauke, 1969. Bonzel, H.P., Gjostein, N.A. : In situ measurementsof surface self-diffusion of metals, in: “Molecular Processes on Solid Surfaces,” p. 533, Drauglis, E., Gretz, R.G., Jaffee, R.I. (eds.), New York: McGraw-Hill, 1969. Hirano, K., Tanaka, R. : Surface self-diffusion on metals. Nippon Kinzoku Gakkai Kaiho 9 (6) (1970) 341. Gjostein, N.A. : Surface, grain boundary, and dislocation pipe diffusion, in: “Techniques of Metals Research,” Vol. IV, Part 2, p. 405, Bunshah, R.F., Rapp, R.A. (eds.), New York: Wiley Interscience, 1970. Neumann, G., Neumann, G.M. : Surface self-diffusion of metals. Diffusion Monograph Series,Wohlbier, F.H., (ed.), Bay Village, Ohio: Diffusion Inform. Center, 1972. Geuss, JW.: Mobility of atoms and molecules over solid surfaces. Ned. Tijdschr. Vacuum Technol. 10 (1972) 59. Bonzel, H.P. : Surface’‘diffusion of metals, in: “Structure and Properties of Metal Surfaces”, Vol. 1, p. 248, Shimodaira, S., (ed.), Tokyo: Maruzen, 1973. Gjostein, N.A.: Short circuit diffusion, in: “Diffusion”, Aaronson, H. (ed.), Metals Park, Ohio: Am. Sot. for Metals, 1973.
Land&-Biimstein New Series III/26
Bonzel
13.12 References for 13
744
Ehrlich, G.: Surface self-diffusion. CRC Critical Rev. Solid State Sci. 4 (1974) 205. Bonzel, H.P.: Transport of matter at surfaces, in: “Surface Physics of Materials”, Vol. 2, p. 279, Blakely, J.M. (ed.), New York: Academic Press, 1975. Kellog. G.L., Tsong. T.T., Cowan, P.: Direct observation of surface diffusion and atomic interaction on metal surfaces. Surface Sci. 70 (1978) 485. Ehrlich, G., Stolt, K.: Ann. Rev. Phys. Chem. 31 (1980) 603. Binh. Vu Thien (ed.): Surface mobilities on solid materials. NATO-AS1 Series B, Vol. 86, New York: Plenum Press. 1983. Ehrlich, G.: Diffusion and interaction of adatoms, in: “The Structure of Surfaces”, p. 375, van Hove, M. A., Tong, S.Y. (eds.), Springer Series in Surface Science, Vol. 2, Berlin, Heidelberg, New York: Springer, 1985. Naumovets. A.G., Vedula. Yu.S.: Surface diffusion of adsorbates. Surf. Sci. Rep. 4 (1985) 365. Tsong. T.T.: Studies of solid surfaces at atomic resolution. Surf. Sci. Rep. 8 (1988) 127.
13.12 Referencesfor 13 32L 57Ml 57M2 58G 59M 60B
Langmuir, I., Taylor, J.B.: Phys. Rev. 40 (1932) 463. Miiller, E.W.: Z. Elektrochem. 61 (1957) 43. Mullins, W.W.: J. Appl. Phys. 28 (1957) 333. Gomer, R.: Discuss. Faraday Sot. 28 (1958) 23. Mullins, WW.: J. Appl. Phys. 30 (1959) 77. Barbour, J.P., Charbonnier, EM., Dolan, WW, Dyke, W.P., Martin, E.E., Trolan, J.K.: Phys. Rev. 117 (1960) 1452.
61B 61G 61M 62B 62C 62K 63B 63Gl 6362 63M 63s
64Bl 64B2 64G 642 65B 65Gl 6562 65M 65Nl 65N2 66A 66C 66E 66N 67Gl 6762 67H 67L
Blakely, J.M., Mykura, H.: Acta Metall. 9 (1961) 23. Gjostein, N.A.: Trans. Metall. Sot. ATME 221 (1961) 1039. Mullins, W.W.: Philos. Mag. 6 (1961) 1313. Blakely, J.M., Mykura, H.: Acta Metall. 10 (1962) 565. Choi, J.Y., Shewmon, P.G.: Trans. Metall. Sot. AIME 224 (1962) 589. King, R.T., Mullins, W.W.: Acta Metall. 10 (1962) 601. Blakely, J.M.: Progr. Mater. Sci. 10 (1963) 395. Geguzin, Ya.E., Kovalev, G.N.: Fiz. Tverd. Tela 5 (1963) 1687; Dokl. Akad. Nauk (USSR) (English Transl.) 142 (1963) 1290. Gjostein, N.A.: Metal Surfaces, Structure, Energetics and Kinetics, p.99, Gjostein, N.A., Robertson, W.D. (eds.), Metals Park Ohio: Am. Sot. for Metals, 1963. Mullins, W.W.: Metal Surfaces, Structure, Energetics and Kinetics, p.17, Gjostein, N.A., Robertson, W.D., (eds.), Metals Park, Ohio: Am. Sot. for Metals, 1963. Shewmon, P.G., Choi, J.Y.: Trans. Metall. Sot. AIME 227 (1963) 515. Bradshaw, F.J., Brandon, R.H., Wheeler, C.: Acta Metall. 12 (1964) 1057. Brenner, S.S.: Surf. Sci. 2 (1964) 496. Geguzin, Ya., Kovalev, G.N., Ovcharenko, N.N.: Fiz. Tverd. Tela 5 (1964) 3580. Zahn, R.: Thesis, Jernkontorets Laboratory for Powder Metall., Stockholm 1964. Bettler, P.C.: AF-AFOSR Report No. 62-297 (1965). Gjostein, N.A., Hirth, J.P.: Acta Metall. 13 (1965) 991, Acta Metall. 14 (1966) 899. Gjostein, N.A.: Coil. Intern. du CNRS No. 152, 97, Paris: Editions du CNRS, 1965. Melmed, A.J.: J. Chem. Phys. 43 (1965) 3057. Nichols, EA., Mullins, W.W.: J. Appl. Phys. 36 (1965) 1826. Nichols, EA., Mullins, W.W.: Trans. Metall. Sot. AIME 233 (1965) 1840. Allen, B.C.: Trans. Metall. Sot. AIME 236 (1966) 915. Collins, H.E., Shewmon, P.G.: Trans. Metall. Sot. AIME 236 (1966) 1354. Ehrlich, G., Hudda, F.G.: J. Chem. Phys. 44 (1966) 1039. Neumann, G.M., Hirschwald, W., Stranski, I.N.: Z. Naturforsch. 21 a (1966) 807. Gjostein, N.A.: Trans. Metall. Sot. AIME 239 (1967) 785. Gjostein, N.A.: Surfacesand Interfaces, I. Chemical and Physical Characteristic, Burke, Reed, Weiss, (eds.), Syracuse University Press, 1967. Ho-Yi, L.: Jernkont. Ann. 151 (1967) 801. Lewis, R., Gomer, R.: Nuovo Cimento., Suppl. Serie I 5 (1967) 506.
Land&-BBmstein New Series 111126
13.12 References for 13 67Ml 67M2 67P 67s 68Bl 68B2 68B3 68G 68M 680 68P 68W 69Al 69A2 69Bl 69B2 69M 69R 69W 70A 70Bl 70B2 70G 70Hl 70H2 70s 71D 71K 710 72A 72H 72Pl 72P2 73B 73Gl 7362 7363 73P 73R 73T 74A 74B 74E 74G 74K 74P 75Bl 75B2 75c 75G 75s
745
Maya, P.S., Blakely, J.M.: J. Appl. Phys. 38 (1967) 698. Melmed, A.J.: J. Appl. Phys. 38 (1967) 1885. Perdereau, J., Rhead, G.E.: Surf. Sci. 7 (1967) 175. Sizmann, R., Englert, G.: Z. Angew. Phys. 23 (1967) 81. Bettler, P.C., Barnes, G.: Surf. Sci. 10 (1968) 165. Bonzel, H.P., Gjostein, N.A.: J. Appl. Phys. 39 (1968) 3480. Bonzel, H.P., Gjostein, N.A.: Phys. Status Solidi 25 (1968) 209. Geguzin, Ya.E., Kaganovskiy, Yu.S., Stoychev, N.V.: Fiz. Met. Metalloved. 26 (2) (1968) 298. McLean, M., Hirth, J.P.: Surf. Sci. 12 (1968) 177. Odishariya, G.A.: Fiz. Tverd. Tela 10 (1968) 1425. Pantor, D.M., Sokolskaya, I.L.: Fiz. Tverd. Tela 10 (1968) 2473. Wynblatt, P., Gjostein, N.A.: Surf. Sci. 12 (1968) 109. Allen, B.C.: Trans. Metall. Sot. AIME 245 (1969) 1621. Allen, B.C.: Trans. Metall. Sot. AIME 245 (1969) 2089, and private communication (1971). Bonzel, H.P., Gjostein, N.A. : in: “Molecular Processes on Solid Surfaces,” p.533, Drauglir E., Gretz, R.G., Jaffee, R.I., (eds.), New York: McGraw-Hill, 1969. Bowden, F.P., Singer, K.E.: Nature 222 (1969) 977. Mills, B., Douglas, P., Leak, G.M.: Trans. Metall. Sot. AIME 245 (1969) 1291. Rhead, G.E.: Surf. Sci. 15 (1969) 353. Wolfe, J.R., Weart, H.W.: in: “The Structure and Chemistry of Solid Surfaces”, p.32-1, Somorja G.A., (ed.), New York: Wiley, 1969. Abramenkov, A.D., Slezov, V.V., Tanatarov, L.V., Fogel, Ya.M. : Fiz. Tverd. Tela 12 (10) (1970) 2929 Sov. Phys. Solid State (English Transl.) 12 (1971) 2365. Bassett, D.W., Parsley, M.J.: J. Phys. D 3 (1970) 707. Bonzel, H.P.: Surf. Sci. 21 (1970) 45. Gjostein, N.A. : in: “Techniques of Metals Research”, Vol.IV, Part 2, p.405, Bunshah, R.F., RapI R.A. (eds.), New York : Wiley Interscience, 1970. Henrion, J., Rhead, G.E. : in: “Diffusion Processes”, Thomas Graham Memorial Symposium, Nel York: Gordon and Breach, 1970. Hough, R.R.: Ser. Metall. 4 (1970) 559. Singer, K.E.: Coll. Intern. du CNRS No. 187 (1970) 199. Delamare, F., Rhead, G.E. : Surf. Sci. 28 (1971) 267. Kleint, Ch.: Surf. Sci. 25 (1971) 411. Olson, D.L.: Ph. D. Thesis, Cornell University, Ithaca, 1971. Allen, B.C.: Metall. Trans. 3 (1972) 2544. Henrion, J.: Ph. D. Thesis, University of Paris, 1972. Peraillon, B., Torrens, I.M., Levy, V.: Ser. Metall. 6 (1972) 611. Pichaud, M., Drechsler, M.: Surf. Sci. 32 (1972) 341. Bonzel, H.P.: in: “Structure and Properties of Metal Surfaces”, Vol.1, p.248, Shimodaira, S. (ed. Tokyo: Maruzen, 1973. Gal, V.V., Gruzin, P.L., Yudina, G.K.: Phys. Status Solidi (a) 15 (1973) 659. Gomer, R.: Surf. Sci. 38 (1973) 373. Graham, W.R., Ehrlich, G.: Phys. Rev. Lett. 31 (1973) 1407. Pichaud, M., Drechsler, M.: Surf. Sci. 36 (1973) 813. Roulet, C.A.: Surf. Sci. 36 (1973) 295. Tsong, T.T.: Phys. Rev. B7 (1973) 4018. Ayrault, G., Ehrlich, G.: J. Chem. Phys. 60 (1974) 281. Bettler, P.C., Bennum, D.H., Case, C.M. : Surf. Sci. 44 (1974) 360. Ehrlich, G.: CRC Critical Rev. Solid State Sci. 4 (1974) 205. Graham, WR., Ehrlich, G.: Surf. Sci. 45 (1974) 530. Korner, W.: Jpn. J. Appl. Phys. Suppl. 2, Pt.2. (1974) 75. Piquet, A., Roux, H., Binh, Vu Thien, Uzan, R., Drechsler, M.: Surf. Sci. 44 (1974) 575. Bonzel, H.P.: in: “Surface Physics of Materials,” Vol. 2, p.279, Blakely, J.M. (ed.), New York Academic Press, 1975. Brailsford, A.P., Gjostein, N.A. : J. Appl. Phys. 46 (1975) 2390. Cowan, P., Tsong, T.T.: Phys. Lett. 53A (1975) 383. Graham, WR., Ehrlich, G.: Thin Solid Films 25 (1975) 85. Sakata, T., Nakamura, S.: Surf. Sci. 51 (1975) 313.
Land&-Bhnstein New Series III/26
Bowel
746 75Tl 75T2 76A 76B1 76B’ 76B3 76Rl 76R2 76s 77B 77E 77P 78B1 78B2 78B3 78K 78R 79B 79c 79H 80B 80C 80D 80El 80E2 8OJ 80T 8OW 81C 81D 81H 81Ml 81M2 81M3 81M4 81R 82B 82C 82Dl 82D2 82G 82L 82P 82V 8381 83B2 83B3 83G 83s 83V 84Bl 84B2 84B3 84C
13.I2 References for 13 Tsong. T.T., Cowan, P., Kellogg, G.: Thin Solid Films 25 (1975) 97. Tsong. T.T., Kellogg. G.: Phys. Rev. B 12 (1975) 1343. Azzerri, N., Colombo, R.L.: Metallogr. 9 (1976) 233. Bassett, D.W.: J. Phys. C 9 (1976) 2491. Binh. Vu Thien, Chaudier, M., Couturier, J.C., Uzan, R., Drechsler, M.: Surf. Sci. 57 (1976) 184. Binh, Vu Thien, Uzan, R., Drcchsler, M.: Surf. Sci. 57 (1976) 118. Reed. D.A., Ehrlich, G.: J. Chem. Phys. 64 (1976) 4616. Roux, H., Piquet, A., Uzan, R., Drechsler, M.: Surf. Sci. 59 (1976) 97. Stolt, K., Wrigley, J.D., Ehrlich, G.: J. Chem. Phys. 65 (1976) 3206. Butz. R., Wagner, H.: Surf. Sci. 63 (1977) 448. Ehrlich, G.: Surf. Sci. 63 (1977) 422. Polak, A., Ehrlich, G.: J. Vat. Sci. Technol. 14 (1977) 407. Bassett. D.W., Webber, P.R. : Surf. Sci. 70 (1978) 520. Bassett, D.W.: Thin Solid Films 48 (1978) 237. Bonzel, H.P., Latta, E.E.: Surf. Sci. 76 (1978) 275. Kellogg. G.L., Tsong. T.T., Cowan, P.: Surf. Sci. 70 (1978) 485. Roux, H., Piquet, A., Pralong, G., Uzan, R., Drechsler, M.: Surf. Sci. 71 (1978) 375. Butz, R., Wagner, H.: Surf. Sci. 87 (1979) 69. Chen, J.R., Gomer, R.: Surf. sci. 79 (1979) 413. Halicioglu, T.: Surf. Sci. 79 (1979) L 346. Bowker, M., King, D.A.: Surf. Sci. 94 (1980) 564. Chen, J.R., Gomer, R. : Surf. Sci. 94 (1980) 456. Di Foggio, R., Gomer, R.: Phys. Rev. Lett. 44 (1980) 1258. Ehrlich, G.: J. Vat. Sci. Technol. 17 (1980) 9. Ehrlich, G., Stolt, K.: Ann. Rev. Phys. Chem. 31 (1980) 603. Jaunet, J.: Ph. D. Thesis, University of Paris, 1980. Tung. R.T., Graham, W.R.: Surf. Sci. !)7 (1980) 73. Wrigley, J.D., Ehrlich, G.: Phys. Rev. Lett. 44 (1980) 661. Cousty, J., Peix, R., Perraillon, B.: Surf. Sci. 107 (1981) 586. Drechsler, M., Mttois, J.J.,Heyraud, J.C.: Surf. Sci. 108 (1981) 549. Hok, S., Drechsler, M.: Surf. Sci. 107 (1981) L362. Mazenko, G., Banavar, J.R., Gomer, R.: Surf. Sci. 107 (1981) 459. Morin, R., Drechsler, M.: Surf. Sci. 111 (1981) 128. Morin, R., Drechsler, M.: Surf. Sci. 107 (1981) 140. Mruzik, M.R., Pound, G.M.: J. Phys. F: Met. Phys. 11 (1981) 1403. Reed, D.A., Ehrlich, G.: Surf. Sci. 102 (1981) 588. Binnig. G., Rohrer, H., Gerber, Ch., Weibel, E.: Phys. Rev. Lett. 49 (1982) 57. Casanova, R., Tsong. T.T.: Thin Solid Films 93 (1982) 41. Dabrowski, A., Kleint, Ch.: Surf. Sci. 119 (1982) 118. De Lorenzi, G., Jacucci, G., Pontikis, V.: Surf. Sci. 116 (1982) 391. Geguzin, Ya.E., Kaganovski, Yu.S., Mikhailov, E.G.: Ukr. Fiz. Zh. 27 (1982) 1887. Loburets, A.T., Naumovets, A.G., Vedula, Yu.S.: Surf. Sci. 120 (1982) 347. Poelsema, B., Verheij, L.K., Comsa, G.: Phys. Rev. Lett. 49 (1982) 1731. Viswanathan, R., Burgess,jr., D.R., Stair, P.C., Weitz, E.: J. Vat. Sci. Technol. 20 (1982) 605. Bassett, D.W.: in: “Surface Mobilities on Solid Materials,” Binh, Vu Thien (ed.), NATO ASI Series B, Vol.86, p.74, New York: Plenum Press, 1983. Bayat, B., Wassmuth, H.W.: Surf. Sci. 133 (1983) I. Bonzel, H.P.: in: “Surface Mobilities on Solid Materials,” Binh, Vu Thien (ed.), NATO AS1 Series B, Vol.86, p.195, New York: Plenum Press, 1983. Gomer, R.: in: “Surface Mobilities on Solid Materials,” Binh, Vu Thien (ed.), NATO ASI SeriesB, ~01.86,p.7, New York: Plenum Press, 1983. Schrammen, P., H6lzl, J.: Surf. Sci. 130 (1983) 203. Venables, J.A., Spiller, G.D.T.: in: “Surface Mobilities on Solid Materials,” Binh, Vu Thien (ed.), NATO AS1 Series B, Vol.86, p.341, New York: Plenum Press, 1983. Blaszczyszyn, M.: Surf. Sci. 136 (1984) 103. Bonzel, H.P., Preuss, E., Steffen, B.: Appl. Phys. A 35 (1984) 1. Bonzel, H.P., Preuss, E., Steffen, B.: Surf. Sci. 145 (1984) 20. Ciszewski, A., Melmed, A.J.: Surf. Sci. 145 (1984) L 509. Bonzel
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13.12 References for 13 84R 85Bl 85B2 85E 85Fl 85F2 85G 85K 85N 85T 86B 86G 86K
747
Roux, H., Pique& A., Uzan, R., Drechsler, M.: Surf. Sci. 141 (1984) 301. Binh, Vu Thien, Melinon, P.: Surf. Sci. 161 (1985) 234. Blaszczyszyn, M.: Surf. Sci. 151 (1985) 351. Ehrlich, G.: in: “The Structure of Surfaces,” p.375, van Hove, M.A., Tong, S.Y., Springer Series in Surface Science, Vo1.2, Berlin: Springer, 1985. Freyer, N.: Ph. D. Thesis, RWTH Aachen; Report Jill-2003, 1985. Futamoto, M., Hanbiicken, M., Harland, C.J., Jones, G.W., Venables, J.A.: Surf. Sci. 150 (1985) 430. George, SM., De Santolo, A.M., Hall, R.B.: Surf. Sci. 159 (1985) L 425. Kellogg, G.L.: J. Chem. Phys. 83 (1985) 852. Naumovets, A.G., Vedula, Yu.S.: Surf. Sci. Rep. 4 (1985) 365. Tringides, M., Gomer, R. : Surf. Sci. 155 (1985) 254. Binnig, G., Fuchs, H., Stoll, E.: Surf. Sci. 169 (1986) L 295. Gomer, R.: Appl. Phys. A 39 (1986) 1. Kay, G.W.C., Laby, T.H. : Tables of Physical and Chemical Constants, 15th ed., London: Longman, 1986.
86Ml 86M2 86M3 86P 86Sl 8682 86V 87Bl 87B2 87B3 87G 87Kl 87K2 87Ml 87M2 87M3 88B 88D 88F 88J 88K 88M 88N 88R 88Sl 8882 8833 88Tl 88T2 88W 882 89F
Mak, C.H., Brand, J.L., Decker& A.A., George, S.M. : J. Chem. Phys. 85 (1986) 1676. Morris, M.A., Barnes, C.J., King, D.A.: Surf. Sci. 173 (1986) 618. Mullins, D.A., Roop, B., White, J.M.: Chem. Phys. Lett. 129 (1986) 511. Preuss, E., Freyer, N., Bonzel, H.P. : Appl. Phys. A 41 (1986) 137. Seebauer,E.G., Schmidt, L.D.: Chem. Phys. Lett. 123 (1986) 129. Stepien, Z.M., Kukulka, J., Lenkow, W.: J. Phys. (Paris) Colloq. C 7, 47 (1986) 165. Villain, J.: Europhys. Lett. 2 (1986) 531. Beben, J., Klein& Ch., Meclewski, R.: Z. Phys. B, Cond. Matter 69 (1987) 319. Beben, J., Kleint, Ch., Meclewski, R.: J. Phys. (Paris) Colloq. C6, 48 (1987) 545. Binh, Vu Thien, Uzan, R.: Surf. Sci. 179 (1987) 540. Gong, YM., Gomer, R.: J. Phys. (Paris) Colloq. C6, 48 (1987) 15. , Kellogg, G.L.: Surf. Sci. 187 (1987) 153. Kozlowski, G., Surma, S.: J. Phys. (Paris) Colloq. C6 48 (1987) 27. Mak, C.H., Brand, J.L., Koehler, B.G., George, S.M.: Surf. Sci. 188 (1987) 312. Mak, C.H., Brand, J.L., Koehler, B.G., George, S.M.: Surf. Sci. 191 (1987) 108. Mullins, D.R., Roop, B., Costello, S.A., White, J.M.: Surf. Sci. 186 (1987) 67. Brand, J.L., Mak, C.H., Deckert, A.A., Koehler, B.G., George, SM.: J. Vat. Sci. Technol. A 6 (1988) 842. Deckert, A.A., Brand, J.L., Arena, M.V., George, S.M. : J. Vat. Sci. Technol. A 6 (1988) 794. Frenken, J.W.M., Toennies, J.P., W611,Ch.: Phys. Rev. Lett. 60 (1988) 1727. Jaklevic, R.C., Elie, L.: Phys. Rev. Lett. 60 (1988) 120. Kleint, Ch.: Surf. Sci. 200 (1988) 472. Mak, C.H., Koehler, B.G., George, SM. : J. Vat. Sci. Technol. A 6 (1988) 856. Naumovets, A.G., Poplavsky, V.V., Vedula, Yu.S.: Surf. Sci. 200 (1988) 321. Reutt-Robey, J.E., Doren, D.J., Chabal, Y.J., Christman, S.B.: Phys. Rev. Lett. 61 (1988) 2778, J. Vat. Sci. Technol. A 7 (1989) 2227. Schneir, J., Sonnenfeld, R., Marti, O., Hansma, P.K., Demuth, J.E., Hamers, R.J. : J. Appl. Phys. 63 (1988) 717. Schwoebel, P.R., Kellogg, G.L.: Phys. Rev. B 38 (1988) 5326. Seebauer,E.G., Kong, A.C.F., Schmidt, L.D. : J. Chem. Phys. 88 (1988) 6597. Tsong, T.T.: Rep. Prog. Phys. 51 (1988) 759. Tsong, T.T.: Surf. Sci. Rep. 8 (1988) 127. Wang, S.C., Ehrlich, G.: Surf. Sci. 206 (1988) 451. Zhu, X.D., Rasing, Th., Shen, Y.R.: Phys. Rev. Lett. 61 (1988) 2883. Frenken, J.W.M., Hinch, B.J., Toennies, J.P., Wdll, Ch.: Phys. Rev. (to be published).
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