Table Of ContentOther Pergamon Titles of Interest
ASHBY and BROWN Perspectives in Creep Fracture
ASHBY and JONES Engineering Materials 1
ASHBY and JONES Engineering Materials 2
ASHWORTH Ion Implantation into Metals
COMINS and CLARK Specialty Steels and Hard Materials
FULLENWIDER Hydrogen Entry and Action in Metals
MCQUEEN Strength of Metals and Alloys (3 Volumes)
VEZIROGLU Metal-Hydrogen Systems
Pergamon Journals of Related Interest
Acta Metallurgica
Canadian Metallurgical Quarterly
Corrosion Science
Materials & Society
Materials Research Bulletin
Metals Forum
Scripta Metallurgica
The Physics of Metals & Metallography
PERSPECTIVES
IN
HYDROGEN IN METALS
Collected Papers on the Effect of Hydrogen
on the Properties of Metals and Alloys
Edited by
M. F. ASHBY
University Engineering Department, Cambridge, U. K.
and
J. P. HIRTH
Metallurgical Engineering Department, Ohio State University
Columbus, Ohio, U.S.A.
PERGAMON PRESS
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Copyright © 1986 Pergamon Books Ltd.
All Rights Reserved. No part of this publication may be reproduced,
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First edition 1986
Library of Congress Cataloging in Publication Data
Perspectives on hydrogen in metals.
"Previously published in various numbers of the journals Acta
metallurgica and Scripta metallurgica, 1981-1985"—T.p. Verso.
Includes index.
I. Metals—Hydrogen content. I. Ashby, M. F.
II. Hirth, John Price, 1930-
TN690.2.P45 1986 669'.94 86-21228
British Library Cataloguing in Publication Data
Perspectives on hydrogen in metals: collected
papers on the effects of hydrogen on the
properties of metals and alloys.
1. Metals—Hydrogen content
I. Ashby, Michael F. II. Hirth, J. P.
IH. Acta metallurgica IV. Scripta metallurgica
669'.92 TN690
ISBN 0-08-034813-0
Previously published in various numbers of the journals Acta
Metallurgica and Scripta Metallurgica 1981-1985.
Printed in Great Britain by A. Wheaton & Co. Ltd., Exeter
FOREWORD
Over the past decade there has been a significant advance in our understanding of the effects of hydrogen on
the physical and mechanical properties of metals and alloys. Work on the subject burgeoned in the same
period, stimulated by interest in hydrogen as a fuel source and the longer term concern about hydrogen
embrittlement. Many of these advances were reported in Acta Metallurgica and Scripta Metallurgica, in
some cases as an extended series of papers on the same subject. Also, hydrogen was the topic o fa number of
Overviews and of one Viewpoint Set.
The contributions included work on hydrogen in amorphous materials, solubility and other thermo-
dynamical properties, diffusi vity, stress induced diffusion, trapping, hydride formation, plastic deformation
and embrittlement. Because of the cohesiveness of this body of work and in order to provide a convenient
reference work in the subject, the recent papers are combined here in a single volume.
February 1986 J. P. HIRTH
M. F. ASHBY
SOLID SOLUTIONS OF Pd CONTAINING HYDROGEN
AND A NOBLE METAL SUBSTITUTIONAL COMPONENT—I.
THERMODYNAMIC BEHAVIOR
M. YOSHIHARA and R. B. McLELLAN
Department of Mechanical Engineering and Materials Science,
Rice University, Houston, TX 77001, U.S.A.
{Received 20 November 1980: in revised form 2 April 1981)
Abstract—Elastic data have been measured for Pd-based solid solutions containing Cu, Au. and Ag in
the concentration range 0-50 at.° of substitutional solute and in the temperature range 300-1200 K.
0
The elastic data have been used to evaluate a statistical mechanical model for solid solutions of
hydrogen in Pd-based solutions containing noble metals. The elastic data are used to calculate that
contribution to the partial thermodynamic functions of the dissolved interstitial atoms which arises due
to the change in the specific volume of the metal lattice as the substitutional atom concentration is
varied.
Résumé—Nous avons mesuré les propriétés élastiques de solutions solides à base de Pd contenant une
concentration en soluté substitutionnel Cu, Au et Ag comprise entre O et 50at.°o, dans le domaine de
températures compris entre 300 et 1200 K.
Nous avons utilisé ces mesures élastiques pour appliquer un modèle de mécanique statistique aux
solutions solides de Thydrogène dans des solutions solides à base de Pd contenant des métaux nobles.
Ces mesures d'élasticité servent à calculer la partie de la contribution des atomes interstitiels dissous aux
fonctions thermodynamiques partielles, qui provient du changement du volume spécifique du réseau
métallique lorsqu'on change la concentration en atomes substitutionnels.
Zusammenfassung—Elastische Daten sind an einer Reihe Pd-reicher Mischkristalle mit Cu, Au, und Ag
im Konzentrationsbereich 0-50 At. ° und im Temperaturbereich 300-1200 K gemessen worden.
0
Die elastischen Daten sind dazu verwendet worden, ein statistisch mechanisches Modell für Pd-
Edelmetall-Mischkristalle, die auch Wasserstoff enthalten, auszuwerten. Die elastischen Daten ermögli
chen die Berechung des Beitrages zu den partiellen thermodynamischen Funktionen der gelösten Zwis
chengitteratome, der durch die als Folge der Änderung der Edelmetallkonzentration stattfindende
Änderung des spezifischen Volumens des Metallgitters entsteht.
INTRODUCTION The object of the present work is to make an
exhaustive series of elastic measurements on the Pd-
In a recent treatment [1] of the thermodynamic based alloys containing Au, Ag and Cu spanning the
properties of solid solutions of an interstitial species i temperatures and composition ranges in which
in a 'binary solvent* lattice with V and U substi thermodynamic data are available. This will enable a
tutional atoms, the partial thermodynamic functions more rigorous evaluation of the statistical model to
of the /-species was written in terms of a 'statistical be undertaken.
contribution* which is derived from considering the The alloys Pd-(Ag, Cu>-H are also interesting in
distributions of the /-atoms in the octahedral inter that the diffusivity of H in the V-U matrix is unaffec
stitial sites (ceils) in the V-U lattice. The second part ted by the presence of large Ag concentrations, and
of the thermodynamic functions is a "volume term* mildly depressed by Cu. In a second paper, diffusivi-
which accounts for the change in specific volume of ties of H in Pd-Au solutions will be reported and the
the V-U-solution as the U-concentration changes. relation between the thermodynamic and kinetic
The exact forms of the relationships [1] will be given properties of the Pd-based alloys containing hydrogen
in a later section. The evaluation of the validity of this will be discussed.
model depends upon having available elastic data in
the form of the variation of the bulk modulus of the
EXPERIMENTAL PROCEDURE
V-U binary system with both temperature and
U-concentration. It has been shown [2] that for sol Sample preparation
utions of hydrogen in Pd-Ag, Pd-Au, and Pd-Cu The wires needed for the thin-line ultrasonic elastic
alloys the model is in reasonable accord with experi measurements were made by arc melting MARZ-
mental measurements of the partial enthalpy of sol grade elements under a protective atmosphere of
ution of H in the limit of infinite dilution of i and the argon. Wires were drawn from the bulk alloys and
limited elastic data for the pure solvent metal (Pd). were ^0.1 m. in length and -3 x 10~Am. in diam-
3
4 M. Yoshihara and R. B. McLellan
the shear wave were attenuated greatly at the higher
temperatures and measurements could only be made
near room temperature.
Experimental results
The measured data for the Young's modulus Ey of
the three alloy systems are shown as functions of tem
perature in Fig. 1 [U = Au], Fig. 2 [U = Ag], and
Fig. 3 [U = Cu]. Each different symbol represents a
different U concentration, as indicated on the dia
gram and the common symbol (Δ) is used for the
pure solvent metal (Pd). It will be noted that the data
for all 4 pure metals involved show a non-linear vari
ation of Ey with temperature. This phenomenon is
also reflected in the alloys.
A better pictorial idea of the variation of μ or Ey
with 9 a given temperature is given in Fig. 4, which
U
shows the actual data points for Ey and μ measured
at room temperature for all three alloy systems.
In auxiliary experiments on the pure metals, the
elastic properties (including μ) were investigated using
samples of very different grain sizes and also using a
copper single crystal wire to measure C and C in
44 u
the [100] direction. All these measurements are in
0.5' ' ' ■ 1 1 1 i Ì 1 —NI good agreement with those shown in Figs 1, 2 and 3
20Û 400 600 800 1000 1200 and will be published separately on account of their
T (K)
relevance to self-diffusion in the noble metals.
Fig. 1. Temperature variation of the Young's modulus of The actual number of data points represented by-
Pd-Au solid solutions. Figs 1, 2 and 3 is very large. Assuming that the Pois-
son's ratio is independent of temperature, the value of
μ measured at room temperature can be used to cal-
eter. Before making the elastic measurements, the
wires were annealed at 900CC for 10 h under vacuum
(^ 10~4 N/m2). The compositions of the wires varied
·'— Ας
in the range 1-50 at% U. 0 — 75%
* — 50 %
Elastic measurements A —30%
2—20%
The elastic measurements were made using the Φ — 10%
thin-line ultrasonic technique in which the velocities
of longitudinal and transverse waves in the wire are
measured by introducing elastic waves into the wire
using a magnetostrictive lead-in wire coupled to an
electronic recording system. The details of the experi
mental equipment, exact measurement of the wire-
length and density, and details of the temperature
control and measurement have been given in a pre
vious publication [3].
The Young modulus Ey and the shear modulus μ
can be obtained from the relations
Ey = p V\
μ = ρν\
where V and V are the longitudinal and transverse
i t
wave velocities and p is the density. The ratio of the
diameters of the lead-in wire to the sample wire was
^3:1, which yields a large amplitude of the end- T(K)
reflection echoes for the longitudinal wave over the Fig. 2. Temperature variation of the Young's modulus of
temperature range measured. However, the echoes for Pd-Ag solid solutions.
Solid Solutions of Pd Containing Hydrogen — I 5
hedral sites in the f.c.c. V-U lattice (V - Pd solvent,
U = substitutional solute metal), the variation of the
partial molar enthalpy of the /-species at infinite dilu
tion of i, H?\ as a function of the atom ratio of U, 0,
U
is given by
r0u VAVB
R?-m- | ^(i-«T)de
u
JO s V
A€xz(l-e f-»9
u u
Φ
where
ψ = χζ(1 -0 )(2-υ0 + (1 -0J* (3)
Μ Μ
In these equations V is the partial molar volume of
{
the i-atoms, AV = V° - V° (V° = molar volume of
u v
pure component), B is the bulk modulus of the sol
ution, a its thermal expansivity, and Ae = 6e- - e\ is
the difference between the energies needed to intro
duce an i-atom into an octahedral %ceir with no
U-atoms (€°) and one U atom (€*).
The quantity x is exp (Αε/kT), V is the molar
s
volume of the V-U-solution, z is the number of lattice
atoms in the shell of atoms surrounding a given site
(6) and Hll is the partial enthalpy of the i-species in
7' ' ' I 1 1 1 i 1 1 1 the V-i binary system.
200 400 600 800 lOOO 1200
T(K) This expression for Hj° takes into account the dila
tion of the 'binary solvent lattice' when B changes.
u
Fig. 3. Temperature variation of the Young's modulus of This 'volume correction' is the integral term in equa
Pd-Cu solid solutions. tion (2). The integral term is a macroscopic quantity
culate the bulk modulus B as a function of T and Pd-Cu
U-concentration. In auxilliary experiments using only
Cu, both μ and Ey were measured up to 1200 K and
Poisson's ratio found to be constant. A least-squares
programming technique was used to fit the data to
the representational form
B = B' + αθ„ - be T
0 u
where 0 is the atom fraction of U and B, a, and b
M 0
are constants. This formulation was shown, by differ
ence techniques, to be valid in the range 0 = 0 - 0.1
U
with an uncertainty of < 5%. The results found are as
follows expressing B in units of N/m2 :
B = (1.797 + 1.436 x 10~2 0 - 9.42 x 10"6
Cu M
ej) io"
B = (1.722 + 0.989 x 10"2 0 - 3.89 x HT6 [1]
Au M
0 T) x 10"
M
B = (1.879 + 0.534 x 10~2 0„ - 4.24 x 10"6
Ag
0 T) x 10"
U
The compositions of some randomly selected wires
were checked by microprobe analysis. In all cases the
results were within 1% of the composition fixed
nominally by the weights of materials.
' ' I l I I i i i \ I
0 10 20 30 40 50 60 70 80 90 100
100 Au
Pd Concentration (At. %) Jj
DISCUSSION
Fig. 4. Variation of the Young's modulus Ey and the shear
In terms of a statistical model given recently [1] in modulus μ for Pd-based alloys containing Au, Ag, and Cu
which the interstitial (i) atoms are distributed in octa at room temperature.
6 M. Yoshihara and R. B. McLellan
derived from bulk thermodynamic reasoning [1] and calculated at T = 555 K and is indicated on Figs 5
does not depend on the details of the atomic distribu and 6. There is virtually no difference between σ for
tion. The last term in this relation is the statistical Ag and Au.
part of the enthalpy resulting from the distribution of Now Ag and Au act as antitrapping sites for
the i-atoms between the various sites [1]. It should be H-atoms in palladium. This is implied by the diffusion
noted that cells with more than one U-atom are not data for H in Pd containing Au or Ag [1] and implies
considered and that Δε is strictly constant. The V-U that Ae < 0 (see paper II in this series). In this case φ
lattice in this model is not held rigid whilst the i-atom is not sensitive to the numerical value of te/kT and φ
is being introduced, but merely maintained at its for the two values -4 and -lOkJ/mole have been
molar volume for which <9 = 0 prior to forming the included in Fig. 5. The dashed line represents Hf>
U
ternary solution. For Au and Ag the effect of the calculated from σ and φ (Δέ = -5kJ/mole). This is
U-atoms is to dilate the metal lattice (AV - 1.35 and to be compared with the measured partial enthalpies.
1.4cm3/mole respectively) for the Cu there is a com The agreement is satisfactory, especially when it is
pression of the lattice (ΔΚ = -1.71). remembered that^ the energy changes are very small.
A limited discussion of the validity of equation (1) The measured Er changes only by -4kJ/mole on
has been given in [2] based on the then available data going from 0 to 10% of Au or Ag, ie a change of less
for B in the limit when 9 = 0. The current elastic than 0.05 eV. The case of copper is interesting. The
U
measurements on Pd-based solutions containing Au, measured data points (O) show a slight dip, and then
Ag and Cu enable a more thorough evaluation of the an increase in H? with increasing ^-values. Recent
solid solution model to be undertaken. diffusivity measurements [8] for H in Pd-Cu alloys at
The elastic data represented in Figs 1, 2 and 3 have 300K indicate that Cu probably acts as a trap site in
been condensed into the form Pd-Cu solutions. This point will be discussed in more
detail in the second paper of this series. Thus the
B = Bo - à9
u appropriate values of Ae are positive. In this case φ is
by evaluating B from the equation [1] at the tempera very sensitive to the numerical value of Ae/kT as the
ture of T = 555 K, at which temperature thermodyn family of φ-curves in Fig. 6 for Ae = 4, 5.6, and 6.0 kJ/
amic data are available. This formalism is valid up to mole show. These curves have been combined with
about θ = 0.1. the σ calculated in equation (5) to yield the calculated
ν
For ease of discussion, let us write equation (2) in Er - curves shown in Fig. 6 concomitant to each Ae.
the form It is interesting to note that the calculation_predicts
an initial decrease and then an increase in H·30 as 0
H? = ff? - σ -φ (4) U
increases. Again the general agreement is satisfactory,
where φ represents the final term in equation (2) and
a represents the elastic term. Combining equations (4)
and (2) and using tables of standard integrals [4] and 210
the approximation 1 > zT yields the following ex
pression for (j.t
214
V£V
wl
δθ« - B, -|,n„ ΨΘ )\ (5)
+ Μ
218}-
where V- is the partial molar volume of i, and
x
φ = AV/V° . Since for the three L/-species considered, o
V
E
ψ ^ 0.1 and we can consider 0-yalues up to only
u
about 6 ~ 0.1, since otherwise the statistical con 222
U
siderations used in calculating φ fail[l], ln(l + φθ^ 8-
IX
can be replaced by ψθ„ and equation (5) becomes
I
2261
σ= ν-^-Βφθ (6)
0 α
Now Er has been measured by Kleppa and his co- 2301
workers. Their data, referring to 555 K, are given in
Fig. 5 for Au (D symbols) [5] and for Ag (O symbols)
[6], and for Cu in Fig. 6 [7]. For Au and Ag, H*
234
becomes more negative as 0 increases. The effect is 0.5
U
reversed in the case of Cu. The quantity σ has been
Fig. 5. Measured and calculated ( ) variation of the_par
t In evaluating the integral note that σ depends on U0 tial molar enthalpy of Hydrogen at infinite dilution Er at
only through B (i.e. B - B - δθ ) and V = V° 0 + V5°55 K in Pd-Au-H and Pd-Ag-H solid solutions as a
0 α s u U v
d - eu) = K? + eu ΔΚ function of the atom fraction 0U of Au or Ag.
Solid Solutions of Pd Containing Hydrogen — I 7
206 Hvi in the semi-rigid lattice model. This is the enthalpy
change in introducing an i-atom into pure V (at con
stant pressure). In the constant-pressure model for the
ternary solution, cf can no longer be identified with
Hvi since cf is now a function of 0„ due to the uniform
dilation of the lattice. Thus let us replace €?, in the
A€ · 4 kj/mof) semi-rigid lattice model, by e* q = €° in the constant-
pressure situation. When Q = 0, q « i. Since Ae is
u
UC-5.6 kj/mol) also constant in this case since both types of cell are
affected uniformly by the bulk concentration change
we can write
..—C«
Af«6.0kJ/mol)
IX
Thus comparing this equation with equation (4) yields
€Γ(1-*)«σ. (8)
Using the approximate value of σ given by equation (6)
φ(Δ€»4 kj/mol)
gives
φ(Δ€·5.6 kJ/mol) VJAVBQII/Θ.
4 = 1-
φ(Δ€«6.0 kJ/mel)
220, 0.1 0_.12_ 0.3 0.4 0.5 so that
e. ,-4-S^M,].
(9)
Fig. 6. Measured and calculated ( ) variation of the
partial molar enthalpy of Hydrogen at infinite dilution H*
Writing this in the form,
555 K for Pd-Cu-H solid solutions as a function of the
atom fraction 6U of Cu. The three uppermost solid ( ) €?«€n;i-00j (10)
curves are derived by combining a (the uppermost curve)
with the corresponding values of φ (lower curves).
and using the appropriate values of the constants K°„
V ΔΚ Bo, Ψ> and e?0 (=/??) for the three w-species
h
being considered yields the results:
but it is clear that much more thermodynamic data in
the region 0 = 0-0.15 are required. It must also be
U U g
pointed' out that for Ac > 0, the statistical model is
reasonably valid only at very low values of 0 since in
U Au -0.208
this case the i-atoms will tend to cluster in the sites
Ag -0.191
with U-atoms in their metal atom shell so that ignor
Cu 4-0.242
ing shells with more than one U-atoms becomes
much more serious than in the case when Δε < 0.
These considerations have shown that the thermo The partial enthalpy of the i-species at infinite dilu
dynamics of Pd-(Cu, Au, Ag)-H solutions can be tion of i may now be written from equations (10 and
understood in terms of a simple statistical cell model (4) in the form
in which the V-U lattice is constrained to have a
constant molar volume prior to inserting the i-atom. ΗΓ-Ηϊ(1-ρθη)-φ (11)
The value of Ae includes a contribution arising from Substitution of the values of q given above and the
the lattice dilation associated with inserting an /-atom calculated values of φ for given Ae-values into equa
into an appropriate cell. Thus Ae is strictly a constant tion (11) results in H^-values close to those calculated
in this semi-rigid lattice model and the term σ rep from equation (2) and presented in Figs 5 and 6. They
resents a macroscopic Volume correction'. are not exactly equal since the approximate form (6)
Let us now ask the following question: can the was used to calculate σ.
measured elastic data be used to formulate a con
stant-pressure model which may be compared directly
to experimental data? In order to attempt an answer
CONCLUSIONS
to this question, let us assume that the addition of the
U-species causes a uniform positive or negative dila 1. The elastic properties of Pd-(Cu, Au, Ag) solid
tion of the metal lattice such that €? and e} are func solutions have been measured in the temperature
tions of the U-concentration. Now in deriving [1] range (300-1200 K) and up to compositions of
equation (2), the term €? was identified correctly with 0 = 0.5, using MARZ-grade polycrystalhne material.
U
8 M. Yoshihara and R. B. McLellan
2. The measured elastic data enable the simple cell with T and 0M and' is not a relation derived a priori
model for solutions consisting of an interstitial species from first principles.
(i) in a substitutional 'solvent matrix' (V-U) to be 6. The conclusions reached in the current analysis
tested using measured thermodynamic data for must, if they are correct, be consistent with the dif
Pd-(Cu, Au, Ag)-H. fusion behavior of hydrogen in Pd-based noble metal
3. The model is compatible with the experimental alloys. This will be demonstrated in the second paper
partial enthalpies of solution of hydrogen. Sites near of this series.
est-neighbor to Au and Ag atoms are antitrapping
Acknowledgement—The authors are grateful for the sup
sites for H-atoms with a 'negative trapping depth'. port provided by the U.S. Army Research Office and the
The thermodynamic properties of the solution are Robert A. Welch Foundation.
relatively insensitive to Δε.
4. Sites nearest-neighbor to Cu atoms are trapping REFERENCES
sites for H-atoms whose depth lie ~* 6.0 kJ/mole lower
1. R. B. McLellan and R. Kirchheim, Phvsics Chem.
than those for H in pure Pd. In the case of U = Cu,
Solids 41, 1281 (1980).
the agreement must be regarded as somewhat fortui
2. R. B. McLellan, Scripta metali 14, 875 (1980).
tous because of the high U-concentration. Since 3. W. J. Arnoult and R. B. McLellan, Acta metali 23, 51
Δ£ > 0, i-atom clustering at trapping sites renders the (1975).
assumptions of the model questionable for θ„ > 0.05. 4. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals,
Series and Products, Academic Press, New York (1965).
5. The measured elastic data can be used to formu-
5. M. Shamsuddin and O. J. Kleppa, J. chem. Phys. 71,
*
5154 (1979).
late an equation [ie equation (11)] giving the vari 6. C. Picard, O. J. Kleppa and G. Boureau, J. chem. Phvs.
ation of the partial enthalpy of the interstitial solute 70, 2710 (1979).
as a function of the measured elastic data. This re 7. O. J. Kleppa, S. Shamsuddin, and C. Picard, J. chem.
Phys. 71, 1656 (1979).
lation does not, however, represent an 'elastic theory
8. R. Kirchheim and R. B. McLellan, Acta metali 28,
of solutions' since its form depends upon the experi 1549 (1980).
mentally determined variation of the bulk modulus
