Solubility and diffusivity of hydrogen in palladium and Pd77Ag23 containing lattice defects

748

Journal of the Less-Common

Metals, 172-l 74 (1991) 748-758

Solubility and diffusivity of hydrogen in palladium and Pd,,Ag,, containing lattice defects R. V. Bucur and N. 0. Ersson Institute of Chemistry,

University of Uppsala, Box 531, Uppsala, Sweden

X. Q. Tong Department of Chemistry, Queen’s University, Belfast BT9 5AG (U.K.) and Department of Materials Science and Engineering, Tsinghua University, Beijing (People’s Republic of China)

Abstract The energy of interstitial sites in a palladium alloy depends considerably on the nature and concentration of the alloying substituent. However, the microstructure of the sample (e.g. grain boundaries, dislocations) may also contribute to a certain extent to these alterations. In some cases it is expected that the effect of these defects may be opposite to that of the substituent, while in other cases both contributions have similar directional influences. In either circumstance the strength of the interaction of hydrogen atoms with the interstitial sites will be affected. The aim of this paper is to investigate the contribution of defects to the solubility and diffusivity of hydrogen in Pd,,Ag,, alloy. The measurements have been carried out on samples with and without defects, in the Sieverts domain (2933335 K) using a computer-assisted electrochemical method. The results are discussed in terms of Oriani’s two-state model and compared with similar data obtained with palladium samples.

1. Introduction Defects in the host lattice of palladium influence both the solubility and diffusivity of hydrogen. Since Flanagan et al. first reported on the effect of mechanical deformation on the solubility of hydrogen in palladium [l], numerous papers have been published on the subject. Following the generation of defects either by mechanical processing [2-71 or by the cxG p phase transition [&lo], all the data show a solubility enhancement in the low concentration c1 phase. In addition, a decrease of hydrogen diffusivity has been found [4,7,9, lo]. This overall lower mobility of hydrogen has been attributed to its interaction with the defects. The fraction of the lattice containing defects acts as a trapping region where the mean residence time of hydrogen atoms is sensibly longer than in the defect-free regions. These defects may include dislocations, with their accompanying stress fields, grain boundaries, vacancies and voids. By contrast with the case of pure palladium, there has been little published on the interaction of hydrogen with defects in palladium alloys.

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749

Also, little is known about the dual influence of foreign atoms and defects in the host palladium lattice on the behaviour of dissolved hydrogen. The data published by Sakamoto et al. on both the solubility and diffusivity of hydrogen in some Pd-Ag and Pd-Au alloys (composition O-50 at.%) have, however, shown differences between annealed and cold-worked samples [7]. Although they recognized the role of the trapping sites in solubility enhancement and reduction of hydrogen diffusivity, no systematic investigations were reported. The purpose of this paper is to compare the effect of defects introduced into palladium and the well-known palladium alloy Pd,,Ag,, on the behaviour of dissolved hydrogen. This has been accomplished by carrying out simultaneous measurements of the solubility isotherm and apparent diffusion coefficient on the same sample using combined transient potentiostatic and galvanostatic methods assisted by a computer technique [ll]. Attempts have been made to interpret the results within the framework of the two-state model proposed to explain interactive effects between hydrogen and defects in palladium [lo].

2. Experimental A permeation cell divided by bielectrode membranes with large active surface area was used [12]. The membranes, with a geometrical surface area of 8.30 cm’, were composed of cold-rolled samples of palladium and Pd,,Ag,,. The following thicknesses (L) and degrees of deformation (d) were employed: palladium, L = 2.06 x lop3 cm, d = 84%; Pd,,Ag,,, L = 1.71 x 1O-3 cm, d = 93% and L = 2.88 x lop3 cm, d = 87%. After performing an initial set of measurements, the membranes were pretreated before further series of measurements (I) by heating for 1 h at 850 “C in vacuum (for palladium) or under argon (for Pd,,Ag,,) and (II) by subjection to the c1G- p phase transition as a result of cathodic charging with hydrogen at 1 A for 20 min to a saturation hydrogen content followed by removal through anodic oxidation. This latter procedure was applied twice to the palladium membrane and 10 times to the Pd,,Ag,, one (L = 2.88 x 10e3 cm). In further sections the following notation will be used: cw-Pd and cw-Pd,,Ag,, for cold-rolled samples; (a-p)-Pd and (a-p)-Pd,,Ag,, for samples subjected to cycles of u + p phase transitions. Desorption isotherms were measured by the potentiostatic transient method. The hydrogen pressure was calculated from measurements of the electrode potential of the membrane with respect to a Pt-H, electrode in the same solution; the corresponding hydrogen content was determined from the anodic charge required for oxidation of hydrogen contained in the membrane [13]. Combinations of hydrogen diffusion coefficient and concentration were measured by the galvanostatic permeation method according to an experimental procedure described in detail elsewhere [12]. A solution of 1N H,SO, was used for the solubility measurements and of 1N NaOH for the permeation

750

O’O’ c 0.06 Pd 3

0.05 -

,a e % s. 0.04 z B 6 z! 5

0.03 -

0.02 -

0.01 -

0

1

2

3

4

Hydrogen cont.

5

6

, n=(H/M)

Fig. 1. Solubility data for hydrogen in palladium: x , annealed; CLz+ p phase transition; -, calculated with eqn. (1).

7 x10-3 0, cold-worked;

+, subjected

to

measurements. Temperatures within the range from 293 to 335 K were controlled (circulatory water bath) to fO.l K.

3. Results 3.1. Hydrogen

solubility

3.1.1. Palladium The solubility isotherms of hydrogen in the diluted a-phase region of both palladium and Pd,,Ag,, exhibit very similar features as far as the influence of defects is concerned. As a result of the direct interaction of hydrogen atoms with the traps, a deviation of the solubility data from Sieverts’ linear law is found at low hydrogen pressure. For a sufficiently high hydrogen pressure the traps approach their saturation state and the solubility data again obey a linear relationship similar to that of a material free of defects, but shifted along the abscissa. This is well illustrated in Fig. 1, where some solubility data for hydrogen in palladium at 293 K are shown. Compared to results for the annealed sample (line 3 of Fig. l), there is an evident solubility enhancement for the other two samples which is more pronounced for the u-p sample (line 1) than for the cold-worked sample (line 2). The slight displacement from the origin of the isotherm for the annealed palladium could be accounted for in terms of surface hydrogen adsorption. Values of the experimental solubility enhancement E, calculated at different

751 TABLE

1

Experimental lO$‘/”

(6,) and calculated

(atm’iz)

0.16

0.26 0.48 0.69 1.60 2.10 2.65 3.28 3.79 4.06 4.47 Average

(c,) solubility

enhancement

of hydrogen in palladium at 293.5 K

1O’p”’ (atm”‘)

c,(cw, 84%) -0.243 0.63 1.01 1.05 1.20 1.22 1.25 1.26 1.31 1.31 1.26

-0.317 0.57 1.03 1.14 1.23 1.24 1.25 1.25 1.25 1.25 1.25

1.26

1.25

0.19 0.38 0.60 0.92 1.13 1.43 1.70 1.99 2.56 3.16 3.42

0.943

2.09 2.32 2.37 2.39 2.36 2.32 2.36 2.36 2.31 2.35

0.872 1.95 2.20 2.31 2.34 2.36 2.37 2.37 2.38 2.38 2.38

Average

2.35

2.37

equilibrium pressures for the cw- and (a-S)-Pd are given in Table 1. The solubility enhancement is defined as E, = (n” - n”)/n, where nd is the measured solubility in deformed palladium, IZ is the solubility in annealed palladium and no is the intercept on the concentration axis of relationships over the linear domain of the isotherm [a]. It can be seen that the solubility enhancement is constant within the linear domain but tends to decrease towards negative values in the curved domain, i.e. at low hydrogen pressures. Values of C, are comparable with those reported in gas phase or electrochemical measurements for cw-Pd [2,4] but are larger in the case of (a-P)-Pd, which can be ascribed to a more intensive c( S fl phase transition treatment than in ref. 8. 3.1.2. Pd,,Ag,, Experimental solubility enhancements for Pd,,Ag,, at different hydrogen pressures, s,, for both cold-worked (d = 87%) and cr-p samples are given in Table 2. It may be noted that for the same measure of deformation the same solubility enhancement was found in Pd,,Ag,, as in palladium. Moreover, the intercepts no also have comparable values, namely 3.8 x lop4 for Pd,,Ag,, and 4.10 x 10m4 for palladium. On the other hand, electrolytic saturation of Pd,,Agz3 with hydrogen has had little influence on the solubility enhancement since its microstructure has been much less affected by hydrogen introduction and removal than in the case of palladium [14]. 3.2. Hydrogen

diffusivity

3.2.1. Palladium Variations of the (apparent) diffusion coefficient D with hydrogen concentration in palladium are illustrated in Fig. 2 for the three cases discussed above.

752 TABLE 2 Experimental

(E,) and calculated

(E,) solubility

enhancement

of hydrogen in Pd,,Aga,

at 293.5 K

103p”s (atm1/2)

E,(CW, 87%)

103p1” ( atmli2)

&,(a-8)

0.19 0.54 0.92 1.30 1.67

1.23 1.30 1.28 1.29 1.28

Average

1.28

0.44 0.64 0.84 1.09 1.27 1.49 1.68

1.04 1.03 1.01 1.02 1.03 1.04 1.03

Average E, z K./K;

= 1.28

E, z KS/K;

1.03 = 1.03

4.5 Pd

4-

293K -_ Df

3.5-

3

3.13 ___I._-__w_-2.85 _-_

__2.08

0 0

i 0.002

1 0.004 Hydrogen

0.006

I 0.008

0.01

0.012

cone, n4HIM)

Fig. 2. Diffusion data (divided by 10e7) for hydrogen in palladium: x , annealed; 0, cold-worked; +, subjected to a c$ p phase transition; -, calculated with two-state model [lo]; D,, limiting diffusion coefficient.

As already reported [lo], the diffusion coefficient increases smoothly with increasing concentration of hydrogen and finally tends towards a concentration-independent limiting value Dr. Figure 2 also shows that both the rate of increase of the diffusion coefficient and its limiting value depend on the degree of deformation, whether effected either by the degree of mechanical cold work or by the number of cycles of 01e p phase transitions. Values of the limiting diffusion coefficient calculated in accordance with the procedure already described [lo] are D, = 3.13 x 10m7cm2 s-l for the annealed, D,= 2.85 x 10e7 cm2 s-l for the cold-worked and D,= 2.08 x lop7 cm2 s-l for the u-p sample.

753

3.5 -

;; 3

E g

3-

PmAg23

293K

-

2.5-

4

0 0

1

2

3 Hydrogen

4

cw,

L 5

Qf-

__-,___ -u" - 229

6

7

n = (HIM)

Fig. 3. Diffusion data (divided by 10m7) for hydrogen in Pd,,Ag,,: worked (L = 1.71 x lo-" cm) and (L = 2.88 x 10.’ cm), respectively; model [lo]; D,, limiting diffusion coefficient.

x , annealed; 0, cold; and f, -,

calculated

with two-state

3.2.2. Pd,, Ag,, Figure 3 illustrates that the variation of the diffusion coefficient with hydrogen concentration in Pd,,Ag,, differs from the case of palladium. While the variation of the diffusion coefficient as a function of hydrogen concentration is different for annealed and cold-worked Pd,, Ag,, , its limiting value seems not to be markedly affected by the plastic deformation [15]. The calculated limiting values of the diffusion coefficient are D, = 2.29 x 10e7 cm2 s-l for the annealed and D,= 2.20 x 10e7 cm2 s-l for the cold-worked samples.

4. Discussion The effects of the mechanical deformation upon the behaviour of hydrogen in palladium reported so far in the literature have been mainly interpreted within the framework of the strain field model [l-5,8,16]. However, this model has not given completely satisfactory agreement either in regard to calculation of the chemical potential at low hydrogen concentration [5] or to calculation of the temperature dependence of the solubility enhancement at high hydrogen concentration [2]. Nor has this model been satisfactory for analysing the solubility data shown in Fig. 1 for both cw- and (E-P)-Pd; the variation of the chemical potential with hydrogen concentration markedly deviates from the theoretical predictions [ 51. The limited possibilities of the strain field model to explain satisfactorily the interaction of hydrogen with defects in palladium could be due to poor

754

correlation with values of the interaction energy in the vicinity of core dislocations based on linear elasticity relationships. As has been suggested by Tyson [17], the variation in magnitude of the interaction energy might alternatively be limited and its value might therefore be considered to be approximately constant (“extended core model” with monoenergetic traps). In view of these facts, a two-state model using the relationships derived from Oriani’s model [18] could still be considered to be an acceptable alternative approach’ for analysing both the solubility and diffusivity data. Within the framework of this model the following relationship has been deduced for the solubility isotherm [lo]: nop’lZ n=K+p112

l/Z

+p KS

(1)

where n is the hydrogen concentration, no is the concentration of available traps, K is the equilibrium constant for hydrogen in the traps and KS is Sieverts’ constant. The first term on the right-hand side of eqn. (1) gives the contribution corresponding to occupation of the traps, while the second term corresponds to occupation of normal sites in the long-range stress field. From the temperature variation of Sieverts’ constant K, and the trapping constant K the thermodynamic parameters of hydrogen in the two states have been estimated. These values are given in Table 3 for palladium and where AH and AS’ are the partial molar enthalpy and standard Pd,,Ag,,, entropy of hydrogen respectively (relative to ;H, (gas, 1 atm)). Here are included the transport parameters as well, i.e. the frequency factor D" and the activation energy for diffusion, Q. These values have been calculated from Arrhenius plots of the limiting diffusion coefficient D,.It can be seen from Table 3 that palladium and Pd,,Ag,, subjected to the same degree of deformation exhibit practically the same trap concentration no and solubility enhancement E,. Simultaneously, the heats of solution of hydrogen in the normal sites become more exothermic by the same amount of about 1 kJ mol-’ in both cases. The electrolytic saturation of palladium by hydrogen generates similar but amplified effects compared with cold working in regard to trap concentration and solubility enhancement. Hence the heat of solution in the normal sites is much more exothermic, AH, = - 15.5 kJ mol-‘, and the heat of trapping is AH, = -23 &-2 kJ mol-‘. This value agrees well with that reported for deformed palladium in gas phase measurements, AH, = -23.8 kJ mol-’ 131. Using the solubility parameters given in Table 3 and the two-state isotherm described by eqn. (l), the solubility isotherms for hydrogen in cw- and (a-P)-Pd have been calculated and displayed in Fig. 1, lines 1 and 2 respectively. However, for the same degree of deformation the limiting diffusion coefficient Df changes in different ways for palladium and Pd,,Ag,,. Thus for palladium there is a significant decrease of D, from the annealed to the cold-working conditions simultaneously with an increase of the activation energy for diffusion of about 2 kJ malll. In contrast, deformation of

i:,, experimental

Cold rolled (87%)

n”, trap concentration;

Pd,,Ag,,

Annealed

solubility

38

5

7 42 64

Annealed Cold rolled (84%) r + 6 phase transition

Pd

loj?z”

Treatment

1.28

1.26 2.35

6,

21.6 + 1.1

20.3 k 1.1

10.9 11.9 15.5 * 0.5 23 & 2

-AH (kJ mol-‘)

and Pd,,Agas

67 + 3

6424

61 64 69 + 1

-AS” (Jmol

AH and AS”. thermodynamic

in palladium

enhancement;

of hydrogen

Sample

parameters

and transport

3

Thermodynamic

TABLE

parameters;

‘K-‘)

22.20

22.02

21.83 23.7 + 0.5 22.2 & 0.5

Q (kJ atom-.‘)

D” and Q. transport parameters.

1.99

1.86

2.48 4.69 1.82

lO"l30 (cm’s “)

Pd,,Ag,, has practically no influence on either the limiting diffusion coefficient or the activation energy for hydrogen diffusion. The solubility enhancement sC can be calculated immediately from eqn. (1) and is given by the relationship

(2) where KS is Sieverts’ constant for the annealed sample and K: for the deformed one. For a sufficiently high hydrogen pressure, pllz $ K and the solubility enhancement attains a constant value

where AHd and AH, are the partial molar enthalpies of hydrogen in the deformed and annealed samples respectively. As can be seen both in Tables 1 and 2, the calculated solubility enhancement E, agrees very well with the experimental one E, in regard both to its variation with hydrogen pressure and to its constant average value. Moreover, eqn. (3) predicts quite well the variation of the solubility enhancement as a function of temperature, as can be seen in Table 4, for (E-fi)-Pd. A plot of Inse us. l/T gives F, = 0.3657 exp ( -4539/T). It follows that AH;, = -15.4 kJ mol-“, taking a value of AH, = - 10.9 kJ mol-’ from ref. 13, which is in good agreement with the value given in Table 3. These results provide good support for the proposals represented by eqns. (l)-( 3). The two-state model also gives a good fit to the data for hydrogen diffusivity in both palladium and Pd,,Ag,, within the temperature range investigated here. The good fits do not in themselves prove that the model is valid. However, in spite of its approximate nature, the model seems to be able to satisfactorily predict the behaviour of hydrogen in both palladium and Pd,,Agz3 containing defects and offers a simple and complementary way of analysing the experimental data.

TABLE

4

Experimental

(c)

and calculated

(E,) solubility

enhancement

at different

temperatures

(a-@)-Pd T(K)

G

E, s KS/K;

293.5 303.5 313.8 323.6 335.0

2.35 2.25 2.05 1.94 1.90

2.39 2.26 2.09 1.96 1.92

for

5. Conclusions (1) Palladium and Pd,,Ag,, subjected to the same degree of deformation exhibit practically the same variations of trap concentration and overall solubility enhancement. Simultaneously, the heats of solution of hydrogen become more exothermic by the same amount of about 1 kJ malll in both cases. (2) However, for the same degree of deformation the limiting diffusion coefficient D, changes in different ways for palladium and Pd,,Ag,,. For palladium there is a significant decrease of D, from the annealed to the cold-worked condition simultaneously with an increase of the activation energy for diffusion of about 2 kJ mall’. In contrast, deformation of Pd,,Ag,, has practically no influence on either the limiting diffusion coefficient or the activation energy for hydrogen diffusion. (3) Electrolytic saturation of palladium by hydrogen can generate similar but amplified effects compared with cold working in regard to trap concentration and solubility enhancement. An additional consequence is the lowering of limiting values of the diffusion coefficient. No such effects have been observed as a consequence of hydrogen introduction into Pd,,Ag,,. (4) Despite its approximate nature, the two-state model is able to predict the behaviour of hydrogen in palladium and Pd,,Ag,, containing defects in a fairly satisfactory manner.

Acknowledgements The authors wish to thank Professor T. B. Flanagan and Dr. F. A. Lewis for critical reading of the manuscript. Financial support (R.V.B.) from the Swedish Natural Science Research Council and from the Goran Gustafsson Foundation is gratefully acknowledged. Thanks are also due to JohnsonMatthey PLC for providing the Pd,,Ag,, alloy.

References 1 T. B. Flanagan, J. F. Lynch, J. D. Clewley and B. van Turkovich, J. Less-Common Met., 49 (1976) 13. 2 T. 8. Flanagan and J. F. Lynch, J. Less-Common Met., 49 (1976) 25. 3 T. B. Flanagan and S. Kishimoto, in P. Jena and C. B. Satterthwaite (eds.), Electronic Structure and Properties of Hydrogen in Metals, Plenum, New York, 1982, p. 623. 4 R. Kirchheim, Actu Metall., 29 (1981) 835. 5 R. Kirchheim, Acta Metall., 29 (1981) 845. 6 H.-G. Schimeich, U. Bilitewski and H. Ziichner, 2. Phys. Chem. N.F., 143 (1985) 97. 7 Y. Sakamoto, S. Hirata and H. Nishikawa, J. Less-Common Met., 88 (1982) 387. 8 J. F. Lynch, J. D. Clewley, T. Curran and T. B. Flanagan, J. Less-Common Met., 55 (1977) 153. 9 R. V. Bucur and E. Indrea, Acta Metall., 35 (1987) 1325. 10 R. V. Bucur, J. Muter. Sci., 22 (1987) 3402. 11 R. V. Bucur and V. Klimecki, 2. Whys. Chem. N.F.. 167 (1990) 175.

758 12 R. V. Bucur, Znt. J. Hydrogen Energy, 10 (1985) 399; Z. Phys. Chem. N.F., 145 (1985) 217. 13 R. V. Bucur, Electrochim. Acta, 31 (1986) 385. 14 F. A. Lewis, The Palladium/Hydrogen System, Academic, London, 1967; Z. Phys. Chem. N.F., 146 (1985) 17. 15 R. V. Bucur and F. A. Lewis, Ser. Metall. Mater., 24 (1990) 2071. 16 R. Kirchheim, Prog. Muter. Sci., 32 (1988) 261. 17 W. R. Tyson, J. Less-Common Met., 70 (1980) 209. 18 R. W. Oriani, Acta Metall., 18 (1970) 147.