A.
2160
c. n/IAKRIDES
Absorption of Hydrogen by Silver-Palladium Alloys
by A. C. Makrides Tyco Laboratories, I n c . , W a l t h a m , Massachusetts
(Received February 1, 1964)
Time-potential curves were obtained during the absorption of hydrogen froin aqueous solution by Ag-Pd electrodes and the extent of absorption was determined by potentiostatic techniques. Silver has the following effects on the absorption isotherms: (a) the pressure, po, of the a-fl transition decreases with silver content up to about 25 atom % silver; (b) the a-fi transition does not occur above 30 atom yo silver; (c) the solubility po) increases with silver content; (d) the heat of soluof hydrogen a t low pressures ( p tion at po increases with silver content; (e) the maximum solubility ( p >> po) decreases with silver content. The above results are discussed in terms of a model, frequently proposed for H-I'd, in which hydrogen is assumed to dissolve as protons with the electrons occupying d-states in the conduction band. I t is suggested that interactions between electrons which provide Fermi screening for the protons are responsible for an attractive hydrogen-hydrogen interaction leading to a phase transition in the isotherm. A similar interaction between silver and hydrogen is postulated to account for the changes of po observed with the alloys. The decrease of the maximum solubility (approximated by the solubility a t P H p= 1 atm.) is attributed to a decrease in the number of available elcctron states in the d-band. The eliniination of the phase transition with alloys of 30 atom % or more silver is attributed to the decrease of the maximum so1ubilit)yof hydrogen below a calculated critical value.
lo0 niv.) to zero without any arrest. The Solubility of Hydrogen in Ag-Pd Alloys. The amount of dissolved hydrogen was determined for 10.4, 23.8, and 30.5 atom % Ag-Pd alloys a t a series of potentials between zero and 120 mv. us. H*-H2 in the same solution. I n each case, the palladized alloy was charged potentiostatically at 0 mv. us. H+-HZ until the current dropped to zero. The potential was then adjusted to a desired value within the range given above and the current was followed with time until it again decayed to zero; the electrode was then discharged a t 600 mv. us. H+-Hz. The current-time curves were integrated to obtain the total amount of hydrogen oxidized between zero and the selected potential, and between the selected potential and 600 mv. The sun1 of these two integrals was constant and was equal to the value obtained by discharging directly, a t 600 mv., electrodes which had been charged with hydrogen at 0 mv. us. I-I+-Hz. The results are presented in Fig. 3 and in Table I. Figure 3 gives essentially isotherms for the solution of hydrogen in these alloys, the potential scale corresponding to a logarithmic scale for the pressure of The Journal of Physical Chemistry
0.2
04 [Hl/[Mel
0.6
Figure 3. The amount of dissolved hydrogen, as determined from potentiostatic discharge a t 600 mv., a t various potentials for a series of Ag-Pd alloys. These curves are equivalent to isotherms with E = 0.030 log p , where p = 1 atm. hydrogen (see text).
Table I : Hydrogen Solubility a t P H = ~ 1 atm. a t 30" Atom % silver
0 10 10.4 20.0 23.8 26 30.5 40.0 50 Q
H/M0
0.70
...
H/Pd
0.69 0.57
...
0.582 0.49 0.384
0.45
...
0.36
0.340
... ...
... ... 0.24 0.15
0.70 0.63 0.64 0.61 0.50 0.49 0.49 0.40 0.30
Lewis and Schurter, ref. 22.
hydrogen ( E = -RT/2F In PHJ. In general, the isotherms for the Ag-Pd alloys resemble those of palladium with two modifications: the a-0 transformation, indicated by the horizontal portion of the isotherm, occurs at progressively more positive potentials (lower equivalent hydrogen pressures), while the hydrogen solubility (at an equivalent P H ~= 1 atm.) decreases uniformly as the silver content increases. Temperature coefficients at the a+ transformation were obtained from the temperature dependence of the potential plateau. Heats calculated from these results are plotted as a function of silver content in Fig. 4.
Discussion The isotherms presented in Fig. 3 and the potentials corresponding to the a-p transformation are in general
2165
ABSORPTION OF HYDR,OGEN BY SILVER-PALLADIUM ALLOYS
action between interstitial hydrogenlo or an attractive interaction (clustering) between vacancies (see above). l1 The equations derived from these models are essentially the same, but the interpretation of the terms differs Hydrogen interaction
Vacancy interaction % Ag
Figure 4. Energies of sollution, per mole of hydrogen, calculated from the temperature coefficient of the plateau potential, as a function of silver content.
agreement with other results reported for this system.19-22 There are, however, some differences, particularly in relation to the a-0 transformation observed with the alloys. Vert and TverdovskiiZ1determined isotherms for the absorption of hydrogen by Ag-Pd alloys from galvanostatic charging curves. They interpreted their results as showing an a+ transformation up to about 50 atom % silver. The present study and the X-ray results reported previouslyz3 show that the ~0 transition does not occur a t or above 30 atom % Ag. Lewis and SchurterZ2obtained time-potential curves for a series of alloys up to 50 atom % Ag. They found that the potential plateau becomes more positive with increasing silver content up to about 26 atom yo silver, and subsequently decreases rapidly (3 mv. a t 40 atom % silver). Our results show that the potential plateau disappears a t about 30 atom Yo silver; it is certainly not observed at 40 atom % silver. Therefore, it is likely that the potential arrests observed by Lewis and Schurterz2a t a few (3-6 mv.) millivolts for the 30 and 40 atom % silver alloys are due to some other cause peculiar to their experimental system and not to an a-0 transformation. The amount of dissolved hydrogen determined by potentiostatic discharge a t PH, = 1 stm. (E = 0.000 v.) is in good agreement with the results of Lewis and Schurter,zzwho measured the solubility by vacuum degassing of electrodes which had attained a potential of zero volts us. the R2-Pt electrode. However, these solubilities are uniformly higher than the values determined by Vert and Tverdovskii21 by galvanostatic charging. A possible cause for the lower values reported in ref. 21 is failure to attain equilibrium a t any given potential during galvanostatic charging. The Absorption Isotherms. The Pd-H isotherms can be described either by assuming an attractive inter-
In eq. 1, p o is the pressure of the transition, e is the fraction of available sites occupied by hydrogen, xi is the number of nearest neighbors for each interstitial hydrogen, and Eii is the interaction energy for each pair of interstitials (Eii > 0 for attractive interaction). In eq. 2, s is the stoichiometric hydrogen to metal ratio, n is the H/M ratio at p , and E,, is the energy of interaction of a pair of hydrogen vacancies. In the case of the Pd-H system, eq. 2 does not fit the experimental results if a stoichiometric Pd-H is assumed; a reasonably good fit (however, see below) is obtained only if s is set equal to the maximum solubility observed experimentally (s = H/Pd = 0.70 at 25’ and 0.61 at 290’). With this assumption, eq. 2 is reduced to exactly the same equation as (1). I n the following discussion, the terminology of eq. 1 is used. We adopt as a working hypothesis the suggestionlZ that hydrogen dissolved in palladium exists essentially as protons which are screened by Fermi electrons. This hypothesis explains in a simple way most of the known facts about the system and is in accord with the admittedly approximate theoretical conclusions about the state of dissolved hydrogen. The interactions between dissolved protons which give rise to the flat portion of the isotherm are probably a result of interactions between the electrons which provide screening. It is known26J7that there occur, around a solute (impurity) atom, changes of electronic density which oscillate with distance and which are fairly long range. These long-range fluctuations of electronic charge are responsible, for example, for the magnetic coupling of nuclei via the conduction electronszs and for changes of the Knight shift caused by solute atom^.^^^^^ It is suggested here than an interaction exists between the ‘(tails”of the electron density (26) T. J. Rowland, Phys. Rev., 119, 900 (1960); 125, 459 (1962). (27) A. Blandin, E. Daniel, and J. Friedel, PhiZ. Mag., 4, 180 (1959) ; A. Blandin and E. Daniel, J . Phys. Chem. Solids, 10, 126 (1959). (28) N. Bloembergen and T. J. Rowland, Phys. Rev., 97, 1679 (1956).
Volume 68, Number 8
August, 2964
A. C. ~IAKRIDES
2166
distributions around dissolved protons, which is attractive in character. Hydrogen in the palladium metal lattice probably occupies interstitial octahedral positions to form a rock-salt type structure.29 The distance between the centers of hydrogen atoms in such a structure is about 2.8 8. and the number of nearest neighbors is 12. The attractive interaction postulated here involves relatively small energies, i e . , about 0.4 kcal. per hydrogen pair. Of the total energy of solution (-57 kcal./niole hydrogen), the contribution of a hydrogen interaction with the lattice is by far the largest term, and is about 55 kcal./mole hydrogen. This energy corresponds to introducing a hydrogen ion interstitially in the palladium lattice and an electron in the conduction band. In screening by Fermi electrons, the solute atom merely displaces states in the zone of the conduction band without creating new ones. Thus, one more state is occupied for every attracted electronic charge. Therefore, the solubility is expected to correspond approximately to the number of available states with low-lying energies and these, in the case of palladium, are essentially d-states amounting to about 0.6 per palladium atom. 12,30 There are two observations which we might make in connection with this model. First, although the model predicts a “limiting” solubility, it is clear that a sharp cut-off point is not expected but rather a gradual decrease in the amount of hydrogen dissolved per unit increment of pressure, once a composition of approximately 0.6 H/Pd is reached. Second, the heat of solution, Ei, is probably not constant but actually decreases with the hydrogen concentration. This change is unrelated to the solute-solute interactions given by Eii and is due to the distribution of the available empty states in the d-band over an energy range of approximately 0.1-0.15 ~ . v . ~ O These two effects are probably responsible for the deviation of the isotherms from what is predicted by eq. 1. According to this equation, the isotherms should be symmetrical about 0 = 0.5.13 In fact (see Fig, 5), the Pd-H isotherms are not symmetrical about this point, the solubility a t high pressures decreasing considerably more gradually than expected from eq. 1. It may be argued that this deviation from the predicted isotherm arises from the approximation made in deriving eq. 1, specifically, from the assumption of random distribution of hydrogen (Bragg-Williams approximation31). However, the next approximation (the quasi-chemical approximation) also predicts isotherms which are symmetrical about 0 = 0.5.31 Other correct,ions32933 to the basic eq. 1, e.g., Rushbrooke’s treatment32which includes a dependence of the internal The Journal of Physical Chemistry
CC H 2 / ? . Pd
Figure 5 . The H-Pd isotherm a t 30.0’ from data of Gillespie and Ha1l.O The midpoint of the transition falls considerably below e = 0.5 so that the isotherm is not symmetrical. Instead, there is an extended “tail” on the high pressure side indicating that the solubility approaches a limiting value more slowly than predicted by eq. 1. The isotherms for the Ag-Pd alloys (see Fig. 3) have the same characteristic.
partition function in the absorbed state on 8, yield isotherms which are symmetrical about 0 > 0.5, whereas the midpoint of the transition for the hydrogen isotherms occurs at 0 < 0.5. Thus, it is likely that the basic assumptions on which eq. 1 is based, namely, a fixed number of available sites and a constant Ei, are only approximately true for the Pd-H system. The Ag-Pd-H Isotherms. There are three basic changes in the absorption isotherms produced by alloy(29) J. E. Worsham, M. K. Wilkinson, and C. G. Shull, J . Phys. Chem. Solids, 3, 303 (1957). (30) F. E. Noare, J. C. Matthews, and J. C. Walling, Proc. Roy. SOC. (London). A216, 502 11953). (31) R. Fowler and E. A. Gumenheim. “Statistical Thermodvnarnics,” Cambridge University &em, London, 1960, pp. 429-443, 658-563. (32) G. H. Rushbrooke, Proc. Cambridge Phil. SOC.,34, 424 (1938). (33) B. B. Fisher and W. G. McMillan, J . Chem. Phys., 28, 555 (1958).
2167
ABSORPTION OF HYDROGEN BY SILVER-PALLADIUM ALLOYS
ing palladium with silver. First, the transition pressure is shifted to smaller values (Fig. 3) and, a t sufficiently high silver content ( 330 atom %), the transition no longer occurs. Second, the heat of solution of hydrogen, Ei, in the alloy increases with silver content, the increase being approximately proportional to X a g . Third, the solubility a t P H = ~ 1atm. decreases approximately linearly with silver content (see Fig. 6). The isotherms with the Ag-Pd alloys show that PO decreases with silver content according to -log po
rY1' )P
E 2.30RT
= -~
=
1.63
+ 6.0X~g
=
1.0
- 0.0 - 0.6
. . I
1 -0.4
P 5
- 0.2
(3)
where X A s is the attom fraction of silver in the uncharged alloy. The pressure for this transformation is related to the energy of absorption by log PO
-
log K ( T ) -
where In K ( T ) varies only slowly with temperature. Consequently, to a very good approximation
where Ei is the heat of solution of hydrogen at an interstitial site where all the neighboring sites are unoccupied and Do is the heat of dissociation of hydrogen. Figure 4 shows that the right-hand side of eq. 5 increases from (about4.8kcal./g.-atom of hydrogen (9.5 kcal./mole of Hz) for pure palladium to 5.8 kcal./ g. atom of hydrogen for the 20.4 atom % silver alloy. The solubility of hydrogen in the alloys a t PnZ = 1 atm. (E = 0) decreases as silver is introduced in the lattice. Table I shlows that the R/Pd ratio also decreases from about 0.70 for pure palladium to 0.30 for the 50 atom % silver alloy. It is clear that silver produces two distinct effects: an increase of solubility a t low pressures but, also, a decrease of the limiting solubility (here approximated by the solubility a t PHt = 1 atm.). These effects probably have a different origin; the first is likely a resuk of an interaction between an interstitial hydrogen and a silver ion, while the second is probably caused by changes of the electronic structure of the solid which accompany the introduction of silver atoms in the lattice. The increase of the right-hand side of eq. 5 with silver content may be due to a change of either Ei or of Eii. The isotherms suggest that Eii remains unaltered as silver is introduced in the lattice. The value of e a t the end of the transition can be used to estimate xiEii from eq. 1. The calculation is imprecise and the
-0
I
I 20
I
I 40
I
I 60
I
A t % A9
Figure 6. The mass su~ceptibility3~ and the hydrogen solubility as a function of silver content. The solubility in the alloys is given in terms of the hydrogen solubility in palladium.
estimate is not very good as judged from results with pure palladium. This is probably because the isotherms do not follow eq. 1 rigorously for the reasons given above. However, this calculation still shows that Eii for the alloys is probably the same as for pure palladium. Thus, the increase of the r.h.s. of eq. 5 with silver content is probably due to an increase in the energy of solution of hydrogen at an isolated interstitial site and not an increase of the energy of interaction between dissolved hydrogen. The above discussion suggests that the shift of po to smaller values (and the increase of Ei) is due to an attractive interaction between silver and hydrogen. This interaction is probably similar to that between interstitial hydrogens, uiz., it arises from exchange interactions between the electrons which provide screening for protons and for silver ions. It is not possible to state in advance whether this effect should be attractive or repulsive. I n view of its small magnitude (-2-3 kcal. or 0.1 e.v./hydrogen), it is doubtful whether even a detailed calculation would show whether an attractive or repulsive effect is to be expected. If such an attractive interaction exists, and if it is treated as an additive. pair interaction, then it is clear that there must be differences in the heat of absorption of hydrogen at different sites in Ag-Pd alloys, i.e., the heat will be larger for sites with a greater number of nearest neighbor silver atoms. Since the Ag-Pd solid solutions are random, the various sites will be randomly distributed. It is not immediately obvious that the adsorption isotherm for such a system will Volume 68,Number 8
August, 1964
A. C. MAKRIDES
2168
show an a-p transition as it does for pure palladium, A detailed treatment of this problem will be presented elsewhere; suffice it to state here that, if the Ag-H interaction energy is small, the main features of the isotherm are not altered and an a-p transition is still expected in agreement with the experimental observations for the palladium-rich alloys. The pressure, po, of the transition is expected to decrease, as is found experimentally. Therefore, it is permissible to assume that the addition of silver essentially increases EL and that the shift of the transition to lower pressures is due to the increase of Ei. If the above assumptions are correct, the shift of p o with X A should ~ correspond to the increase of the heat of solution. Using the experimental data of Fig. 4 and relations 4 and 5, we calculate a t 303OK.
which is in fair agreement with eq. 3. The solubility of hydrogen at PH*= 1 atm. (>>PO) decreases linearly with silver content (Fig. 6). Using the model discussed above for absorption by pure palladium, the decrease of solubility is attributed to a decrease in the number of unoccupied d-states when silver is introduced in the lattice. The number of d-band holes may be taken to be proportional to the magnetic susceptibility of the alloys30 according to the wellknown account given by Nlott and Jones.12 A comparison of the decrease in magnetic susceptibility and hydrogen solubility is given in Fig. 6. Although both quantities decrease more or less linearly with silver content, the magnetic susceptibility drops much faster than the solubility. Furthermore, the susceptibility drops to zero at somewhat lower Ag content (-50 atom % silver) than the extrapolated value for zero hydrogen solubility (-65 atom % silver). An effect, which is not included in the above description and which may account for these discrepancies, is the attractive interaction between silver and hydrogen which increases the energy of solution, and hence the solubility of hydrogen. This interaction in effect makes it possible to utilize electronic energy states lying above the d-states and still maintain a net negative free energy of solution for hydrogen. It should be pointed out that attempts to describe the H-Ag-Pd system in terms of a compound between palladium and hydrogen have been made. The main difficulty in such analysis is the continuously decreasing H/Pd rati? (Table I and ref. 21) which changes from about 0.7 for pure palladium to about 0.15 at 65 atom yo silver. A suggestion that the H/Pd ratio remains constant if only the amount involved in the T h e Journal of Physical Chemistry
wp transition is consideredz1 has no theoretical justification and cannot be correct since the or-p transformation itself does not exist above 30 atom % Ag. The decrease of the maximum solubility, irrespective of its origin, accounts for the suppression of the a-/3 transformation a t about 30 atom yo silver. The simplest way of showing this is to refer to the derivation of eq. 1 or 2 (see ref. 11 and 31). If it is assumed that there are N, sites available in pure palladium and each site has x i neighbors, then the number of pairs of neighboring occupied sites, assuming a completely random distribution of adsorbed hydrogen (BraggWilliams approximation) , is given by
N"
1
=
- x~NH',", 2
(7)
This formula is derived (ref. 31, p. 431) by assuming that each site has a probability NA/N, of being occupied. In the case of the alloys, the maximum solubility (PH2 >> p o ) is less than N,, the absorption being reduced because Ei decreases sharply when the dband holes are all filled. In these cases, therefore, the probability of a site being occupied is (NJN,) (S(alloy)/ S(Pd)), where S is the maximum solubility of hydrogen. Using this result, we find that the relation between p and 0 is modified for the alloys to read In p
=
constant
e + 2 In + i - e
where 0 is now calculated with reference to pure palladium. According to eq. 8, there are two values of 6' for each value of p over a range of e-values, provided xiEii
S (alloy) (Pd)
> 4kT
(9)
For pure palladium, xiEii can be calculated from the critical temperature as 4.6 kcal. (ref, 31) or from a detailed analysis of the isotherms as a 4.2 kcal. (ref. l l ) . Taking a mean of about 4.4 kcal., we find that at (S(alloy)/S(Pd)) = 0.5 the inequality (9) is no longer satisfied at room temperature. Consequently, the isotherm is expected to be continuous and a twophase region should not be observed. The above ratio of solubilities corresponds to the 30 atom yosilver alloy (see Fig. 3) for which an a-p transition is, in fact, not observed . In summary, the H-Ag-Pd system can be described in terms of an extension of the model which has been suggested for the H-Pd system. The main effects of
ABSORPTION OF HYDROGEN BY SILVER-PALLADIUM ALLOYS
silver are a decrease of the hydrogen pressure corresponding to the c r P transition (and an eventual elimination of this transition at about 30 atom % silver) and a decrease of tlhe solubility at PHs = 1 atm. The first effect can be described by an attractive interaction
2169
between silver and hydrogen, which is similar to that between dissolved hydrogens. The second can be attributed to a decrease in the unoccupied electron states in the d-band of the alloy resulting from the random substitution of silver for palladium.
Volume 68, Number 8
August, 1964
