Thermoelectric power of hydrogenated palladium and some of its dilute alloys, between 80 and 300 K

Journal of Alloys and Compounds 316 (2001) 82–89

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Thermoelectric power of hydrogenated palladium and some of its dilute alloys, between 80 and 300 K ´ * A.W. Szafranski Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44 /52, 01 -224 Warsaw, Poland Received 14 July 2000; accepted 4 December 2000

Abstract Thermoelectric power and electrical resistance of Pd and PdMe (Me5Ti, Nb, Zr, Ce, Be and Ge) saturated with hydrogen at high pressure have been simultaneously measured between 80 and 300 K. Several experimental runs have been carried out on samples of successively decreasing hydrogen content. The results have been analysed in terms of the Nordheim–Gorter rule. The phonon and disorder diffusion contribution to the thermoelectric powers could be estimated.  2001 Elsevier Science B.V. All rights reserved. Keywords: Hydrogenated palladium alloys; Thermoelectric power; Electrical resistance

1. Introduction Hydrogen easily dissolves in palladium [1] forming an interstitial alloy PdH c with hydrogen atoms occupying octahedral sites. Two phases can form in the Pd–H system, the a-phase with a very small (few percent) hydrogen content and the b-phase (hydride) of non-stoichiometric composition (0.6 # c # 1). The latter forms when palladium is in equilibrium with gaseous hydrogen at a pressure exceeding |0.03 bar (at room temperature). At lower pressures the two phases coexist. Both have fcc crystal structure, which differs in the lattice parameter. The two phases differ much in their electron properties which results from the donating of hydrogen 1s electrons to the hybridized 4d–5s band of palladium. The electron bands change to some extent but the general feature of the band structure is preserved (see [2]). Above the energy region with a high density of states (high-DOS, mainly of dcharacter) there is an energy region where the density of states (low-DOS, mainly of s-character) is nearly one order of magnitude lower. The essential difference between aand b-phase is the location of the Fermi level. In Pd and a-Pd–H it is located in the high-DOS region while in b-Pd–H it is shifted in energy to the low-DOS region. Therefore all physical properties of both phases related to values of the density of states at the Fermi level, differ much. The specific heat and magnetic susceptibility can be cited as examples. Another qualitative difference between ´ *E-mail address: [email protected] (A.W. Szafranski).

both phases has been found in the phonon spectrum. Palladium is a metal with Debye temperature equal to 270 K. The presence of light hydrogen atoms results in the formation of optical phonon band located above the ‘normal’ acoustic band, at energies (E /k) exceeding 600 K (see [3]). These optical phonons give rise to additional electron scattering, hence to a substantial increase of the phonon electrical resistivity [4]. The coupling of electrons to these optical phonons, together with the decay of paramagnetism, present in palladium, is the source of superconductivity of palladium hydride [5]. The thermoelectric power of PdHc alloys (c#0.7) has been measured by Fletcher et al. [6], Schindler et al. [7] and Foiles [8] in the temperature range up to 20, 110 and 273 K, respectively. Kopp et al. measured hydride samples with compositions close to stoichiometry (0.915 # c # 0.996) between 10 and 170 K [9]. One should note that in the temperature range between 50 and 80 K and for hydrogen contents 0.5 # c # 0.85 the so-called 55 K anomaly exists in the Pd–H system in the behaviour of TEP [7] and electrical resistance [10,11]. Skoskiewicz has investigated TEP of the Pd–H system at room temperature at a high hydrogen pressure [12]. He observed positive values of the thermopower and its decrease with increasing pressure. No explanation for this behaviour has been proposed. The attempts of Foiles [13] failed to predict the temperature dependence of thermopower of highly concentrated Pd–H alloys, based on the available limited data of different authors.

0925-8388 / 01 / $ – see front matter  2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 00 )01507-3

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In this paper we present experimental results for PdMeH c -alloys performed on samples of a wide range of hydrogen content (0 # c # 0.95), including the pure bphase region (c $ 0.6 in Pd–H), and in the temperature range where the anomaly mentioned does not exist. The solute elements belong to transition (Ti, Nb, Zr), rare-earth (Ce) or non-transition metals (Be,Ge). The thermoelectric power, while relatively easy as to measurements, is rather difficult to interpret because it is strongly influenced by subtle details of the electronic structure. Nevertheless it has been successfully used for the detection of hydride-phase formation in metal–hydrogen systems under high-pressure conditions (see [14] and references given in [15]). In a recent paper [15] we showed that important information could be obtained from moderately low-temperature TEP results obtained for hydrogenated nickel alloyed with some transition metals (V, Fe or Co). It has been concluded that these nickel-based hydrides belong to Kondo systems. The aim of this study is to obtain more information about electron transport in single-phase PdMe hydride when the concentration of hydrogen, and hence the conduction electron concentration, changes. For this purposes both thermoelectric power and electrical resistance have been investigated. According to the Mott theory and the Nordheim–Gorter rule in the case of elastic electron scattering, they can be tightly correlated (see e.g. [16]).

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and thermopower turned back to their values prior to saturation with hydrogen. The thermoelectric forces generated in the samples were measured against copper leads. The temperature gradient was measured with use of a Pd 0.2 Ag 0.8 reference sample. The accuracy of the TEP measurements in the moderately low temperature range (80–300 K) was estimated to be 60.5 mV/ K. The method applied is less accurate as compared to the conventional method where the samples are long with one end kept at constant temperature. The present method can hardly be applied in the lower temperature range, i.e. much below 80 K where the accuracy in the determination of temperature gradient across the samples is highly reduced. On the other hand, at higher temperatures the phonon drag is less important and the disturbing effect of the 55 K anomaly mentioned vanishes. Simultaneous measurements of TEP and electrical resistance are possible in this method thus enabling correlation of both quantities with use of the Nordheim–Gorter rule. More experimental details can be found in [15] where results of TEP measurements of NiMe hydrides have been presented. Unfortunately, hydrogen contents corresponding to subsequent runs could not be determined. In the case of PdH c alloys the c values have been estimated from electrical resistance using available r(T,c) data [10,11,18]. In the case of Pd alloys electrical resistance was used for monitoring decrease of hydrogen content.

2. Experimental 3. Results Pure palladium and several palladium alloys, Pd 12x Me x , where Me5Be, Ge (x50.05), Ti, Nb, Zr (x50.04) and Ce (x50.03), in a form of small foil samples (10 mm long31 mm wide30.02 mm thick), have been saturated with hydrogen at room temperature. The pressure of gaseous hydrogen ranged from 0.4 to 0.8 GPa. The equilibrium hydrogen content in palladium hydride exceeds 0.9 [17] but is usually lower upon addition of a second element (Ni and Rh are known to be exceptions). The hydrides are unstable at normal conditions because hydrogen easily desorbs. Thus the samples were taken off the pressure chamber after cooling it down to |170 K. At this temperature the rate of desorption is highly reduced. The simultaneous measurements of thermoelectric power and electrical resistance have been performed starting at liquid nitrogen temperature. The upper temperature limit of the first experimental run was |220 K. This corresponded to the beginning of desorption. In the subsequent runs the limit was successively increased. It this way samples of successively decreasing hydrogen content have been obtained and measured. Desorption rates are reduced much for smaller hydrogen content, corresponding to two-phase region. In order to achieve its further decrease the samples were kept at or above room temperature (up to 325 K) for several hours or even days. Finally the samples’ resistance

The temperature dependence of thermopower and electrical resistance for the PdH c alloys is given in Figs. 1 and 2, respectively. The palladium sample was saturated with hydrogen at 0.5 GPa, at room temperature. According to Tkacz and Baranowski [17] the equilibrium hydrogen content, c, at this pressure is 0.95. The labels 2, 4, 7 etc. denote the run number. It is seen that the TEP of palladium hydride is positive. The extrapolation of the run 2 to room temperature gives for TEP a value of 15.5 mV/ K. It is ´ equal to that measured at 298 K by Skoskiewicz [12] at hydrogen pressure of 0.4 GPa. The values of run 2 (hydrogen content, c50.94, estimated from electrical resistance) are up to 1 mV/ K lower than that of Kopp et al. [9] for their sample of highest hydrogen content (c5 0.996). In the latter case the S(T ) dependence was far from linearity — dS / dT decreases with increase of temperature suggesting possible existence of plateau or maximum above 170 K. The initial hydrogen desorption results in increase of TEP — the subsequent S(T ) curves move up, attain a maximal position for run 7 (above 200 K) or 9 (below 200 K), and then decrease toward the pure Pd curve. It is interesting that all curves labelled 9–14 cross each other in the temperature region close to 80 K. Fletcher et al. [6]

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Fig. 1. Temperature dependence of thermoelectric power of Pd–H alloys, s and d, this work. The labels denote the run number. — — —, Pd [8]; - - -, PdH 0.63 [8]; – ? –, PdH 0.996 [9]; ———, PdH (hypothetical, see text); – ? ? –, Cu [28]. The vertical bar denotes the range of room´ temperature, high-pressure results of Skoskiewicz [12]. The solid lines for runs 2–9 are best fits according to (6) with a dis 5 1 0.04 mV/ K 2 and a ph 5 10.005 mV/ K 2 (runs 2–7) or a ph 5 20.04 mV/ K 2 (run 9); the solid lines for runs 10–13 derived according to (9b) with ub 5 0.82, 0.62 and 0.40, respectively, see text. The estimated hydrogen contents for runs 2, 4, 7, 9, 10, 12 and 14 are 0.94, 0.86, 0.70, 0.66, 0.59(0.54), 0.47(0.41) and 0.34(0.26), respectively; the numbers in brackets derived from ub values.

pointed out that such a crossing indicates two-phase nature of the system. The changes of TEP are accompanied by the corre-

Fig. 2. Temperature dependence of the reduced electrical resistance, r, of Pd–H alloys. r ; R /R 0 , R is the actual resistance of a sample and R 0 is the resistance of the same sample measured at room temperature prior to saturation with hydrogen. The labels denote the run number.

sponding changes in electrical resistance (see Fig. 2). The maximal values of resistance have been observed in run 7 (r51.52 and 1.8 at 200 K and room temperature, respectively). Run 9 with its room-temperature value of r51.7 is the one that corresponds to b-PdH c with c ¯ 0.65 (see [1]). As can be seen in Fig. 1, the temperature dependence of TEP in run 9 is not monotonic. A maximum in the S(T ) relationship is observed at 220 K. This curve is in an excellent agreement with the S( T) dependence given by Folies [8] for his PdH 0.63 sample. In Fig. 3 thermoelectric power of PdH c alloys at 200 K is given as a function of hydrogen content estimated from electrical resistance. The data of Folies [8] and Kopp et al. [9] is shown for comparison. The relationship between electrical resistance and hydrogen content (taken from [10,11,18]) is also given. It is seen that both quantities attain maximal values for c ¯ 0.7, the value slightly exceeding the composition corresponding to the two-phase, a1bub, boundary (c a1bub ¯ 0.6). The maximum in the r(c) relationship (at c 5 c r,m ) is tightly related to the disorder of the hydrogen sublattice. In an ideal case, if details of electronic structure, phase diagram, and any change of phonon resistivity upon hydrogenation are neglected, then, according to the Nordheim rule, c r,m should be equal to 0.5. In either case, c r,m $ c a1bub . The results for TEP and electrical resistance for hydrogenated palladium alloyed with few percent of germanium or beryllium, are similar to those of the Pd–H system. In Fig. 4 the data set for the PdGe–H system is given as an example. The thermoelectric power of the b-phase alloys (c r,m , c # 1, see runs 2–6 in Fig. 4) increases with temperature. In the two-phase region (where r decreases

Fig. 3. Hydrogen content dependence of thermoelectric power (d, this work; m, [9]; j, [8]; ♦, estimated for PdH, see text) and electrical resistance of PdH c alloys (h, [10]; n, [11]; 쏻, [18], s, this work) at 200 K. Two phase region: (- - -) TEP calculated according to (9b); (? ? ?) ER calculated according to (9a).

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Fig. 4. Temperature dependence of thermoelectric power of Pd 0.95 Ge 0.05 and Pd 0.95 Ge 0.05 –H alloys. The labels denote the run number. ( ] ] ]) hypothetical S(T ) dependence of H-free alloy below 85 K.

with reduction of hydrogen content, c , c r,m ), the S(T ) dependence is no longer monotonic in shape. A maximum appears that successively shifts to lower temperatures with decreasing hydrogen content. The crossing mentioned above occurs close to 85 and 115 K for PdBe–H and PdGe–H alloys, respectively. The temperature dependence of TEP and ER for PdMe– H alloys (Me5Ti, Nb, Zr, Ce; see Figs. 5 and 6 for PdCeH c as an example) is qualitatively similar to that described above but the effect of hydrogen desorption on the data set (S,r) is different. In Fig. 7 thermoelectric power is plotted against reduced

Fig. 5. Temperature dependence of thermoelectric power of Pd 0.97 Ce 0.03 and Pd 0.97 Ce 0.03 –H alloys. The labels denote the run number.

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Fig. 6. Temperature dependence of electrical resistance of Pd 0.97 Ce 0.03 –H alloys. The labels denote the run number.

electrical resistance, r /r m , where r m denotes the highest value of r attained during the desorption process (for c 5 c r,m ), both quantities measured at 200 K. The experimental points lying extreme of the left and of the right correspond to the run with H-free metal and to run 1, respectively. Two groups of data can be distinguished in this figure. In the case of the first group (Pd–H, PdGe–H and PdBe–H) the TEP attains a maximal value (at c 5 c S,m ) for r /r m 5 1. i.e. both quantities, ER and TEP, attain maximal values at the same state of hydrogen desorption (see Figs. 1 and 2), i.e. c S,m 5 c r,m 5 c m , The PdMe–H alloys with Me5Nb, Ti, Zr or Ce form the second group.

Fig. 7. Thermoelectric power of PdH c and Pd 12x Me x H c alloys, at 200 K as a function of relative electrical resistance (see text). d, Pd; j, Me5Ge, x50.05; 쏻, Me5Be, x50.05; ., Me5Nb, x50.04; S, Me5 Ti, x50.04; m, Zr, x50.04; ♦, Ce, x 5 0.03; s, PdH (S, estimated, see text; r, after [18]).

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In the latter case the hydrogen contents corresponding to maximal values of TEP measured at 200 K, c S,m , are apparently lower than that corresponding to the maximal values of the electrical resistance, c r,m (see run 13 in Fig. 5 and run 5 in Fig. 6 for PdCe–H, see also Fig. 7). The hydrogen content corresponding to the a1bub boundary in the Pd 0.95 Ce 0.05 –H system (c a1bub ¯0.25 [19]) is much lower than that for Pd–H (c a1bub ¯0.6). So we assume that TEP of Pd 0.97 Ce 0.03 H c attain maximal values at c S,m 5 c a1bub , with 0.25 , c a1bub , 0.6. This is the probable reason for the observed inequality c S,m , c r ,m .

content. By a combination of expressions (1) and (3) we obtain rph rdis S 5 ]Sph 1 ]Sdis (4) r r where

F

G

F

G

p 2 k 2 T dln rph Sph 5 ]] ]] 3e dE

EF

(5a)

and

p 2 k 2 T dln rdis ]] ]] Sdis 5 3e dE

EF

(5b)

4. Discussion

Combining (4) and (5) we obtain a modified version of the Nordheim–Gorter (NG) rule

Total thermoelectric power is the sum of diffusion thermopower and phonon drag. The latter is important in very dilute alloys, in moderately low temperatures. Hence we expect it can be neglected in the analysis of the present results. According to Mott and Jones [20] the diffusion thermoelectric power and electrical resistivity are correlated

rdis S(T ) /T 5 a ph 1 ]](a dis –a ph ) r (T )

2 2

F

p k T dln r (T ) S(T ) 5 ]] ]]] 3e dE

G

EF

(1)

where k, e, r, EF are the Boltzmann constant, electron charge, electrical resistivity and Fermi energy, respectively. This equation can be valid if electron scattering is elastic. This restriction is satisfied at very low (T < QD , QD — Debye temperature) and high (T . 2 / 3QD ) temperatures or if phonon resistivity is less than the residual resistivity [21]. From the present r(T ) measurement we can see that the third restriction is fulfilled in the case of b-PdMe–H alloys with exception of highly hydrogenated Pd–H and PdBe–H alloys. Hence we expect Eq. (1) to approximately hold in the whole temperature range of present measurements. The resistivity can be presented as a sum of terms, each corresponding to i-th scattering mechanism

Or

r5

i

(6)

where a ph 5 Sph /T and a dis 5 Sdis /T. So if the experimental data set for a given alloy is plotted in coordinates hS /T, 1 /r j then it is expected to be fitted by a straight line S /T 5 A 1 B(1 /r ). From the fit parameters, A and B, the quantities a ph and a dis can be easily obtained if the residual resistivity for that alloy is known. In general, all this quantities, a ph , a dis and rdis , can be dependent on the alloy composition. As an example the results for Pd–H alloys are shown in Fig. 8 where it is seen that Eq. (6) is indeed roughly fulfilled. It is rather strange that relationship (6) holds in the two-phase range as well. The values of the a ph and a dis , derived from the NG plots for H-rich Pd–H and PdMe–H, alloys are given in Fig. 8. A general feature is the occurrence of positive values of a dis , decreasing if the hydrogen content tends to stoichiometry. The quantity a ph is small and positive for

(2)

i

The main scatterings involved are (1) scattering by phonons and (2) scattering resulting from the lattice disorder. So

r 5 rph 1 rdis

(3)

The disorder resistivity can also be split into two terms — one corresponding to disorder of metal lattice (here substitutional Pd 12x Me x alloy) and the other corresponding to disorder of hydrogen sublattice (if not all octahedral sites are occupied, i.e. if we deal with non-stoichiometric composition, Pd 12x Me x H c , with c , 1). If no phase transition occurs at lower temperatures then rdis is temperature independent and can be identified as residual resistivity. In principle, both terms in (3) depend on hydrogen

Fig. 8. Modified NG plots for Pd–H alloys. The labels denote the run number.

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high hydrogen contents but it changes sign and decreases to large, negative values for decreasing hydrogen contents. As was already stated in Section 1 there are two kinds of phonons — acustical and optical. In the case of Pd–H alloys the phonon thermopower can be analysed in more detail. The contributions from acoustical and optical phonons can be estimated as follows. By analogy to expression (3) the phonon thermoelectric power, Sph 5 a ph T, can be split in two components

r ac r opt ph ph opt ]] a ph 5 ]a ac 1 a rph ph rph ph

(7)

where ac rph 5 r ph 1 r opt ph

(8)

is a sum of contributions to electrical resistivity from electron scattering on acoustical and optical phonons. The opt ac quantities a ac ph and a ph are defined by (5a) with r ph and opt r ph substituted for rph . According to Chiu and Devine [22] the optical phonon resistivity gradually vanishes if the hydrogen content decreases down to c ¯ 0.7. Thus we conclude from (7) and the data given in Fig. 9 that 2 a ac ph 5 20.04 mV/ K for c ¯ 0.6 and it increases to small, positive values, | 10.005 mV/ K 2 for c ¯ 0.7. This value is in excellent agreement with the value of Sph /T (5 10.0048

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mV/ K 2 ) derived from the NG plots for silver [23] where only acustical phonons are believed to be present as they are in copper [24]. As r opt ph 50 for c , 0.7 then one can conclude from (7) that there is no contribution of optical phonons to TEP for hydrogen content in the range 0 # c # 0.7. More accurate measurements of TEP and ER would be needed for estimation of acustical and optical contributions at higher hydrogen contents. As we have already noted, a maximum in the temperature dependence of thermopower could be seen in the case of partially desorbed samples of Pd–H and PdMe–H alloys (see Figs. 1, 4 and 5). Its origin is not clear. (1) It can be attributed to phonon drag, (2) it is a manifestation of the two-phase nature of the alloy or (3) it is an intrinsic property of the diffusion thermopower. The analysis of the values of the resistances and their changes resulting from hydrogen desorption suggests that run 9 of Pd–H corresponds to the b-phase of hydrogen content, c ¯ 0.66, slightly higher than c a1bub 5 0.6). The S(T ) relationship for this run is in excellent agreement with the results of Folies [8] measured for the PdH 0.63 alloy. The set of hS(T ),r(T )j data fulfils the Northeim–Gorter rule as shown in insert of Fig. 8. So we conclude that the maximum in this S(T ) relationship does not originate from phonon drag (as generally accepted to do in pure Pd) but from the temperature dependence of resistance, with phonon and disorder thermopowers simply proportional to temperature. The temperature dependence of thermoelectric power of b-PdH c alloys has been calculated according to Eq. (6) with resistivities, r, substituted by relative resistances, r, and using averaged a ph and a dis values. The results are given in Fig. 1 (runs 2–9). If an alloy is a mixture of two phases, a and b, which differ in resistance ( ra and rb ) and thermopower (Sa and Sb ), then the effective resistance and thermopower of the two-phase mixture ( ra1b and Sa1b , respectively) is expected to be intermediate between thermopower and resistivity values characteristic for both phases. Their actual values should depend mainly on relative amount of both phases, ua and ub . Fletcher et al. [6] have shown that in the case of Pd–H system the following relations is approximately valid at low temperatures in the two-phase region ln ra1b 5 ua ln ra 1 ub ln rb

(9a)

and Sa1b 5 ua Sa 1 ub Sb

Fig. 9. Phonon (a ph ) and disorder (a dis ) thermopowers for Pd–H (d), Pd–Be–H (앳), Pd–Ce–H (♦), Pd–Ge–H (h), Pd–Ti–H (S), Pd–Nb– H (.) and Pd–Zr–H (m). s, PdH (estimated, see text, r after [18]).

(9b)

where ua 1 ub 5 1 TEP values of Pd–H, corresponding to runs 10 through 14 (two-phase region) have been calculated from expression (9b), with Sa approximated by thermopower of pure Pd, and Sb approximated by thermopower of run 9, with ub taken as a fit parameter. The results are given in Figs. 1 and 3. A similar procedure has been applied for the

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electrical resistance using (9a), see Fig. 3. The apparent agreement between the experimental and calculated relationships supports the approximate validity of the assumptions (9). The S(T ) curves for hydrogen-free dilute Pd alloys pass through a maximum located below |100 K and tend to negative values at high temperatures. The S values corresponding to the H-rich hydrides are positive and increase with temperature. Thus in the case of two-phase alloy, having in view (9b), one can expect a non-monotonic temperature dependence with a maximum located above 100 K. Its position should depend on the hydrogen content. In fact, this is observed as can be seen in Figs. 1, 4 and 5.

4.1. Thermoelectric power of Pd–H system under high pressure of gaseous hydrogen From the measurements of palladium–hydrogen system performed at room temperature in the pressure range between 0.05 and 1.4 GPa of H 2 it is known that thermopower is positive and decreases with increase of pressure, i.e. with increase of hydrogen content. TEP of Pd–H system (298 K), is given in Fig. 10 as a function of log of hydrogen fugacity [12] (at low densities hydrogen fugacity is equal to pressure but at higher pressures the difference between them becomes very appreciable as hydrogen highly deviates from the ideal behaviour). This pressure range corresponds to hydrogen content in the range 0.85 # c # 0.99 [17]. Such behaviour of TEP can be explained in terms of the Nordheim–Gorter rule. The TEP values have been calculated from the expression

Fig. 10. Thermoelectric power of Pd–H system at 298 K as a function of log of hydrogen fugacity. The averaged, experimental data of ´ Skoskiewicz [12] and the calculated values are denoted by thick and thin solid lines, respectively; calc., calculated according to (10); (a) (r ph /r)a ph T RT ; (b) (r dis /r)a dis T RT .

S( p) 5 1 /r( p) ? (r dis a ph T RT 1 r ph a ph T RT )

(10)

a modified version of expression (6). Here r( p) is the relative resistance of the Pd–H sample measured at a hydrogen pressure p and temperature T RT 5 298 K and r ph 5 r( p) 2 r dis . The r( p) values were taken from [25], the values of r dis , i.e. the residual resistances were taken from [10] and / or estimated from the present measurements. We have taken the averaged values for the phonon and disorder thermopowers, a ph 5 1 0.005 and a dis 5 1 0.031 mV/ K 2 , respectively, as derived from the present low-temperature measurements of b-Pd–H. The S( p) values calculated according to (10) are shown in Fig. 10. The contributions of phonon scattering, (r ph /r( p))a ph T RT (a), and disorder, (r dis /r( p))a dis T RT (b), to total thermopower (calc.) are also indicated. Basing on Eq. (10), the room-temperature TEP of stoichiometric PdH (where r dis 5 0) can be estimated as 11.5 mV/ K (see insert in Fig. 10). A direct extrapolation of the experimental data, S vs. r dis /r to r dis /r 5 0 yields 12.5 mV/ K for TEP of PdH, see insert of Fig. 10. Both values are close to the values of thermopower of noble metals Cu, Ag and Au: 11.8, 11.5 and 11.9 mV/ K, respectively [26] and of stoichiometric nickel hydride: 11 mV/ K ([12], see also [15]). The hypothetical, linear, temperature dependence of the diffusion thermopower of stoichiometric PdH is then S 5 a ph T, with a ph ¯ 1 0.008 mV/ K, as shown in Fig. 1, see also Fig. 9. This gives 11.7 mV/ K at 200 K (see Fig. 7). There is a disagreement between the present results and the experimental data of Kopp et al. for nearly stoichiometric PdH c (c50.996). In the latter case the S(T ) dependence was far from linearity — dS / dT decreased with increase of temperature suggesting possible existence of plateau or maximum above 170 K. It is hard to explain this nonlinearity in terms of diffusion thermopower of the ordered compound like PdH. Perhaps, the phonon drag could be responsible for such a behaviour. However this supposition is in contrast with other experimental findings in similar systems: The S(T ) dependence observed in NiH 0.87 above 85 K was nearly linear [27]. Having in view that NiH is the main component of this two-phase alloy, one can conclude that phonon drag is negligibly small in stoichiometric nickel hydride, in this temperature range. In pure copper and silver (the TEP of the former [28] is shown for comparison in Fig. 1), which can be treated, from the point of view of electronic structure, as analogues of NiH and PdH [2], the estimated phonon drag is maximal at 80 K and does not exceed 10.7 and 10.25 mV/ K, respectively. TEP of both noble metals is proportional to temperature above |150 K. In either case, total, diffusion1phonon drag, thermopower of stoichiometric PdH is expected not to exceed 2 mV/ K at 170 K. This value should be compared with 3.8 mV/ K measured by Kopp et al. at this temperature for PdH c with hydrogen content, claimed by the authors to be, 0.996.

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If we take into account that the values of most quantities involved in expression (10), have been derived from the measurements performed at quite different conditions, then the agreement between the experimental and calculated values can be claimed to be satisfactory. So, one can conclude that the observed negative value of pressure derivative, dS / dpH 2 (and dS / dc as well) results from the decreasing contribution of the residual resistance to the total resistance when hydrogen pressure (and hydrogen content) increases, together with the fact that disorder thermopower (a dis T ) is much greater than phonon thermopower (a ph T ). Kopp et al. [9] qualitatively explained decrease of TEP of PdH c , observed by them for c in the range 0.915 # c # 0.996, also with use of the Nordheim–Gorter rule. They arbitrary assumed that S opt ph 50 and attributed the decrease mentioned to the increasing contribution of optical phonon resistivity in the total phonon resistivity. However, they completely neglected disorder of the hydrogen sublattice, i.e. contribution of disorder thermopower.

5. Summary It was shown that the total thermopower of hydrogenated palladium and its dilute alloys is, in a simple manner, related to the electrical resistance. The results of simultaneous measurements of temperature dependence of thermoelectric power and electrical resistance could be analysed in terms of the Nordheim– Gorter rule. Thus two main components of the diffusion thermoelectric power could be estimated, one corresponding to scattering of electrons on phonons and the other corresponding to disorder of the crystal lattice. The room-temperature value of TEP of stoichiometric PdH has been estimated and found to be similar to that for noble metals.

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