Configurational and communal entropies of formation of non-stoichiometric PdHx at the glass transition temperature and the critical temperature

Abstract

Non-stoichiometric palladium hydride (PdHx) with vacancies for hydrogen exhibits a glass transition temperature (Tg), resulting in generation of both configurational and communal entropies. The communal entropy was evaluated under a given configurational entropy with a suitable hydrogen occupation of tetrahedral and octahedral sites of Pd using the standard molar entropy of formation (ΔfSm(exp.)°) calculated from the equilibrium pressures in pressure–composition–temperature (PCT) curves and the spectroscopic entropies of molecular hydrogen and PdHx.PCT curves with little hysteresis between hydrogenation and dehydrogenation processes were obtained just below the critical temperature Tc, at which the lattice volume mismatch between α and β phases of PdHx is almost negligible. The ΔfSm(exp.)° value calculated from the PCT curves was −83.4 ± 1.3 J/(K·molH2) in the hydrogenation process and −87.3 ± 1.7 J/(K·molH2) in the dehydrogenation process, showing only a relatively small discrepancy between the two.Based on data from the literature, we assumed that the α phase, with its lower hydrogen concentration, was PdH0.006, and that the β phase, with its higher hydrogen concentration, was PdH0.6 in the equilibrium hydrogenation reaction between α and β phases. We then estimated the difference in communal entropy (ΔScom.°) between PdH0.006 and PdH0.6 in terms of the ΔfSm(exp.)° value, the hydrogen molar entropy (Sm,H2°), the vibrational entropy (ΔSvib.°), the electronic entropy (ΔSele.°), and given configurational entropy (ΔSconf.°). We found that near Tc, H atoms occupied both the octahedral and tetrahedral sites in PdH0.6, with ΔScom.° approaching the value of the gas constant R. On the other hand, ΔScom.° approached 0 J/(K·molH) near the glass transition temperature Tg, with H atoms occupying only all the octahedral sites in PdH0.6.