Configurational and communal entropies of formation of non-stoichiometric PdH 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 ( Δ f S m ( e x p . ) ° ) 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 Δ f S m ( e x p . ) ° 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 ( Δ S c o m . ° ) between PdH0.006 and PdH0.6 in terms of the Δ f S m ( e x p . ) ° value, the hydrogen molar entropy ( S m , H 2 ° ), the vibrational entropy ( Δ S v i b . ° ), the electronic entropy ( Δ S e l e . ° ), and given configurational entropy ( Δ S c o n f . ° ). We found that near Tc, H atoms occupied both the octahedral and tetrahedral sites in PdH0.6, with Δ S c o m . ° approaching the value of the gas constant R. On the other hand, Δ S c o m . ° approached 0 J/(K·molH) near the glass transition temperature Tg, with H atoms occupying only all the octahedral sites in PdH0.6.