Models for the Phase Diagram of Palladium Hydride Including O-site and T-site Occupation

Abstract

Early statistical mechanics models for palladium hydride allowed for a good description of the phase diagram based on a simple parameterization of the O-site energy. In this work we study generalizations of these models to include higher-order dependence on loading, temperature-dependent O-site energies, and also to include T-site occupation. Experimental data sets for 10 isotherms were assembled, and augmented with additional extrapolated points for the low-pressure α-phase region as well as the high pressure β-phase region. Loading-dependent O-site energies are optimized by minimizing the mean square error in the chemical potential between the model and data set. The resulting models give a good match to the phase diagram. If the O-site energy is allowed to be temperature dependent then the fit is better, but the resulting optimum is a mathematical optimum not so closely connected with the physical system. Models were studied in which O-site and T-site occupation occurs. When optimized these models are able to provide a good match to the phase diagram. When the O-site to T-site excitation energy is fixed according to estimates developed in earlier studies, the resulting temperature-dependent O-site energies are physically plausible. When the excitation energy are optimized together with the O-site energy, the resulting optimum is a mathematical one much less connected to the physical system. An earlier analysis of solubility in the α-phase led to a strong argument that T-site occupation occurs in palladium hydride and in palladium deuteriude; the present study supports this conclusion based on an independent data set. Keywords: Mean field model; Palladium hydride; Phase diagram; Statistical mechanics; T-site occupation