Ab initio thermodynamics of fcc H-Zr and formation of hydrides

Abstract

In order to elucidate the currently debated stability of zirconium hydrides, the energetics of fcc H-Zr was investigated by means of ab initio-based cluster expansions (CEs) including the effect of long-range interactions, the latter being possibly important due to the interstitial H site occupancy in fcc-Zr. Allowing a detailed temperature- and composition-dependent evaluation of the configuration part of free energies in fcc H-Zr, our modelling provides new insights into the controversial properties of the γ-ZrH compound: (i) at low temperature, γ is metastable with respect to α-Zr+ε-ZrH2−x, (ii) there exists a temperature domain around 500K in which γ becomes stable, in agreement with recent experiments, (iii) contrasting with the ill-defined off-stoichiometry of the stable δ-ZrHy (y∼1.5) and ε-ZrH2−x hydrides, γ is a line-compound undergoing a γ→δ order/disorder transition at moderate temperature (∼800K), (iv) the γ composition domain corresponds to a strong failure of the usual random approximation for the configurational entropy. Relying on a large set of ab initio data, our results also reveal an intricate energetic behaviour of fcc H-Zr around the δ domain. This complex behaviour could not be not reliably captured by CE modelling, which implies that, contrary to experiments, our proposed theoretical H-Zr phase diagram contains no δ+ε domain. Moreover, the coupling between phonons and chemical order, much more significant at ZrH composition than for higher H contents, may be responsible for a lowering of the order–disorder transition temperature of γ. Our work therefore indicates that including phonons into CEs should be a promising direction for high-quality modelling of Zr hydrides.