Ab initio thermodynamics of zirconium hydrides and deuterides

•We model thermodynamic and elastic properties of zirconium hydrides.•We calculate phonon dispersion and density of states for all hydrides.•Thermodynamic and elastic results agree well with experimental measurements.•Gamma hydride is found to be mechanically stable. We report the results of a systematic ab initio study of the elastic and thermodynamic properties of γ-ZrH, δ-ZrH1.5,γ-ZrD, and δ-ZrD1.5. In addition, pure α-Zr as well as the ε-ZrH2 and ε-ZrD2 phases are evaluated for reference. The calculations are performed using quantum mechanical density functional theory (DFT) with the frozen core projector augmented wave (PAW) approach and a generalised gradient approximated (GGA) exchange–correlation functional. To capture the variations of the thermodynamic quantities over a wide range of temperatures (0≲T⩽1000K), the quasi-harmonic approximation approach is adopted where the influence of the vibrational and electronic free energies are included by means of the phonon and electron densities of state. This allows for quantifying the contributions of the electron density of states, which were not accounted for in the previous studies. All the pertinent elastic constants and phonon properties for the considered hydride/deuteride phases are calculated and compared with experimental data; which were not done before. We have further computed the entropy, heat capacity and enthalpy as well as low temperature thermodynamic properties such as the Debye temperature and the electronic heat capacity constant for all the hydride and deuteride phases. The results of our computations concur well with the corresponding data obtained by measurements that are reported in the literature and offer the necessary data and basis for multiscale modelling of zirconium alloys.