First-principle calculations of thermodynamic properties of ZrC and ZrN at high pressures and high temperatures

Ab initio calculations for the thermal properties of ZrC and ZrN have been performed by using the projector augmented-wave (PAW) method within the generalized gradient approximation (GGA). Pressure-temperature-dependent thermodynamic properties including the bulk modulus, thermal expansion, thermal expansion coefficient, heat capacity at constant volume and constant pressure were calculated using three different models based on the quasi-harmonic approximation (QHA): the Debye-Slater model, Debye-Grüneisen model and full quasi-harmonic model (that requires the phonon density of states at each calculated volume). Also the empirical energy corrections are applied to the results of three models. The calculated values are in good agreement with experimental results. It is found that the full quasi-harmonic model provides more accurate estimates in comparison with the other models.