Theoretical study of the thermodynamic properties of cubic Zr3N4 and Hf3N4 under high pressures

The crystal structure and elastic properties of two nitrides c-Zr3N4 and c-Hf3N4 with Th3P4 structure are investigated using density functional theory within the local density approximation (LDA). The results at zero pressure are in good agreement with the available theoretical and experimental values. Through the quasi-harmonic Debye model, the variations of the Debye temperature, internal energies, entropy, heat capacity and the thermal expansion under pressure range from 0 to 100 GPa and temperature range from 0 to 600 K are successfully obtained and discussed.