High pressure study on the phonon spectra and thermal properties in hafnium nitride and zirconium nitride

We report ab initio calculations of the thermal properties for transition metal nitrides, hafnium and zirconium nitride at ambient and high pressures. The assessment of thermodynamical properties like lattice specific heat, vibrational energy, internal energy and entropy for two nitrides has been carried out. The basic calculations of ingredient phonon density of states for the determination of thermal properties have been done using density functional perturbation theory including external perturbations like strains and electric fields in periodic systems. The ground state properties such as equilibrium lattice constants and bulk modulus obtained for two nitrides are in good agreement with the available experimental value. The calculated pressure variation of the phonon density of states shows trend similar to the experimental pressure dependent Raman spectra. The lattice specific heat, internal energy, entropy and Helmholtz energy increases with pressure.