First-principles calculations on the elastic and thermodynamic properties of NbN

The elastic and thermodynamic properties of NbN at high pressures and high temperatures are investigated by the plane-wave pseudopotential density functional theory (DFT). The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) method is used to describe the exchange-correlation energy in the present work. The calculated equilibrium lattice constant a(0), bulk modulus B-0, and the pressure derivative of bulk modulus B-0' of NbN with rocksalt structure are in good agreement with numerous experimental and theoretical data. The elastic properties over a range of pressures from 0 to 80.4 GPa are obtained. Isotropic wave velocities and anisotropic elasticity of NbN are studied in detail. It is indicated that NbN is highly anisotropic in both longitudinal and shear-wave velocities. According to the quasi-harmonic Debye model, in which the phononic effect is considered, the relations of (V - V-0)/V-0 to the temperature and the pressure, and the relations of the heat capacity C-V and the thermal expansion coefficient a to temperature are discussed in a pressure range from 0 to 80.4 GPa and a temperature range from 0 to 2500 K. At low temperature, C-V is proportional to T-3 and tends to the Dulong-Petit limit at higher temperature. We predict that the thermal expansion coefficient a of NbN is about 4.20 x 10(-6)/K at 300 K and 0 GPa.