Phase transition and elastic properties of NbN under hydrostatic pressure

First-principles pseudopotential calculations are performed to investigate the phase transition and elastic properties of niobium nitrides (NbN). The lattice parameters a0 and c0/a0, elastic constants Cij, bulk modulus B0, and the pressure derivative of bulk modulus B0′ are calculated. The results are in good agreement with numerous experimental and theoretical data. The enthalpy calculations predict that NbN undergoes phase transition from NaCl-type to NiAs-type structure at 13.4 GPa with a volume collapse of about 4.0% and from AsNi-type to CW-type structure at 26.5 GPa with a volume collapse of about 7.0%. Among the four types of structures, CW-type is the most stable structure. The elastic properties are analyzed on the basis of the calculated elastic constants. Isotropic wave velocities and anisotropic elasticity of NbN are studied in detail. The longitudinal and shear-wave velocities, VP, VS and Vm increase with increasing pressure, respectively. The Debye temperature ΘD increases monotonically with increasing pressure except for NiAs-type structure. Both the longitudinal velocity and the shear-wave velocity increase with pressure for wave vector along all the propagation directions, except for VTA([100]) and VTA[001]([110]) with NaCl structure and VTA[010]([100]) with the other three types of structures.