Theoretical study of the structural phase transition and elastic properties of HfN under high pressures

• We investigate the phase transition of six types of structure of HfN.
• The transition pressure from B1 to CsCl (B2) phase is ca. 277.3 GPa.
• The elastic parameters of B1 and B2 phases increase monotonically with pressure.
• The anisotropy of B1 and B2 phases become more extreme as the pressure increases.

The effect of hydrostatic pressure on the structures of HfN at 0 K was investigated by using the projector augmented wave (PAW) within the Perdew–Burke–Ernzerhof (PBE) form of the generalized gradient approximation (GGA). The transition pressure between NaCl (B1) and CsCl (B2) structures is predicted to be 277.3 GPa. This value is consistent with that reported by Kroll, while in contrast to the results obtained by Ojha et al. and Meenaatci et al. Moreover, the elastic properties of B1-HfN and B2-HfN under high pressures are successfully obtained. It is found that the elastic constants, bulk modulus B, shear modulus G, compressional and shear wave velocities increase monotonically with increasing pressure. The Debye temperature Θ calculated from the elastic constants of HfN is in good agreement with the experimental values. The anisotropies of B1-HfN and B2-HfN at zero pressure have also been discussed.