First-principles calculations of phase transition, elasticity, phonon spectra, and thermodynamic properties for hafnium

Abstract

In this work, structural transformation, elastic behaviors, phonon spectra, and thermodynamic properties upon hydrostatic compression of hafnium are investigated by using first-principle density functional theory. Our calculated equilibrium structural parameters and the transition pressures of α→ω→β are well consistent with experiments. At ambient pressure, the elastic constants indicate that the α and ω phases are mechanically stable while the β phase is unstable. The thermal properties including bulk modulus, entropy, and heat capacity in wide range of pressure and temperature for α-Hf are predicted. We present results of the phonon spectra and phonon density of states for the three experimentally observed phases and discuss the effects of pressure and temperature on those properties. The β-Hf is mechanically and dynamically stable at high pressure or at high temperature. Employing the quasiharmonic approximation as well as the Debye model, we calculate the Gibbs free energy and predict the pressure-temperature phase diagram.