Phonon mode softening and elastic properties of hafnium under pressure

Abstract

The effect of pressure on the zone-center optical phonon modes and the elastic properties of hafnium has been studied by both experimental (Raman scattering) and theoretical (DFT) approaches. It was found an anomaly dependence of the phonon frequency of E$_{2g}$ mode in the pressure range from 0 to 67 GPa. The calculated electronic structure of hafnium shows significant changes under pressure, which have a pronounced spatial anisotropy similar to the anisotropy of the observed phonon properties. The dependencies of the elastic properties on pressure including the components of the elasticity tensor, bulk and shear modulus, Poisson ratio and Universal anisotropy index obtained during the calculations has characteristic features indicating the occurrence of the structural phase transition.