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 have been studied employing both experimental (Raman scattering) and theoretical (density-functional theory) approaches. An anomaly dependence of the phonon frequency of the E2g mode was found 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 from the calculations have characteristic features indicating the occurrence of a structural phase transition. © 2018 American Physical Society.