Pressure-induced softening of shear modes in wurtzite ZnO: A theoretical study

Abstract

Recent ultrasonic experiments on single-crystal specimens of the wurtzite $(B4)$ phase of ZnO have shown that, under pressure, this material becomes softer against shear-type acoustic distortions. In the light of these results, we have performed atomistic calculations based on an interatomic pair potential within the shell-model approach. The focus is on the behavior of the elastic moduli ${C}_{\mathrm{ij}}$ as function of pressure. A linear evolution under pressure is observed for the two longitudinal modes ${C}_{11}$ and ${C}_{33}$ with a pressure derivative $\ensuremath{\partial}C/\ensuremath{\partial}P$ of 3.18 and 1.72, respectively. In contrast, the shear moduli ${C}_{44}$ and ${C}_{66}$ exhibit a negative pressure dependence throughout the pressure range with $\ensuremath{\partial}{C}_{44}/\ensuremath{\partial}P=\ensuremath{-}0.30,$ and $\ensuremath{\partial}{C}_{66}/\ensuremath{\partial}P=\ensuremath{-}0.84.$ We show that this behavior can be related to the wurtzite-rocksalt phase transition. Besides, the effect of phonons and the role of bond-bending forces as function of pressure in causing the elastic softening are discussed.