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

Recent ultrasonic experiments on single-crystal specimens of the wurtzite $\mathrm{}\left(B4\mathrm{}\right)\mathrm{}$ 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 $\partial C/\partial P$ 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 $\partial C_{44}/\partial P=-0.30,$ and $\partial C_{66}/\partial P=-\mathrm{0.84.}$ 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.