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

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 Cᵢⱼ as function of pressure. A linear evolution under pressure is observed for the two longitudinal modes C₁₁ and C₃₃ with a pressure derivative ∂C/∂P of 3.18 and 1.72, respectively. In contrast, the shear moduli C₄₄ and C₆₆ exhibit a negative pressure dependence throughout the pressure range with ∂C₄₄/∂P=-0.30, and ∂C₆₆/∂P=-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.