The effect of cation order on the elasticity of omphacite from atomistic calculations

Omphacite, a clinopyroxene mineral with two distinct crystallographic sites, M1 and M2, and composition intermediate between diopside and jadeite, is abundant throughout the Earth’s upper mantle and is the dominant mineral in subducted oceanic crust. Unlike the end-members, omphacite exists in two distinct phases, a P2/n ordered phase at low temperature and a high-temperature C2/c disordered phase. The crystal structure and full elastic constants tensor of ordered P2/n omphacite have been calculated to 15 GPa using plane-wave density functional theory. Our results show that several of the elastic constants, notably C₁₁, C₁₂, and C₁₃ deviate from linear mixing between diopside and jadeite. The anisotropy of omphacite decreases with increasing pressure, and at 10 GPa, is lower than that of either diopside or jadeite. The effect of cation disorder is investigated through force-field calculations of the elastic constants of special quasi-random structures supercells with simulated disorder over the M2 sites only, and over both cation sites. These show that cation order influences the elasticity, with some components displaying particular sensitivity to order on a specific cation site. C₁₁, C₁₂, and C₆₆ are sensitive to disorder on M1, while C₂₂ is softened substantially by disorder on M2, but insensitive to disorder on M1. This shows that the elasticity of omphacite is sensitive to the degree of disorder, and hence the temperature. We expect these results to be relevant to other minerals with order–disorder phase transitions, implying that care must be taken when considering the effects of composition on seismic anisotropy.