Elasticity of grossular–andradite solid solution: an ab initio investigation

Abstract

Grossular and andradite are garnet end-members stable under upper mantle conditions. We perform ab initio simulations to investigate the dependence of the bulk modulus on chemical composition of the grossular–andradite solid solution, Ca₃Fe_2−2xAl_2x(SiO₄)₃. All-electron local basis sets of Gaussian-type orbitals and the hybrid B3LYP density functional are used. Our calculations predict a linear modulus-composition trend, in contrast to previous conjectures based on “heterogeneous” experimental measurements. We estimate the largest deviation from linearity to be about 0.5 GPa under ambient conditions, and to progressively reduce to less than 0.2 GPa at pressure P = 20 GPa. The bulk modulus is computed over the whole composition range 0 ≤ x ≤ 1 following two independent approaches: fitting energy–volume data to an equation-of-state and calculating elastic tensors. Results from the two methods are in perfect agreement, assuring consistency and high numerical accuracy of the adopted algorithms.