Theoretical study of the structure, lattice dynamics, and equations of state of perovskite-type MgSiO₃ and CaSiO₃

Abstract

The structural distortions, lattice dynamics, and equations of state of the high-pressure perovskite phases of MgSiO₃ and CaSiO₃ are examined with a parameter-free theoretical model. A theoretical ionic description of the crystal charge density is constructed from shell-stabilized ions, whose wavefunctions are calculated from Hartree-Fock theory. The short-range forces are then calculated in the pairwise-additive approximation from modified electron gas theory. The resulting many-body-corrected pair potentials are used to study the lattice dynamics in the quasiharmonic approximation. The cubic structure of MgSiO₃ perovskite (Pm3m) is found to be dynamically unstable at all pressures, with imaginary quasiharmonic phonons occurring at the edge of the Brillouin zone. In contrast, the cubic phase of CaSiO₃ perovskite is found to be stable at low pressures but becomes dynamically unstable at ∼ 109 GPa (1.09 Mbar). Energy minimization of MgSiO₃ in an orthorhombic cell (Pbnm) is performed to obtain a distorted perovskite structure that is dynamically stable. The calculated unit cell parameters at zero pressure and room temperature are within 2 percent of those determined by x-ray diffraction. The theoretical equation-of-state calculations predict a lower compressibility and thermal expansivity for the two silicate perovskites than does the available experimental data on these compounds. Extensions of the present ionic model for more accurate predictions will require the inclusion of polarization of charge density and vibrational anharmonicity.