Equation of state of MgSiO3 perovskite and its thermoelastic properties under lower mantle conditions

Abstract

A simple four‐parameter model for calculating thermoelastic properties of MgSiO3 perovskite is presented based on the Vinet model for static lattice and the Debye approximation for lattice vibration. The input parameters are the volume of the unit cell, V0, the bulk modulus, K0, its pressure derivative, K0′, and the Debye temperature, Θ0, in the static lattice at zero pressure. For V0, K0 and K0′ the theoretical values by Stixrude and Cohen [1993] are used and Θ0 is determined to reproduce the experimental value at ambient conditions, 980 K, by Akaogi and Ito [1993]. The resulting isobars are in good agreement with experimental data to 1300 K and 11 GPa by Wang et al. [1994], with those to 1200 K at 20 GPa by Utsumi et al. [1995], and with those to 1500 K and to 2000 K, respectively, by Kato et al. [1995] and Funawori et al. [1996] both at 25 GPa. Using the present equation of state together with the method for calculating adiabatic Lamé constants λS and μS for isotropic medium given in the present paper, density ρ, and sound velocities νp and νs of MgSiO3 perovskite under lower mantle conditions have been calculated where the constant‐entropy model is assumed with the temperature at the core‐mantle boundary being taken to be 3000 K. The results for ρ, νp, and νs are in agreement with the preliminary reference Earth model (PREM) within −2.4%∼ −3.7%, +3.3%∼+1.1%, and +0.8%∼−6.8%, respectively, over the lower mantle from 670 to 2891 km in depth. The calculated thermal expansivity under lower mantle conditions is in good agreement with that of the lower mantle estimated by Anderson [1982]. Using the present model with the parameters determined from experimental data at room temperature by Knittle and Jeanloz [1987], assuming Θ0 to be the same as that of MgSiO3 perovskite, thermoelastic properties of (Mg0.9, Fe0.1)SiO3 perovskite under lower mantle conditions have been calculated. The density becomes in much better agreement (+0.4%∼−0.8 %) with PREM and νp and νs remain almost unchanged from those of MgSiO3 perovskite.