EQUATION OF STATE OF MGSIO3 PEROVSKITE AND ITS THERMOELASTIC PROPERTIES UNDER LOWER MANTLE CONDITIONS

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, V-0, the bulk modulus, K-0 , its pressure derivative, K-0', and the Debye temperature, Theta(0), in the static lattice at zero pressure. For V-0, K-0, and K-0', the th eoretical values by Stixrude and Cohen [1993] are used and Theta(0) is determined to reproduce the experimental value at ambient conditions, 980 K, by Akaogi and Ito [1993]. The resulting isobars are in good ag reement with experimental data to 1300 K and 11 GPa by Wang et al. [19 94], 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 Funamori et al. [1996] both at 25 GPa. Using the present equation of state together with the method for calculating adiabatic Lame constant s lambda(S) and mu(S) for isotropic medium given in the present paper, density rho, and sound velocities upsilon(p) and upsilon(s) of MgSiO3 perovskite under lower mantle conditions have been calculated where t he constant-entropy model is assumed with the temperature at the core- mantle boundary being taken to be 3000 K. The results for rho, upsilon (p), upsilon(s) are in agreement with the preliminary reference Earth model (PREM) within -2.4%similar to-3.7%, +3.3%similar to+1.1%, and +0 .8%similar to-6.8%, respectively, over the lower mantle from 670 to 28 91 km in depth. The calculated thermal expansivity under lower mantle conditions is in good agreement with that of the lower mantle estimate d by Anderson [1982]. Using the present model with the parameters dete rmined from experimental data at room temperature by Knittle and Jeanl oz [1987], assuming Theta(0) to be the same as that of MgSiO3 perovski te, thermoelastic properties of (Mg-0.9, Fe-0.1)SiO3 perovskite under lower mantle conditions have been calculated. The density becomes in m uch better agreement (+0.4%similar to-0.8%) with PREM and upsilon(p) a nd upsilon(s) remain almost unchanged from those of MgSiO3 perovskite.