Thermoelastic properties of MgSiO3 perovskite using the Debye approach

MgSiO3 perovskite is shown to be a Debye-like mineral by the determination of specific heat, C-V, entropy, S, and thermal pressure, Delta P-Th, using the Debye theory up to 1800 K. Sound velocities and bulk moduli at ambient conditions published by Yeganeh-Haeri were used to find the ambient acoustic Debye temperature, Theta(D)(ac). The variation of Theta(D)(ac) with T was assumed to be a curve parallel to the Theta(D)(ac) vs. T curves previously found for Al2O3, MgO, and MgSiO3, enabling Theta(D)(ac)(T) to be given up to 1800 K. To determine C-P, the thermal expansivity, alpha, and the isothermal bulk modulus, K-T, are needed. After considering several sets of alpha(T), the alpha(T) data of Funamori and his colleagues were chosen. Using the ambient K-T and the values of (partial derivative K-T/partial derivative T)(P) vs. T reported by Jackson and Rigden, K-T(T) up to 1800 K was found. Then C-P(T) up to 1800 K was found assuming quasiharmonicity in C-V. The data behind the C-P(T) calculation are also sufficient to find the Gruneisen parameter, gamma(T), and the Anderson-Gruneisen parameters, delta(T) and delta(S), up to 1800 K. The value of q = (partial derivative ln gamma/partial derivative ln V)(T) was found, and with gamma and rho, Delta P-Th vs. V and T was determined. The three sound velocities, nu(s), nu(p), and nu(b) = root K-s/rho, were then determined to 1800 K. From nu(s) and nu(p), Poisson's ratio and the isotropic shear modulus, G, were found to 1800 K. MgSiO3 perovskite is one of a small, select group of Debye-like minerals for which thermoelastic properties and the equation of state (EOS) are calculable from acoustic data.