Thermoelastic properties of MgSiO ₃ perovskite using the Debye approach

University of California at Los Angeles, Department of Earth and Space Sciences, Los Angeles, CA, United States

MgSiO ₃ 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 ^ac _D . The variation of Theta ^ac _D with T was assumed to be a curve parallel to the Theta ^ac _D vs. T curves previously found for Al ₂ O ₃ , MgO, and MgSiO ₃ , enabling Theta ^ac _D (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 (theta K _T /theta 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 = (theta ln gamma /theta ln V) _T was found, and with gamma and rho , Delta P _Th vs. V and T was determined. The three sound velocities, v _s , v _p , and v _b = K (sub s/rho ) , were then determined to 1800 K. From v _s and v _p , Poisson's ratio and the isotropic shear modulus, G, were found to 1800 K. MgSiO ₃ 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.

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