ANALYSIS OF P-V-T DATA - CONSTRAINTS ON THE THERMOELASTIC PROPERTIES OF HIGH-PRESSURE MINERALS

The availability of precise determinations of unit cell volumes of man tle minerals as functions of both pressure and temperature through syn chotron-based X-ray diffraction has motivated a re-evaluation of the c apacity of such data to constrain various higher-order thermoelastic p arameters. Alternative parameterisations of the thermal pressure, base d upon integration of the thermodynamic identity (partial derivative P /partial derivative T)(V) = alpha K-T and upon the simple Mie-Gruneise n-Debye model for the vibrational energy have been compared through ap plication to recently published P-V-T data for beta-(Mg,Fe)(2)SiO4 and MgSiO3 perovskite. Each of these approaches provides an adequate repr esentation of the available P-V-T data. However, the Mie-Gruneisen-Deb ye equation-of-state, with its explicit incorporation of an approximat e model for the vibrational energy, is preferred because it describes more faithfully the temperature dependence of thermal expansion, and a llows internally consistent conversion between isothermal experimental conditions and the adiabatic conditions more relevant to understandin g the Earth's deep interior. Evaluation of formal errors in thermoelas tic properties obtained from 'thermodynamic' least-squares fits of a s ynthetic dataset for a phase with the properties of beta-(Mg,Fe)(2)SiO 4 indicates that values of (partial derivative K-T/partial derivative T)(p) and partial derivative(2)K(T)/partial derivative P partial deriv ative T should be resolvable within 10% and 50% respectively for state -of-the-art P-V-T data. Excellent agreement is obtained between values determined for (partial derivative K-T/partial derivative T)(p) and p artial derivative(2)K(T)/partial derivative P partial derivative T fro m the two thermodynamic and Mie-Gruneisen-Debye methods, particularly when average values over an appropriate temperature range are compared . For the temperature interval between 300 K and 1600 K (the potential temperature appropriate for the lower-mantle adiabat in an isochemica l model mantle), preferred average values of alpha are 3.6 x 10(-5) K- 1 and 2.6 x 10(-5) K-1 for beta-(Mg,Fe)(2)SiO4 and MgSiO3 perovskite, respectively. For (K-T/T)(p) and (K-S/T)(p) the preferred average valu es are -0.028 GPaK(-1) and -0.019GPaK(-1) for beta-(Mg,Fe)(2)SiO4 and -0.027GPaK(-1) and -0.017GPaK(-1) for MgSiO3 perovskite, In agreement with independent estimates of partial derivative(2)K(T)/partial deriva tive P partial derivative T of (1-3) x 10(-4) K-1 for a range of oxide and silicate minerals, this analysis yields values near 2 x 10(-4) K- 1 and 1 x 10(-4) K-1 for the beta-phase and perovskite, respectively. It appears likely, however, that the more seismologically relevant par ameter [partial derivative(partial derivative K-S/partial derivative P )(S)/partial derivative T](p) is almost an order of magnitude smaller for both phases.