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 mantle minerals as functions of both pressure and temperature through synchotron-based X-ray diffraction has motivated a re-evaluation of the capacity of such data to constrain various higher-order thermoelastic parameters. Alternative parameterisations of the thermal pressure, based upon integration of the thermodynamic identity (partial derivative P/partial derivative T)(V) = alpha K-T and upon the simple Mie-Gruneisen-Debye model for the vibrational energy have been compared through application to recently published P-V-T data for beta-(Mg,Fe)(2)SiO4 and MgSiO3 perovskite. Each of these approaches provides an adequate representation of the available P-V-T data. However, the Mie-Gruneisen-Debye equation-of-state, with its explicit incorporation of an approximate model for the vibrational energy, is preferred because it describes more faithfully the temperature dependence of thermal expansion, and allows internally consistent conversion between isothermal experimental conditions and the adiabatic conditions more relevant to understanding the Earth's deep interior. Evaluation of formal errors in thermoelastic properties obtained from 'thermodynamic' least-squares fits of a synthetic dataset for a phase with the properties of beta-(Mg,Fe)(2)SiO4 indicates that values of (partial derivative K-T/partial derivative T)(p) and partial derivative(2)K(T)/partial derivative P partial derivative 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 partial derivative(2)K(T)/partial derivative P partial derivative T from 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 isochemical 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 values 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 derivative 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 parameter [partial derivative(partial derivative K-S/partial derivative P)(S)/partial derivative T](p) is almost an order of magnitude smaller for both phases.