HIGH-TEMPERATURE ELASTIC-CONSTANT DATA ON MINERALS RELEVANT TO GEOPHYSICS

The high-temperature measurements of elastic constants and related temperature derivatives of nine minerals of interest to geophysical and geochemical theories of the Earth's interior are reviewed and discussed. A number of correlations between these parameters, which have application to geophysical problems, are also presented. Of especial interest is alpha, the volume coefficient of thermal expansion, and a section is devoted to this physical property. Here we show how alpha can be estimated at very high temperatures and how it varies with density. An estimate of alpha for Mg-perovskite at deep-mantle conditions is made. The formula for the Gruneisen ratio-gamma as a function of V and T is presented, including plots of the numerical values of gamma over a wide T and V range. An example calculation of gamma for MgO is made. The high-T-high-P values of gamma calculated here agree well with results from the ab initio method of calculation for MgO. The use of the thermoelastic parameters is reviewed, showing application to the understanding of thermal pressure, thermal expansivity, enthalpy, and entropy. We review an extrapolation formula to determine K(S), the adiabatic bulk modulus, at very high T. We show that the thermal pressure is quite linear with T up to high temperatures (approximately 1800 K), and, as a consequence, the anharmonic contribution to the Helmholtz free energy is sufficiently small, so that it can and should be ignored in thermodynamic calculations for mantle conditions.