PURE SILICATE PEROVSKITE AND THE PREM LOWER MANTLE MODEL - A THERMODYNAMIC ANALYSIS

A recently published thermodynamic theory enables one to calculate alpha, the volume thermal expansivity; Delta V/V-0, the thermal expansion; and rho, the density in V, T space or P, T space, based on the values of seven thermoelastic parameters evaluated at P = 0. These parameters are themselves based on high-pressure and high-temperature measurements of V. Especially useful are calculated isobars of Delta V/V-0, versus T or isentropes of rho versus P, because with these, seismic models of the earth can be compared with the perovskite compositional model. There is general agreement on the thermoelastic parameters of V-0, K-T0, and K-0' for perovskite, but not on the value of delta(T0), the dimensionless Anderson-Gruneisen parameter, or of gamma(0), the Gruneisen ratio. In comparing the calculated isentrope of rho(P) with the geotherm of rho(P) from the PREM seismic model, we find the most sensitive parameter is gamma(0). We also find a number of reasons to select gamma(0) = 1.5 +/- 0.2 for perovskite. This range of gamma(0) values leads to the conclusion that perovskite satisfies the PREM model of density in the lower mantle without the addition of heavy elements, like iron or silicon. The value range gamma(0) > 1.9 for perovskite would require a significant amount of iron or silicon to satisfy PREM, but we cannot justify a value of gamma(0) that high.