Pure silicate perovskite and the PREM lower mantle model: a thermodynamic analysis

Abstract

A recently published thermodynamic theory enables one to calculate α, the volume thermal expansivity; , the thermal expansion; and ϱ, 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 versus T or isentropes of ϱ 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 V₀, K_{T0 and K′0 for perovskite, but not on the value of δT0, the dimensionless Anderson-Grüneisen parameter, or of γ0, the Grüneisen ratio. In comparing the calculated isentrope of ϱ(P) with the geotherm of ϱ(P) from the PREM seismic model, we find the most sensitive parameter is γ0. We also find a number of reasons to select γ0 = 1.5 ± 0.2 for perovskite. This range of γ0 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 γ0 > 1.9 for perovskite would require a significant amount of iron or silicon to satisfy PREM, but we cannot justify a value of γ0 that high.}