Thermoelasticity of (Mg, Fe)SiO 3 perovskite and a comparison with the lower mantle

Abstract

A re-examination of the classical theory of the thermal Grüneisen parameter, γ, for the case of a polyatomic anisotropic crystal yields a zero pressure value for silicate perovskite at high temperature, γ 0 = 1.30 ± 0.09. Corresponding values of volume expansion coefficient are α(290K) = 14.0 × 10 −6 K −1, α(1000 K) = 23.8 × 10 −6 K −1, α(2000 K) = 26.8 × 10 −6 K −1. These are used to calculate densities at high temperatures for comparison with the lower mantle. For this purpose lower mantle properties are extrapolated to the foot of the adiabat (temperature T 0) using the dK dP vs P K equation-of-stater, with the following results: K 0 = 204.5 ± 1.3 GPa, μ 0 = 129.0 ± 1.0 GPa, ϱ 0 = 3973 ± 6 kg m −3. Matching both density and incompressibility for a perovskite-magnesiowustite mixture to these values, it is shown that both minerals must have appreciable iron contents and that a substantial magnesiowustite fraction is required. The favoured solution requires about 6% Fe in the perovskite, 15% Fe in the magnesiowustite and a mineral mix with 28% magnesiowustite by volume (26.7% by mass), giving a mean atomic weight for the mixture of 20.97. Although the analysis is simplistic in the sense that additional minor elements and minerals must be present in the lower mantle, it gives no encouragement to the supposition that the lower mantle is enriched in either iron or silicon.