Abstract

By assuming an ideal two-component mixture of (Mg,Fe)SiO3 perovskite (MgPv) and (Mg,Fe)O magnesiowüstite (Mw), and by using a thermoelastic model for mantle minerals developed previously, we can reproduce the PREM values of density and velocities vP and vS of compressional and shear waves of the lower mantle within ±0.12%, ±0.28%, and ±0.56% except for the transition layers at the both boundaries. The molar fractions and atomic fractions of iron for MgPv and Mw were adjusted to reproduce the PREM values of ρ, vP, and vS above the point of z = 871 km (which is slightly inside the lower mantle) under constant-entropy condition. This depth avoids the boundary effect. The adiabatic bulk and shear moduli of the mixture are calculated by the Hashin-Shtrikman method for MgPv and Mw and then arithmetically averaged. The temperature profile was calculated assuming that the lower mantle is adiabatic and T(670 km) = 1873 K. The temperature at the top of D″ becomes 2444 K. Being added the temperature increment of 840 K over D’’ (z = 2741–2891 km) estimated by Stacey and Loper (1983) to our value, the temperature at the core-mantle boundary (CMB) becomes 3284 K in agreement with T(CMB) of 3300 ± 500 °C by Brown and McQueen. The molar ratios of Fe/(Mg + Fe) and (Mg + Fe)/Si become 0.12 and 2.10. The calculated thermal expansivity, α, of the mixture under lower mantle conditions is in agreement with α of the lower mantle calculated directly from PEM data by Brown and Shankland, and Anderson. For the addition of 5 mol% of CaSiO3 perovskite to our model, the essential feature of the result is unchanged and the wt% of SiO2, MgO, FeO, and CaO become 40.7, 44.6, 11.0, and 3.7.

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