Thermoelasticity of silicate perovskites and magnesiowustite and its implications for the Earth's lower mantle

By assuming an ideal two-component mixture of (Mg,Fe)SiO3 perovskite (MgPv) and (Mg,Fe)O magnesiowustite (Mw), and by using a thermoelastic model for mantle minerals developed previously we can reproduce the PREM values of de nsity and velocities nu(P) and nu(S) of compressional and shear waves of th e lower mantle within +/-0.12%, +/-0.28%, and +/-0.56% except for the trans ition layers at the both boundaries. The molar fractions and atomic fractio ns of iron for MgPv and Mw were adjusted to reproduce the PREM values of rh o, nu(P), and nu(S) 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 cal culated by the Hashin-Shtrikman method for MgPv and Mw and then arithmetica lly averaged. The temperature profile was calculated assuming that the lowe r 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 degrees C by Brown and McQueen. The molar ratio s of Fe/(Mg + Fe) and (Mg + Fe)/Si become 0.12 and 2.10. The calculated the rmal expansivity, alpha, of the mixture under lower mantle conditions is in agreement with alpha 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.