Compositional constraints on the equation of state and thermal properties of the lower mantle

By extrapolating the lower mantle equation of state (EoS) to P = 0, T = 290 K, we determine the EoS parameters that are compatible with a mixture of (Mg, Fe)SiO3 perovskite (with a small admixture of Al2O3), (Mg, Fe)O magnesiowustite and CaSiO3 perovskite in arbitrary proportions and with arbitrary Fe/(Fe + Mg) ratio. The parameters fitted are density, rho, adiabatic incompressibility, K-S, and its pressure derivative, K'(S) =(partial derivativeK(S)/partial derivativeP)(S). The first stage is adiabatic extrapolation to P = 0, T = T-0, that is, to the foot of the lower mantle adiabat, at which k'(0)(T-0) is allowed to have any value between 3.8 and 4.6, and 1500 K less than or equal to T-0 less than or equal to 2000 K. It is important to use an equation for which the lower mantle fitting does not prescribe K'(0)(T-0) and this rules out the third-order Birch theory, which gives a seriously wrong value. The further extrapolation to 290 K at P = 0 uses thermodynamic relationships with maximum generality, allowing all of the following thermoelastic parameters to be arbitrary functions of temperature: K; rho; Gruneisen parameter, gamma; q = (partial derivative 1n gamma/partial derivative 1n V)(T), where V is volume; volume coefficient of thermal expansion, alpha; adiabatic Anderson-Gruneisen parameter, delta (S) = (1/alpha) (partial derivative 1n K-S/partial derivativeT)(P); and the mixed P, T derivative (partial derivativeK'(S)/partial derivativeT)(P). The heat capacity at constant volume, C-V, is assumed to follow the Debye function, so alpha is controlled by that. The temperature dependences of the dimensionless parameters gamma, q and delta (S) at P = 0 are slight. We find gamma to be precisely independent of T at constant V. The parameter dK'(0)/dT increases strongly with T, as well as with the assumed value of K'(0)(T-0), where K'(0) is K'(S) at P = 0. The fitting disallows significant parameter ranges. In particular, we find solutions only if K'(0)(T0)greater than or equal to4.2 and the 290 K value of K'(0) for Mg perovskite is less than 3.8. Conclusions about composition are less secure, partly because of doubt about individual mineral properties. The volume of magnesiowustite is found to be between 10 and 25 per cent for respective T-0 values of 2000 and 1500 K, but the Ca-perovskite volume is no more than 6 per cent and has little influence on the other conclusions. The resulting overall Fe/(Fe + Mg) ratio is 0.12 to 0.15. Although this ratio is higher than expected for a pyrolite composition, the ratio depends critically on the assumed mineral densities; some adjustment of the mineral mix may need to be considered.