Using Stishovite to Constrain Semi-Empirical Density Functional Models of Silicates, Such as Aluminous Perovskites

Recent experiments indicate that aluminum, which is believed to comprise only a few weight percent of the Earth's mantle, may play an important role in the properties of the most abundant mantle mineral, (Mg,Fe)SiO₃ perovskite. In particular, aluminum may aid in the incorporation of ferric iron into perovskite, thus affecting the partitioning of iron among lower mantle phases, and therefore the densities and elastic properties of these phases. The mechanism of Al solubility in perovskite and its pressure dependence are not well understood. Such mechanisms can be explored with realistic simulations based on accurate computations of the free energy as a function of lattice configuration. The density-functional-based VIB model of ionic interactions has been shown to be accurate and efficient enough to allow practical simulations of crystals containing hundreds of atoms and structural degrees of freedom. However, due to the significant covalency of the Si-O bond, the model tends to underestimate the compressibility of some silicates by as much as 20%. To correct for this, we have used recent data on the compressibility of stishovite to constrain a simple covalent correction to VIB. This correction is based on charge transfer between ions, in order to equalize electronegativities. We find that the empirical parameters that bring the calculated properties of stishovite into agreement with experimental data also yield excellent results for mantle silicates, such as forsterite (T = 300K, V_o = 287.8 ų, K_o = 128.0 +/- .7 GPa, K' = 4.13 +/- .05 [Bukowinski and Downs 2000]) as well as MgSiO₃ (T = 300K, V_o = 162.7 +/- .02 ų, K_o = 257.0 +/- 2.0 GPa, K' = 4.2 +/- .01) and CaSiO₃ (T = 300K, V_o = 45.9 +/- .02 ų, K_o = 227.5 +/- 2.0 GPa, K' ≈ 4.3 +/- .01 [Akber, Bukowinski, and Matas 2001]) perovskites. In this study, we report progress on simulations designed to examine the effects of aluminum concentration on the density and compressibility of magnesium perovskite. In addition, we compare the energetics of various substitution mechanisms of aluminum into the Mg and Si sites in the lattice. Preliminary calculations using VIB without a covalent correction (for an Al substitution of both Mg and Si at an Al concentration of 12.5%: Mg₇Al₂Si₇O₂₄) suggest that aluminous perovskites are less dense and more compressible than the pure magnesian end-member.