AB INITIO THEORETICAL PREDICTIONS OF HIGH-PRESSURE AND HIGH-TEMPERATURE PROPERTIES OF LOWER MANTLE MINERAL PHASES

Constraints on the chemical composition and mineralogy of the earth's lower mantle are obtained using theoretically derived estimates of high-temperature and high-pressure thermodynamic properties of candidate mineral phases. Using first-principles approaches, we have investigated the static and dynamic properties of SiO{dollar}sb{lcub}2{rcub}{dollar} fluorite, a proposed post-rutile phase of silica. The equation of state is computed from the augmented plane-wave method and the phonon spectrum is computed from lattice dynamics employing electron-gas force fields. Our analysis indicates that it is unlikely that the density of the fluorite phase exceeds that of stishovite anywhere in the mantle. The theoretical phonon spectrum of fluorite exhibits a dynamic instability at pressures below 170 GPa, suggesting that even if this phase were produced at high pressure, it would be unquenchable and hence unobservable in unloaded experimental samples. Lattice dynamical studies of MgSiO{dollar}sb3{dollar} and CaSiO{dollar}sb3{dollar} perovskites are also presented. Calculations of the room-temperature equation of state and zero-pressure thermal expansion are in very good agreement with data. The results indicate that the lower mantle perovskite phase exists in an orthorhombic structure and is stable to the core mantle boundary. The degree of distortion in MgSiO{dollar}sb{lcub}3{rcub}{dollar} perovskite from the ideal cubic structure is predicted to increase with pressure. The model further predicts that at high temperatures and low pressures MgSiO{dollar}sb{lcub}3{rcub}{dollar} perovskite will exhibit critical soft-mode behavior undergoing successive second-order phase transitions to higher symmetry polymorphs. We discuss implications of this critical behavior on constraints of lower mantle composition models that are based on extrapolated properties. Finally, we construct compositional models of the lower mantle based on comparisons of seismic properties with those computed for hypothetical mineral assemblages using theoretical estimates for the properties of the component mineral phases. We have also presented a further extension of the electron-gas theory of crystals which includes the effects of many-body forces that arise from both electrostatic and overlap interactions. In this extension, spherical relaxation of the component ion charge densities is incorporated through a minimization of the crystal binding energy. This treatment leads to improvements in calculated equations of state and elastic properties of alkaline earth oxides over prior electron-gas methods.