THEORETICAL INVESTIGATIONS OF CHEMICAL BONDING IN MINERALS (ELECTRON GAS, POLARIZATION, QUARTZ, SILICA, MAGNESIUM OXIDE)

In this thesis we present theoretical models of oxide minerals. The short range interactions are calculated using the modified electron gas model. In chapters 1 and 2 we consider only ionic bonding. In chapters 3-5 we also allow for polarization. We study the role of anion energy and electron density in determining lattice structure and stability.; In chapter 1 we investigate crystal structures for MgO. The B1 phase is favored at zero pressure. The lattice constant is about 2% too large. The bulk modulus is slightly smaller than experiment. The lattice energy agrees with experimental measurement. Above about 650 GPa the CsCl phase is most stable. The ZnS structure is only favored for negative pressure. Finally, the hexagonal NiAs phase is never stable relative to B1.; In chapter 2 we investigate high pressure silica structures. The stishovite structure agrees reasonably well with experiment. CaCl(,2) and (alpha)-PbO(,2) are comparable in energy to stishovite at high pressure. The defect NiAs structure is slightly less stable than stishovite, but our model neglects entropy which would favor the defect structure at high temperature. The CaF(,2) and ZrO(,2) structures are less stable than stishovite for all pressures considered. Anatase and brookite are only stable at low pressures, where four-coordinated silica is stable.; In chapter 3 we present a two-shell polarization model for the (alpha)-quartz and (alpha)-cristobalite structures. Polarization corrects the problems of an ionic treatment of tetrahedrally coordinated silica. The shell model zero pressure structures agree with experiment. The compressional properties of the shell model (alpha)-quartz lattice dramatically improve over the distorted ionic lattice.; In chapter 4 we investigate cubic and orthorhombic MgSiO(,3)-perovskite. High pressure favors the orthorhombic lattice. The ionic structure agrees fairly well with experiment, but is not compressible enough. By allowing for polarization, we determine that covalent corrections are important for both the cubic and distorted lattices.; Finally, in chapter 5 we investigate the olivine and spinel phases of Mg(,2)SiO(,4). The ionic model gives adequate structures of the two phases. However, in order to understand the stability of these lattices polarization must be considered. The ionic model predicts an olivine to spinel phase transition of 5 GPa, below the thermally assisted experimental value of 20 GPa. The polarization model predicts a transition at 80-100 GPa.