Electron-gas theory of some phases of magnesium oxide

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Abstract
In this paper we investigate the relative stability of the B1 (NaCl), B2 (CsCl), B3 (ZnS), B4 (BeO), and B8 (NiAs) structures for MgO using an ionic bonding model with the short-range repulsions calculated using the modified electron-gas (MEG) model. The short-range pair potentials are generated from anion wave functions which are consistent with the electrostatics of the crystal lattice. We include corrections for the van der Waals energy. Our predictions for the zero-pressure B1 lattice constant and bulk modulus agree with experiment. The MEG ionic model, with van der Waals energy terms included, accounts for all of the experimental lattice energy. The B2 phase becomes stable relative to B1 at pressures above about 600 GPa. The B3 structure is less stable than B4 by about 8 kJ/mole for all calculated volumes. Finally, the hexagonal B8 packing arrangement is never stable relative to B1. In order to understand more fully the high-pressure behavior of oxides, we propose an additional self-consistency criterion for the calculation of the oxide electron density in future theoretical investigations of bonding in minerals. The charge on the Watson sphere used to stabilize the anion wave function should be consistent with the total charge inside the sphere, i.e., the size of the oxide ion. A charge of 1.7 a.u. on a Watson sphere, instead of 2.0, gives denser and more stable zero-pressure B1 and B2 structures. This may have ramifications for the modeling of oxide structures and phase stability at extreme pressures.