EQUILIBRIUM PROPERTIES OF SOME SILICATE MATERIALS: A THEORETICAL STUDY (MAGNESIUM OXIDE, ALUMINUM OXIDE, SILICON DIOXIDE)
Equilibrium properties of the MgO-Al(,2)O(,3)-SiO(,2) (MAS) system are modeled using techniques from statistical and quantum mechanics. The fundamental structural units in this model are the closed shell ions: Mg('2+), Al('3+), Si('4+), and O('2-). The equilibrium properties of the MAS system are determined by the interactions among these ions and by the environment (i.e. temperature and pressure). The interactions are modeled using coulombic, dispersion, and repulsive forces. Two parameters appearing in the repulsive terms for each cation-oxygen interaction are fitted from properties of quartz, corundum, and periclase crystals. The effects of the environment on the liquid and solid compositions found in this system are calculated using a Monte Carlo technique involving the generation of a Markov chain of configurations; each configuration being a "snapshot" of the particles in the liquid or solid material being studied. The properties of the material are derived from averaging appropriate quantities over all the configurations. Enthalpies of formation, heat capacities, and volumes of seven compositions in the MAS system have been calculated using this method. All are within three percent of the corresponding experimental values. Radial distribution functions for these runs show the competition among the cations for the common anion, oxygen, under charge and mass balance constraints.
The electronic structure of several molecular clusters in the MAS system are examined using ab initio linear combinations of atomic orbitals (LCAO) techniques. The assumptions used in LCAO calculations are examined and a small, balanced basis set for the MAS system is presented. The Mg-, Al-, and Si-O interactions are all found to be highly ionic using this basic set. Using a first principles technique, the two body effective pair potentials assumed for the Monte Carlo calculations were shown to be physically reasonable.