Mathematical Modeling of the Structures and Bulk Moduli of TX2 Quartz and Cristobalite Structure-Types, T = C,Si,Ge and X = O,S

Models of the oxide and sulfide structure-types of quartz and cristobalite have been made using potential energy surfaces derived from MO calculations on small molecules. The bond length and angle and the volume compressibility data calculated for quartz match those observed for pressures up to 40 kbars. An analysis of the force constants that define the potential energy surface indicates that the bulk modulus of the mineral is governed primarily by the bending force constant of the bridging angle. Similar calculations were completed for the GeO2 form of quartz, but the agreement with the observed data is somewhat poorer. A modeling of the CO2 form of quartz predicts that it would be significantly harder, more incompressible and show less expansibility than the SiO2 form.