A modeling of the structure and compressibility of quartz with a molecular potential and its transferability to cristobalite and coesite

Abstract

Several computer models of quartz were devel- oped and tested. A simple model based on a potential energy function, derived in large part from quantum me- chanical calculations on the molecule H6Si2Ov, was found to reproduce the compressibility curve for quartz up to pressures of 8 GPa. The potential includes quadra- tic expressions for the SiO bond lengths, the OSiO angles and a parameter spanning the SiOSi angle together with an exponential OO repulsion term for non co-dimer O atoms. The variations in the cell edges and in the SiOSi angle, as a function of pressure, parallel observed trends when the bond lengths and angles calculated for the mol- ecule are used as regressor values. Poisson ratios calcu- lated using the model match those observed. Two config- urations for quartz related by the Dauphin6 twin law are generated as minimum energy structures of the model with about equal frequencies as observed in nature. It is shown that the model, devised for quartz, can also be applied to the silica polymorph cristobalite, giving reasonable estimates of its compressibility curve, struc- tural parameters and its negative Poisson ratio. When the observed bond lengths and angles are used as regres- sor values, the model generates the absolute coordinates of the atoms and the cell dimensions for quartz to within 0.005 It and those of cristobalite to within 0.001 ~, on average, both at zero pressure. When applied to coesite, the model yields a zero pressure structure that is close to that observed but which is significantly softer than observed. The resulting SiO bond lengths are linearly correlated withfs(O), as observed for coesite, despite the use of a single bond length and a single SiOSi angle as regressor values in the calculation. When the struc- tures are optimized assuming P1 space group symmetry and triclinic cell dimensions, the resulting frameworks of silicate tetrahedra exhibit the translational, rotational and reflection symmetries observed for quartz, cristoba- lite and coesite. The fact that the resulting frameworks exhibit observed space group symmetries is evidence that the symmetry adopted by the silica polymorphs can be explained by short ranged forces.