Abstract
Several computer models of quartz were developed and tested. A simple model based on a potential energy function, derived in large part from quantum mechanical calculations on the molecule H6Si2O7, was found to reproduce the compressibility curve for quartz up to pressures of 8 GPa. The potential includes quadratic 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 molecule are used as rgressor values. Poisson ratios calculated using the model match those observed. Two configurations for quartz related by the Dauphiné 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, structural parameters and its negative Poisson ratio. When the observed bond lengths and angles are used as regressor values, the model generates the absolute coordinates of the atoms and the cell dimensions for quartz to within 0.005 Å and those of cristobalite to within 0.001 Å, 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 with f s (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 structures 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, cristobalite 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.
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Boisen, M.B., Gibbs, G.V. A modeling of the structure and compressibility of quartz with a molecular potential and its transferability to cristobalite and coesite. Phys Chem Minerals 20, 123–135 (1993). https://doi.org/10.1007/BF00207206
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DOI: https://doi.org/10.1007/BF00207206