Systematic ab initio study of the compressibility of silicate garnets

The structural properties of the silicate garnets andradite, Ca₃Fe₂Si₃O₁₂, uvarovite, Ca₃Cr₂Si₃O₁₂, knorringite, Mg₃Cr₂Si₃O₁₂, goldmanite, Ca₃V₂Si₃O₁₂, blythite, MnMnSi₃O₁₂, skiagite, FeFeSi₃O₁₂, calderite, MnFeSi₃O₁₂, and khoharite, Mg₃FeSi₃O₁₂, have been investigated with a quantum-mechanical model as a function of applied pressure. The study has been performed with the density functional theory code CASTEP, which uses pseudopotentials and a plane-wave basis set. All structural parameters have been optimized. The calculated static geometries (cell parameters, internal coordinates of atoms and bond lengths), bulk moduli and their pressure derivatives are in good agreement with the experimental data available. Predictions are made for those cases where no experimental data have been reported. The data clearly indicate that the elastic properties of all silicate garnets are dominated by the compressibility of the dodecahedral site. The compression mechanism is found to be based on a bending of the angle between the centers of the SiO₄ tetrahedra and the adjacent octahedra, as in the aluminosilicate garnets. An analysis of the relationship between ionic radii of the cations and the compressibility of silicate garnets is presented.