Charge distribution from least-energy structure in Ca - Mg orthosilicates

Calcium-olivine, γ-Ca₂SiO₄, larnite, β-Ca₂SiO₄, merwinite, Ca₃Mg(SiO₄)₂, and monticellite, CaMgSiO₄, are considered. According to a rigid oxyanion scheme, eulerian orientation angles of the SiO₄ tetrahedra and translation coordinates of Ca and Si atoms are specified as structural variables τk. All derivatives of the static energy (Born model) contain atomic charges and repulsive parameters as unknowns; the minimum energy conditions ?E _L/?τ_k=0 yield 34 equations which are solved by a least-squares method. The set of energy parameters fitting structural properties of all four phases together is: z _Ca=1.50, z _o=?1.10 e, r _Ca=1.05, ρ=0.25 Å; the Mg charge was fixed at 1.38 e, from a previous study on forsterite. An average shift of 0.04 Å is observed between experimental and least-energy calculated atomic positions. Results are compared with those of Mg₂SiO₄, where the fit was based both on thermoelastic and on structural properties. If no charge values were fixed “a priori”, just ratios between charges could be determined by fitting them to structural data only.