An interatomic potential-function model for Mg, Ca and CaMg olivines

Abstract

The structures of Mg(forsterite), Ca and CaMg(monticellite) olivines have been investigated by lattice energy calculations, where the silicate ions are treated as rigid bodies. The lattice energy was approximated to be the sum of electrostatic and repulsive terms. The net charges on the Si and O atoms in the silicate ion and the repulsive radii of the atoms concerned were derived using the two known crystal structures, Mg and Ca olvines, by a least-squares fit. The results are as follows: qo(lel) = -1.569, qsi = +2.276, R o (A) = 1.998, Rug = 1.164, and Rca = 1.581. The repulsive interactions of the Si atoms were neglected, since the Si atom would be screened by the outermost four O atoms of the silicate ion. The reliability and the transferability of the potential model presented were tested by the calculation of the energy-minimized structure for CaMg olivine, with the result that the observed structure was very well reproduced.

Crystal elasticity and inner strain: a computational model

“…In the first paper the elastic properties were computed indirectly by a numerical procedure, and the Zing charge was kept fixed at the ideal value ÷2 without optimization. A subsequent refinement (Matsui & Matsumoto, 1985), where the ZMg charge was relaxed and bond-distance-stretching (Si-O) and bond-angle-bending (O-Si-O) energy terms were introduced, gave an average relative deviation of 11.9%. In the second paper, the computation followed the method of Catlow & Mackrodt (1982), using a Morse potential to account for Si-O interactions instead of the rigid-body model.…”

Crystal structure and elastic constants of β-Mg2SiO4 under high pressure simulated from a potential model

“…Modeling of these polymorphs in terms of potential-energy calculations has been performed by Miyamoto & Takeda (1980, Catti (1981Catti ( , 1982, Matsui & Matsumoto (1982), Catlow & Parker (1982), Price & Parker (1984), and Matsui & Busing (1984a). Matsui & Busing (1984a, b) emphasized that a realistic model of the mineral should be obtained so as to reproduce not only the observed crystal structure but also the experimental elastic properties; they showed that two early models for a-MgESiO4 (Miyamoto & Takeda, 1980;Matsui & Matsumoto, 1982) succeeded in reproducing the observed atmospheric-pressure 0108-7681 / 85/060377-06501.50 structure fairly well; however, they failed to reproduce the experimental elastic constants.…”

“…Matsui & Busing (1984a, b) emphasized that a realistic model of the mineral should be obtained so as to reproduce not only the observed crystal structure but also the experimental elastic properties; they showed that two early models for a-MgESiO4 (Miyamoto & Takeda, 1980;Matsui & Matsumoto, 1982) succeeded in reproducing the observed atmospheric-pressure 0108-7681 / 85/060377-06501.50 structure fairly well; however, they failed to reproduce the experimental elastic constants. Horiuchi & Sawamoto (1981) have determined the crystal structure of/3-Mg2SiO4 by single-crystal X-ray analysis.…”

Lattice-Energy Conformational Analysis of Orthosilicate Ca3OSiO4(C3S): Regularizing Ca-Sublattice versus Deforming SiO4−4Anions

“…However, we were not interested in the Si charge, as we did not consider any Si-OC or Si-Ca atomic interactions, first because we assumed rigid SiO 4 , so its internal contribution to U(VDW) becomes constant, and second, to avoid the reported screening effect of the four oxygens between Si and Ca (7). We had to evaluate, however, the charge of the four oxygens of SiO 4 , which we four electrons of the anion are on the short Si-OC bonds (see Fig.…”