The energetics of polytypic structures: a computer simulation of magnesium silicate spinelloids

Abstract

A computer simulation technique is used to predict the lattice energies, structures and physical properties of magnesium silicate spinelloids from given interatomic potentials. Two types of potential models are considered, a fully ionic model, which includes electrostatic, short-range and dispersive terms, and a partially ionic model, in which fractional charges are allocated to the component ions and a Morse function is included to describe the effect of covalency in the Si-O bond. The calculated energies of the spinelloid polytypes are analysed in terms of the interaction energies between component structural units. The calculated spinelloid energetics are discussed in the light of recently developed models of polytypism. The predicted values of the interaction energy terms are tested by using them to calculate the energy of a 1/21101](010) stacking fault in the naturally occurring magnesium silicate spinelloid wadsleyite. The calculated stacking-fault energies are in excellent agreement with the value inferred from transmission electron microscopy.

Electron microscopy of high-pressure phases synthesized from natural olivine in diamond anvil cell

“…(172). This fault is a low energy one in the spinel structure (Veyssiere et al 1975, Price et al 1985. It has been previously observed in germanate spinel Kohlstedt 1981, Rubie andChampness 1987), in the Fe2SiO4 spinel synthesized in diamond-anvil cell (Lacam et al 1980), and in the (Mgo.v4Feo.26)2SiO, spinel (ringwoodite) of the Tenham meteorite (Putnis and Price 1979, Price et al 1979, 1983.…”

A short-range interaction model for polytypism and planar defect placement in sapphirine

“…Price et al 1985). It therefore seems reasonable to approximate stacking fault energies in terms of the short-range interaction parameters, neglecting phononic effects.…”

“…10 A), and take a typical J2 value for Finero sapphirine of, say, + 1.8kT/C, then using a geologically reasonable temperature T= 1100 K gives us an absolute value for J2 of around 9 • 10 -3 J/m e. This compares very reasonably with interac- Table 2. 1 error boxes are marked tion energies and stacking fault energies calculated for the Mg2SiO~ spinelloids by Price et al (1985), who quote values of the order of a few 10-2 j/m 2. Multiplying by the unit mesh area in the layer plane and by Avogadro's number, such values correspond to ground-state energy differences between principal polytypes of a few kJ/mol.…”

Structures of the nickel gallosilicate spinelloids

“…Overall, the prediction and explanation of the relative stabilities of individual spinelloid phases (see, for example, Price & Yeomans, 1984;Price et al, 1985) in pseudobinary systems, such as NiAI2Oa-Ni2SiO4, NiGa2Oa-Ni2SiO4, MgGa2Oa-Mg2GeO4, MgFe2Oa-Mg2GeO4 or Fe3Oa-Fe2SiO4, must involve a complex combination of compositional, structural and thermodynamic effects. Besides their dependence on the pressure and temperature variables, the spinelloid phase relations in these various systems clearly also depend, in a subtle way, on the nature of the atomic species involved.…”

“…The sustained interest in the spinelloid structural family stems from the facts that its members are closely related to the spinel structure type (see, for example, Ma, 1974;Horiuchi, Horioka & Morimito, 1980), that they possibly play a role as intermediates in the high-pressure olivine ~ spinel transformation (see, for example, Hyde, White, O'Keeffe & Johnson, 1982;Madon& Poirier, 1983;Guyot, Gwanmesia & Liebermann, 1991) and that they belong to the broad class of polytypic compounds (see, for example, Price, 1983;Price, Parker & Yeomans, 1985).…”