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

Abstract

A computational model based on energy minimization has been developed for/3-MgESiO4. The potential energy of the model includes Coulomb and repulsive interactions between non-bonded atoms as well as bond-distance-stretching energy terms for Si-O distances and bond-angle-bending energy terms for O-Si-O angles. Some of the energy parameters are treated as common to a-and /3-Mg2SiO4, and are obtained by varying these parameters until both the calculated atmospheric-pressure structure and the elastic constants of a-Mg2SiO4 agree as closely as possible with the experimental ones. Other necessary energy parameters for the modeling of fl-Mg2SiO4 are derived to reproduce the observed atmosphericpressure structure of fl-Mg2SiO4. The potential model obtained is successfully used for the calculation of the elastic constants of fl-Mg2SiO4. Subsequently, the model is applied to the simulation of crystal structures of fl-MgESiO4 under high pressure. The pressure derivatives of the elastic constants of fl-MgESiO4 are also evaluated using the model. The present model is compared with a recently proposed one for /3-Mg2SiO4.

The lattice dynamics of forsterite

“…ijk where kiSjk is a derivable spring constant, Oqk is the O-Si-O bond angle, and 0 o is the tetrahedral angle. A similar approach to the problem of modelling the Si-O bond has been adopted with some considerable success by Matsui and co-workers (Matsui and Busing, 1984;Matsui and Matsumoto, 1985) in their elegant studies ofbeta-Mg2SiO 4 and diopside.…”

“…Early studies concentrated upon the use of pair-wise additive interatomic potentials, and ignored the role of many-body interactions. Recent successes, however, in modelling more complex silicates by using bond-bending terms to simulate some aspects of three-body interactions (Matsui and Busing, 1984;Sanders et al, 1984;Catlow et al, 1986) have provided the impetus for this study of forsterite, in which we have included O-Si-O bond-bending terms within our potential model to simulate the directional bonding thought to be important in silicate phases. In the following sections we describe in detail the potentials used in this study, and outline how they were used to calculate the Brillouin zone centre vibrational behaviour (infrared and Raman spectra) of forsterite.…”

The ionic model: Extension to spatial charge distributions, derivation of an interaction potential for silica polymorphs

“…Therefore a modified ionic model, hereafter referred to as the spherosymmetrical charge distribution model (SCD), has been developed that takes in account the spatial extent of the ions -rather than representing them by point charges -and variations thereof within the limit of spherical atoms. In this paper i Adams and McDonald (1974), Catlow et al (1977), Sangster and Atwood (1978), Catlow et al (1982), Matsui and Matsumoto (1982), Matsui and Busing (1984a, b), Catlow et al (1984), Matsui and Matsumoto (1985), Parker and Price (1985), Hostetler (1985), Post and Burnham (1986), Matsui et al (1987), Docka et al (1987), Post and Burnham (1987), Jackson and Catlow (1988), Wall and Price (1988), Kubicki and Lasaga (1988), Tsuneyuki et al (1988), Abbott et al (1989), , Aoki and Tsuneyuki (1989), Dove (1989), Tomlinson et al (1989), Yagi (1989, 1990), Purton and Catlow (1990), Dove et al (1992), Collins and Catlow (1992) this modified ionic model is applied to derive an atomic interaction potential for II-IV-coordinatcd silica polymorphs in order to investigate further the descriptive abilities of the "ionic model" for silicates with a high degree of polymerisation.…”

Modelling of structural and elastic changes of forsterite (Mg2SiO4) under stress

“…The computed unit-cell volume shows a small decrease of 0.5%. Atomic charges are fairly similar to those determined by Matsui and Matsumoto (1985) in their potential based on a nonrigid SiO4 group; however, repulsive parameters differ much more, and the overall agreement with the experimental structure seems to be slightly worse in that case (the volume In order to calculate the structural and elastic evolution of forsterite under an applied stress, the first step begins at the equilibrium zero-stress configuration (experimental structure after Hazen 1976). The elastic tensor C and the inner strain tensor T are computed by the method developed (Catti 1989) and using the optimized parameters of the potential.…”