Explaining the dependence of M-site diffusion in forsterite on silica activity: a density functional theory approach

Experimentally, silica activity (aSiO₂) has been shown to have an effect on Mg diffusion in forsterite, but no fully satisfactory mechanism has yet been proposed. We calculated the effects of aSiO₂ and aluminium content (the main contaminant in some recent experimental studies), and their co-effect, on Mg diffusion in forsterite, using thermodynamic minimisations of defect formation energies [calculated using density functional theory (DFT)] and a Monte-Carlo diffusion model. These two variables, in isolation, do not appreciably change the defect concentrations of forsterite and thus do not affect the diffusivity of Mg. However, when elevated together, they cause large increases in the Mg vacancy content and thus can increase the Mg diffusivity by one to six orders of magnitude depending on temperature, with little pressure dependence. This effect is largely independent of Al₂O₃ concentration above ~ 1 wt. ppm, and thus, for all practical purposes, should occur wherever forsterite is in the presence of enstatite. It is also largely dependent upon configurational entropy and is thus highly sensitive to the chemistry of the crystal. A low concentration of structurally bound hydroxyl groups at low temperatures (1000 K) suppresses this effect in pure forsterite, but it is likely robust in the presence of water either when alternative water sinks (such as Ti or Fe) are present, or at high temperatures (> 1500 K). This effect is also robust in the presence of ferrous iron (or other substitutional Mg defects) at all temperatures. Fe₂O₃ can operate like Al₂O₃ in this reaction and should enhance its effect. These findings explain the experimentally observed dependency of Mg diffusion of aSiO₂, and elucidate how chemical activity variations in both experiments and natural settings could affect not only the diffusivity of Mg in forsterite, but of olivine-hosted cations in general.