Thermodynamic model for diffusion controlled reaction rim growth in a binary system: Application to the forsterite-enstatite-quartz system

We present a thermodynamic model for diffusion controlled growth of a reaction rim of phase γ between the phases α and β in a two component system. We investigate the case, where the reactant phase α has planar, cylindrical and spherical geometry and is embedded in a matrix of phase β. We find that for non planar geometry and for the general case, where the molar volumes of the reactant phases are different, the rim growth rate depends on the matrix-inclusion arrangement. The model is applied to growth of enstatite reaction rims that form at quartz-forsterite interfaces. Two different geometrical setups are considered, namely a spherical grain of forsterite in a quartz matrix and a spherical quartz grain in a forsterite matrix. The enstatite rims are polycrystalline and transfer of the MgO and SiO₂ components across the growing rim occurs by a combination of volume− and grain boundary diffusion. For enstatite rims that were grown at experimental conditions of 1000°C and 1 GPa (Milke and others, 2008) bulk mass transfer may be described by effective diffusion coefficients in the range of 1.8 · 10⁻¹⁷m²s⁻¹ ≤ DSiO₂ ≤ 1.1 · 10⁻¹⁶m²s⁻¹ and 2.7 · 10⁻¹⁷m²s⁻¹ ≤ DMgO ≤ 1.6 · 10⁻¹⁶m²s⁻¹.