Modeling diffusion in ionic, crystalline solids with internal stress gradients

Intracrystalline diffusion is an invaluable tool for estimating timescales of geological events. Diffusion typically modeled using gradients in chemical potential caused by variations composition. However, derived uniform pressure and temperature conditions therefore cannot be used to model when there are stress. Internal stress minerals will create strain energy which, addition composition, drive diffusion. Consequently, it necessary have a method that incorporates into models. To address this issue, we flux expression allows ionic, crystalline solids under arbitrary states. Our approach consistent with standard petrological methods but instead utilizes thermodynamic called “relative potential.” Relative accounts the lattice constraint quantifying changes free due exchanges constituents on sites conditions. relative can not (i.e., non-hydrostatic stress). We apply our derivation common quaternary garnet solid solution almandine–pyrope–grossular–spessartine. The rates directions divalent cation response determined endmember molar volume or parameters, elastic moduli, non-ideal activity interaction parameters. results predict internal one hundred MPa more required shift compositions at least few hundredths mole fraction. Mineral inclusions present environment test stress-driven approach, as ranging from hundreds GPa-level observed predicted around such inclusions. ability stress-induced may provide new information about magnitudes both intracrystalline stresses during which they occurred, imparting better understanding large-scale tectono-metamorphic processes.