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Intracrystalline diffusion is an invaluable tool for estimating timescales ofgeological events. Diffusion is typically modeled using gradients in chemicalpotential. However, chemical potential is derived for uniform pressure andtemperature conditions and therefore cannot be used to model diffusion whenthere are gradients in stress. Internal stress variations in minerals creategradients in strain energy which will drive diffusion. Consequently, it isnecessary to have a method that incorporates stress variations into diffusionmodels. We derive a flux expression that allows diffusion to be modeled inionic, crystalline solids under arbitrary stress states. Our derivationutilizes gradients in a thermodynamic potential called relative chemicalpotential which quantifies changes in free energy due to the exchanges ofconstituents on lattice sites under arbitrary stress conditions. We apply ourderivation to the common quaternary garnet solid solutionalmandine-pyrope-grossular-spessartine. The rates and directions of divalentcation diffusion in response to stress are determined by endmember molar volumeor lattice parameters, elastic moduli, and non-ideal activity interactionparameters. Our results predict that internal stress variations of one hundredMPa or more are required to shift garnet compositions by at least a fewhundredths of a mole fraction. Mineral inclusions in garnet present a potentialenvironment to test and apply our stress-driven diffusion approach, as stressvariations ranging from hundreds of MPa to GPa-level are observed or predictedaround such inclusions. The ability to model stress-induced diffusion mayprovide new information about the magnitudes of both intracrystalline stressesand the timescales during which they occurred, imparting a better understandingof large-scale tectono-metamorphic processes.

Modeling diffusion in ionic, crystalline solids with internal stress gradients