Gibbs free energy, the fundamental thermodynamic potential used to calculate equilibrium mineral assemblages in geological systems, does not apply to non-hydrostatically stressed solids. Consequently, there is debate over the significance of non-hydrostatic stress in petrological and geophysical processes. To help resolve this debate, we consider the effects of non-hydrostatic stress on the polymorph pairs kyanite/sillimanite, graphite/diamond, calcite/aragonite, and quartz/coesite. While these polymorphs are most relevant to metamorphic processes, the concepts developed are applicable to any single-component solid reaction. We quantitatively show how stress variations normal to an interface alter equilibrium temperatures of polymorph pairs by approximately two orders of magnitude more than stress variations parallel to an interface. Thus, normal stress controls polymorph stability to first order. High-pressure polymorphs are expected to preferentially nucleate normal to and grow parallel to the maximum stress and low-pressure polymorphs, the minimum stress. Nonetheless, stress variations parallel to an interface allow for the surprising possibility that a high-pressure polymorph can become more stable relative to a low-pressure polymorph as stress decreases. The effects of non-hydrostatic stress on mineral equilibrium are unlikely to be observed in systems with interconnected, fluid-filled porosity, as fluid-mediated reactions yield mineral assemblages at approximately constant pressures. In dry systems, however, reactions can occur directly between elastic solids, facilitating the direct application of non-hydrostatic thermodynamics. Non-hydrostatic stress is likely to be important to the evolution of metamorphic systems, as preferential orientations of polymorphic reactions can generate seismicity and may influence fundamental rock properties such as porosity and seismic anisotropy.

Mineral compositions are used to infer pressures, temperatures, and timescales of geological processes. The thermodynamic techniques underlying these inferences assume a uniform, constant pressure. Nonetheless, convergent margins generate significant non-hydrostatic (unequal) stresses, violating the uniform pressure assumption and creating uncertainty. Materials scientists F. Larché and J. Cahn derived an equation suitable for non-hydrostatically stressed geologic environments that links stress and equilibrium composition in elastic, multi-component crystals. However, previous works have shown that for binary solid solutions with ideal mixing behavior, hundreds of MPa to GPa-level stresses are required to shift mineral compositions by a few hundredths of a mole fraction, limiting the equation’s applicability. Here, we apply Larché and Cahn’s equation to garnet, clinopyroxene, and plagioclase solid solutions, incorporating for the first time non-ideal mixing behavior and more than two endmembers. We show that non-ideal mixing increases predicted stress-induced composition changes by up to an order of magnitude. Further, incorporating additional solid solution endmembers changes the predicted stress-induced composition shifts of the other endmembers being considered. Finally, we demonstrate that Larché and Cahn’s approach yields positive entropy production, a requirement for any real process to occur. Our findings reveal that stresses between tens and a few hundred MPa can shift mineral compositions by several hundredths of a mole fraction. Consequently, mineral compositions could plausibly be used to infer stress states. We suggest that stress-composition effects could develop via intracrystalline diffusion in any high-grade metamorphic setting, but are most likely in hot, dry, and strong rocks such as lower crustal granulites.