Quantifying the Effects of Non-Hydrostatic Stress on Multi-Component Minerals

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. Larche 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 Larche 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 Larche 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. Plain Language Summary The chemical compositions of many minerals found in rocks are sensitive to the pressure and temperature conditions at which the minerals form. Thus, we can use mineral compositions to deduce the formation conditions of rocks, giving us insights into important geological processes such as the global carbon cycle and continent formation. The techniques we use to determine these conditions assume that pressure is equal in all directions. However, minerals sometimes form in settings where there is significantly more pressure, or stress, in one direction than another due to, for example, colliding tectonic plates. As a result, there is uncertainty as to how to interpret the compositions of such minerals. In this work, we apply a theory developed by materials scientists that provides a way to quantify the expected compositions of different types of minerals based on the directions and magnitudes of stresses. This approach will enable us to use mineral compositions to learn more about the pressure and stress conditions in important geological settings such as within subduction zones and mountain belts.

Automated summary

Mineral compositions can be used to infer the pressure states in geological processes. However, previous research has limited understanding of non-ideal mixing behavior and multi-endmember cases. In this study, a new theory is applied to examine the stress-induced composition changes in minerals, considering non-ideal mixing and multiple endmembers. The results indicate that non-ideal mixing amplifies the predicted composition changes, and the presence of additional solid solution endmembers affects the stress-induced composition shifts of other endmembers. The findings suggest that mineral compositions can be used to infer stress states under certain conditions.