Quantifying the Effects of Non-Hydrostatic Stress on Single-Component Polymorphs

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. Plain Language Summary Geoscientists are interested in determining at what temperatures and pressures different minerals are stable in the Earth. This is because the breakdown and formation of minerals are important for processes such as the generation of earthquakes and the geochemical cycling of elements such as hydrogen and carbon. However, a key problem is that the calculations we use to determine if minerals are stable assume that pressure is equal in all directions. But if this were true, there would be no mountains or earthquakes which are caused by unequal pressures deep within our planet. This leaves the question of how do we determine mineral stability when pressure is not equal in all directions? In our work, we show that the pressure on each side of a mineral determines whether each side is stable. This means, for example, if one squeezes graphite hard enough in one direction, the squeezed sides will start to form diamond while the other sides remain graphite. Consequently, when pressure is not equal in all directions, minerals will break down or form in certain directions. This could create cracks for earthquakes, or allow water to enter rocks more easily, influencing subsurface fluid flow and element cycling.