Does non-hydrostatic stress influence the equilibrium of metamorphic reactions?

Abstract

We address the questions: are the temperature and thermodynamic pressure significantly different for thermodynamic equilibrium under hydrostatic versus non-hydrostatic stresses? Moreover, is the nature of the equilibrium state comprising the number of phases and their microstructure different? Only closed thermodynamic systems are considered involving both fluid present and fluid absent mineral reactions. Distinctions are drawn between hydrostatic, fluid, mechanical and thermodynamic pressures. The thermodynamic pressure is always equal to the mechanical pressure (the mean stress) for a linear elastic material but differs from the mechanical pressure if processes involving dissipative volume changes operate. The fundamental principle governing equilibrium in a crystalline aggregate under a non-hydrostatic stress at a given temperature and mean stress is that the elastic energy be minimised. This can be attained in a vast number of ways that involve changes in chemical composition and crystalline structure, as in the growth of garnet on biotite, subtle changes in chemical composition, as in a solid solution series or an order–disorder transition, microstructural rearrangements, as in subgrain formation, and combinations of all of these as in myrmekite formation. All involve changes in the elastic energy of the system and force a new conceptual approach to the definition of a phase and a phase diagram. A microstructural phase rule needs to be considered in conjunction with a mineral phase diagram. For practical purposes the thermodynamic pressure generally is close to the mean stress. A chemical potential for a stressed solid can always be defined if diffusive processes operate. For solid/fluid systems the difference in conditions defining equilibrium for hydrostatic and non-hydrostatic conditions is a second order effect; multiple equilibrium states can exist. Departures from hydrostatic conditions are marked by the form of the phase rule (that is, the topology of the phase diagram) and hence there must be either changes in the Clapeyron slope or the position of the equilibrium phase boundary unless all the modifications to the phase rule are achieved by microstructural rearrangements and subtle changes in chemical composition. For solid/solid systems the shift in equilibrium conditions for non-hydrostatic stresses can, in principle, be very large but such effects can be mitigated by softening of the elastic moduli at phase transitions and are also limited by the difference between the mean stress and the equilibrium hydrostatic pressure. For natural situations the difference between the non-hydrostatic and hydrostatic equilibrium temperature is not likely to exceed 20K. For non-hydrostatic conditions if soft mode nucleation and growth processes dominate, departures from hydrostatic conditions are again marked by changes in the form of the phase rule. Departures in the phase rule from hydrostatic conditions in both fluid present and fluid absent reactions are expressed as variations in chemical composition and differences in the number of phases and their microstructural arrangements at equilibrium under non-hydrostatic as opposed to hydrostatic conditions. The types of microstructures expected at equilibrium under non-hydrostatic conditions include those well documented as arising from internal “spontaneous” stresses in crystals as well as distinct new mineral phases. If the couplings between elastic lattice distortions and diffusive processes, or plastic deformation, are strong then softening modes are suppressed or enhanced and large departures from the hydrostatic Clapeyron slope are possible.