Thermodynamic equilibrium at heterogeneous pressure

Recent advances in metamorphic petrology point out the importance of grain-scale pressure variations in high-temperature metamorphic rocks. Pressure derived from chemical zonation using unconventional geobarometry based on equal chemical potentials fits mechanically feasible pressure variations. Here, a thermodynamic equilibrium method is presented that predicts chemical zoning as a result of pressure variations by Gibbs energy minimization. Equilibrium thermodynamic prediction of the chemical zoning in the case of pressure heterogeneity is done by constrained Gibbs minimization using linear programming techniques. In addition to constraining the system composition, a certain proportion of the system is constrained at a specified pressure. Input pressure variations need to be discretized, and each discrete pressure defines an additional constraint for the minimization. The Gibbs minimization method provides identical results to a geobarometry approach based on chemical potentials, thus validating the inferred pressure gradient. The thermodynamic consistency of the calculation is supported by the similar result obtained from two different approaches. In addition, the method can be used for multi-component, multi-phase systems of which several applications are given. A good fit to natural observations in multi-phase, multi-component systems demonstrates the possibility to explain phase assemblages and zoning by spatial pressure variations at equilibrium as an alternative to pressure variation in time due to disequilibrium.