The Gibbs method and Duhem's theorem: The quantitative relationships among P, T, chemical potential, phase composition and reaction progress in igneous and metamorphic systems

Abstract

The Gibbs method permits simultaneous evaluation of the relationships among all intensive thermodynamic variables of a heterogeneous system in equilibrium. Addition of mass balance constraints permits simultaneous evaluation of both intensive and extensive variables so that changes in phase chemistry and modes may be monitored. Assumption of closed system behavior results in a system of equations with two degrees of freedom, regardless of the thermodynamic variance, as specified by Duhem's theorem. Open system behavior increases the number of degrees of freedom by the number of components to which the system is open. The methodology presented is therefore a formal statement of the constraints among the differential of all of the intensive and extensive variables of a heterogeneous system.

Examples of the application of this formalism include contouring pressure-temperature space for mineral composition, modal changes and reaction progress; contouring reaction space with pressure, temperature and mineral composition; and calculation of compositional and modal changes of phases for prescribed changes in pressure and temperature, as, for example, in the calculation of synthetic garnet zoning profiles or liquid lines of descent in crystallizing magmas.