Truth and beauty in metamorphic phase equilibria: Conjugate variables and phase diagrams

In using calculated equilibria among minerals to understand metamorphic processes, there are usually natural choices of axes to use on phase diagrams, depending on the geological supposition of the processes operating in rocks. Thermodynamic variables come in conjugate pairs, intensive and extensive, and the natural choice of which to use as an axis of a phase diagram depends on which of the pair leads to paths for metamorphic processes that are easiest to visualize. An unnatural choice leads to diagrams on which paths are not intuitively obvious, and these diagrams usually have to be calculated. Ideas relating to conjugate pairs are illustrated using mineral equilibria for the upper amphibolite to granulite facies, calculated for an aluminous pelite composition in the system Na2O-CaO-K2O-FeO-MgO-Al2O3-SiO2-H2O (NCKFMASH). We look specifically at the pressure volume conjugate pair and the H2O content-aH(2)O pair (i.e., the H2O-mu(H20) pair). P-T versus V-T and T-M-H2O versus T-a(H2O) diagrams are used to consider metamorphic processes. We show that the less obvious variable, for example V rather than P, may be more useful in considering certain situations, usually transient.