Divariant and trivariant reaction line slopes in FMAS and CFMAS: Theory and applications

The theory of divariant reactions is investigated in some detail and approaches involving simultaneously operating reactions and X_mg isopleths are combined. Using the Gibbs' method (Spear et al. 1982), a general equation is derived for X_mg isopleth slopes in FMAS and CFMAS, which may be applied to any divariant assemblage in these systems. Isopleth slopes are calculated for a number of divariant FMAS and CFMAS reactions inferred to have operated in Sri Lankan granulites, giving more rigorous constraints on the local P-T path. Isopleth slopes are also calculated for the trivariant CFMAS reaction orthopyroxene + plagioclase = garnet + quartz. The resulting dP/dT range from +8 to +18 bar/K. Application to Sri Lankan granulites confirms an earlier hypothesis (Faulhaber and Raith 1991) that a retrograde path with a dP/dT of ∼10-15 bar/K may cause garnet growth in charnockites and garnet breakdown in metabasites. It is shown here that dP/dT depends primarily on the Ca contents of garnet and plagioclase. Large variations in isopleth and reaction line slopes are possible, due to the thermodynamic effect of additional components in solid solutions, e.g. albite in plagioclase. This has a good potential for the assessment of the exact form of P-T paths. Equations to calculate isopleth slopes could be included in software packages aimed at defining P-T estimates, enabling geologists to derive realistic P-T paths.