Mixing behavior in quaternary garnet solid solution and an extended Ellis and Green garnet-clinopyroxene geothermometer

Applications of the different formulations of garnet-clinopyroxene geothermometers to crustal granulites and particularly to metamorphosed manganese formations show a wide scatter of estimates. This is primarily related to the uncertainty associated with the formulation of the activity-composition relationship in garnet solid solution besides that in the clinopyroxene solid solution. The largest uncertainty appears to have resulted from the adopted Mg-Mn interaction parameter in garnet which is yet to be experimentally determined. A fresh statistical regression of eleven pairs of garnet and clinopyroxene equilibrated at identical P-T conditions from a manganese formation in India yields W_Mg-Mn^Gt(=W_Mn-Mg) value of 1600±500 cal/mols. An extension of the Ellis and Green (1979) geothermometer, known to work well in normal granulites, incorporating terms associated with the activity coefficients of the exchangeable cations, now yields consistent temperature estimation from normal granulites as well as from metamorphosed manganese formations. The geothermometer, however, will not work well for garnet having X_Fe0.65 and clinopyroxenes containing appreciable Na, Al and/or Fe³⁺.