Empirical calibration of six geobarometers for the mineral assemblage quartz+muscovite+biotite+plagioclase+garnet

Six equilibria among quartz, plagioclase, biotite, muscovite, and garnet were empirically calibrated using mineral composition data from 43 samples having the assemblage quartz+muscovite+biotite+garnet+plagioclase+Al₂SiO₅ (sillimanite or kyanite). Pressures and temperatures in the data set used for calibration were determined through the simultaneous application of garnet-biotite geothermometry and garnet-quartz-plagioclase-Al₂SiO₅ geobarometry. Thermodynamic expressions for four of the six equilibria incorporate interaction parameters that model non-ideality in the mixing of cations in the octahedral sites of both muscovite and biotite. With pressure chosen as the dependent variable, multiple regression was used to solve for unknowns in the equilibrium thermodynamic expressions. The regressions yielded multiple correlation coefficients ranging from 0.983 to 0.999, with corresponding standard deviations of 338 and 92 bars in the residuals. The standard deviations in the residuals may be explained largely or entirely by the propagation of errors associated with electron microprobe analysis. These equilibria enable the determination of pressures from equilibrium assemblages of quartz+garnet+plagioclase+muscovite+biotite, and give results closely comparable to the experimentally calibrated garnet-quartz-plagioclase-Al₂SiO₅ geobarometer. Geobarometric applications should be restricted to rocks in which equilibrium constants and compositional variables fall within the same ranges as those used for calibration.