Equilibria within the mineral assemblage quartz + muscovite + biotite + garnet + plagioclase, and implications for the mixing properties of octahedrally-coordinated cations in muscovite and biotite

Abstract

Interaction parameters derived using empirical calibration methods indicate strong non-ideality in the mixing of octahedrally-coordinated cations in muscovite and biotite. The data set used for calibration comprises mineral compositions from 49 samples containing quartz, muscovite, biotite, garnet, plagioclase and Al₂SiO₅ (kyanite or sillimanite). Pressures and temperatures in the data set were determined through the simultaneous application of geothermometry based on the garnet-biotite FeMg₁ exchange equilibrium and geobarometry based on the anorthite-breakdown equilibrium. Two equilibria yielded simple expressions from which binary interaction parameters for octahedrally-coordinated cations in biotite could be directly determined. A four-component (Fe²⁺, Mg, Al, Ti) regular symmetric mixing model was assumed for biotite. One equilibrium yielded a simple expression from which an interaction parameter for the mixing of the MgAl-celadonite component in muscovite could be directly determined. Two sets of calculations were performed utilizing different calibrations of the garnet-biotite geothermometer and the anothite-breakdown geobarometer and different garnet activity models. Both placed samples within or near the stability field of the Al₂SiO₅ phase present in each sample and both yielded similar values for the interaction parameters within narrow uncertainties, indicating that the values are insensitive to differences in the underlying methods. Using the derived interaction parameters, activity models were formulated for the annite, phlogopite, eastonite, and siderophyllite components of biotite, and for the MgAl-celadonite component of muscovite. These were utilized for the empirical calibration of 45 fluid-independent equilibria involving unique combinations of phase components from the mineral assemblage garnet + plagioclase±biotite±muscovite±quartz. Forty-three of the equilibria may be applied as geobarometers to equilibrium assemblages of quartz + muscovite + biotite + garnet + plagioclase when care is taken to insure that applications are restricted to valid compositional ranges. For these, the calibrations yielded multiple correlation coefficients ranging from 0.953 to 0.998 and standard deviations of the residuals ranging from 597 to 118 bars.