Titanium in muscovite, biotite, and hornblende: Modeling, thermometry, and rutile activities of metapelites and amphibolites

Ideal mixing on octahedral or octahedral plus tetrahedral sites and a non-ideal van Laar solution model yield the best regression results for thermodynamic fit parameters, with R-2 values of 0.98-1.00. Isopleths of the equilibrium constant (K-eq) show minimal pressure dependencies of <1 degrees C/kbar, implying that the equilibria are poor barometers. Model reproducibility of the ideal portion of the equilibrium constant (K-id) is excellent (ca. +/- 0.1 to 0.3, 2 sigma), but the absolute value of the combined term Delta S+K-id is quite small (absolute values from 0 to 4), so calibration residuals propagate to temperature errors >+/- 50-100 degrees C, 1 sigma. Whereas the consistency of a mica or hornblende composition with a known T can be evaluated precisely, Ti chemistry in these reactions is sensitive to composition and does not resolve T (or P) well. The activity of TiO2 in rutile [a(rt)] was also evaluated using both the garnet-rutile-ilmenite-plagioclase-quartz (GRIPS) equilibrium and our new calibrations in rutile-absent, ilmenite-bearing rocks whose peak P-T conditions are otherwise known. Metapelites have average a(rt) of 0.9 (GRIPS) and 0.8 (RI), whereas amphibolites have a(rt) of 0.95 (GRIPS and R3). A value for a(rt) of 0.80 +/- 0.20 (metapelites) and 0.95 +0.05/-0.25 (amphibolites) is recommended for trace-element thermomobarometers in ilmenite-bearing, rutile-absent rocks. The dependence of Ti contents of minerals on a(rt) and the reequilibration of Ti during metamorphic reactions both deserve further exploration, and may affect application of trace-element thermobarometers.