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

Reactions involving the VI Ti IV Al- VI Al IV Si exchange in muscovite, biotite, and hornblende were calibrated thermodynamically using a set of experimental and natural data in rutile- plus quartz/ coesite-bearing assemblages. The specific respective reactions are K(Al 2 )(AlSi 3 )O 10 (OH) 2 + TiO 2 = K(AlTi)(Al 2 Si 2 )O 10 (OH) 2 + SiO 2 (R1) K(□MgAl)Si 4 O 10 (OH) 2 + TiO 2 = K(□MgTi)AlSi 3 O 10 (OH) 2 + SiO 2 (R2) Ca 2 Mg 3 Al 2 Al 2 Si 6 O 22 (OH) 2 + 2TiO 2 = Ca 2 Mg 3 Ti 2 Al 4 Si 4 O 22 (OH) 2 + 2SiO 2 . (R3) 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 R2 values of 0.98-1.00. Isopleths of the equilibrium constant (K eq ) show minimal pressure dependencies of <1 °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, 2σ), but the absolute value of the combined term ΔS+K id is quite small (absolute values from 0 to 4), so calibration residuals propagate to temperature errors >±50-100 °C, 1σ. 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 TiO 2 in rutile [a(rt)] was also evaluated using both the garnetrutile- 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 (R1), 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 traceelement 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.