Reactions involving the VITiIVAl-VIAlIVSi 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

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 (Keq) 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 (Kid) is excellent (ca. ±0.1 to 0.3, 2σ), but the absolute value of the combined term ΔS+Kid 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 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 (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 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.

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