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

Abstract

Reactions involving the ^VITi^IVAl-^VIAl^IVSi 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(Al₂)(AlSi₃)O₁₀(OH)₂ + TiO₂ = K(AlTi)(Al₂Si₂)O₁₀(OH)₂ + SiO₂ (R1)

K(□MgAl)Si₄O₁₀(OH)₂ + TiO₂ = K(□MgTi)AlSi₃O₁₀(OH)₂ + SiO₂ (R2)

Ca₂Mg₃Al₂Al₂Si₆O₂₂(OH)₂ + 2TiO₂ = Ca₂Mg₃Ti₂Al₄Si₄O₂₂(OH)₂ + 2SiO₂. (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 TiO₂ 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.