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The Ti content of biotite can serve as a geothermometer for graphitic, peraluminous metapelites that contain ilmenite or rutile and have equilibrated at roughly 4-6 kbar. The relationship between Ti-content, temperature, and Mg/ (Mg + Fe) value was calibrated empirically using an extensive natural biotite data set (529 samples) from western Maine and south-central Massachusetts in combination with the petrogenetic grid of Spear et al. (1999). The calculated Ti-saturation surface is curved such that for a given Mg/ (Mg + Fe) value, Ti concentration increases as a function of temperature in a nonlinear fashion, and for a given temperature Ti concentrations decrease with an increase in Mg/ (Mg + Fe). The fit to the Ti-saturation surface can be reformulated as the geothermometric expression: T = In (Ti) - a - c (XMg) 3 /b0. 333, in which T is temperature in degrees Celsius, Ti is the number of atoms per formula unit (apfu) normalized on the basis of 22 O atoms, XMg is Mg/ (Mg + Fe), a = -2. 3594, b = 4. 6482 × 10-9 and c = -1. 7283. The calibration range for this expression is XMg = 0. 275-1. 000, Ti = 0. 04-0. 60 apfu, and T = 480-800 °C. Precision of the Ti-in-biotite geothermometer is estimated to be ±24 °C at the lower temperature range and improves to ±12 °C at higher temperatures. Application of the Ti-in-biotite geothermometer to ilmenite- or rutile-bearing, graphitic, peraluminous metapelites equilibrated at 3-6 kbar is generally consistent with independent temperature determinations, but with some deviations that represent local reequilibration. Consequently, the Ti systematics in biotite can also serve as the basis of a very sensitive indicator of chemical equilibrium, or lack thereof. Application of the geothermometer to metapelites not containing the requisite mineral assemblages can lead to minor-to-significant errors in estimated temperatures. Biotite Ti-subst itution mechanisms are controlled by several factors. Based on the biotite calibration data set, magnesian biotites (XMg > 0. 65) incorporate Ti in accordance with the exchange vector TiAl2R-11Si-2, where R is the sum of the divalent cations Mg + Fe + Mn. This substitution mechanism is primarily a response to misfit of the octahedral and tetrahedral layers in magnesian biotites. Intermediate biotites (XMg <0. 65), particularly at higher temperatures, exhibit enhanced Ti concentrations, most consistent with the Ti-deprotonation TiO2R-1 (OH) 2 exchange vector. Dominance of Ti-deprotonation substitution is largely a function of reduction of H2O activity at higher metamorphic grades. Supplementary biotite data from metaluminous amphibolites and mafic granulites, metamorphosed isothermally with variable H2O activities, reveal that low-Al biotite incorporates significantly higher concentrations of Ti relative to peraluminous biotite as a result of a combination of the exchange vectors TiO2R-1 (OH) -2 and RSiAl-2 substituting in roughly an 8: 1 ratio.
Darrell J. Henry (Tue,) studied this question.