Titanium substitution in biotite: an empirical model with applications to thermometry, O 2 and H 2O barometries, and consequences for biotite stability

Abstract

An empirical model for solution of Ti in biotite is developed and calibrated on the basis of various equilibria among biotite and Ti-saturating assemblages. Sources of data used for the calibration include both experimental products and published analyses of natural assemblages. Ti solution in biotite can be satisfactorily modelled by means of the exchange component TiFe −2, whose non-ideal behavior can be approximated empirically by means of a linear function of the relative concentrations of Ti and octahedral Al in biotite. Within assemblages which fix the chemical potential of the exchange component TiFe −2, the concentration of this component in biotite is very sensitive to temperature and oxygen fugacity, making it possible to use biotite+oxide assemblages to obtain reliable T and f(O 2) estimates in igneous and metamorphic rocks. In assemblages which also contain alkali feldspar, it is possible to use breakdown equilibria of Ti additive components in biotite to estimate H 2O fugacity. Such uses are likely to find important applications in rocks in which other assemblages sensitive to temperature, f(O 2) and/or f(H 2O) are absent (in general, rocks containing a single oxide phase plus biotite as the only mafic silicate phase, ±alkali feldspar). The empirical model for solution of Ti in biotite also allows to calculate the loci of various terminal reactions for the assemblage titanian biotite+quartz, which, by comparison with equivalent equilibria in Ti-free systems, provide insight into the effect of Ti on the stability of biotite. Solubility of Ti in biotite increases with temperature in a strongly non-linear fashion. As a consequence, calculations predict that the effect of Ti on the stability of biotite is very small up to conditions typical of the beginning of the granulite facies of metamorphism, but beyond those conditions Ti concentration increases markedly and biotite is rendered very refractory. At mid to deep crustal pressures (≥ 10 kbar), the vapor-absent solidus of biotite+quartz in rocks containing Ti-saturating phases is likely to exceed 900°C, even in bulk compositions with subequal concentrations of Fe and Mg.