β-Factors of Titanite and Oxygen Isotope Fractionation in the Titanite-Ilmenite-Rutile System

New O-18/O-16 beta-factors have been calibrated against temperature for titanite (considering the principal isomorphic substitutions Al + F double left right arrow Ti + O, Ti + O double left right arrow Al + OH, Ti + O double left right arrow Fe-3(+) + OH) and ilmenite (accounting for Fe double left right arrow Mg substitution) for the first time using the frozen-phonon approach of the density functional theory. The equilibrium oxygen isotope fractionation factors between titanite (CaTiSiO5), ilmenite (FeTiO3), and rutile (TiO2) are expressed as: 1000 ln alpha(ttn-ilm) = 1000 ln beta(ttn) - 1000 ln beta(ilm) = 1.96836x - 0.10514x(2) + 0.00319x(3), 1000 ln alpha(ttn-rt) = 1000 ln beta(ttn) - 1000 ln beta(rt) = 1.80155x - 0.09262x(2) + 0.00288x(3), x = 10(6)/T-2 (K-2). The results can be applied to geothermometry, particularly in calc-silicate and calc-alkaline rocks of magmatic, metamorphic, and metasomatic origins.