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

New 18O/16O β-factors have been calibrated against temperature for titanite (considering the principal isomorphic substitutions Al + F ⇔ Ti + O, Ti + O ⇔ Al + OH, Ti + O ⇔ Fe3+ + OH) and ilmenite (accounting for Fe ⇔ 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 αttn–ilm = 1000 ln βttn – 1000 ln βilm = 1.96836x – 0.10514x2 + 0.00319x3, 1000 ln αttn–rt = 1000 ln βttn – 1000 ln βrt = 1.80155x – 0.09262x2 + 0.00288x3, x = 106/T2 (K–2). The results can be applied to geothermometry, particularly in calc–silicate and calc–alkaline rocks of magmatic, metamorphic, and metasomatic origins.