Equilibrium Inter-Mineral Titanium Isotope Fractionation: Implication for High-Temperature Titanium Isotope Geochemistry
Equilibrium Ti isotope fractionation factors among major Ti-bearing minerals are critical for understanding Ti isotope fractionation during magmatic processes. We use the first-principles calculations based on the density functional theory (DFT) to obtain Ti isotope reduced partition function ratios (103lnβ of 49Ti/47Ti) in a series of important Ti-bearing minerals, including Ti-doped clinopyroxene, orthopyroxene, olivine, and pyrope, geikielite-ilmenite solid solutions, and rutile. There is a large variation in our calculated 103lnβ, which are linearly correlated to their Ti force constants, a parameter related to the average TiO bond length and the Ti valence state. Among all studied minerals, silicates with Ti4+ occupying the tetrahedral Si site have the highest 103lnβ, and rutile has the lowest 103lnβ. The valence state also significantly controls the 103lnβ. Typically, Ti3+-doped silicates have lower 103lnβ than those of Ti4+-doped silicates. At the natural abundance levels, the 103lnβ of Ti4+Si-doped and Ti3+Mg-doped (Ti3+ occupying the Mg site) silicate minerals show no concentration effect. That is, their 103lnβ do not vary with their Ti4+ and Ti3+ contents, respectively. In contrast, the 103lnβ of geikielite-ilmenite solutions significantly decrease with increasing Fe/(Fe + Mg) ratio. Our calculations predict no significant Ti isotope fractionation among Ti4+Si-doped clinopyroxene, orthopyroxene, olivine, and pyrope (<0.08 % at 1200 K), whereas the 103lnα between geikielite-ilmenite solutions and Ti4+Si-doped clinopyroxene ranges from ∼−0.67‰ to −0.49‰ at 1200 K, supporting the hypothesis that FeTi oxides are important fractionating Ti isotopes during magma differentiation. Finally, the large equilibrium Ti isotope fractionation between geikielite-ilmenite solutions and clinopyroxene suggests that Ti isotopes can be used as a thermometer with precision comparable to that of elemental geothermometer.