First-principles calculations of equilibrium fractionation of O and Si isotopes in quartz,albite, anorthite,and zircon

In this study, we used first-principles calculations based on density functional theory to investigate silicon and oxygen isotope fractionation factors among the most abundant major silicate minerals in granites, i.e., quartz and plagioclase (including albite and anorthite), and an important accessory mineral zircon. Combined with previous results of minerals commonly occurring in the crust and upper mantle (orthoenstatite, clinoenstatite, garnet, and olivine), our study reveals that the Si isotope fractionations in minerals are strongly correlated with SiO₄ tetrahedron volume (or average Si–O bond length). The ³⁰Si enrichment order follows the sequence of quartz > albite > anorthite > olivine ≈ zircon > enstatite > diopside, and the ¹⁸O enrichment follows the order of quartz > albite > anorthite > enstatite > zircon > olivine. Our calculation predicts that measurable fractionation of Si isotopes can occur among crustal silicate minerals during high-temperature geochemical processes. This work also allows us to evaluate Si isotope fractionation between minerals and silicate melts with variable compositions. Trajectory for δ³⁰Si variation during fractional crystallization of silicate minerals was simulated with our calculated Si isotope fractionation factors between minerals and melts, suggesting the important roles of fractional crystallization to cause Si isotopic variations during magmatic differentiation. Our study also predicts that δ³⁰Si data of ferroan anorthosites of the Moon can be explained by crystallization and aggregation of anorthite during lunar magma ocean processes. Finally, O and Si isotope fractionation factors between zircon and melts were estimated based on our calculation, which can be used to quantitatively account for O and Si isotope composition of zircons crystallized during magma differentiation.