Reduced partition function ratios of iron, magnesium, oxygen, and silicon isotopes in olivine: A GGA and GGA + U study

Olivine, typically occurring as a forsterite-fayalite solid solution, is a major rock-forming mineral in mafic and ultramafic igneous rocks, and it is important for understanding the genesis, evolution, and alteration of its host rocks. In this study, both GGA and GGA + U methods were employed to calculate the reduced partition function ratios of Fe, Mg, O, and Si isotopes for the forsterite-fayalite solid solution, aiming to elucidate the impacts of Fe content and Hubbard U correction on the isotope fractionation signatures of Fe, Mg, O, and Si in olivine. On the whole, the β_Fe-factor, β_Mg-factor, β_O-factor, and β_Si-factor decrease with increasing Fe content. The linear correlations between β-factors and bond lengths obtained from GGA + U are better compared to those from GGA. The Hubbard U correction can increase the β_Fe-factor. When Fe/(Fe + Mg) ≤ 1/8, ≤ 1/2, and ≤ 1/2, the effect of Hubbard U correction on β_Mg-factor, β_O-factor, and β_Si-factor can be considered negligible, respectively, suggesting that the β_Mg-factor, β_O-factor, and β_Si-factor of Fe-bearing olivine calculated using GGA + U and those of Fe-free minerals calculated using GGA can be combined to derive 10³lnα and trace geological processes. Furthermore, equilibrium fractionation of Fe, Mg, O, and Si isotopes between olivine and other minerals, including troilite, clinopyroxene, and garnet, were also calculated. Our results are helpful in interpreting the observed data regarding Fe, Mg, O, and Si isotopic compositions of olivine, leading to a comprehensive understanding of relevant geological processes.