First-principles calculations of equilibrium Ca isotope fractionation: Implications for oldhamite formation and evolution of lunar magma ocean

Abstract

Calcium is a major element of the Earth, the Moon, terrestrial planets, and rocky meteorites. Here we present equilibrium Ca isotope fractionation factors of Ca-bearing minerals using the first-principles calculations based on density functional theory (DFT). The sequence of minerals from the isotopically heaviest to the lightest in Ca is forsterite > orthopyroxene (opx) > grossular ∼ pigeonite > diopside > anorthite > oldhamite. Overall, the equilibrium fractionation of Ca isotopes is mainly controlled by the average bond lengths. Although oldhamite is enriched in light Ca isotopes relative to silicate minerals in equilibrium, natural oldhamite of enstatite chondrites are isotopically heavier than coexisting silicate materials. This implies that enstatite chondrites oldhamites should have been formed during solar nebular gas condensation instead than during parent body processing.Following previous models for crystallization of the Lunar Magma Ocean (LMO), we simulated Ca isotopic fractionation of the LMO based on our calculated equilibrium Ca isotope fractionation factors. It shows that the δ44/40Ca of the lunar anorthositic crust should be lower than the average of the bulk Moon by 0.09–0.11‰. Considering that the lunar mantle might have overturned and mixed after solidification of the LMO, we further predict that the lunar mantle should be isotopically heavier than the bulk Moon by 0.17–0.26‰ if the mantle was fully overturned, or only by 0.06–0.08‰ for the case of fully mixing. Therefore, we predict that the potential offset of Ca isotopic composition between the anorthositic crust and the lunar mantle can be used to test LMO evolution models.