Theoretical Calculations Of The Equilibrium Ca Isotope Fractionation Factors

Calcium is a major element of the Earth,the Moon,terrestrial planets,and rocky meteorites in the inner solar system.Here we investigate equilibrium Ca isotope fractionation factors of Ca-bearing minerals using the first-principles calculations based on density functional theory(DFT).The enrichment sequence of heavy Ca isotopes is forsterite>orthopyroxene(opx)>grossular?pigeonite>butschliite>lime?fluorite>tremolite?diopside>dolomite?anhydrite>titanite>anorthite>perovskite?gehlenite?aragonite?richterite>akermanite>oldhamite.Overall,the equilibrium fractionation of Ca isotopes is mainly controlled by the average bond length,whereas other factors,such as the coordination number and polyhedral distortions,also show significant contributions.Although oldhamite should be enriched in light Ca isotopes relative to silicate minerals in equilibrium,oldhamite in enstatite chondrites was reported to have a higher ?44/40 Ca than the coexisting silicate materials.This implies that oldhamite may form during solar nebular gas condensation and the enstatite chondrites may not be significantly modified by igneous processes-Following previous models for cooling and crystallization of the Lunar Magma Ocean(LMO),we simulated Ca isotopic fractionation of the LMO based on our calculated equilibrium Ca isotope fractionation factors.Our results show that the 844/4oCa of the lunar anorthositic crust could 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 cooling of the LMO,we further predict that the lunar mantle could be enriched in heavy Ca isotopes 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 offset of Ca isotopic composition between the anorthositic crust and the lunar mantle can be used to constrain the LMO cooling and evolution processes.