First-principles Investigation Of The Concentration Effect On Equilibrium Fractionation Of Ca Isotopes Between Forsterite And Upper Mantle Minerals

Previous theoretical studies have found that the concentration variations within a certain range shows a significant effect on inter-mineral equilibrium isotope fractionation(103 lna).Based on the density function theory(DFT)method,we investigated the effect of Ca content in forsterite(Fo)on its average Ca-0 bond length and the reduced partition function ratios(103 ln?)of 44Ca/40Ca.Our results show that the average Ca-0 bond length in forsterite decreases from 2.327 A to 2.267 A when the Ca/(Ca+Mg)decreases from 2/16 to 1/64.However,when Ca/(Ca+Mg)is lower than 1/64,the average Ca-0 bond length is insensitive to Ca content and maintains a constant.Because the 103 ln? is negatively correlated to the average Ca-0 bond length,the 103 ln? significantly increases with decreasing Ca/(Ca+Mg)when 1/64<Ca/(Ca+Mg)<2/16.As a consequence,the 103 lna of 44Ca/40Ca between forsterite and other minerals also strongly depends on Ca content in forsterite.Combining previous studies with our results,we find the enrichment sequence of heavy Ca isotopes in minerals is:forsterite>orthopyroxene>clinopyroxene>calcite?diopside>dolomite>aragonite.Olivine and pyroxenes are enriched in heavy Ca isotope relative to carbonates.Although the 103 lna between forsterite with a Ca/(Ca+Mg)of 1/64 and clinopyroxene(Ca/Mg=1/1,i.e.diopside)is up to?0.64‰ at 1200 K,forsterite plays a less prominent role in the Ca isotope variations during the magmatic processes,because forsterite has a much lower Ca content than pyroxenes in igneous rocks.However,the large 103 ln?Fo-diopside relative to the current analytical precision for Ca isotope measurements suggests that the dependence of 103 ln?Fo-diopside on temperature can be used as a thermometer,similar to the one based on the 103 lna of 44Ca/40Ca between orthopyroxene and diopside.These two Ca isotope thermometers both have a precision comparable to elemental thermometers and provide independent constraints on temperature.