First-principles investigation of the concentration effect on equilibrium fractionation of Ca isotopes in forsterite

Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation (10(3)ln alpha). Based on the density functional theory, we investigated how the average Ca-O bond length and the reduced partition function ratios (10(3)ln beta) and 10(3)ln alpha of Ca-44/Ca-40 in forsterite (Fo) are affected by its Ca concentration. Our results show that Ca-O bond length in forsterite ranges from 2.327 to 2.267 angstrom with the Ca/(Ca + Mg) varying between a narrow range limited by an upper limit of 1/8 and a lower limit of 1/64. However, outside this narrow range, i.e., Ca/(Ca + Mg) is lower than 1/64 or higher than 1/8, Ca-O bond length becomes insensitive to Ca concentration and maintains to be a constant. Because the 10(3)ln beta is negatively correlated with Ca-O bond length, the 10(3)ln beta significantly increases with decreasing Ca/(Ca + Mg) when 1/64 < Ca/(Ca + Mg) < 2/16. As a consequence, the 10(3)ln alpha between forsterite and other minerals also strongly depend on the Ca content in forsterite. Combining previous studies with our results, the heavier Ca isotopes enrichment sequence in minerals is: forsterite > orthopyroxene > clinopyroxene > calcite approximate to diopside > dolomite > aragonite. Olivine and pyroxenes are enriched in heavier Ca isotope compared to carbonates. The 10(3)ln alpha between forsterite with a Ca/(Ca + Mg) of 1/64 and clinopyroxene (Ca/Mg = 1/1, i.e., diopside) is up to similar to 0.64 parts per thousand at 1200 K. The large 10(3)ln alpha(Fo-diopside) relative to the current analytical precision for Ca isotope measurements suggests that the dependence of 10(3)ln alpha(Fo-diopside) on temperature can be used as a thermometer, similar to the one based on the 10(3)ln alpha of Ca-44/Ca-40 between orthopyroxene and diopside. These two Ca isotope thermometers both have a precision approximate to that of elemental thermometers and provide independent constraints on temperature.