First-principles calculations of equilibrium Mg isotope fractionations between garnet, clinopyroxene, orthopyroxene, and olivine: Implications for Mg isotope thermometry

Equilibrium fractionation factors of Mg isotopes at high temperature and pressure are investigated for pyrope, majorite, clinopyroxene, orthopyroxene, and olivine using density functional theory. The calculated equilibrium fractionation factors are in good agreement with previous study (Schauble, 2011), suggesting that our calculations are reliable and accurate. The results reveal significant inter-mineral Mg isotope fractionations due to different coordination environment of Mg in minerals. Specifically, pyrope, where Mg is in eight-fold coordination, is more enriched in light Mg isotopes than olivine and pyroxene where Mg is in six-fold coordination. The calculated isotope fractionation for Mg isotopes between clinopyroxene and pyrope is consistent with observations from natural eclogites (Li et al., 2011; Wang et al., 2012). Our calculation also reveals substantial pressure effect on Mg isotope fractionations among garnet, pyroxene, and olivine. brium fractionation of Mg isotopes between pyrope and pyroxene (and olivine) could be used as a novel and independent thermometry with precision much better than the traditional garnet–clinopyroxene Fe–Mg exchange thermometry because such fractionation is significantly greater than the current uncertainties of Mg isotope analyses (∼0.05‰ amu−1). These Mg isotope thermometries could have wide applications in high-temperature mafic igneous and metamorphic rocks where garnet co-exists with pyroxene or olivine. Equations for equilibrium Mg isotope fractionation factors between garnet (pyrope and majorite) and pyroxene and between garnet and olivine as a function of temperature and pressure are also presented in this study.