First-principles investigation of equilibrium magnesium isotope fractionation among mantle minerals: Review and new data

Abstract

Equilibrium inter-mineral Mg isotope fractionation factors (103lnα) are key to using Mg isotopes to investigate high-temperature geochemical processes. First-principles calculations based on density functional theory (DFT) have been proven to be a reliable approach to predict the reduced partition function ratio (103lnβ) and the inter-mineral 103lnα values, and there are large amounts of data calculated based on different methods in the literature. We here review previous DFT calculations on inter-mineral 103lnα of Mg isotopes, complement new calculations for some minerals, and thoroughly discuss and compare results from different methods. Two types of approximations, the local density approximation (LDA) and the generalized gradient approximation (GGA), are adopted to model the exchange-correlation potential in DFT calculations. Static calculations and quasi-harmonic approximation (QHA) are both used to calculate the 103lnα. In theory, the QHA method is more reliable but more computationally expensive than the static method, because the former derives the pressure- and temperature-dependent 103lnβ from its volume- and temperature-dependent form via the equation of states.The structural and vibrational properties of mantle minerals predicted by the LDA calculations agree well with experimental results, while the GGA calculations overestimate the volumes and MgO bond lengths. There are systematic differences between the calculated 103lnβ values using static LDA and GGA calculations; however, both approaches predict similar inter-mineral 103lnα values at high temperatures because the systematic difference between two 103lnβ values cancels out. Furthermore, the inter-mineral 103lnα values predicted by the static LDA method generally agree with those from the LDA + QHA method, which is used to calculate the pressure effect on 103lnα. Two sets of inter-mineral 103lnα values of 26Mg/24Mg calculated by static LDA and LDA + QHA methods are present as a function of temperature and/or pressure in this review. Large Mg isotope fractionation exists between some minerals, and inter-mineral 103lnα values could be significantly affected by pressure due to the difference in the pressure slopes of their 103lnβ. The measured forsterite-magnesite and spinel-magnesite Mg isotope fractionation factors in previous experiments are consistent with the calculated results within uncertainties. Using the calculated data, we examine the degree to which the observed inter-mineral Mg isotope fractionation in natural rocks represents equilibrium and model the Mg isotope fractionation during late-stage basalt differentiation.