Theoretical calculation of equilibrium Mg isotope fractionation between silicate melt and its vapor

Abstract

Isotope fractionation during the evaporation of silicate melt and condensation of vapor has been widely used to explain various isotope signals observed in lunar soils, cosmic spherules, calcium–aluminum-rich inclusions, and bulk compositions of planetary materials. During evaporation and condensation, the equilibrium isotope fractionation factor (α) between high-temperature silicate melt and vapor is a fundamental parameter that can constrain the melt’s isotopic compositions. However, equilibrium α is difficult to calibrate experimentally. Here we used Mg as an example and calculated equilibrium Mg isotope fractionation in MgSiO3 and Mg2SiO4 melt–vapor systems based on first-principles molecular dynamics and the high-temperature approximation of the Bigeleisen–Mayer equation. We found that, at 2500 K, δ25Mg values in the MgSiO3 and Mg2SiO4 melts were 0.141 ± 0.004 and 0.143 ± 0.003‰ more positive than in their respective vapors. The corresponding δ26Mg values were 0.270 ± 0.008 and 0.274 ± 0.006‰ more positive than in vapors, respectively. The general $$\alpha - T$$ equations describing the equilibrium Mg α in MgSiO3 and Mg2SiO4 melt–vapor systems were: $$\alpha_{{{\text{Mg}}\left( {\text{l}} \right) - {\text{Mg}}\left( {\text{g}} \right)}} = 1 + \frac{{5.264 \times 10^{5} }}{{T^{2} }}\left( {\frac{1}{m} - \frac{1}{{m^{\prime}}}} \right)$$ and $$\alpha_{{{\text{Mg}}\left( {\text{l}} \right) - {\text{Mg}}\left( {\text{g}} \right)}} = 1 + \frac{{5.340 \times 10^{5} }}{{T^{2} }}\left( {\frac{1}{m} - \frac{1}{{m^{\prime}}}} \right)$$ , respectively, where m is the mass of light isotope 24Mg and m′ is the mass of the heavier isotope, 25Mg or 26Mg. These results offer a necessary parameter for mechanistic understanding of Mg isotope fractionation during evaporation and condensation that commonly occurs during the early stages of planetary formation and evolution.