First-principles computation of diffusional Mg isotope fractionation in silicate melts

© 2020 Elsevier Ltd Diffusional isotope fractionation occurs in geochemical processes (such as magma mixing, bubble growth, and crystal growth), even at magmatic temperatures. Isotopic mass dependence of diffusion is commonly expressed as [Formula presented], where Di and Dj are diffusion coefficients of two isotopes whose masses are mi and mj. How the dimensionless empirical parameter β depends on temperature, pressure, and composition remains poorly constrained. Here, we conducted a series of first-principles molecular dynamics simulations to evaluate the β factor of Mg isotopes in MgSiO3 and Mg2SiO4 melts using pseudo-isotope method. In particular, we considered interactions between Mg isotopes by simultaneously putting pseudo-mass and normal-mass Mg atoms in a simulation supercell. The calculated β for Mg isotopes decreases linearly with decreasing temperature at zero pressure, from 0.158±0.004 at 4000 K to 0.121±0.017 at 2200 K for MgSiO3 melt and from 0.150±0.004 at 4000 K to 0.101±0.012 at 2200 K for Mg2SiO4 melt. Moreover, our simulations of compressed Mg2SiO4 melt along the 3000 K isotherm show that the β value decreases linearly from 0.130±0.006 at 0 GPa to 0.060±0.011 at 17 GPa. Based on our diffusivity results, the empirically established positive correlation between β and solvent-normalized diffusivity (Di/DSi) seems to be applicable only at constant temperatures or in narrow temperature ranges. Analysis of atomistic mechanisms suggests that the calculated β values are inversely correlated with force constants of Mg at a given temperature or pressure. Good agreement between our first principles results with available experimental data suggests that interactions between isotopes of major elements must be considered in calculating β for major elements in silicate melts. Also, we discuss diffusion-controlled crystal growth by considering our calculated β values