First-principles calculations of equilibrium barium isotope fractionation among silicate minerals

Barium isotopes have been increasingly applied to trace igneous processes, but the applications are hindered by the lack of equilibrium Ba isotope fractionation factors between silicate minerals. In this study, the reduced partition function ratios (RPFRs) of the major Ba-hosting silicate minerals, including muscovite, phlogopite, tremolite, richterite, microcline, albite, and epidote, as well as witherite and barite, are obtained using first-principles calculations. The effect of Ba concentration on the RPFR of those silicate minerals was examined, and no significant effect was observed in the natural range of Ba concentrations. Our results show a heavy Ba isotope enrichment order of tremolite > epidote > albite > witherite similar to richterite similar to microcline similar to barite similar to muscovite similar to phlogopite. The RPFRs are controlled by the force constant of Ba and affected by the BaO bond length. The lattice environment of substituted ions controls the equilibrium Ba isotope fractionation factors of trace elements. For instance, the replacement of Ba2+ with Mg2+ or K+ in phlogopite introduces an approximately 0.16 parts per thousand offset of Ba isotope ratios (Ba-138/Ba-134) at 1000 K. In general, light Ba isotopes are preferentially enriched in crystalline positions with larger ion radii. Equilibrium Ba isotope fractionation among silicate minerals is up to 0.08 parts per thousand at 1000 K, which can be well resolved by the current analytical precision (similar to 0.05 parts per thousand for delta Ba-138/134). This study provides the calculated equilibrium fractionation factors, which are the key to understanding Ba isotope fractionation in natural rocks.