Site-specific isotope effect: Insights from equilibrium magnesium isotope fractionation in mantle minerals

Abstract

The equilibrium Mg isotope fractionation factors (lnα) derived from both theoretical calculation and experimental studies are not consistent with the values from natural sample observation. Different cation sites, which have identical coordinate numbers but different bond strengths, contribute equally to lnα in theoretical calculations. These non-equivalent sites might complicate the inter-mineral equilibrium isotope fractionations. Here, we investigate reduced partition function ratios (103lnβ) of non-equivalent Mg cation sites (e.g., M1, M2, and M3) in forsterite, orthoenstatite, clinoenstatite, tremolite, omphacite, pyrope and spinel to explore the site-specific effect on the intra- and inter-mineral equilibrium isotope fractionation. Based on all-electron first-principles calculations, 103lnβ in different cation sites decreases in the following sequence of spinelM1 > tremoliteM3 > orthoenstatiteM1 > forsteriteM1 > omphaciteM1 > tremoliteM1 > tremoliteM2 > clinoenstatiteM1 > forsteriteM2 > orthoenstatiteM2 > clinoenstatiteM2 > pyropeM1. These findings suggest that cation sites with larger polyhedron volumes prefer light Mg isotopes to those with smaller polyhedron volumes inside minerals, and the different contribution of intra-mineral cation sites could result in significant variations of equilibrium Mg isotope fractionation between minerals. The range of lnα between minerals induced by specific sites is defined as the equilibrium isotope fractionation domain. The site-corrected lnα can provide better evaluation of equilibrium fractionation factor of Mg isotopes between spinel and olivine and clarify the equilibrium state between mantle minerals. In addition, we establish spinel-olivine and omphacite-pyrope Mg isotope geothermometers based on the site-specific effect. This study suggests that the site-specific effect could be prevalent in solid materials and thus important for other isotope systems.