The magnitude of equilibrium isotope fractionation of Mg between forsterite, diopside and melt at liquidus temperatures

Bram de Winter, Andrew Walker , Elena Melekhova, Xiao-Ning Liu, Tim Elliott

We examine the equilibrium fractionation of Mg isotopes between forsterite, diopside, and a coexisting melt at liquidus temperatures using a combination of analyses of petrological-experiment products and atomic-scale simulations. Our experiment yields ∆²⁶Mgol/melt = -0.058 ± 0.032 ‰ (2s.e.) and ∆²⁶Mgcpx/melt = 0.060 ± 0.034 ‰ (2s.e.) for crystals grown from a near-cotectic basaltic melt in the CMAS system, which combine to give ∆26Mgcpx/ol = 0.131 ± 0.045 ‰ at 1300 °C. The value of ∆²⁶Mgol/melt is within the uncertainty of the mean olivine-melt fractionation determined for unzoned phenocrysts and naturally quenched glass from ocean island and mid-ocean ridge basalts. We compare the experimentally determined Mg isotope fractionation between olivine and clinopyroxene with ab initio calculations using different DFT functionals. We demonstrate that when using the revised Perdew–Burke–Ernzerhof (PBESOL) exchange-correlation functional, accounting for thermal expansion, and site-averaging for forsterite, our ab initio results are in good agreement with our experiments, yielding ∆26Mgcpx/ol = 0.134‰ at 1300°C. Using the Local Density Approximation (LDA) or other Generalised Gradient Approximation (GGA) functionals, or neglecting thermal expansion, lowers ∆26Mgcpx/ol values to approximately 0.03–0.06 ‰ below the experimentally measured values. Neglecting site-averaging in forsterite results in positive (using only M1) or negative (using only M2) deviations in fractionation of 0.08‰ from averaged isotope ratios. Comparison of our experimentally and theoretically derived ∆26Mgcpx/ol values with empirical estimates from natural samples reveals a systematic offset, underscoring the need to distinguish equilibrium mineral–mineral fractionation from empirically derived relationships that may incorporate kinetic or compositional effects.