Controls on Mg isotopic fractionation between deep mantle phases and relict signatures of a terrestrial magma ocean

We use density functional theory to investigate the fractionation of Mg isotopes between phases in the lower mantle. Our results support previous work and show that coordination number plays an important role in controlling isotopic fractionation, with bridgmanite (perovskite-structured MgSiO3) preferentially incorporating lighter Mg isotopes into its highly coordinated site compared to periclase (MgO). A trade-off between pressure (which enhances fractionation) and temperature (which reduces it) allows this preference to be evident across all lower mantle conditions explored, even to the high temperatures of the chondritic liquidus (e.g. Δ26/24MgPer-Bdm is 0.04‰ at 4200 K and 87 GPa). In additional numerical experiments we separate the effect of coordination number from differences in bond length between different phases and these allow us to build an ionic model which parameterises magnesium isotope fractionation as a function of bond length, coordination number, and temperature. This model provides us with a preliminary means to describe isotope partitioning between solid and liquid phases when making predictions of Mg isotopic differences generated during terrestrial magma ocean crystallisation. We find that Mg isotopic fractionation between bridgmanite and melt, at lower mantle conditions, is sufficient to generate detectable differences in the Mg isotopic compositions of a residual melt or solid cumulate phase, relative to bulk Earth. More specifically, we show that isolation of a reservoir of cumulate bridgmanite that is some 3-15 percent by mass of the mantle could account for the super-chondritic 26Mg/24Mg of accessible terrestrial peridotite samples. Long-standing problems remain in physically retaining such a reservoir at the core mantle boundary over Earth history, but our results help quantify possible tests of such a scenario.