Alfred Wilson , Monica Pozzo, Chris Davies , Andrew Walker , Dario Alfè 

We examine magnesium and potassium solubility in liquid Fe mixtures, representative of Earth’s core composition, in equilibrium with liquid silicate mixtures representative of an early magma ocean. Our study is based on the calculation of the chemical potentials of MgO and K2O in both phases, using density functional theory. For MgO, we also study stability against precipitation of the solid phase. We use thermal evolution models of the core and mantle to assess whether either radiogenic heating from 40K decay or Mg precipitation from the liquid core can resolve the new core paradox by powering the geodynamo prior to inner core formation. Our results on K show that concentrations in the core are likely to be small and the effect of 40K decay on the thermal evolution of the core is minimal, making it incapable of sustaining the early geodynamo alone. Our results also predict small concentrations of Mg in the core although these might be sufficient to power the geodynamo prior to inner core formation, depending on the process by which it is transported across the core mantle boundary.