Towards reconciling experimental and computational determinations of Earth's core thermal conductivity

Abstract

The thermal conductivity (κ) of Earth's core is a critical parameter that controls predictions of core cooling rate, inner core age and the power available to the geodynamo. However, the values of core thermal conductivity inferred from recent studies span a wide range due to the challenges of extrapolating to the pressure-temperature-composition (P-T-C) conditions of the core liquid. In particular, extrapolations of κ from direct experimental determinations are lower than ab initio calculations conducted at core conditions. We have performed density functional theory (DFT) calculations to determine the thermal conductivity and resistivity (ρ) of solid FeSi alloys with two compositions, 4 mol % and 15 mol % Si, at a range of temperatures (850-4350 K) and pressures (60-144 GPa) for ease of comparison with recent directly measured κ values. In agreement with recent experiments, our calculations show that for the larger Si composition the resistivity of the mixture increases substantially, compared to pure Fe, reaching its saturated value already at the lowest temperature investigated. As a result, the thermal conductivity of the mixture is also correspondingly reduced. We also analysed the effect of possible errors in the DFT calculations due to the neglect of electron-electron scattering (EES) processes. Our results show that experimental and EES-corrected DFT calculations of κ are actually consistent within uncertainties when compared directly at overlapping P-T-C conditions. We present new core thermal history models using our EES-corrected estimates of κ=75−81 Wm−1K−1 at core-mantle boundary (CMB) conditions, which support previous determinations of late inner core formation around 400-700 Myrs ago and an early molten lower mantle.