Electrical resistivity and thermal conductivity of liquid Fe alloys at high P and T, and heat flux in Earth's core

Abstract

Earth's magnetic field is sustained by magnetohydrodynamic convection within the metallic liquid core. In a thermally advecting core, the fraction of heat available to drive the geodynamo is reduced by heat conducted along the core geotherm, which depends sensitively on the thermal conductivity of liquid iron and its alloys with candidate light elements. The thermal conductivity for Earth's core is very poorly constrained, with current estimates based on a set of scaling relations that were not previously tested at high pressures. We perform first-principles electronic structure computations to determine the thermal conductivity and electrical resistivity for Fe, Fe-Si, and Fe-O liquid alloys. Computed resistivity agrees very well with existing shock compression measurements and shows strong dependence on light element concentration and type. Thermal conductivity at pressure and temperature conditions characteristic of Earth's core is higher than previous extrapolations. Conductive heat flux near the core-mantle boundary is comparable to estimates of the total heat flux from the core but decreases with depth, so that thermally driven flow would be constrained to greater depths in the absence of an inner core.

Fig. 1.

Computed electrical resistivity (ρ_el), thermal conductivity (k_el), and corresponding Lorenz numbers (λ). Solid lines (top row) and dashed lines (middle and bottom rows) show the Bloch–Grüneisen models of Fe liquid; the horizontal dotted line indicates the value of the Lorenz number expected via the Wiedemann–Franz relation (W-F). Hugoniot temperatures (25) for selected shock compression datapoints [K71 (10), M77 (12), B02 (11)] are shown to guide comparisons. Other experimental data (see text): R83 (17), B61 (18), T71 (28), S89 (27), V80 (26).

Fig. 2.

Temperature dependence of electrical resistivity for pure Fe liquid at 136 GPa, determined using the model in Table 1 (solid red line), agrees very well with the resistivity measurement of Keeler (10) at the same pressure. Stacey and Anderson (8) used ρ_el ∝ T (dashed line) in their extrapolation of this measurement to temperatures of the core near the core–mantle boundary. The shaded region indicates the T range near the core–mantle boundary from the range of candidate adiabats used (see text).

Fig. 3.

(Top) Electrical resistivity and (Middle) electronic thermal conductivity for the various compositions considered in this study, evaluated using the models in Table 1 along a range of candidate core adiabats (see text). (Bottom) Corresponding heat flux values computed as 4πr²k_el∇T, where r is the radius, compared to geophysical estimates of core–mantle boundary (CMB) heatflux (5).