Impurity Resistivity of fcc and hcp Fe-Based Alloys: Thermal Stratification at the Top of the Core of Super-Earths

It is widely known that the Earth's Fe dominant core contains a certain amount of light elements such as H, C, N, O, Si, and S. We report the results of first-principles calculations on the band structure and the impurity resistivity of substitutionally disordered hcp and fcc Fe based alloys. The calculation was conducted by using the AkaiKKR (machikaneyama) package, which employed the Korringa-Kohn-Rostoker (KKR) method with the atomic sphere approximation (ASA). The local density approximation (LDA) was adopted for the exchange-correlation potential. The coherent potential approximation (CPA) was used to treat substitutional disorder effect. The impurity resistivity is calculated from the Kubo-Greenwood formula with the vertex correction. In dilute alloys with 1 at. % impurity concentration, calculated impurity resistivities of C, N, O, S are comparable to that of Si. On the other hand, in concentrated alloys up to 30 at. %, Si impurity resistivity is the highest followed by C impurity resistivity. Ni impurity resistivity is the smallest. N, O, and S impurity resistivities lie between Si and Ni. Impurity resistivities of hcp-based alloys show systematically higher values than fcc alloys. We also calculated the electronic specific heat from the density of states (DOS). For pure Fe, the results show the deviation from the Sommerfeld value at high temperature, which is consistent with previous calculation. However, the degree of deviation becomes smaller with increasing impurity concentration. The violation of the Sommerfeld expansion is one of the possible sources of the violation of the Wiedemann-Franz law, but the present results could not resolve the inconsistency between recent electrical resistivity and thermal conductivity measurements. Based on the present thermal conductivity model, we calculated the conductive heat flux at the top of terrestrial cores, which is comparable to the heat flux across the thermal boundary layer at the bottom of the mantle. This indicates that the thermal stratification may develop at the top of the liquid core of super-Earths, and hence, chemical buoyancies associated with the inner core growth and/or precipitations are required to generate the global magnetic field through the geodynamo.