Seismic observations suggest that the Earth’s inner core has a complex structure (e.g., the isotropic layer at the top, innermost inner core, and hemispherical dichotomy). These characteristics are believed to reflect the history of dynamics and temperature profile of the inner core. One critical physical property is the inner core’s thermal conductivity. The thermal conductivity of metals can be estimated from their electrical resistivity using the Wiedemann-Franz law. Recent high-pressure and temperature experiments revealed that the temperature dependence of electrical resistivity is small for Fe-Si alloys. The small temperature coefficient means that it is essential to determine the impurity resistivity of Fe alloys to constrain the inner core’s thermal conductivity. Therefore, this study systematically calculated the impurity resistivities of 4- and 6-component alloys at inner core pressure by combining the Korringa-Kohn-Rostoker method with the coherent potential approximation. As a result, we obtained the thermal conductivity of the inner core to be 150-263 W/m/K. The inner core cannot maintain thermal convection with such a high thermal conductivity, resulting in a flat temperature profile. In materials science, it is widely known that polycrystals soften suddenly at high temperatures a few percent below their melting temperature. If such a pre-melting occurs in the inner core, the flat temperature profile due to high thermal conductivity causes variations in the attenuation within the inner core. This may explain the observation that the upper inner core is more strongly attenuated than the innermost inner core.

Composition, chemical disorder, and magnetism significantly affect the volume and bulk modulus of iron–silicon (Fe–Si) alloys at ambient pressure. Here, we computed the equations of state for bcc-like (ordered B2 and disordered bcc) Fe–Si alloys available up to the inner-core pressure using the first-principles Korringa–Kohn–Rostoker method. Ferromagnetic (FM) and nonmagnetic (NM) states over a wide composition range, from Fe to FeSi, were investigated. The results revealed that magnetism and chemical disorder increased the volume and decreased the bulk modulus even at high pressures. Comparing the results with the preliminary reference Earth model, we found that an unrealistically large temperature gradient is required if the inner core is composed of a bcc-like Fe–Si alloy.

While hydrogen is one of plausible major light elements in the core, the high-temperature equation of state (EoS) of Fe-H alloy has not been experimentally examined to the core pressure range. Here we measured the volume (V) of non-magnetic (NM) fcc FeH at high pressure and temperature (P-T) to 142 GPa and 3660 K in a laser-heated diamond-anvil cell (DAC) and obtained its P-V-T EoS. An increase in the lattice volume of Fe per H atom, ΔVH, determined as functions of P and T is found to be substantially smaller than the volume of metallic H that has been used to estimate H concentration in Fe-H alloy. The ΔVH is almost identical between fcc and dhcp phases in the NM state, suggesting that it is applicable to hcp. The extrapolation of ΔVH to inner core conditions indicates its maximum H content to be 0.8–0.9 wt%.