Impurity Resistivity of the Earth's Inner Core

Abstract

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.

Electrical Resistivity and Phase Evolution of Fe–N Binary System at High Pressure and High Temperature

“…Under these conditions, Fe-1N and Fe-2N are stable in the γ phase-field, while Fe-6.4N and Fe-10N form nitride phases according to our recovery experiments. As shown in Figure 4, N has a positive effect on the resistivity of Fe, similar to Si and other elements such as C, S, O, P, and H [29,30,33,38]. The resistivity of all Fe-N compositions shows a weak temperature dependence at high temperatures.…”

“…We also examined the validity of Matthiessen's rule by calculating the elementary resistivity of N based on the experimental data. Matthiessen's rule is usually used to describe the alloying effect of the solute atoms on the resistivity of pure metals [18,20,25,27,33,38,88]. This rule gives the resistivity ρ total of dilute alloys as a sum of the resistivity of the pure metal matrix ρ 0 (T) and the impurity term as a function of the solute concentration C i , ρ total (C i , T) = ρ 0 (T) + ∑ ρ i C i , where ρ i is the elementary resistivity of solute i, which is only dependent on the impurity species.…”

“…It suggests that N would have enormous effect on the thermal conductivity of Fe and therefore the heat transport in the planetary core. However, the most recent computational studies suggest that the resistivity of the Fe-N system is comparable to other Fe alloys in the Fe-Si, Fe-C, Fe-O, Fe-S, Fe-H, and Fe-P systems [38]. Furthermore, recent experimental findings by Ma et al [81] reported that the bulk Fe 2 N synthesized under high pressure conditions exhibits good metallic conductivity, with a resistivity of 172 × 10 −8 Ωm at ambient condition, similar to the experimental results for Fe alloys mentioned above.…”