[S-IT19] Deep Earth Sciences

[SIT19-P06] Impurity resistivity of the inner core

*Hitoshi Gomi¹, Kei Hirose^1,2 (1.Tokyo Institute of Technology, 2.The University of Tokyo)

Keywords:impurity resistivity, KKR-CPA, inner core, thermal conductivity

The Earth's inner core has various seismological features (anisotropy, hemispherical asymmetry, inner-inner core). To consider the origin of these features, the possibility of thermal convection, and hence the thermal conductivity, is important. The thermal conductivity of metals can be estimated from their electrical resistivity using the Wiedemann-Franz law. The impurity resistivity of hexagonal close-packed iron (hcp Fe) has been determined for substitutional alloys up to ternary systems by the first principles Korringa-Kohn-Rostoker (KKR) method combined with the coherent potential approximation (CPA). In this study, we extend the method by Gomi and Yoshino (2018) to calculate the impurity resistivity of alloys containing both substitutional and interstitial impurities. By using the Kubo-Greenwood formula, we computed the electrical resistivity of hcp Fe_1-x-yNi^s_xL^s_yLⁱ_z (L^s = Si, C, N, O, P, S, or H, Lⁱ = C, N, O, or H), where the superscript s represents the substitution site and the superscript i represents the octahedral interstitial site. The impurity concentration was set to 0 <= x <= 0.15, 0 <= y <= 0.3, and 0 <= z <= 0.5. Linear regression was performed on the electrical resistivity of the resultant 6105 alloys. We set the concentration of each impurity element as the explanatory variable, considering Mathiesen's rule. The results of the substitutional hcp Fe_0.9-yNi^s_0.1L^s_y (L= Si, C, N, O, P, S, or H) ternary alloy were compared with a previous study (Zidane et al. 2020) with the same composition, which shows that the previous calculation systematically overestimated the impurity resistivity of the inner core. The previous study also showed that hydrogen has a higher impurity resistivity than other impurities, but no such feature was found in the present study. The results for hcp FeHⁱ_z, an interstitial alloy, showed that hydrogen in the interstitial sites hardly contributes to the electrical resistivity, consistent with previous experiments (Ohta et al. 2019). A linear regression on hcp Fe_1-x-yNi^s_xL^s_yLⁱ_z (L^s = Si, C, N, O, P, S, or H, Lⁱ = C, N, O, or H) quaternary alloy with both substitutional and intrusive impurities shows that the constant term in the regression is 33 micro Ohm. As a result, the prediction performance was significantly different at around ~40 micro Ohm cm. This behavior may be due to the resistivity saturation. Furthermore, we performed calculations for a six-component alloys of Fe_1-x-yNi^s_x(Si,S)^s_y(H,C)ⁱ_z (0 <= x <= 0.05, 0 <= y <= 0.3, 0 <= z <= 0.5), which have two light elements each at the substitutional and interstitial sites. The results confirmed that the linear regression model of the quaternary alloy correctly predicted the results of the six-component alloys. Thus, we successfully obtained a highly predictive regression model in the region where the saturation is significant, which is important for discussing the impurity resistivity of the inner core. In the composition range of the present study, the impurity resistivity is expected to be less than ~100 micro Ohm cm, and the inner core is considered to have such high thermal conductivity that thermal convection is impossible.