Electrical resistivity of substitutionally disordered hcp Fe–Si and Fe–Ni alloys: Chemically-induced resistivity saturation in the Earth's core

Abstract

The thermal conductivity of the Earth's core can be estimated from its electrical resistivity via the Wiedemann-Franz law. However, previously reported resistivity values are rather scattered, mainly due to the lack of knowledge with regard to resistivity saturation (violations of the Bloch-Grüneisen law and the Matthiessen's rule). Here we conducted high-pressure experiments and first-principles calculations in order to clarify the relationship between the resistivity saturation and the impurity resistivity of substitutional silicon in hexagonal-close-packed (hcp) iron. We measured the electrical resistivity of Fe-Si alloys (iron with 1, 2, 4, 6.5, and 9 wt.% silicon) using

The influence of sulfur on the electrical resistivity of hcp iron: Implications for the core conductivity of Mars and Earth

“…The P-R relation of the hcp Fe-Si-S alloy shown in Figure 1a was converted to P-ρ relation (Figure 1b). This result clearly shows that the resistivity of the hcp Fe-Si-S alloy is larger than those of hcp Fe and hcp Fe-Si alloy at 300 K [Gomi et al, 2013[Gomi et al, , 2016Seagle et al, 2013], indicating that S plays a role as an additional electron scatterer in the Fe-based alloy.For a single-phase alloy, Matthiensen's rule gives the electrical resistivity of a dilute alloy (ρ alloy ) as a function of solute concentrations of element i (χ i ):…”

“…Our estimate shows that the thermal conductivity of the Martian core increases from 46 W/m/K at CMB to 62 W/m/K at its center. However, all of these studies [Gomi et al, 2016], and black broken line is the predicted ρ S from the ρ Si and the Norbury-Linde rule [Gomi et al, 2013[Gomi et al, , 2016. However, all of these studies [Gomi et al, 2016], and black broken line is the predicted ρ S from the ρ Si and the Norbury-Linde rule [Gomi et al, 2013[Gomi et al, , 2016.…”

“…Fitting of the resistivity of hcp Fe-Si-S alloy via equations (3) and (4) yielded F 1 = 1.15 (+0.88/À0.50), F 2 = 1.14 (+0.02/À0.02), and F 3 = À1.06 (+0.42/ À0.30). Gomi et al [2013Gomi et al [ , 2016 approximated ρ S based on their value of ρ Si and the Norbury-Linde rule; the impurity resistivity for metal alloys is proportional to Z i 2 , where Z i is the difference in valence between the impurity element and host metal [Norbury, 1921;Linde, 1932] (broken line in Figure 2). Gomi et al [2013Gomi et al [ , 2016 approximated ρ S based on their value of ρ Si and the Norbury-Linde rule; the impurity resistivity for metal alloys is proportional to Z i 2 , where Z i is the difference in valence between the impurity element and host metal [Norbury, 1921;Linde, 1932] (broken line in Figure 2).…”

“…The obtained electrical resistivity of the hcp Fe-Si-S was analyzed to reveal the influence of S on the electrical resistivity of Fe alloy in combination with the reported resistivities of Fe and Fe-Si alloy at high pressures [Gomi et al, 2013[Gomi et al, , 2016. The obtained electrical resistivity of the hcp Fe-Si-S was analyzed to reveal the influence of S on the electrical resistivity of Fe alloy in combination with the reported resistivities of Fe and Fe-Si alloy at high pressures [Gomi et al, 2013[Gomi et al, , 2016.…”

Stochastic generation of MAC waves and implications for convection in Earth’s core

“…Wave frequencies for the case of a dipolar background magnetic field converge toward the analytical (diffusion-free) solutions of Braginsky (1993) when the effects of magnetic diffusion are reduced. Lowering η by a factor of four in the numerical calculations from our preferred value of η = 0.8 m 2 s −1 (Pozzo et al 2012;Gomi et al 2016) reproduces the analytical solution to within 0.1 per cent. Numerical convergence is achieved with a resolution of 80 × 80 grid points in the x and r coordinates.…”