Review of Electrical Resistivity Measurements and Calculations of Fe and Fe-Alloys Relating to Planetary Cores

Abstract

There is a considerable amount of literature on the electrical resistivity of iron at Earth’s core conditions, while only few studies have considered iron and iron-alloys at other planetary core conditions. Much of the total work has been carried out in the past decade and a review to collect data is timely. High pressures and temperatures can be achieved with direct measurements using a diamond-anvil cell, a multi-anvil press or shock compression methods. The results of direct measurements can be used in combination with first-principle calculations to extrapolate from laboratory temperature and pressure to the relevant planetary conditions. This review points out some discrepancies in the electrical resistivity values between theoretical and experimental studies, while highlighting the negligible differences arising from the selection of pressure and temperature values at planetary core conditions. Also, conversions of the reported electrical resistivity values to thermal conductivity via the Wiedemann-Franz law do not seem to vary significantly even when the Sommerfeld value of the Lorenz number is used in the conversion. A comparison of the rich literature of electrical resistivity values of pure Fe at Earth’s core-mantle boundary and inner-core boundary conditions with alloys of Fe and light elements (Si, S, O) does not reveal dramatic differences. The scarce literature on the electrical resistivity at the lunar core suggests the effect of P on a wt% basis is negligible when compared to that of Si and S. On the contrary, studies at Mercury’s core conditions suggest two distinct groups of electrical resistivity values but only a few studies apply to the inner-core boundary. The electrical resistivity values at the Martian core-mantle boundary conditions suggest a negligible contribution of Si, S and O. In contrast, Fe-S compositions at Ganymede’s core-mantle boundary conditions result in large deviations in electrical resistivity values compared to pure Fe. Contour maps of the reported values illustrate ρ(P, T) for pure Fe and its alloys with Ni, O and Si/S and allow for estimates of electrical resistivity at the core-mantle boundary and inner-core boundary conditions for the cores of terrestrial-like planetary bodies.

Deviation of Mercury's Spin Axis From an Exact Cassini State Induced by Dissipation

“…strength of the radial component of the field at the ICB and $$${\mathcal{F}}_{icb}=\frac{\sigma \delta }{{{\Omega}}_{o}{\rho }_{s}{r}_{s}},$$$ where σ is the electrical conductivity (assumed equal in the fluid and solid core) and $$\delta =\sqrt{2/\left(\sigma \mu {{\Omega}}_{o}\right)}$$ is the magnetic skin depth with μ = 4 π × 10 −7 N A −1 the magnetic permeability of free space. We use σ = 10 6 S m −1 , a reasonable value for Mercury's core (e.g., Berrada & Secco, 2021). This parameterization is valid, provided EM coupling remains in a weak‐field regime which, as detailed in D21, is a reasonable assumption for Mercury.…”

“…where σ is the electrical conductivity (assumed equal in the fluid and solid core) and 𝐴𝐴 𝐴𝐴= √ 2∕ (𝜎𝜎𝜎𝜎Ω𝑜𝑜) is the magnetic skin depth with μ = 4π × 10 −7 N A −1 the magnetic permeability of free space. We use σ = 10 6 S m −1 , a reasonable value for Mercury's core (e.g., Berrada & Secco, 2021). This parameterization is valid, provided EM coupling remains in a weak-field regime which, as detailed in D21, is a reasonable assumption for Mercury.…”

Deviation of Mercury's spin axis from an exact Cassini state induced by dissipation

“…We use σ = 10 6 S m −1 , a reasonable value for Mercury's core [e.g. Berrada and Secco, 2021]. This parameterization is valid provided EM coupling remains in a weak-field regime which, as detailed in D21, is a reasonable assumption for Mercury.…”

Electrical Resistivity of Fe and Fe‐3 wt%P at 5 GPa With Implications for the Moon's Core Conductivity and Dynamo

“…We can therefore estimate the thermal conductivity of a terrestrial planet's metallic core by measuring the electrical resistivity of iron and its alloys. To date, numerous studies have investigated the electrical resistivities of Fe and Fe‐L systems (L is light elements, such as S, C, Si, and P) under various pressure‐temperature conditions (see the review paper of Berrada and Secco [2021]). Electrical resistivity has been used to discuss the thermal evolution of the Earth (Gomi & Hirose, 2015; Inoue et al., 2020; Ohta et al., 2016; Yong et al., 2019; Y. Zhang et al., 2020, 2021), Moon (Berrada et al., 2020; Yin, Zhai, et al., 2019), Mars (Suehiro et al., 2017), Ganymede (Littleton et al., 2021; Pommier, 2020), and Mercury (Berrada et al., 2021; Manthilake et al., 2019; Pommier, 2018; Pommier et al., 2019; Silber et al., 2018).…”