Thermal Conductivity and Electrical Resistivity of Solid Iron at Earth’s Core Conditions from First Principles

Abstract

We compute the thermal conductivity and electrical resistivity of solid hcp Fe to pressures and temperatures of Earth's core. We find significant contributions from electron-electron scattering, usually neglected at high temperatures in transition metals. Our calculations show a quasilinear relation between the electrical resistivity and temperature for hcp Fe at extreme high pressures. We obtain thermal and electrical conductivities that are consistent with experiments considering reasonable error. The predicted thermal conductivity is reduced from previous estimates that neglect electron-electron scattering. Our estimated thermal conductivity for the outer core is 77±10 W m^{-1} K^{-1} and is consistent with a geodynamo driven by thermal convection.

Heat Flow in Earth's Core From Invariant Electrical Resistivity of Fe‐Si on the Melting Boundary to 9 GPa: Do Light Elements Matter?

“…On the core side of the CMB, we estimate κ to be between 65 and 73 W/m · K assuming that temperatures at CMB are in the range 4,000-4,500 K (e.g., Badro et al, 2014;Zhang, Jackson, et al, 2016) and ρ of~150 μΩcm. These estimates are in a reasonable agreement with the lower end of the recent theoretically and experimentally obtained values (e.g., Gomi et al, 2013Gomi et al, , 2016Gomi & Hirose, 2015;de Koker et al, 2012;Pozzo et al, 2012Pozzo et al, , 2013Seagle et al, 2013;Xu et al, 2018). Comparatively, our κ values are also in a reasonable agreement with estimates of thermal conductivity at the CMB based on models of heat flow through the CMB (e.g., Davies, 2015;Davies et al, 2015;Gubbins et al, 2015;Olson, 2016).…”

“…Assuming that the Wiedemann-Franz law (κ = LT/ρ) holds at the CMB and ICB conditions, which is predicated on the minimal role of inelastic electron scattering at core conditions (e.g., Williams, 2018), we can then evaluate κ at the ICB and CMB using the Sommerfeld value (2.445 × 10 −8 W 2 /K 2 ) of the Lorenz number. This number agrees well with a total Lorenz value of 2.10-2.15 × 10 −8 W 2 /K 2 derived for the entire outer core region from calculated total electrical resistivity and total thermal conductivity in a recent study that showed significant electron-electron scattering in pure hcp Fe (Xu et al, 2018). On the outer core side of the ICB, κ is estimated to be 104-131 W/m · K relying on the current uncertainties in ICB temperatures (5,500-6,000 K; e.g., Anzellini et al, 2013).…”

Advances in geodynamo modelling

“…Ab initio simulations by Pourovskii et al (2016) argue that the electron-electron scattering contribution to the thermal resistivity is stronger than in previous calculations, while its contribution to the electrical conductivity remains negligible. Newer calculations based on the same idea (Xu et al 2018) now suggest a thermal conductivity value of 70-75 W m −1 K −1 at Earth's CMB, not quite as high as those by de Koker and Steinle-Neumann (2012) and Pozzo et al (2012) but definitely not in the range of the older low values. Its worth keeping in mind that high pressure experiments as well as ab initio calculations are extremely challenging.…”

“…Recent estimates of the electrical conductivity σ and thermal conductivity k at Earth coremantle boundary conditions based on experimental data and ab initio calculations. Xu et al (2018) All listed experiments are Diamond Anvil Cell (DAC) setups while older experiments used shock waves. Gomi et al (2013) and the older experiments measured the electrical conductivity, highlighted in bold, and use the Wiedemann-Franz Law to calculate the thermal conductivity.…”

FeO Content of Earth’s Liquid Core

“…Standard evolution models (those not including precipitation) that incorporate new high core thermal conductivity estimates [22][23][24] require cooling rates exceeding 100 K Gyr −1 and predict supersolidus temperatures until the last 0.5-1.0 Ga [3,20,25]. Even with lower values of the thermal conductivity [26,27], these models predict supersolidus temperatures for approximately the first 1 Gyr [28] after core formation. Concerns over the inefficiency of sustaining the ancient dynamo with high thermal conductivity led to a new class of models arguing that precipitation of MgO [4] or SiO 2 [6] began shortly after core formation, though these models still predict supersolidus temperatures until the last 1-2 Ga. All evolution models predict that the inner core is ≲1.5-Ga old, and so FeO exchange between a fully molten core and a molten lower mantle should have occurred over much of Earth's history.…”