Lorenz number and transport properties of Fe: Implications to the thermal conductivity at Earth's core-mantle boundary

Abstract

Abstract The electrical resistivity (ρ) and thermal conductivity (κ) of the Earth's core compositions are essential parameters for constraining the core's thermal state, the inner core age, and the evolutionary history of the geodynamo. However, controversies persist between experimental and computational results regarding the electronic transport properties (ρ and κ) of the Earth's core. Iron is the major element in the core, and its transport properties under high pressure and high temperature conditions are crucial for understanding the core's thermal state. We measured the ρ values of solid iron using the four-wire van der Pauw method at 300 K and pressures ranging from 3 to 26 GPa within a multi-anvil press. For comparison, we calculated the ρ and κ values of hexagonal close-packed (hcp) iron at conditions of 300-4100 K and 22-136 GPa using the first-principles molecular dynamics (FPMD) method. Our calculations generally align with prior studies, indicating that the electrical resistivity of solid hcp iron at Earth's core-mantle boundary (CMB) conditions is ~76-83 μΩ∙cm. The resistivity of hcp iron changes small as it melts from solid to liquid at pressures from 98 to 134 GPa. The impact of temperature and pressure on the Lorenz numbers of solid hcp iron are investigated according to our calculation results and previous studies. Under the CMB's pressure conditions, the κ of hcp iron initially decreases with increasing temperature and subsequently increases. The electron-electron scattering plays a dominant role at low temperatures and causes the decrease in κ. At high temperatures, the increase of electronic specific heat significantly increases the Lorentz number and κ. Overall, we estimate the κ of solid hcp iron at CMB's condition to be 114 ± 6 W/m/K, slightly lower than the room temperature value of 129 ± 9 W/m/K at the same pressure. Our model shows that a 0-525 km thickness of a thermally stratified layer may exist beneath the Earth's CMB depending on the core's heat flow and thermal conductivity.