Electrical resistivity, thermal conductivity, and viscosity of Fe-H alloys at Earth's core conditions

Abstract

The transport properties (electrical resistivity, thermal conductivity, and viscosity) of iron-hydrogen alloy are of great significance in the stability and evolution of planetary magnetic fields. Here, we investigate the thermal transport properties of iron doped with varying hydrogen content as functions of pressure (P) and temperature (T) for the top and bottom of Earth's outer core and beyond, corresponding to pressures of about 130 to 300 GPa and temperatures of 4000 to 7000 K. Using first-principles density functional theory molecular dynamic simulations (FPMD), we verify that crystalline FeH$_x$ is superionic with H diffusing freely. We find a low frequency viscosity of 10-11 mPa$\cdot$s for liquid Fe-H alloys at Earth's outer core conditions by the linear response Green-Kubo formula. Using the KKR method within density functional theory (DFT) plus Dynamical mean-field Theory (DMFT), we find saturation of electrical resistivity with increasing temperatures in liquid iron at outer core conditions. The effect of H on electrical and thermal transport we find is small, so that the exact H content of the core is not needed. The primary effect of H is on the equation of state, decreasing the density at constant P and T. We find the Lorenz number is smaller than the ideal value, and obtain for X(H)= 0.20, or 0.45 wt% H , thermal conductivity $\kappa$ of $\sim$105 and $\sim$190 $Wm^{-1}K^{-1}$, respectively, at conditions near the core-mantle and inner-outer core boundary.