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

The transport properties (electrical resistivity, thermal conductivity, and viscosity) of iron-hydrogen alloys 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 380 GPa and temperatures of 4000 to 7000 K. Using first-principles density functional theory molecular dynamic simulations (FPMD), we verify that crystalline ${\mathrm{FeH}}_{x}$ is superionic with H diffusing freely. We find a low-frequency viscosity of 10--11 $\text{mPa}\phantom{\rule{0.16em}{0ex}}\text{s}$ for liquid Fe-H alloys at Earth's outer core conditions. We find resistivity saturation with increasing temperatures in liquid Fe-H alloy at core pressures. 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 $\ensuremath{\kappa}$ of $\ensuremath{\sim}105$ and $\ensuremath{\sim}190\phantom{\rule{4pt}{0ex}}{\text{Wm}}^{\ensuremath{-}1}\phantom{\rule{0.28em}{0ex}}{\text{K}}^{\ensuremath{-}1}$ at conditions near the core-mantle and inner-outer core boundary, respectively.