Electrical Resistivity of Fe-C Alloy at High Pressure: Effects of Carbon as a Light Element on the Thermal Conductivity of the Earth's Core

We measured the electrical resistivity of iron, Fe₉₉C₁, Fe₃C, and Fe₇C₃ up to ~80 GPa using the van der Pauw method in a diamond anvil cell. The electrical resistivity of disordered Fe₉₉C₁ at high pressure shows a strong impurity resistivity of carbon. The ferromagnetic-paramagnetic transition in Fe₃C and Fe₇C₃ is associated with the flattening of the resistivity pressure gradient at ~6 GPa. Fe₇C₃ exhibits the highest electrical resistivity among all iron-light element alloys, and Fe₃C and Fe₇C₃ disobey the Matthiessen's rule by showing a lower electrical resistivity than a disordered iron-carbon alloy because of chemical ordering. A comparison of the impurity resistivity between silicon, sulfur, nickel, and carbon shows that carbon has an exceedingly stronger alloying effect than other elements. If the chemical ordering observed in Fe-Si system is held true for the Fe-C system, the chemical ordering in Fe₇C₃ possibly increases the thermal conductivity of the inner core and enlarges the thermal and electrical conductivity gap at the inner-core boundary. Models of the thermal conductivity of liquid Fe₇₀C₃₀ with 8.4 wt % carbon show a low thermal conductivity of 38 Wm⁻¹ K⁻¹ at the pressure-temperature conditions of the topmost outer core. The corresponding heat flow of 6 TW at the core-mantle boundary is notably lower than previous electrical resistivity results on Fe and Fe alloys. The alloying effect of carbon on the electrical and thermal conductivity of iron can thus play a significant role in understanding the heat flux at the core-mantle boundary and the thermal evolution of the core.