Electrical Resistivity Measurements of Fe-Si With Implications for the Early Lunar Dynamo

The effect of impurities on the electrical resistivity of Fe at core conditions is controversial due to the challenges of measuring transport properties of Fe alloys under high-pressure and high-temperature conditions. In this study we describe an innovative technique to make wires of Fe-Si samples initially in powder form for measuring electrical resistivity. The electrical resistivity of Fe-2, Fe-8.5, and Fe-17 wt%Si was measured at 3, 4, and 5 GPa at temperatures into the liquid state and compared to results of Fe-4.5 wt%Si and Fe from prior studies. Isothermal electrical resistivity increases linearly with increasing Si content. Yet the effect of Si content on the magnitude of the electrical resistivity compared to that of Fe diminished as temperature increased at all experimental pressures. This implies the contribution to the electrical resistivity due to Si impurities is dependent on temperature, in disagreement with Matthiessen's rule. Thermal conductivity of Fe-Si alloys calculated using the Wiedemann-Franz law indicates a nonnegligible influence of the Si content on the thermal conductive properties of Fe-Si alloys. The results are used to calculate the adiabatic heat flux of an Fe-Si lunar core and date the end of the high magnetic field intensity era of the lunar dynamo to be in the range 3.32-3.80 Ga. Plan Language Summary The heat flux at the top of the core of terrestrial bodies is usually inferred by determining the thermal conductivity at the corresponding pressure and temperature conditions of core mimetic composition. It is difficult to measure directly the thermal conductivity of a metallic material at high pressures and temperatures, especially in the liquid state. Fortunately for metallic samples, thermal conductivity can be calculated from electrical resistivity, which is a property that is more accessible to experimental measurements. We measured the electrical resistivity of various Fe-Si alloys (2, 8.5, and 17 wt%Si) at 3, 4, and 5 GPa at temperatures into the liquid state. Compared to the electrical resistivity of pure Fe, our results show a temperature-dependent Si contribution, which violates the well-known Matthiessen's rule. The corresponding calculated thermal conductivity indicates a nonnegligible influence of Si on the thermal conductivity of Fe-Si alloys at high pressures and in the solid state, but in the high-temperature liquid state, thermal conductivity values for different Si contents begin to converge. This suggests estimates of heat flux at the top of the core may be insensitive to the impurity content in an Fe-Si core. Finally, the heat flux at the lunar core-mantle boundary is calculated using our data at 5 GPa. Our conducted heat flux results are in general lower than values in the literature, suggesting that the heat transport mechanism of thermal convection was enough to power the lunar dynamo during the high-intensity magnetic era and could explain the remanent magnetization in lunar core samples formed as late as 3.56 Ga.