Outer Core Heat Flux in Small Terrestrial Bodies from Electrical Resistivity Measurements of Liquid Fe-8S-4.5Si at High Pressure

The thermal conductivity values through Earth’s core and planetary cores have important implications for the thermal evolution and magnetism of these bodies. For the outer cores of small terrestrial planetary bodies, this study constrains the thermal conductivity of liquid Fe-8wt%S-4.5wt%Si at pressures 2-5 GPa. Thermal conductivity was estimated using the Wiedemann-Franz Law from electrical resistivity measurements of a small Fe alloy sample at high pressures and high temperatures in a 1000-ton cubic anvil press. The powder samples were prepared by mixing powders of three compositions: Fe, FeS, and Fe-9wt%Si. Electron microprobe analysis and micro X-ray diffraction verified the elemental composition and crystallographic structure of the sample material both before and after pressurization.

Resistivity-temperature plots of the Fe-8wt%S-4.5wt%Si data display trends common to Fe mixed with significant amounts of Si: a general rise in resistivity to a peak, a drop in resistivity through the melt, and a leveling of resistivity through the liquid state. Two reversals in slope occur between 800 K and 1000 K. At each integral pressure value between 2-5 GPa, an electrical resistivity in the range 300±100 μΩ·cm was found. Using the Sommerfeld value of the Lorenz number, thermal conductivities in the range 15±5 W/m/K were estimated. Comparative plots including resistivity data of Fe, Fe-4.5wt%Si, Fe-17wt%Si, and Fe-20wt%S are instructive to illuminate the relative effects of S and Si on the resistivity and thus the thermal conductivity and adiabatic heat flow of core mimetic Fe alloys. If the pressure at the top of the core is constrained using the assumptions of hydrostatic equilibrium and a bulk silicate mantle, then these thermal conductivity results may be applied to a number of known small terrestrial bodies, such as Io, in the case of a dominantly Fe-S-Si liquid outer core.