Equations of state in the Fe-FeSi system at high pressures and temperatures

Earth's core is an iron-rich alloy containing several weight percent of light element(s), possibly including silicon. Therefore, the high pressure-temperature equations of state of iron-silicon alloys can provide understanding of the properties of Earth's core. We performed X-ray diffraction experiments using laser-heated diamond anvil cells to achieve simultaneous high pressures and temperatures, up to similar to 200 GPa for Fe-9 wt % Si alloy and similar to 145 GPa for stoichiometric FeSi. We determined equations of state of the D0(3), hcp + B2, and hcp phases of Fe-9Si, and the B20 and B2 phases of FeSi. We also calculated equations of state of Fe, Fe11Si, Fe5Si, Fe3Si, and FeSi using ab initio methods, finding that iron and silicon atoms have similar volumes at high pressures. By comparing our experimentally determined equations of state to the observed core density deficit, we find that the maximum amount of silicon in the outer core is similar to 11 wt %, while the maximum amount in the inner core is 6-8 wt %, for a purely Fe-Si-Ni core. Bulk sound speeds predicted from our equations of state also match those of the inner and outer core for similar ranges of compositions. We find a compositional contrast between the inner and outer core of 3.5-5.6 wt % silicon, depending on the seismological model used. Theoretical and experimental equations of state agree at high pressures. We find a good match to the observed density, density profile, and sound speed of the Earth's core, suggesting that silicon is a viable candidate for the dominant light element.