Sound velocities of Fe and Fe-Si alloy in the Earth’s core

<jats:p>Compressional wave velocity-density (<jats:italic>V</jats:italic><jats:sub><jats:italic>P</jats:italic></jats:sub> - <jats:italic>ρ</jats:italic>) relations of candidate Fe alloys at relevant pressure-temperature conditions of the Earth’s core are critically needed to evaluate the composition, seismic signatures, and geodynamics of the planet’s remotest region. Specifically, comparison between seismic<jats:italic>V</jats:italic><jats:sub><jats:italic>P</jats:italic></jats:sub> - <jats:italic>ρ</jats:italic>profiles of the core and candidate Fe alloys provides first-order information on the amount and type of potential light elements—including H, C, O, Si, and/or S—needed to compensate the density deficit of the core. To address this issue, here we have surveyed and analyzed the literature results in conjunction with newly measured<jats:italic>V</jats:italic><jats:sub><jats:italic>P</jats:italic></jats:sub> - <jats:italic>ρ</jats:italic>results of hexagonal closest-packed (hcp) Fe and hcp-Fe<jats:sub>0.85</jats:sub>Si<jats:sub>0.15</jats:sub>alloy using in situ high-energy resolution inelastic X-ray scattering and X-ray diffraction. The nature of the Fe-Si alloy where Si is readily soluble in Fe represents an ideal solid-solution case to better understand the light-element alloying effects. Our results show that high temperature significantly decreases the<jats:italic>V</jats:italic><jats:sub><jats:italic>P</jats:italic></jats:sub>of hcp-Fe at high pressures, and the Fe-Si alloy exhibits similar high-pressure<jats:italic>V</jats:italic><jats:sub><jats:italic>P</jats:italic></jats:sub> - <jats:italic>ρ</jats:italic>behavior to hcp-Fe via a constant density offset. These<jats:italic>V</jats:italic><jats:sub><jats:italic>P</jats:italic></jats:sub> - <jats:italic>ρ</jats:italic>data at a given temperature can be better described by an empirical power-law function with a concave behavior at higher densities than with a linear approximation. Our new datasets, together with literature results, allow us to build new<jats:italic>V</jats:italic><jats:sub><jats:italic>P</jats:italic></jats:sub> - <jats:italic>ρ</jats:italic>models of Fe alloys in order to determine the chemical composition of the core. Our models show that the<jats:italic>V</jats:italic><jats:sub><jats:italic>P</jats:italic></jats:sub> - <jats:italic>ρ</jats:italic>profile of Fe with 8 wt % Si at 6,000 K matches well with the Preliminary Reference Earth Model of the inner core.</jats:p>