Equation of State of hcp Fe-C-Si Alloys and the Effect of C Incorporation Mechanism on the Density of hcp Fe Alloys at 300 K

Si and C are cosmochemically abundant elements soluble in hcp Fe under pressure and temperature and could therefore be present in the Earth's inner core. While recent ab initio calculations suggest that the observed inner core density and velocities could be matched by an Fe-C-Si alloy, the combined effect of these two elements has only recently started to be investigated experimentally. We therefore carried out synchrotron X-ray diffraction measurements of an hcp Fe-C-Si alloy with 4 at% C and 3 at% Si, up to similar to 150 GPa. Density functional theory calculations were also performed to examine different incorporation mechanisms. These calculations suggest interstitial C to be more stable than substitutional C below similar to 350 GPa. In our calculations, we also find that the lowest-energy incorporation mechanism in the investigated pressure range (60-400 GPa) is one where two C atoms occupy one atomic site; however, this is unlikely to be stable at high temperatures. Notably, substitutional C is observed to decrease the volume of the hcp Fe, while interstitial C increases it. This allows us to use experimental and theoretical equations of state to show unambiguously that C in the experimental hcp Fe-C-Si alloys is not substitutional, as is often assumed. This is crucial since assuming an incorrect incorporation mechanism in experiments leads to incorrect density determinations of similar to 4%, undermining attempts to estimate the concentration of C in the inner core. In addition, the agreement between our experiments and calculations supports Si and C as being light elements in the inner core.