Fe–C and Fe–H systems at pressures of the Earth's inner core

The solid inner core of Earth is predominantly composed of iron alloyed with several percent Ni and some lighter elements, Si, S, O, H, and C being the prime candidates. To establish the chemical composition of the inner core, it is necessary to find the range of compositions that can explain its observed characteristics. Recently, there have been a growing number of papers investigating C and H as possible light elements in the core, but the results were contradictory. Here, using ab initio simulations, we study the Fe–C and Fe–H systems at inner core pressures (330–364 GPa). Based on the evolutionary structure prediction algorithm USPEX, we have determined the lowest-enthalpy structures of all possible carbides (FeC, Fe$_2$C, Fe$_3$C, Fe$_4$C, FeC$_2$, FeC$_3$, FeC$_4$, Fe$_7$C$_3$) and hydrides (Fe$_4$H, Fe$_3$H, Fe$_2$H, FeH, FeH$_2$, FeH$_3$, FeH$_4$) and have found that Fe$_2$C (space group Pnma) is the most stable iron carbide at pressures of the inner core, while FeH, FeH$_3$, and FeH$_4$ are the most stable iron hydrides at these conditions. For Fe$_3$C, the cementite structure (space group Pnma) and the Cmcm structure recently found by random sampling are less stable than the I-4 and C2/m structures predicted here. We have found that FeH$_3$ and FeH$_4$ adopt chemically interesting thermodynamically stable crystal structures, containing trivalent iron in both compounds. We find that the density of the inner core can be matched with a reasonable concentration of carbon, 11–15 mol.% (2.6–3.7 wt.%) at relevant pressures and temperatures, yielding the upper bound to the C content in the inner core. This concentration matches that in CI carbonaceous chondrites and corresponds to the average atomic mass in the range 49.3–51.0, in close agreement with inferences from Birch's law for the inner core. Similarly made estimates for the maximum hydrogen content are unrealistically high: 17–22 mol.% (0.4–0.5 wt.%), which corresponds to the average atomic mass of the core in the range 43.8–46.5. We conclude that carbon is a better candidate light alloying element than hydrogen.