The solid inner core of the 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 are contradictory. Here, using ab initio simulations, we study the Fe-C and Fe-H systems at inner core pressures (330-364 GPa). Using the evolutionary structure prediction algorithm USPEX, we have determined the lowest-enthalpy structures of possible carbides (FeC, Fe 2 C, Fe 3 C, Fe 4 C, FeC 2 , FeC 3 , FeC 4 and 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 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 found here. We have found that FeH 3 and FeH 4 adopt chemically interesting thermodynamically stable structures, in both compounds containing trivalent iron. 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. 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 the 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 in the range 43.8-46.5. We conclude that carbon is a better candidate light alloying element than hydrogen.
Using the evolutionary crystal structure prediction algorithm USPEX, we identify the compositions and crystal structures of thermodynamically stable compounds in the Fe–S system at pressures in the range of 100–400 GPa. We find that at pressures in the Earth’s solid inner core (330–364 GPa) two compounds are stable—Fe2S and FeS. In equilibrium with iron, only Fe2S can exist in the inner core. Using the equation of state of Fe2S, we find that, in order to reproduce the density of the inner core by adding sulfur alone, 10.6–13.7 mol.% (6.4–8.4 wt.%) sulfur is needed. An analogous calculation for silicon (where the only stable compound at inner core pressures is FeSi) reproduces the density of the inner core with 9.0–11.8 mol.% (4.8–6.3 wt.%) silicon. In both cases, a virtually identical mean atomic mass in the range of 52.6–53.3 results for the inner core, which is much higher than inferred for the inner core from Birch’s law. In the case of oxygen (allowing for the equilibrium coexistence of suboxide Fe2O with iron under core conditions), the inner core density can be explained by the oxygen content of 13.2–17.2 mol.% (4.2–5.6 wt.%), which corresponds to between 49.0 and 50.6. Combining our results and previous work, we arrive at four preferred compositional models of the Earth’s inner core (in mol.%): (i) 86% (Fe+Ni)+14% C; (ii) 84% (Fe+Ni)+16% O; (iii) 84% (Fe+Ni)+7% S+9% H; (iv) 85% (Fe+Ni)+6% Si+9% H.
The solid inner core of the 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 are contradictory. Here, using ab initio simulations, we study the Fe-C and Fe-H systems at inner core pressures (330-364 GPa). Using the evolutionary structure prediction algorithm USPEX, we have determined the lowest-enthalpy structures of possible carbides (FeC, Fe 2 C, Fe 3 C, Fe 4 C, FeC 2 , FeC 3 , FeC 4 and 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 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 found here. We have found that FeH 3 and FeH 4 adopt chemically interesting thermodynamically stable structures, in both compounds containing trivalent iron. 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. 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 the 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 in the range 43.8-46.5. We conclude that carbon is a better candidate light alloying element than hydrogen.
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