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.
We report a new hydrogen clathrate hydrate synthesized at 1.2 GPa and 298 K documented by singlecrystal x-ray diffraction, Raman spectroscopy, and first-principles calculations. The oxygen sublattice of the new clathrate hydrate matches that of ice II, while hydrogen molecules are in the ring cavities, which results in the trigonal R3c or R3c space group (proton ordered or disordered, respectively) and the composition of ðH 2 OÞ 6 H 2 . Raman spectroscopy and theoretical calculations reveal a hydrogen disordered nature of the new phase C 0 1 , distinct from the well-known ordered C 1 clathrate, to which this new structure transforms upon compression and/or cooling. This new clathrate phase can be viewed as a realization of a disordered ice II, unobserved before, in contrast to all other ordered ice structures.
The iron-sulfur system is important for planetary interiors and is intensely studied, particularly for better understanding of the cores of Mars and Earth. Yet, there is a paradox about highpressure stability of FeS: ab initio global optimization (at DFT level) predicts a P mmn phase (with a distorted rocksalt structure) to be stable at pressures above ∼ 120 GPa, which has not yet been observed in the experiments that instead revealed a CsCl-type phase which, according to density functional calculations, should not be stable. Using quasiharmonic free energy calculations and the dynamical mean field theory, we show that this apparent discrepancy is removed by proper account of electron correlations and entropic effects.
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