Abstract:
First-principles density functional calculations (beyond the local density approximation) are used to predict the equations of state (EOS) and formation energies of Fe-FeO and Fe-FeS alloys under the pressures of the Earth's core. The accuracy of the static calculations is demonstrated from predicted equations of state and phase transitions of Fe, FeO and FeS. As indicated by the formation energies of Fe3O and Fe4O, solid solution between Fe and FeO remains energetically unfavorable up to core pressures. The instabilities are so large that no reasonable entropy term could stabilize an Fe-FeO solid solution at core temperatures. In contrast, solid solution between Fe and FeS becomes favored at core pressures as indicated by the formation energy of Fe3S. To the extent that the Earth's inner core is not dense enough to be pure iron, it follows that the inner core is most likely an Fe-FeS alloy rather than an Fe-FeO alloy. This, however, requires that the melting point of FeS fall below that of Fe at core pressures. The much lower density of the outer core may reflect either the width of the ''phase loop'' in the Fe-FeS binary or presence of an additional light element which cannot be incorporated into solid iron. Even if an additional light element is present in the outer core, the Earth must be enriched in sulfur relative to potassium. TheK ratio of the Earth must reflect the segregation of the core as an Fe-FeS eutectic during the early differentiation of the Earth.