Light elements in the Earth's core: Fe3X compounds

The nature of the light element (or elements) of the core has been the subject of considerable speculation, because of its bearing on the overall bulk composition of the earth, the conditions under which the core formed, the temperature regime in the core and the continuing process of core-mantle reaction. The correct thermodynamical and thermochemical properties of iron alloyed with any of the potential major candidate light elements - sulfur, carbon and silicon - are described along solid solutions. At least at low pressures, one of their major eutectic points is found at Fe₃X compositions. Here we study in detail the compressibility and elasticity of these phases, Fe₃S, Fe₃C and Fe₃Si, up to inner core pressures. For this specific stoichiometry Fe - Me = 3 - 1, both the sulfide and the carbide present the cementite orthorhombic structure up to inner core pressures. They exhibit a gradual decrease of the residual magnetic moment, in ferromagnetic configuration. The spin transition occurs largely below the core conditions. The silicide behaves differently. Fe₃Si is not stable as cementite and during the relaxation the structure naturally evolves into a standard face-centered cubic structure, where Si occupies every fourth site. The structure is ferromagnetic with non-vanishing spin even at inner core pressures. The density of all Fe₃X compounds analyzed here is smaller than that of hexagonally-close packed (hcp) iron by about 10-15%. Fe₃S and Fe₃C have similar values of bulk modulus as hcp iron and show smaller values for the shear modulus. Fe₃Si shows considerably smaller values for both elastic moduli. In terms of velocities, Fe₃S presents the closest velocities to hcp iron from all the three Fe₃X candidates in terms of both Vp and Vs. Fe₃Si shows larger Vp than hcp iron by about 4%. The difference in Vs is on the order of 11%. Fe₃C shows the largest difference. Both Vp and Vs of Fe₃C are considerably smaller than of pure iron. However adding carbon to iron is not enough to decrease its velocities enough to match PREM, even if we consider a thermal correction of 5%.