The composition of the Earthʹs core: constraints on S and Si vs. temperature

The Earthʹs core is an alloy of iron and a light element such as sulphur, oxygen or silicon. Starting with static equations of state of Fe, Fe3Si, Fe7S, Fe3S and FeS, calculated from density functional theory, we can estimate the core composition as a function of thermal pressure. We can relate the thermal pressure at a given density to temperature using the Mie-Grüneisen formalism. There is a significant (4%) excess volume of mixing along the Fe-FeS binary at core pressures. Consequently, the density of the Earthʹs core can be explained using much less sulphur (2.0–8.0 wt%) than that previously estimated. However, the amount of sulphur required is still greater than that expected from the abundance of less volatile elements and suggests that a second light element is needed. The equation of state of Fe3Si shows that the core can accommodate as much 8.7% Si at geophysically reasonable thermal pressures. A core composition of 7.3% Si and 2.3% S, as proposed by Allègre et al. [10] for a chondritic bulk EarthSi/Mg, implies a thermal pressure of 15 GPa at the core-mantle boundary assuming a −3% density change of melting for Fe. A 15 GPa thermal pressure, in turn, requires a temperature of 3000 K for a Grüneisen parameter γ = 1.38. At the inner core boundary, a core composition of 7.3% Si and 2.3% S implies a thermal pressure near 35 GPa which, in turn, implies a temperature near 4400 K. Somewhat higher core temperatures would result if the sulphur content were as low as that recently proposed. It appears that a sulphur-depleted Earth with a chondriticMg/Si ratio (with excess Si incorporated into the core) is consistent with the observed density of the core, the calculated equations of state, and the estimated thermal pressures. Finally, the results obtained here completely remove any need to accommodate oxygen in the core; this is consistent with the previously found [14] extreme instability of Fe-FeO alloy phases.