Core formation and chemical equilibrium in the Earth—I. Physical considerations

Current models of planetary formation suggest a hierarchy in the size of planetesimals from which planets were formed, causing formation of a hot magma ocean through which metal-silicate separation (core formation) may have occurred. We analyze chemical equilibrium during metal-silicate separation and show that the size of iron as well as the thermodynamic conditions of equilibrium plays a key role in determining the chemistry of the mantle (silicates) and core (iron) after core formation. A fluid dynamical analysis shows that the hydrodynamically stable size of iron droplets is less than ∼ 10 ^-2 m for which both chemical and thermal equilibrium should have been established during the separation from the surrounding silicate magma. However, iron may have been separated from silicates as larger bodies when accumulation of iron on rheological boundaries and resultant large scale gravitational instability occurred or when the core of colliding planetesimals directly plunged into the pre-existing core. In these cases, iron to form the core will be chemically in dis-equilibrium with surrounding silicates during separation. The relative role of equilibrium and dis-equilibrium separation has been examined taking into account of the effects of rheological structure of a growing earth that contains a completely molten near surface layer followed by a partially molten deep magma ocean and finally a solid innermost proto-nucleus. We show that the separation of iron through a completely molten magma ocean likely occurred with iron droplets assuming a hydrodynamically stable size (∼ 10 ^-2 m) at chemical equilibrium, but the sinking iron droplets are likely to have been accumulated on top of the partially molten layer to form a layer (or a lake) of molten iron which sank to deeper portions as a larger droplet. The degree of chemical equilibrium during this process is determined by the size of droplets which is in turn controlled by the size and frequency of accreting planetesimals and the rheological properties of silicate matrix. For a plausible range of parameters, most of the iron that formed the core is likely to have been separated as large droplets or bodies and chemical equilibrium with silicate occurred only at relatively low temperatures and pressures in a shallow magma ocean or in their parental bodies. However, a small portion of iron that separated as small droplets was in chemical equilibrium with silicate at high temperatures and pressures in a deep magma ocean during the later stage of core formation. Therefore the chemistry of the core is mostly controlled by the chemical equilibrium with silicates at relatively low temperatures and pressures, whereas the chemistry of the mantle controlled by the interaction with iron during core formation is likely to have been determined mostly by the chemical equilibrium with a small amount of iron at high temperatures and pressures.