A model of core formation is presented that involves the Earth accreting heterogeneously through a series of impacts with smaller differentiated bodies. Each collision results in the impactor's metallic core reacting with a magma ocean before merging with the Earth's proto-core. The bulk compositions of accreting planetesimals are represented by average solar system abundances of non-volatile elements (i.e. CI-chondritic), with 22% enhancement of refractory elements and oxygen contents that are defined mainly by the Fe metal/FeO silicate ratio. Based on an anhydrous bulk chemistry, the compositions of coexisting core-forming metallic liquid and peridotitic silicate liquid are calculated by mass balance using experimentally-determined metal/silicate partition coefficients for the elements Fe, Si, O, Ni, Co, W, Nb, V, Ta and Cr. Oxygen fugacity is fixed by the partitioning of Fe between metal and silicate and depends on temperature, pressure and the oxygen content of the starting composition. Model parameters are determined by fitting the calculated mantle composition to the primitive mantle composition using least squares minimization. Models that involve homogeneous accretion or single-stage core formation do not provide acceptable fits. In the most successful models, involving 24 impacting bodies, the initial 60-70% (by mass) of the Earth accretes from highly-reduced material with the final 30-40% of accreted mass being more oxidised, which is consistent with results of dynamical accretion simulations. In order to obtain satisfactory fits for Ni, Co and W, it is required that the larger (and later) impactor cores fail to equilibrate completely before merging with the Earth's proto-core, as proposed previously on the basis of Hf-W isotopic studies. Estimated equilibration conditions may be consistent with magma oceans extending to the core-mantle boundary, thus making core formation extremely efficient. The model enables the compositional evolution of the Earth's mantle and core to be predicted throughout the course of accretion. The results are consistent with the late accretion of the Earth's water inventory, possibly with a late veneer after core formation was complete. Finally, the core is predicted to contain ~5 wt.% Ni, ~8 wt.% Si, ~2 wt.% S and ~0.5 wt.% O.
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