  The liquid metal-liquid silicate partitioning of molybdenum and tungsten
during core formation must be well-constrained in order to understand the
evolution of Earth and other planetary bodies, in particular because the Hf-W
isotopic system is used to date early planetary evolution. We combine 48 new
high pressure and temperature experimental results with a comprehensive
database of previous experiments to re-examine the systematics of Mo and W
partitioning. W partitioning is particularly sensitive to silicate and metallic
melt compositions and becomes more siderophile with increasing temperature. We
show that W has a 6+ oxidation state in silicate melts over the full
experimental fO2 range of $\Delta$IW -1.5 to -3.5. Mo has a 4+ oxidation state
and its partitioning is less sensitive to silicate melt composition, but also
depends on metallic melt composition. DMo stays approximately constant with
increasing depth in Earth. Both W and Mo become more siderophile with
increasing C content of the metal, so we fit epsilon interaction parameters. W
and Mo along with C are incorporated into a combined N-body accretion and
core-mantle differentiation model. We show that W and Mo require the early
accreting Earth to be sulfur-depleted and carbon-enriched so that W and Mo are
efficiently partitioned into Earth's core and do not accumulate in the mantle.
If this is the case, the produced Earth-like planets possess mantle
compositions matching the BSE for all simulated elements. However, there are
two distinct groups of estimates of the bulk mantle's C abundance in the
literature: low (100 ppm), and high (800 ppm), and all models are consistent
with the higher estimated carbon abundance. The low BSE C abundance would be
achievable when the effects of the segregation of dispersed metal droplets
produced in deep magma oceans by the disproportionation of Fe2+ to Fe3+ plus
metallic Fe is considered.
