Redox systematics of a magma ocean with variable pressure-temperature gradients and composition

Oxygen fugacity in metal-bearing systems controls some fundamental aspects of the geochemistry of the early Earth, such as the FeO and siderophile trace element content of the mantle, volatile species that influence atmospheric composition, and conditions for organic compounds synthesis. Redox and metal-silicate equilibria in the early Earth are sensitive to oxygen fugacity (fO(2)), yet are poorly constrained in modeling and experimentation. High pressure and temperature experimentation and modeling in metal-silicate systems usually employs an approximation approach for estimating fO(2) that is based on the ratio of Fe and FeO [called "ΔIW (ratio)" hereafter]. We present a new approach that utilizes free energy and activity modeling of the equilibrium: Fe + SiO(2) + O(2) = Fe(2)SiO(4) to calculate absolute fO(2) and relative to the iron-wüstite (IW) buffer at pressure and temperature [ΔIW (P,T)]. This equilibrium is considered across a wide range of pressures and temperatures, including up to the liquidus temperature of peridotite (4,000 K at 50 GPa). Application of ΔIW (ratio) to metal-silicate experiments can be three or four orders of magnitude different from ΔIW (P,T) values calculated using free energy and activity modeling. We will also use this approach to consider the variation in oxygen fugacity in a magma ocean scenario for various thermal structures for the early Earth: hot liquidus gradient, 100 °C below the liquidus, hot and cool adiabatic gradients, and a cool subsolidus adiabat. The results are used to assess the effect of increasing P and T, changing silicate composition during accretion, and related to current models for accretion and core formation in the Earth. The fO(2) in a deep magma ocean scenario may become lower relative to the IW buffer at hotter and deeper conditions, which could include metal entrainment scenarios. Therefore, fO(2) may evolve from high to low fO(2) during Earth (and other differentiated bodies) accretion. Any modeling of core formation and metal-silicate equilibrium should take these effects into account.