Mechanisms of metal–silicate equilibration in the terrestrial magma ocean

It has been proposed that the high concentrations of moderately siderophile elements (e.g. Ni and Co) in the Earth’s mantle are the result of metal–silicate equilibration at the base of a deep magma ocean that formed during Earth’s accretion. According to this model, liquid metal ponds at the base of the magma ocean and, after equilibrating chemically with the overlying silicate liquid at high pressure (e.g. 25–30 GPa), descends further as large diapirs to form the core. Here we investigate the kinetics of metal–silicate equilibration in order to test this model and place new constraints on processes of core formation. We investigate two models: (1) Reaction between a layer of segregated liquid metal and overlying silicate liquid at the base of a convecting magma ocean, as described above. (2) Reaction between dispersed metal droplets and silicate liquid in a magma ocean. In the liquid-metal layer model, the convection velocity of the magma ocean controls both the equilibration rate and the rate at which the magma ocean cools. Results indicate that time scales of chemical equilibration are two to three orders of magnitude longer than the time scales of cooling and crystallization of the magma ocean. In the falling metal droplet model, the droplet size and settling velocity are critical parameters that we determine from fluid dynamics. For likely silicate liquid viscosities, the stable droplet diameter is estimated to be ∼1 cm and the settling velocity ∼0.5 m/s. Using such parameters, liquid metal droplets are predicted to equilibrate chemically after falling a distance of <200 m in a magma ocean. The models indicate that the concentrations of moderately siderophile elements in the mantle could be the result of chemical interaction between settling metal droplets and silicate liquid in a magma ocean but not between a segregated layer of liquid metal and overlying silicate liquid at the base of the magma ocean. Finally, due to fractionation effects, the depth of the magma ocean could have been significantly different from the value suggested by the apparent equilibration pressure.