Core growth and siderophile element depletion of the mantle during homogeneous Earth accretion

Abstract

A simple mechanism is put forward to explain the abundances of siderophile elements in the Earth's mantle. Within the frame of a homogeneous accretion hypothesis, the model involves repeated equilibrium fractionation, in a portion of the mantle, between solid and liquid silicate and metal phases. Fractionation events are followed by segregation of metal phases into the core and extensive mixing of different materials (newly accreted matter, terrestrial unfractionated matter, and silicate mantle material which has undergone fractionation) within the mantle. The time scale of a fractionation and mantle mixing event is very short compared to that of accretion. The process leads to a decrease of the metal fraction in the mantle with time. Therefore, the modelling was done in two stages. In the first, envisaged during accretion, metal fractions around 0.1 were considered. A second stage is set after the completion of accretion and metal fractions modelled are around 0.001. The depletion in the mantle by such a two-stage process was calculated for seven involatile siderophile elements, characterized by different partitioning between liquid metal, solid metal, liquid silicate, and solid silicate. In the first stage, the mantle is depleted equally in all siderophile elements irrespective of differences in partition coefficients: Abundances are controlled solely by the mass balance of metal and silicate phases within the fractionation events. In the second stage, abundances of the moderately siderophile elements (W, Co, Ni) are not changed, while strongly siderophile elements (Re, Ir, Au) are further depleted. Calculated depletions for five of the seven elements agree well with the observed concentrations (Cl and Al normalized), as follows: W = 0.053, Co = 0.074, Re = 0.0047, Ir = 0.0062, and Au = 0.0056. Results for Ni = 0.028 and Mo = 0.0046 are by factor 2.5 and 5 below the observed concentrations, respectively. An implication of the model is that the (mainly convective) remixing flux within the silicate mantle during accretion was about ten times larger than the metal flux into the core. The silicate mantle is depleted in Pb by a factor 2.5 during core formation. The already large increase in μ value caused by volatilization of Pb is thus augmented. With the probable time scale of accretion taken as around 100 Ma, this means that the discrepancy between meteoritic and terrestrial lead isotope systematics need not be a serious paradox.