Lead isotope evolution during the multi-stage core formation

The evolution of the U-Pb decay system is determined by their initial isotopic composition in the proto-Earth and the subsequent global differentiation. The differentiation is highly complicated because of large-scale evaporation and multi-stage core formation in Earth accretion. We statistically rebuild the accretional history of Earth using a series of N-body simulations. This provides us with an estimation of the amount of silicate melting and thus temperature and pressure at the bottom of the magma oceans driven by continuous planetesimal impacts. We further assumed different evolutionary paths of the redox state and found a reduced process from an oxidized state consistent with the current value of Pb content and μ value (238U/204Pb) in the bulk silicate Earth. Meanwhile, the fraction of the impactor's core that participates in the re-equilibration is around 0.2–0.7. Our model predicts the final μ value equals the observed value, 8.25, regardless of the minor contribution of the late veneer (0.2). The evolution of μ determines the growth rate of radiogenic Pb isotopes. The episodic increase of μ in multi-stage core formation accelerates the growth of radiogenic Pb isotopes (206Pb and 207Pb) and finally causes a slight deviation of the composition of Pb isotopes (206Pb/204Pb and 207Pb/204Pb) to the right of 4.567-Ga Earth Geochron. A multi-stage evolution model for U–Pb system can explain the modern terrestrial μ value, but has little influence on the puzzle of “the first Pb paradox”.