Isotopic constraints on the age of the Earth’s core: Mutual consistency of the Hf-W and U-Pb systems

Abstract

The estimation of the time of Earth’s core formation on the basis of isotopic systems with short-lived and long-lived parent nuclides gives significantly different results. Isotopic data for the 182Hf-182W system with a 182Hf half-life of approximately 9 Myr can be interpreted in such a way that the core was formed 34 Myr after the origin of the solar system assuming complete core-mantle equilibrium. Similar estimates on the basis of the U-Pb isotopic system suggest a significantly longer mean time of core formation of approximately 120 Myr. If the Earth’s core were formed instantaneously, both isotopic systems would have shown identical values corresponding to the true age. The discrepancy between the U-Pb and Hf-W systems can be resolved assuming prolonged differentiation of prototerrestrial material into silicate and metallic phases, which occurred not simultaneously and uniformly in different parts of the mantle. This resulted in the isotopic heterogeneity of the mantle, and its subsequent isotopic homogenization occurred slowly. Under such conditions, the mean isotopic compositions of W and Pb in the mantle do not correspond to the mean time of the separation of silicate and metallic phases. This is related to the fact that the exponential function of radioactive decay is strongly nonlinear at high values of the argument, and its mean value does not correspond to the mean value of the function. There are compelling reasons to believe that the early mantle was heterogeneous with respect to W isotopic composition and was subsequently homogenized by convective mixing. This follows from the fact that the lifetime of isotopic heterogeneities in the mantle is close to 1.8 Gyr for various long-lived isotopic systems. There is also no equilibrium between the mantle and the core with respect to the contents of siderophile elements. Because of this, the mean isotopic ratios of W and Pb cannot be used for the direct computation of the time of metal-silicate differentiation in the Earth. Such estimation requires more sophisticated models accounting for the duration of the differentiation process using several isotope pairs. Given the prolonged core formation, which has probably continued up to now, the question about its age becomes ambiguous, and only the most probable growth rate of the core can be estimated. The combined use of the U-Pb and Hf-W systems constrains the time of formation of 90% of the core mass between 0.12 and 2.7 billion years. These model estimates could have been realistic under the condition of complete disequilibrium between the silicate and metallic phases, which is as improbable as the suggestion of complete equilibrium between them on the whole Earth scale.