Can homogeneous nucleation resolve the inner core nucleation paradox?

The formation of Earth's solid inner core is thought to mark a profound change in the evolution of the deep Earth and the power that is available to generate the geomagnetic field. Previous studies generally find that the inner core nucleated around 0.5–1 billion years ago, but neglect the fact that homogeneous liquids must be cooled far below their melting point in order for solids to form spontaneously. The classical theory of nucleation predicts that the core must be undercooled by several hundred K, which is incompatible with estimates of the core's present-day temperature. This “inner core nucleation paradox” therefore asserts that the present inner core should not have formed, leaving a significant gap in our understanding of deep Earth evolution. In this paper we explore the nucleation process in as yet untested iron-rich systems which may comprise the Earth's early core. We find that 1 mol.% Si and S increase the supercooling required to freeze the inner core compared to pure iron by 400 K and 1000 K respectively. 10 mol.% O reduces the required inner core nucleation supercooling to 730 K and 3 mol.% C to only 612 K, which is close to resolving the paradox but still requires that the inner core formed recently.