Assessing the inner core nucleation paradox with atomic-scale simulations

We investigate the conditions required to freeze liquid iron and iron alloys near the centre of Earth's core. It is usually assumed that inner core growth begins once the ambient core temperature falls below the melting temperature of the iron alloy at Earth's centre; however, additional (under)cooling is required to overcome the energy barrier associated with creating a solid–liquid interface. Predictions based on Classical Nucleation Theory (CNT) have estimated a required undercooling of ∼1000 K, which cannot be reconciled with predicted core cooling rates of ∼100 K Gyr⁻¹. This apparent contradiction has been called the ‘inner core nucleation paradox’. Here we address three major uncertainties in the application of CNT to inner core nucleation using atomic-scale simulations. First, we simulate freezing in Fe and Fe–O liquids at core conditions to self-consistently constrain all parameters required by the CNT equations. Second, we test the basic validity of CNT by directly calculating the waiting time to observe freezing events in Fe and Fe–O liquids. Third, we investigate the influence of wave-like forcings applied to the atomic simulations, which have been suggested as a means to significantly reduce the energy barrier. Our results are consistent with CNT in the computationally accessible parameter regime, though error estimates on the waiting time can reach 50% of the measurement at the largest undercooling temperatures. Using CNT to extrapolate to inner core conditions yields estimated undercooling of 730±20 K for the pure iron system and 675±35 K for the Fe–O system. Forcings corresponding to large pressure variations of O(10) GPa reduce these values by ∼100 K. While our undercooling estimates are significantly lower than previous estimates they are not low enough to resolve the inner core nucleation paradox.