(April 2018)
Using constraints from experiments, simulations, and theory, we show that spontaneous crystallization in a homogeneous liquid iron alloy at Earth‘s core pressures requires a critical supercooling of order 1000 K, which is too large to be a plausible mechanism for the origin of Earth‘s inner core. We consider mechanisms that can lower the nucleation barrier substantially. Each has caveats, yet the inner core exists: this is the nucleation paradox.