On crystallization at the inner core boundary

We made a linear stability analysis of a unidirectionally advancing solid-liquid interface under the ICB conditions. Several values of the liquidus slope as a function of the concentration of light material (mC) were used for the stability analysis. It was confirmed that supercooling and stability may coexist if |mC| is low enough, although too low to be realistic. The estimated amount of supercooling in the layer is of order 0.1 K, and this provides an estimate of the size and population of solid particles in the slurry layer. However, even if |mC| were small enough, the existence of a slurry layer at the ICB would be unlikely due to (i) the difficulty of continuously supplying enough nuclei in the layer and (ii) the Rayleigh-Taylor instability due to the compositional buoyancy. It is, therefore, most probable that a mushy layer exists at the ICB.