  The growth history of the inner core is inherently linked to the thermal
history of the Earth. The crystallization of the inner core may have been
delayed by supercooling, and went through an initial phase of fast growth after
the nucleation barrier has been passed, but so far no evidence or constraint
has been proposed to time this possible event. With two-phase flow dynamics, we
explore the effect of different growth scenarios for the inner core to
determine their effects on its liquid fraction structure. Seismic observations
on the melt fraction inside the inner core at present limit the porosity to a
maximum of 10% of liquid. Our model provides constraints for the delay in
nucleation compared to the time where the first crystal may have started to
nucleate, and we find that the supercooling cannot have exceeded 100K.
