The starting point for study of the rate at which a solidification front advances is to examine the free energy change accompanying the phase transformations. Energy will be released (available to drive the advance) if the free energy of the solid is lower than that of the liquid. This requires that the temperature of the interface, T*, be below the value at which the two phases have the same free energy. The interface is then said to be undercooled (or supercooled).

Click on the solid and liquid labels to show free energy curves for a pure material with an equilibrium fusion temperature of T_f.

An undercooling of DT generates a driving force for solidification of DG_f.

In order to relate this to the rate at which molecules add to the solid, information is needed about the atomic structure of the interface. This is best approached by focusing on the entropy of fusion.