Nucleation in liquid

Crystallization of liquid to solid is initiated by cooling of the melt.

In this case, from the Clausius-Clapeyron relation we can write,

where is defined as, ; ratio of liquid to solid equilibrium vapor pressure.

and are a corresponding temperature (in units of kelvins or other absolute temperature units) and equilibrium vapor pressure of the liquid

and are the corresponding temperature and pressure of the solid at another point

is the molar enthalpy of vaporization

is the universal gas constant

This is valid for , which indicates that subcooling is needed.

At equilibrium we can write,

(heat of fusion) or, molar enthalpy of vaporization.

Then we can get,

where represents the degree of sub cooling, is heat of fusion.