A molecular theory of crystal nucleation from the melt

We construct a molecular theory for the homogeneous nucleation of crystals from pure liquids by combining an order parameter theory of freezing with a square gradient approximation for the nonlocal dependence of free energy on density. We show the results of our theory for the free energy, radius, and shape of crystal nuclei as a function of supercooling, and compare with the conventional nucleation theory based on the capillarity approximation. We argue that the simple picture given by the conventional approach is qualitatively reasonable, although calculated values of the liquid–solid surface free energy may be inaccurate. We point out some of the limitations of our approach and stress the need for additional structural data on supercooled liquids.