A molecular theory of the solid–liquid interface. II. Study of bcc crystal–melt interfaces

We have extended and applied our previously developed order parameter theory for the solid–liquid interface J. Chem. Phys. 74, 2559 (1981). We show how the differential equations for interfacial structure from our earlier work may be reformulated in terms of a variational principle and demonstrate that the quantity minimized gives the surface free energy. We point out a useful analogy between the order parameter equations and the equations of classical dynamics. We carry out explicit calculations of the interfacial structure of the bcc 100 and 111 crystal–melt interfaces and obtain estimates of the solid–liquid interfacial free energy for sodium and potassium; the free energies differ by less than 3% for the two different faces of each crystal. Our calculations suggest the existence of a ’’structured liquid’’ region in the interface, characterized by a liquidlike average density, but solidlike lattice ordering. The interfacial transition zone is quite broad, 16–20 Å in width and comprising 10–15 layers. We compare our results to computer simulation data and discuss their implications for microscopic mechanisms of crystal nucleation and growth from the melt.