A molecular theory for the solid–liquid interface

We present an order parameter theory of the solid–liquid interface which uses structural information about the uniform liquid phase. The order parameters are the coefficients of a Fourier expansion of the nonuniform density in terms of reciprocal lattice vectors characteristic of the uniform solid phase. The theory provides explicit formulas for the interfacial density profile and the surface free energy. Connection is made with recent theories of freezing and of the liquid–vapor interface. Two special cases of particular interest are considered: the flat interface, for which numerical simulations have been attempted, and the spherical ball, which is important in theories of liquid–solid nucleation.