A one order parameter theory for the fluid–solid interface

Abstract
A single order parameter theory for the interface between the flat surface of a single crystal in equilibrium with its melt is developed. Starting with the expression for the free energy as a functional of the nonuniform density, approximations are made which lead to a van der Waals-like formula for the free energy in terms of the order parameter. Expressions for the density profile, interface width, and surface free energy which take into account the crystal structure are derived. Comparison of the theory is made to molecular dynamics simulations.