A theoretical study of the hard sphere fluid–solid interface

Abstract

We investigate in detail the fluid–solid interfaces of hard spheres using the density functional formalism of inhomogeneous systems. The interfacial profiles and surface free energy γ are determined variationally but we avoid the usual square-gradient approximation (SGA) for the nonlocal parts of the free energy. Our findings suggest a narrow interface of 3–4 σ (σ=a hard-sphere diameter) and an upper bound to γ of about 1.7 kBT/σ2. For the low-order crystal planes, γ is almost independent of the crystal orientation, varying less than a few tenths of a percent between the [111] and [110] planes. Our results generally agree with the SGA when a single, hyperbolic-tangent description is used for the inhomogeneous density. However, more realistic variations of the interfacial profiles produce greater disparity between the two methods. We discuss ways in which the SGA might be improved to account for these differences.