On the atomic roughness of solid–vapor interfaces: Significance of many-body interactions

Abstract

It is traditionally assumed that the pair energies of atoms on the surface are site independent and equal to the pair energy in the bulk of the crystal (constant bond energy approach). We have assumed that the internal energy of an atom, ψ, depends nonlinearly on the number of nearest neighbors n in the form ψ(n)=−(an+bn2), where a and b are material constants that can be evaluated from experimentally determined heats of sublimation and energies of bulk vacancy formation. This simple approximation of the actual many-body interactions accommodates site-dependent pair energies. Based on this phenomenological ‘‘variable bond model’’ and the Bragg–Williams approximation, occupation fractions of an equilibrium surface are obtained in two-level and three-level models. These provide a criterion of surface roughness for specific orientations. Application of the criterion to copper, lead, and zinc yields good agreement with experimental observations of anisotropic melting, while the traditional constant bond approach fails. It is shown that in addition to these systems many other metals possess negative b values, i.e., exhibit ‘‘bond strengthening’’ on surfaces. Similar conditions are shown to exist in numerous ionic, covalent, and van der Waals solids. Hence, one must expect that constant bond models underestimate the surface roughness for a large group of materials.