---
abstract: 'Within the solid-on-solid (SOS) approximation, we carry out a calculation of the orientational dependence of the step stiffness on a square lattice with nearest and next-nearest neighbor interactions. At low temperature our result reduces to a simple, transparent expression. The effect of the strongest trio (three-site, non pairwise) interaction can easily be incorporated by modifying the interpretation of the two pairwise energies. The work is motivated by a calculation based on nearest neighbors that underestimates the stiffness by a factor of 4 in directions away from close-packed directions, and a subsequent estimate of the stiffness in the two high-symmetry directions alone that suggested that inclusion of next-nearest-neighbor attractions could fully explain the discrepancy. As in these earlier papers, the discussion focuses on Cu(001).'
author:
- 'T. J. Stasevich'
- 'T. L. Einstein'
- 'R. K. P. Zia'
- 'M. Giesen'
- 'H. Ibach'
- 'F. Szalma'
title: ' The Effects of Next-Nearest-Neighbor Interactions on the Orientation Dependence of Step Stiffness: Reconciling Theory with Experiment for Cu(001) '
---

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Introduction
============

At the nano-scale, steps play a crucial role in the dynamics of surfaces. Understanding step behavior is therefore essential before nano-structures can be self-assembled and controlled. In 