The Effects of Next-Nearest-Neighbor Interactions on the Orientation   Dependence of Step Stiffness: Reconciling Theory with Experiment for Cu(001)
  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). 
T. J. Stasevich, T. L. Einstein, R. K. P. Zia, M. Giesen, H. Ibach, F.   Szalma