The Effects of Next-Nearest-Neighbor Interactions on the Orientation Dependence of Step Stiffness: Reconciling Theory with Experiment for Cu(001)

TL;DR

This paper investigates how next-nearest-neighbor interactions influence the orientation-dependent step stiffness on Cu(001), reconciling theoretical models with experimental observations by extending the SOS approximation.

Contribution

It introduces a calculation incorporating next-nearest-neighbor interactions into the SOS model, improving agreement with experimental data for Cu(001).

Findings

Inclusion of next-nearest-neighbor interactions improves model accuracy.

The effect of trio interactions can be incorporated via modified pairwise energies.

The model reduces to a simple expression at low temperatures.

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).