Orientation dependence of the stiffness of surface steps: an analysis based on anisotropic elasticity

Motivated by recent experimental work that shows that the orientation dependence of the stiffness of steps on Cu surfaces differs significantly from the predictions of Ising and solid-on-solid modes, we study the effect of elastic anisotropy on the stiffness of steps on (1 0 0), (1 1 0) and (1 1 1) surfaces of cubic materials. The contribution to the stiffness due to elastic relaxation is obtained from a regularized continuum model similar to the Peierls–Nabarro model, which is commonly used to study the energetics of dislocations in crystals. Our analysis shows that while the difference in the elastic self-energy of steps between the soft and hard orientations is only about 5 meV/Å, the corresponding difference in stiffness can be as large as 50–100 meV/Å. The latter estimate is found to compare favorably with the experimental data on Cu(0 0 1) surfaces.