Local elastic constants for the Al(001) surface

Restoring forces have been calculated for displacements of a single surface atom of a five-layer Al(001) film using the first-principles scattering-theory method and the local-density-functional approximation. For displacement along the surface normal, the calculated force constant is $k_{\mathrm{zz}}$=-0.88 eV/${\mathrm{bohr}}^2$, while for motion in the surface layer along an Al-Al bond it is $k_{\mathrm{xx}}$=-0.94 eV/${\mathrm{bohr}}^2$. As one would expect, these results are in approximate agreement with corresponding force constants calculated by Ho and Bohnen for periodic disturbances of the same surface.