High-frequency vibrational modes at stepped Pt(111) surfaces

We show that vibrational modes with frequencies above the maximum in the bulk can occur at the steps of the Pt(332) or $6\left(111\right)\mathrm{}\times \left(11\mathrm{}\overline{1}\right)$ surface, as observed by Ibach and Bruchmann, if the largest force constants are increased by ∼ 30—40% at the steps. The calculations are done by applying the recursion method within clusters of thousands of atoms, with a rotationally invariant first- and second-neighbor bond-angle model for the interatomic forces.