A search for high frequency vibrational modes at a stepped surface

In this paper we present a theory of the vibrations of atoms in the vicinity of a stepped surface on a Bravais crystal. The static relaxations in the positions of the atoms in the crystal are determined, and the atomic force constants are then calculated in the relaxed atomic configuration. The general theory is applied to a simple stepped surface, and the local phonon density of states is carried out for atoms at several points on the stepped surface by the real space continued fraction recursion method. No evidence is found for high frequency surface phonons.