Phonon Inelastic Scattering

Abstract

The quantum state of the motion of atoms within a solid with translational symmetry can be described by the phonon dispersion relation and the phonon density of states. At the surface the conditions of motion for the atoms are changed with respect to the bulk. The symmetry is reduced at the surface and the forces acting on the atoms are changed compared to the bulk. Due to these differences phonons localized at the surface (surface phonons) may exist which are not allowed in the bulk. Calculations by de Wette and Benedek revealed discrete phonon modes localized at the surface with dispersion relations in some cases separated from the broad bands of surface projected bulk dispersion curves. Some atomic motions which are inhibited in the bulk for symmetry reasons become possible at the surface by symmetry reduction [11.1,2]. Phonons behave like quasiparticles, characterized by energy and a vector very similar to the momentum vector called quasimomentum. The phonon energy shows a periodic dependence on quasimomemtum for crystals. This is a geometric property, independent of the interaction forces between the atoms and without the need to specify what kind of motion is described by the phonon.