Localized Vibrational Modes at Plane Faces of Defects in Crystal Lattices

The localized modes of vibrations are dicussed for the planes (001), (011), and (111) of impurity atoms in an infinitely extended simple cubic lattice. The frequencies show a band structure according to the translational invariance of the lattice in the impurity plane. It is found that optical and accoustical bands exist, the former lying completely, the latter only partially in the band of the unperturbed lattice. A free surface can be regarded as a special case of these models. Choosing appropriate coupling parameters one obtains localized surface states which have to coincide with the well‐known Rayleigh waves in the limiting case of long waves.