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Localized Vibrational Modes at Plane Faces of Defects in Crystal Lattices
Author(s) -
Lengeler B.,
Ludwig W.
Publication year - 1964
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.19640070211
Subject(s) - limiting , impurity , lattice (music) , condensed matter physics , lattice plane , rayleigh scattering , physics , simple cubic lattice , vibration , rayleigh wave , plane (geometry) , molecular physics , optics , diffraction , surface wave , quantum mechanics , geometry , mathematics , mechanical engineering , statistics , reciprocal lattice , acoustics , monte carlo method , engineering
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.