Landolt-Börnstein - Group III Condensed Matter

4.1.1.3.4 General remarques about surface force constants and surface modes of vibration

Abstract

This chapter discusses characterization of surface modes of vibration and general remarks about surface force constants and surface modes of vibration. The independent surface modes of vibration are characterized in part by the values of the wave vector k|| that lie in the first surface Brillouin zone (SBZ). Most of the materials discussed are associated with the face-centered cubic (fcc) Bravais lattice. For a pair of atoms at or near the surface, an element of the force constant matrix coupling these two atoms may or may not be the same as the corresponding element for a corresponding pair of atoms in the bulk of the crystal. Even if the elements are the same, the effective force constant describing the interaction of a surface atom with its neighbors is generally smaller than that for a bulk atom, because a surface atom interacts with fewer neighbors than does a bulk atom. In order to be a true localized mode, the surface mode frequency must lie in a frequency range that is forbidden for bulk mode frequencies, or in a frequency range such that the surface mode eigenvector is orthogonal to the eigenvectors of nearby bulk modes. Shear horizontal surface modes with a displacement vector parallel to the surface and perpendicular to k|| can also occur in this region. In many crystals there are gaps in the bulk mode spectrum lying above allowed regions of bulk modes and within which surface modes can occur.

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Title
4.1.1.3.4 General remarques about surface force constants and surface modes of vibration
Book Title
Electronic and Vibrational Properties
In
4.1.1.3 Microscopic approach to surface phonons
Book DOI
10.1007/b47750
Chapter DOI
10.1007/10086058_56
Part of
Landolt-Börnstein - Group III Condensed Matter
Volume
24B
Editors
  • G. Chiarotti
  • Authors
  • R. F. Wallis
  • S. Y. Tong
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