Studies of Vibrational Surface Modes. I. General Formulation
Academic Article

 Overview

 Identity

 Additional Document Info

 View All

Overview
abstract

A general formulation is given for studies of the vibrational properties of systems which have twodimensional periodicity and one or two surfaces. Although layered structures and other systems with interfaces fall within the scope of this formulation, the principal motivation is to provide a framework for calculating and interpreting vibrational surface properties. No assumption is made concerning crystal structure, surface orientation, the interaction between particles, or the number of particles per unit cell. Also, the treatment is applicable to reconstructed surfaces, surfaces with adsorbed impurity particles, etc., as well as unreconstructed clean surfaces, provided that the twodimensional periodicity is preserved. A discussion is given of the properties of the vibrational modes: In general, the displacement ellipse for a given mode can have any orientation. For surfaces with "axialinversion symmetry," however, one axis of the ellipse is always normal to the surface. If the surface has "complete reflection symmetry" with respect to a given plane, then for any twodimensional wave vector parallel to the plane the modes will separate into two classes: onethird of the modes will be pure shearhorizontal (SH) modes, and the other twothirds will be polarized strictly in the sagittal plane. It is possible for surface modes of one class to lie within the bulk subbands of the other class. If the crystal has either axialinversion symmetry or a threedimensional center of inversion, then the complex dynamical matrix can be reduced to a real, symmetric matrix of the same size. If both symmetries are present, as is the case for many surfaces of interest, then a further reduction is possible. Finally, notations are suggested for distinguishing twodimensional vectors and for labeling symmetry points in the twodimensional Brillouin zone associated with a surface. © 1971 The American Physical Society.
author list (cited authors)

Allen, R. E., Alldredge, G. P., & de Wette, F. W.
citation count
publication date
publisher
published in
Identity
Digital Object Identifier (DOI)
Additional Document Info
start page
end page
volume
issue