Vibrations of two-dimensional disordered lattices

Abstract

Vibrational spectra are presented for the two-component disordered simple quadratic and honeycomb lattices. These spectra are complex in structure, containing numerous peaks associated with the localized vibrations of clusters of light atoms in predominantly heavy atom local environments. A theorem of Rosenstock & McGill (1962), on the ordering of the displacement eigenfunctions for one-dimensional chains with nearest-neighbour interactions, is generalized.