Extensive numerical and analytic studies of vibrational spectra and normal modes of harmonic systems with varying degrees of substitutional disorder have been made. The effects on frequencies and eigenvectors of random mixtures of two or more species of atoms with differing masses and differing couplings to nearest and next-nearest neighbors have been investigated. Using the IBM-7030 digital computer, spectra for linear chains of 100,000 atoms have been obtained. In order to keep machine running times less than 10 minutes, calculations in two and three dimen¬sions have been limited to arrays of approximately 1000 atoms. Particu¬lar emphasis is placed upon the properties of the vibrational spectra and localized modes of the two dimensional lattices. Varying composition, mass ratio, and order affect the spectra in two and three dimensions in ways analogous to those effected in the linear chain. Mention is made of possible means of verification of some qualitative features of our results.
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