Extensive numerical and analytic studies of vibrational spectra, normal modes, thermodynamic properties, and dynamical properties of harmonic systems with varying degrees of substitutional disorder have been made. The effects on observable properties 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. Calculations in two and three dimensions have been limited to arrays of approximately 1000 atoms. Varying composition, mass ratio, and order affect the spectra in two and three dimensions in ways analogous to those effected in the linear chain. A physical interpretation of the complex nature of the disordered spectrum is given. The effects of disorder on the dynamics of binary disordered harmonic chains have been studied and have been found to be quite pronounced --Abstract, page ii
