Vibrations of Glasslike Disordered Systems. I. Diatomic Chains in Two Dimensions

A computer program has been written to generate disordered, two-dimensional chains of randomly oriented B–A–B V-shaped units with a Gaussian distribution of bond angles between successive units. The radial distribution function of the system shows it to be essentially vitreous in that it exhibits only short-range order. The equations of motion are derived using a simplified valence force potential function, and the distribution of squared normal mode frequencies is obtained using the negative eigenvalue theorem. The frequency spectra are discussed in terms of the ordered chain in two dimensions and the glasslike disordered chain in one dimension. The existence of a band gap is confirmed, but the size and position are complicated by the disorder of the system, as is the over-all shape of the spectrum. A feature in the spectra, near the LO zone-edge frequency of the ordered chain, is found to be the result of wavelength-dependent coupling between “transverse” and “longitudinal” vibrations. The more general results of the present calculations appear applicable to three-dimensional models.