Vibration Frequency Spectra of Disordered Lattices. I. Moments of the Spectra for Disordered Linear Chains

Abstract

By using the theory of random walks on lattices, a combinatorial expression has been obtained for the even moments of the vibrational frequency spectrum of a randomly disordered, two-component, isotopic linear chain as functions of the concentrations of the two kinds of particles and of their mass ratio. Expressions for the even moments up to ${\ensuremath{\mu}}_{20}$ are presented.