The Frequency Spectrum of a Diatomic Linear Chain with Random Isotopic Impurities

Abstract

<p> The frequency spectrum of a diatomic linear chain with randomly placed isotopic impurities is calculated using a Green's function formalism. The calculation follows a method devised by Langer, and yields the density of states exactly to first order in the concentration of impurities. It is found that polarisation mixing causes no problem and the results are analogous to those of Langer for the monatomic chain. Results are presented for various ratios of impurity mass to replaced mass, for which impurity bands are found above the optical band and in the gap between the accoustic and optical bands. A self consistent calculation is also discussed.</p>