On the nature of vibrations in diatomic lattices

Abstract

The lattice dynamics of a one-dimensional diatomic lattice with nearest-neighbour interactions is examined with mathematical techniques involving setting up and solving difference equations. The method gives the exact sets of analytical solutions for the normal modes of vibration. The theory of localised vibrational modes due to local imperfection is developed as a characteristic value problem. The approach seems to have advantages over previous methods used to solve local defect problems in lattices.