Impurity-Induced Localized Modes of Lattice Vibration in a Diatomic Chain

Abstract

The normal modes of vibration and their associated frequencies are found for a diatomic chain containing an impurity of different mass and force constant than the atom which it replaces. Localized modes are found which have appreciable components only near the impurity and whose frequencies are displaced from the continua of the optical and acoustic bands into the forbidden gap or above the optical band. The number of localized modes, their general position (forbidden gap or above optical), and their symmetry (odd or even), engendered by any impurity are presented graphically. It is shown that when a strongly localized mode is present, other modes avoid the impurity.