Localization of vibrations near impurity atoms in semi-infinite and infinite linear chains

Exact analytic expressions for local densities of atoms of the system as functions of the distance to a defect as well as defect parameters (variations of mass and force constants) are derived for an semi-infinite linear chain with an impurity at the end as well as for an infinite linear chain with an interstitial or substitutional impurity (a triatomic defect cluster in the general case). The dependences of the conditions of formation and frequencies of local vibrations and of the amplitudes of vibrations of these frequencies (i.e., the form of their damping) on defect parameters are determined for different atoms of the system. Exact analytic expressions determining the threshold values of the defect parameters as functions of the distance between and impurity atom and the end of the chain are derived and analyzed. (C) 1999 American Institute of Physics.