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 fu nctions of the distance to a defect as well as defect parameters (variation s of mass and force constants) are derived for an semi-infinite linear chai n 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 t he general case). The dependences of the conditions of formation and freque ncies of local vibrations and of the amplitudes of vibrations of these freq uencies (i.e., the form of their damping) on defect parameters are determin ed for different atoms of the system. Exact analytic expressions determinin g the threshold values of the defect parameters as functions of the distanc e between and impurity atom and the end of the chain are derived and analyz ed. (C) 1999 American Institute of Physics.