A METHOD FOR CHARACTERIZING THE LOCALIZED DYNAMICS OF BOUNDARY DEFECTS IN CRYSTALLINE SYSTEMS

A bound semi-infinite two-dimensional crystalline system is considered with an isolated inhomogeneity in the form of a semi-infinite linear atomic chain differing in elastic constants from the rest of the syste m. This is a precursor model to develop a method for determining the f requencies of the localized vibrational modes on the extremity of isol ated inhomogeneities that break the translation symmetry in two direct ions in boundaries. To treat both the localized states and diffraction problems, the mathematical framework of the matching method is genera lized from one to two dimensions. Only the localized modes analysis is presented. This formalism leads to a complete representation of the t wo-dimensional evanescent vibrational field in the neighbourhood of an isolated inhomogeneity, It is an analytical approach that is independ ent of the nanostructure of the isolated inhomogeneity, which makes it easy to extend to a variety of real problems. Numerical results for t he frequencies of the modes localized on the extremity of the semi-inf inite chain in the boundary are given for a case study. The method can be applied systematically to analyze the dynamics of extended surface defects such as steps, ridges or lines of substitute atoms.