A method for characterizing the localized dynamics of boundary defects in crystalline systems

Y. Pennec, A. Khater

    Research output: Contribution to journalArticle

    15 Citations (Scopus)


    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 system. This is a precursor model to develop a method for determining the frequencies of the localized vibrational modes on the extremity of isolated inhomogeneities that break the translation symmetry in two directions in boundaries. To treat both the localized states and diffraction problems, the mathematical framework of the matching method is generalized from one to two dimensions. Only the localized modes analysis is presented. This formalism leads to a complete representation of the two-dimensional evanescent vibrational field in the neighbourhood of an isolated inhomogeneity. It is an analytical approach that is independent of the nanosrructure of the isolated inhomogeneity, which makes it easy to extend to a variety of real problems. Numerical results for the frequencies of the modes localized on the extremity of the semi-infinite 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.

    Original languageEnglish
    Pages (from-to)L82-L88
    JournalSurface Science
    Issue number3
    Publication statusPublished - 10 Mar 1996


    ASJC Scopus subject areas

    • Condensed Matter Physics
    • Surfaces and Interfaces
    • Surfaces, Coatings and Films
    • Materials Chemistry

    Cite this