Vibrational Properties of a Clustered Linear Atomic Chain with Substitutional Impurities

  • M. I. Vasilevskiy
  • O. V. Baranova
Part of the NATO ASI Series book series (NSSB, volume 283)


Theoretical investigation of the lattice dynamics of media with substitutional impurities began with the pioneer work of I.M. Lifshitz (see [1]), but it still attracts a considerable amount of interest (see reviews in [2, 3]). The problem can be solved analytically in the 1D case in the low-concentration limit only, i.e. one can obtain the frequency of the local vibrational mode (in the light impurity case) and the broadening of this mode with increase of impurity concentration by means of perturbation theory. Three types of approach have been used for numerical calculation of the phonon density of states [2–4]:
  1. (i)

    the random-element isodisplacement and cluster isodisplacement (CI) methods, which are based on the solution of averaged equations of motion for some microclusters (MC) ;

  2. (ii)

    Green’s function methods, among which the coherent potential approximation is probably the best;

  3. (iii)

    supercell methods, which deal with direct diagonalization of the dynamical matrix.



Impurity Atom Pair Correlation Function Phonon Density Coherent Potential Approximation Substitutional Impurity 
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Copyright information

© Plenum Press, New York 1992

Authors and Affiliations

  • M. I. Vasilevskiy
    • 1
  • O. V. Baranova
    • 2
  1. 1.Department of PhysicsUniversity of EssexColchester, EssexUK
  2. 2.Faculty of Applied Physics and MicroelectronicsGorky State UniversityGorkyUSSR

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