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Effect of atomic force constant changes on the localized vibrational modes — a perturbation approach
Author(s) -
Croitoru M.,
Grecu D.
Publication year - 1970
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.19700420114
Subject(s) - force constant , perturbation (astronomy) , formalism (music) , lattice (music) , vibration , physics , normal mode , impurity , simple cubic lattice , lattice constant , condensed matter physics , classical mechanics , quantum mechanics , mathematics , molecule , art , musical , statistics , acoustics , diffraction , monte carlo method , visual arts
A general formalism is developed to treat the influence of small perturbations on localized vibration modes. The method is applied to cubic crystals, the perturbation being attributed to the atomic force constant changes between a substitutional impurity and its nearest neighbours. In the first order, the frequencies of the localized modes are obtained from simple equations involving only a few perfect‐lattice Green's functions. For frequencies very high above the perfect‐lattice spectrum these equations are solved leading to asymptotic results in agreement with those of other authors. A comparison with the exact result for a simple cubic lattice is drawn too.