Theoretical analysis demonstrates spatial localization of lattice modes in disordered atomic chains, indicating how structural disorder alters vibrational spectra.
Monatomic and alternating diatomic chains, with nearest neighbour harmonic interactions, are considered; in each case the force constants are governed by a probability distribution function which is continuous and bounded in a well-defined region and zero elsewhere. It is shown that the lattice modes are, in general, spatially localized. In the case of the diatomic chain the condition for a band gap is derived and the positions of the spectral branches are found. Spectra are calculated explicitly for monatomic and diatomic chains of a certain class, and typical displacement eigenvectors for the monatomic chain are depicted.
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P. Dean (1964) studied this question.
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