Abstract
The vibrational modes of an isotopic, disordered binary chain in harmonic approximation including next-nearest neighbour interaction have been studied. The chain and the nearest-neighbour force constant λ are taken to be the same as those chosen by Dean and Bacon to facilitate comparison. The modes at intermediate and high frequencies though remaining localized show a tendency to spread out which increases with increasing next-nearest-neighbour force constant μ. This tendency is particularly marked at intermediate frequencies. The localized modes of the binary chain are found to be directly related to the clusters of light atoms appearing in the chain. To determine the effect of neighbours more distant than the next-nearest, harmonic forces due to all neighbours were introduced. The force constant due to the kth neighbour was assumed to be λ 2 k−1 . The intermediate- and and high-frequency modes continue to be localized in this long-range interaction.
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