The effect of second neighbour interactions on the dynamics of a linear chain with impurities

Abstract

It is usual in lattice-dynamic models to consider nearest neighbour interactions only. Here we extend the range of interactions to second-neighbours also and study the consequent effects on the vibrational modes of a linear monatomic chain containing an impurity. It is shown that besides changes in the frequency spectrum, there may be significant changes in the very nature of the modes, whether localized or wave-like. In particular, it is shown that under suitable conditions there exist localized modes, in which the vibrational amplitude does not decrease monotonically with distance from the impurity site, but is an exponentially damped harmonic function of that distance. It is also shown that resonance scattering can take place if the impurity is sufficiently heavy, though there can be no resonance (in one-dimensional chains) if only nearest neighbour interactions are present.