Lattice vibrations of one-dimensional disordered systems

Abstract

Abstract The study of the effects of defects on the vibrational properties of solids is almost as old as the study of lattice dynamics in crystals. In fact, the effect of certain kinds of defects on the normal–mode vibrational frequencies of a system of particles was first investigated theoretically in the 1890s by Lord Rayleigh. Even earlier, the result that a light atom in a monatomic linear chain gives rise to a nonpropagating mode of vibration was contained in the work of Sir William Rowan Hamilton published in 1841. However, because of the simplifying feature in the geometry of the crystalline solids, elegant theorems were developed so that the studies of normal modes and thermodynamic properties of solids with periodic structures soon became the main stream of research in lattice dynamics. On the other hand, the importance of understanding the dynamic properties of disordered systems is underscored by the fact that the materials we deal with d o not have the simplicity and regularity found in the ph...