Chapter 3 Unusual anharmonic local mode systems

Abstract

Publisher Summary Early far infrared measurements with grating instruments on the low temperature properties of defects in alkali halides produced a variety of sharp features associated with local modes, gap modes, and resonant modes. The loss of periodicity in defect crystals lead to localized vibrational phenomena. The standard description of the dynamics of defect-free periodic lattices in terms of plane wave phonons is so deeply ingrained that it was surprising to many researchers that the presence of strong quartic anharmonicity in perfect lattices can also lead to localized vibrational modes, called “intrinsic localized modes” (ILMs). These papers studied the classical vibrational dynamics of a simple one-dimensional monatomic chain of particles interacting via nearest-neighbor harmonic and quartic anharmonic springs, and they used a rotating wave approximation (RWA), in which just one frequency component was kept in the time dependence. For the case of sufficiently strong positive quartic anharmonicity, it was found that the lattice could sustain stationary localized vibrations having the approximate mode pattern. This pattern is odd under reflection in the central site and is optic mode-like, in that adjacent particles move out of phase. As with all nonlinear vibrations, the ILM frequencies are amplitude dependent. The ILMs can be centered on any lattice site, giving rise to configurational entropy analogous to that for vacancies, and some thermodynamic ramifications, along with speculations about the possible presence of ILMs in strongly anharmonic solids, such as solid He and ferroelectrics.