Phonon Scattering in Disordered Systems

Abstract

It is well known that glasses, which are completely disordered homogeneous solids, display acoustic and thermal properties at low temperature which deviate markedly from those of crystals [1]. This is especially (but not exclusively) true below 1 K, and these differences are explained by the presence of low-lying excitations, described as “Two-Level Systems” (TLS) with a constant energy density of states. The TLS are supposed to be caused by tunnelling motion of a group of atoms in a double-well asymmetric potential [2]. The acoustic experiments have shown that long wavelength phonons exist in a large range of frequency, and are strongly scattered by TLS via resonant and relaxation processes [1]. It has also been established that phonons are responsible for heat transport [3], the resonant scattering by TLS leading to the T² dependence of the thermal conductivity K(T) below 1 K. The tunneling model gives a satisfactory phenomenological description of the acoustic and thermal anomalies below 1 K, but the microscopic nature of the TLS is still unknown. On the other hand, there is no definitively accepted model to describe the anomalies above 1 K, especially the plateau of K(T) around 10 K. In view of these two unresolved problems, a great deal of work has been done during the last years to search for “glassy” properties either in “model” systems where the tunneling units are known or in partly disordered systems.