An asymmetric double-well potential model for structural relaxation processes in amorphous materials

Abstract

Peaks in the ultrasonic attenuation observed in amorphous materials are almost always explained in terms of a classical, thermally activated, structural relaxation process represented by a symmetric double-well potential with a broad distribution of barrier heights. This model suffers from two drawbacks: a low barrier cut-off is required to produce a peak in the attenuation and the magnitude of the attenuation does not scale with the frequency of the acoustic waves, contrary to experimental evidence. This paper presents a model based on an asymmetric double-well potential having distributions of both the barrier height g(V) and the asymmetry f(Δ). Such a model is justified by the random local environments in an amorphous material, and has the advantage that no low barrier cut-off is required, in contrast with the symmetric double-well model. To illustrate the predictions of the model specific forms are assumed for the distribution functions: f(Δ) is taken as constant (valid for temperatures well below the glass transition temperature) and g(V) is chosen as 1/V 0 exp (– V/V 0), where V 0 is of order the glass transition, in order to include the expected high-energy cut-off. The predictions of the model agree well with both the acoustic attenuation and velocity variation at low temperatures as well as with recent experimental data on Raman scattering in vitreous silica, although the scaling with frequency is still not exact. A discussion of the breakdown of the classical model at low temperatures, where quantum effects become important, is also included.