Sound attenuation derived from quenched disorder in solids

TL;DR

This paper analytically and numerically investigates how quenched disorder in spring constants of solids affects sound attenuation, revealing a linear growth of damping with momentum and a characteristic vibrational peak linked to the boson peak phenomenon.

Contribution

It provides an analytical evaluation of the dynamical structure factor in disordered solids with quenched spring constant disorder, connecting vibrational features to the boson peak.

Findings

Damping constant grows linearly with momentum q.

Quenched disorder produces a vibrational density of states peak.

The vibrational peak relates to the boson peak in disordered solids.

Abstract

In scattering experiments, the dynamical structure factor (DSF) characterizes inter-particle correlations and their time evolution. We analytically evaluated the DSF of disordered solids with disorder in the spring constant, by averaging over quenched disorder in the values of lattice bond strength, along the acoustic branch. The width of the resulting acoustic excitation peak is treated as the effective damping constant $\Gamma(q)$, which we found to grow linearly with exchanged momentum $q$. This is verified by numerically calculating a model system consisting of harmonic linear chains with disorder in spring constant. We also found that the quenched averaging of the vibrational density of states produces a characteristic peak at a frequency related to the average acoustic resonance. Such a peak (the excess over Debye law) may be related to the "boson peak" frequently discussed in disordered solids, in our case explicitly arising from the quenched disorder in the distribution of spring constants.