Ioffe-Regel criterion and viscoelastic properties of amorphous solids

TL;DR

This paper investigates how viscoelastic effects influence vibrational damping in amorphous solids, revealing the role of a barrier near the Ioffe-Regel frequency and introducing a stable numerical method for parameter extraction.

Contribution

It introduces a new model describing vibrational relaxation in amorphous solids using a memory function and a stable numerical method based on Chebyshev expansion.

Findings

Viscoelastic effects significantly affect vibrational damping.

A barrier near the Ioffe-Regel frequency reduces vibrational decay.

A numerically stable method for parameter extraction is developed.

Abstract

We show that viscoelastic effects play a crucial role in the damping of vibrational modes in harmonic amorphous solids. The relaxation of a given plane wave is described by a memory function of a semi-infinite one-dimensions mass-spring chain. The initial vibrational energy spreads from the first site of the chain to infinity. In the beginning of the chain, there is a barrier, which significantly reduces the decay of vibrational energy below the Ioffe-Regel frequency. To obtain the parameters of the chain, we present a numerically stable method, based on the Chebyshev expansion of the local vibrational density of states.