Rigidity-based approach to the boson peak in amorphous solids: from sphere packing to amorphous silica

TL;DR

This paper explores the origin of the Boson Peak in amorphous solids, linking it to weak connectivity and rigidity, and demonstrates how these ideas explain vibrational properties in glasses like silica.

Contribution

It introduces a rigidity-based framework connecting the Boson Peak to network connectivity, extending previous theories to rigid covalent glasses and sphere packings.

Findings

Boson Peak arises from weak connectivity in amorphous solids.

In sphere packings, the peak shifts with pressure near jamming.

The approach explains vibrational spectra of amorphous silica.

Abstract

Glasses have a large excess of low-frequency vibrational modes in comparison with continuous elastic body, the so-called Boson Peak, which appears to correlate with several crucial properties of glasses, such as transport or fragility. I review recent results showing that the Boson Peak is a necessary consequence of the weak connectivity of the solid. I explain why in assemblies repulsive spheres the boson peak shifts up to zero frequency as the pressure is lowered toward the jamming threshold, and derive the corresponding exponent. I show how these ideas capture the main low-frequency features of the vibrational spectrum of amorphous silica. These results extend arguments of Phillips on the presence of floppy modes in under-constrained covalent networks to glasses where the covalent network is rigid, or when interactions are purely radial.