Randomness-Induced Redistribution of Vibrational Frequencies in Amorphous Solids

TL;DR

This paper investigates how different types of disorder in amorphous solids affect their vibrational density of states, challenging the universality of the Boson Peak and clarifying the role of various disorder types.

Contribution

It distinguishes the effects of interaction, positional, and coordination disorder on vibrational properties, providing a clearer understanding of frequency softening in amorphous materials.

Findings

Disorder types have distinct impacts on vibrational density of states.

The Boson Peak is not a universal feature of amorphous solids.

Disorder influences elastic moduli and frequency softening in complex ways.

Abstract

Much of the discussion in the literature of the low frequency part of the density of states of amorphous solids was dominated for years by comparing measured or simulated density of states to the classical Debye model. Since this model is hardly appropriate for the materials at hand, this created some amount of confusion regarding the existence and universality of the so- called ``Boson Peak'' which results from such comparisons. We propose that one should pay attention to the different roles played by different aspects of disorder, the first being disorder in the interaction strengths, the second positional disorder, and the third coordination disorder. These have different effects on the low-frequency part of the density of states. We examine the density of states of a number of tractable models in one and two dimensions, and reach a clearer picture of the softening and redistribution of frequencies in such materials. We discuss the effects of disorder on the elastic moduli and the relation of the latter to frequency softening, reaching the final conclusion that the Boson peak is not universal at all.