Acoustic attenuation in glasses and its relation with the boson peak

TL;DR

This paper applies a vibrational dynamics theory to disordered solids, explaining the wavevector dependence of Brillouin peaks and establishing a quantitative link between the boson peak and vibrational broadening, supported by experiments and simulations.

Contribution

It provides a theoretical framework connecting the boson peak with acoustic attenuation in glasses, supported by experimental and numerical validation.

Findings

Confirmed the $k^2$ dependence of $$ in glasses.

Derived a quantitative relation between the boson peak and vibrational broadening.

Supported the theory with experimental and simulation data.

Abstract

A theory for the vibrational dynamics in disordered solids [W. Schirmacher, Europhys. Lett. {\bf 73}, 892 (2006)], based on the random spatial variation of the shear modulus, has been applied to determine the wavevector ($k$) dependence of the Brillouin peak position ($\Omega_k)$ and width ($\Gamma_k$), as well as the density of vibrational states ($g(\omega)$), in disordered systems. As a result, we give a firm theoretical ground to the ubiquitous $k^2$ dependence of $\Gamma_k$ observed in glasses. Moreover, we derive a quantitative relation between the excess of the density of states (the boson peak) and $\Gamma_k$, two quantities that were not considered related before. The successful comparison of this relation with the outcome of experiments and numerical simulations gives further support to the theory.