Neutron scattering investigations of the boson peak

Buchenau Buchenau

doi:10.5488/cmp.22.43601

Abstract

Inelastic neutron scattering is not only capable of determining a generalized vibrational density of states around the boson peak of a glass, but can also be used to get information on the eigenvectors. The eigenvectors determine the dynamic structure factor, which is $Q^2S(Q)$ ($Q$ wavevector) for long wavelength sound waves. This enables the determination of the sound wave fraction below and at the boson peak, done for SiO$_2$, B$_2$O$_3$, polybutadiene and amorphous germanium. The temperature dependence of the boson peak in silica and glycerol is shown. X-ray Brillouin scattering data show that the damping of the longitudinal sound waves in silica and glycerol follows the soft potential model $\omega^4$ prediction in the limit of low frequency.

Highlights

An important part of Giancarlo Ruocco’s scientific work was devoted to the riddle of the low frequency vibrations in glasses
Glasses have the low frequency longitudinal and transverse sound waves which one expects in an elastic solid on the basis of the Debye model, and additional excitations, tunneling states and soft vibrations, which are clearly visible in the heat capacity, the thermal conductivity and the sound absorption at low temperatures [1]
The theoretical basis for neutron scattering studies of the boson peak was supplied by Carpenter and Pelizzari [4], who treated the scattering from low frequency sound waves in an elastically isotropic solid

Summary

Introduction

An important part of Giancarlo Ruocco’s scientific work was devoted to the riddle of the low frequency vibrations in glasses. In scattering techniques (Raman, neutron and x-ray scattering), the additional soft vibrations appear as a broad peak between the frequency zero and the lowest Van Hove singularity of the corresponding crystal. At lower temperatures, it shows the linear temperature increase expected for harmonic vibrations, so it got the name boson peak. Neutrons are a good tool to study the vibrational density of states of a glass and are capable of providing information on the mode eigenvectors If it comes to Brillouin scattering studies of the longitudinal sound absorption in the THz range, x-rays are much better than neutrons, because their energy loss or gain in the Brillouin scattering process is negligible.

Neutron scattering at the boson peak

Low frequency limit of neutron and x-ray Brillouin data

Conclusions