Heterogeneous shear elasticity of glasses: the origin of the boson peak

Abstract

The local elasticity of glasses is known to be inhomogeneous on a microscopic scale compared to that of crystalline materials. Their vibrational spectrum strongly deviates from that expected from Debye's elasticity theory: The density of states deviates from Debye's law, the sound velocity shows a negative dispersion in the boson-peak frequency regime and there is a strong increase of the sound attenuation near the boson-peak frequency. By comparing a mean-field theory of shear-elastic heterogeneity with a large-scale simulation of a soft-sphere glass we demonstrate that the observed anomalies in glasses are caused by elastic heterogeneity. By observing that the macroscopic bulk modulus is frequency independent we show that the boson-peak-related vibrational anomalies are predominantly due to the spatially fluctuating microscopic shear stresses. It is demonstrated that the boson-peak arises from the steep increase of the sound attenuation at a frequency which marks the transition from wave-like excitations to disorder-dominated ones.

Dependence of the atomic level Green-Kubo stress correlation function on wavevector and frequency: Molecular dynamics results from a model liquid

“…These considerations demonstrate that the atomic level sscf can be used to study how lifetimes and ranges of propagation of stress waves depend on their frequency and wavevector. It was also demonstrated that the crossover from quasilocalized to propagating behavior occurs at the frequencies usually associated with the Boson peak, confirming previous results [44][45][46][47]. We found that the ranges of propagation of the shear stress waves for frequencies less than half of the Einstein frequency extend well beyond the nearest neighbor shell.…”

“…This increase correlates with the significant increase in the value of low-frequency viscosity. Our data also show that the change from quasilocalized to propagating behavior happens in the range of frequencies associated with the Boson peak, as expected [44][45][46][47].…”

Stress-Induced Modification of the Boson Peak Scaling Behavior

“…This anomalous feature appears in the signal detected by several techniques, such as inelastic neutron scattering [1], calorimetry [2], nuclear inelastic scattering [3,4], Mössbauer [5], Raman [6] and hyperRaman spectroscopy [7,8]. Despite the long-standing interest in this characteristic feature, its origin still re- mains a source of controversy [9][10][11][12][13][14][15][16].…”

Low-frequency Raman scattering in binary silicate glass: Boson peak frequency and its general expression

“…31),32) Although the frequency of the boson peak was recently suggested to be independent of the bulk modulus on the basis of a simulation using mean field theory, 8) the relationship between the boson peak and bulk modulus has not been experimentally investigated. Therefore, it might fruitful for future studies to experimentally elucidate whether the bulk modulus is linked to the boson peak.…”