Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling

Area of Science:

• Condensed Matter Physics
• Materials Science
• Acoustics

Background:

• Glassy disorder significantly impacts long-wavelength phonon attenuation, a key factor in glass anomalies.
• Understanding the wavenumber (k) dependence of attenuation rate (Γ(k)) in macroscopic glasses is crucial but incomplete.
• Previous work identified a crossover wavenumber (k†) above which phonons are not quantized into bands.

Purpose of the Study:

• To elucidate the scaling of phonon attenuation rate Γ(k) with wavenumber k in finite-size glasses.
• To investigate the role of quasilocalized nonphononic excitations in phonon attenuation.
• To reconcile theoretical predictions with experimental observations of glass anomalies.

Main Methods:

• Combined theoretical analysis with extensive computer simulations.
• Analyzed phonon attenuation scaling in finite-size glasses across different wavenumber regimes.
• Investigated the influence of quasilocalized nonphononic excitations on attenuation.

Main Results:

• Macroscopic low-frequency behavior emerges in finite-size glasses above the crossover wavenumber k†.
• For k < k†, finite-size effects dominate, described by disordered phonon band theory.
• For k > k†, attenuation is influenced by quasilocalized nonphononic excitations, exhibiting Rayleigh scaling (∼k^(d+1)) at low densities and generalized-Rayleigh scaling (∼k^(d+1) log(k0/k)) at higher densities.

Conclusions:

• Finite-size glasses exhibit a crossover in phonon attenuation scaling from Rayleigh to generalized-Rayleigh regimes.
• Macroscopic glasses with suppressed nonphononic excitations show Rayleigh scaling at low k, transitioning to generalized-Rayleigh scaling.
• The findings provide a unified framework for understanding phonon attenuation in disordered materials.