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Elastic moduli fluctuations predict wave attenuation rates in glasses.

Geert Kapteijns1, David Richard1, Eran Bouchbinder2

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|February 28, 2021
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This study clarifies how disorder affects elastic waves in glasses. Computer simulations confirm that wave attenuation scales with frequency, supporting Fluctuating Elasticity Theory (FET) and providing benchmarks for glass property analysis.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Computational Physics

Background:

  • Disorder-induced attenuation of elastic waves is crucial for the low-temperature properties of glasses.
  • Existing literature presents conflicting theories on wave attenuation scaling and its dependence on glass properties.
  • Fluctuating Elasticity Theory (FET) predicts specific low-frequency Rayleigh scattering scaling, but the role of correlation volume (Vc) is debated.

Purpose of the Study:

  • To investigate the low-frequency wave attenuation rate (Γ(ω)) in glasses using extensive computer simulations.
  • To clarify the scaling of Γ(ω) and its dependence on ensemble versus spatial averages of elastic moduli.
  • To test the predictions of Fluctuating Elasticity Theory (FET) in two spatial dimensions.

Main Methods:

  • Extensive computer simulations were employed to model elastic wave propagation in disordered systems.
  • Analysis focused on the low-frequency limit (ω → 0) of the wave attenuation rate Γ(ω).
  • The study examined the statistics of elastic moduli, distinguishing between ensemble and spatial averages.

Main Results:

  • In two dimensions, the wave attenuation rate Γ(ω) was shown to asymptotically satisfy Γ(ω) ∼γω3.
  • The parameter γ was interpreted in terms of ensemble averages, with system size replacing correlation volume (Vc).
  • Anomalous finite-size ensemble statistics of elastic moduli were found, linked to the ω4 density of states of soft quasilocalized modes.

Conclusions:

  • The simulation results strongly support Fluctuating Elasticity Theory (FET) for describing wave attenuation in glasses.
  • The findings provide a rigorous benchmark for coarse-graining methods used to model elastic moduli distributions.
  • This work clarifies the interpretation of key parameters in FET and their relation to system-level properties.