Elastic moduli fluctuations predict wave attenuation rates in glasses

Abstract

The disorder-induced attenuation of elastic waves is central to the universal low-temperature properties of glasses. Recent literature offers conflicting views on both the scaling of the wave attenuation rate $\Gamma (\omega )$ in the low-frequency limit ($\omega \to 0$), and on its dependence on glass history and properties. A theoretical framework -- termed Fluctuating Elasticity Theory (FET) -- predicts low-frequency Rayleigh scattering scaling in $d$ spatial dimensions, $\Gamma (\omega )\sim \gamma {\omega }^{d+1}$, where $\gamma =\gamma (V_{\mathrm{c}})$ quantifies the coarse-grained spatial fluctuations of elastic moduli, involving a correlation volume $V_{\mathrm{c}}$ that remains debated. Here, using extensive computer simulations, we show that $\Gamma (\omega )\sim \gamma {\omega }^3$ is asymptotically satisfied in two dimensions ($d=2$) once $\gamma$ is interpreted in terms of ensemble -- rather than spatial -- averages, where $V_{\mathrm{c}}$ is replaced by the system size. In so doing, we also establish that the finite-size ensemble-statistics of elastic moduli is anomalous and related to the universal ${\omega }^4$ density of states of soft quasilocalized modes. These results not only strongly support FET, but also constitute a strict benchmark for the statistics produced by coarse-graining approaches to the spatial distribution of elastic moduli.

arXiv comment6 pages, 3 figures, accepted manuscript

References in corpus (30)

• Models and algorithms for the next generation of glass transition studies
• Anharmonicity, vibrational instability and Boson peak in glasses
• Crossover to Potential Energy Landscape Dominated Dynamics in a Model Glass-forming Liquid
• Local elasticity map and plasticity in a model Lennard-Jones glass
• Universal Breakdown of Elasticity at the Onset of Material Failure
• Statistics and properties of low-frequency vibrational modes in structural glasses
• On the Microscopic Foundations of Elasticity
• Glass-specific behavior in the damping of acoustic-like vibrations
• Measuring Spatial Distribution of Local Elastic Modulus in Glasses
• Universal non-phononic density of states in 2D, 3D and 4D glasses
• Do Athermal Amorphous Solids Exist?
• The Boson Peak and its Relation with Acoustic Attenuation in Glasses
• Pinching a glass reveals key properties of its soft spots
• Universality of the nonphononic vibrational spectrum across different classes of computer glasses
• Observation of the onset of strong scattering on high frequency acoustic phonons in densified silica glass
• Mean-Field Theory, Mode-Coupling Theory, and the Onset Temperature in Supercooled Liquids
• Phonon transport and vibrational excitations in amorphous solids
• A characteristic energy scale in glasses
• Effect of instantaneous and continuous quenches on the density of vibrational modes in model glasses
• Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling
• Sound attenuation in stable glasses
• Frustration-induced internal stresses are responsible for quasilocalized modes in structural glasses
• Universal disorder-induced broadening of phonon bands: from disordered lattices to glasses
• Nonlinear quasilocalized excitations in glasses. I. True representatives of soft spots
• Finite-size effects in the nonphononic density of states in computer glasses
• Mechanical properties of simple computer glasses
• Sound damping in glasses: interplay between anharmonicities and elastic heterogeneities
• Tracking the connection between disorder and energy landscape in glasses using geologically hyperaged amber
• Impact of elastic heterogeneity on the propagation of vibrations at finite temperatures in glasses
• Analytical prediction of logarithmic Rayleigh scattering in amorphous solids from tensorial heterogeneous elasticity with power-law disorder

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• Disordered crystals reveal soft quasilocalized glassy excitations
• Nonphononic spectrum of two-dimensional structural glasses
• A unified quantifier of mechanical disorder in solids
• Emergence of linear isotropic elasticity in amorphous and polycrystalline materials
• Local and global measures of the shear moduli of jammed disk packings
• Non-phononic density of states of two-dimensional glasses revealed by random pinning
• Variability of mesoscopic mechanical disorder in disordered solids
• Random quench predicts universal properties of amorphous solids
• The Origin of Sound Damping in Amorphous Solids: Defects and Beyond
• Quasi-localized vibrational modes, Boson peak and sound attenuation in model mass-spring networks
• Properties of stable ensembles of Euclidean random matrices
• Scaling regimes and fluctuations of observables in computer glasses approaching the unjamming transition
• Understanding the scaling of boson peak through insensitivity of elastic heterogeneity to bending rigidity in polymer glasses
• A self-consistent current response theory of jamming and vibrational modes in low-temperature amorphous solids
• Effective medium theory for viscoelasticity of soft jammed solids
• Vibrational density of states of amorphous solids with long-ranged power-law correlated disorder in elasticity
• Unified study of viscoelasticity and sound damping in hard and soft amorphous solids
• Sound Attenuation in Glasses
• Finite-size study of the athermal quasistatic yielding transition in structural glasses
• Brittle to ductile transitions in glasses: Roles of soft defects and loading geometry
• Critical fluctuations of elastic moduli in jammed solids