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

Abstract

The attenuation of long-wavelength phonons (waves) by glassy disorder plays a central role in various glass anomalies, yet it is neither fully characterized, nor fully understood. Of particular importance is the scaling of the attenuation rate $\Gamma (k)$ with small wavenumbers $k\to 0$ in the thermodynamic limit of macroscopic glasses. Here we use a combination of theory and extensive computer simulations to show that the macroscopic low-frequency behavior emerges at intermediate frequencies in finite-size glasses, above a recently identified crossover wavenumber $k_{†}$, where phonons are no longer quantized into bands. For $k<k_{†}$, finite-size effects dominate $\Gamma (k)$, which is quantitatively described by a theory of disordered phonon bands. For $k>k_{†}$, we find that $\Gamma (k)$ is affected by the number of quasilocalized nonphononic excitations, a generic signature of glasses that feature a universal density of states. In particular, we show that in a frequency range in which this number is small, $\Gamma (k)$ follows a Rayleigh scattering scaling $\sim k^{d+1}$ ($d$ is the spatial dimension), and that in a frequency range in which this number is sufficiently large, the recently observed generalized-Rayleigh scaling of the form $\sim k^{d+1}\log (k_0/k)$ emerges ($k_0>k_{†}$ is a characteristic wavenumber). Our results suggest that macroscopic glasses --- and, in particular, glasses generated by conventional laboratory quenches that are known to strongly suppress quasilocalized nonphononic excitations --- exhibit Rayleigh scaling at the lowest wavenumbers $k$ and a crossover to generalized-Rayleigh scaling at higher $k$. Some supporting experimental evidence from recent literature is presented.

arXiv comment15 pages, 10 figures (including appendices). v2 includes a new appendix with 2 figures (Fig.7 & Fig.8)

References in corpus (26)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Jamming of Soft Particles: Geometry, Mechanics, Scaling and Isostaticity
• Models and algorithms for the next generation of glass transition studies
• Anharmonicity, vibrational instability and Boson peak in glasses
• Continuum limit of the vibrational properties of amorphous solids
• Statistics and properties of low-frequency vibrational modes in structural glasses
• Fast Monte Carlo algorithm for supercooled soft spheres
• Low-frequency vibrational modes of stable glasses
• Glass-specific behavior in the damping of acoustic-like vibrations
• Universal non-phononic density of states in 2D, 3D and 4D glasses
• Scaling of phononic transport with connectivity in amorphous solids
• Zero-temperature glass transition in two dimensions
• Energy transport in jammed sphere packings
• Phonon transport and vibrational excitations in amorphous solids
• Fast generation of ultrastable computer glasses by minimization of an augmented potential energy
• A characteristic energy scale in glasses
• The Static Lengthscale Characterizing the Glass Transition at Lower Temperatures
• Nonlinear modes disentangle glassy and Goldstone modes in structural glasses
• Effect of instantaneous and continuous quenches on the density of vibrational modes in model glasses
• 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
• Propagative and diffusive regimes of acoustic damping in bulk amorphous material
• Mechanical properties of simple computer glasses
• Low temperature universality in disordered solids
• Introduction to High-Resolution Inelastic X-Ray Scattering

Cited by in corpus (36)

• Pinching a glass reveals key properties of its soft spots
• Low-energy quasilocalized excitations in structural glasses
• A simple and broadly-applicable definition of shear transformation zones
• Nonlinear quasilocalized excitations in glasses. I. True representatives of soft spots
• Elastic moduli fluctuations predict wave attenuation rates in glasses
• Universal low-frequency vibrational modes in silica glasses
• Finite-size effects in the nonphononic density of states in computer glasses
• Unifying description of the vibrational anomalies of amorphous materials
• Low-frequency excess vibrational modes in two-dimensional glasses
• Microscopic analysis of sound attenuation in low-temperature amorphous solids reveals quantitative importance of non-affine effects
• Robustness of Density of Low Frequency States in Amorphous Solids
• Mean-field model of interacting quasilocalized excitations in glasses
• Sound damping in glasses: interplay between anharmonicities and elastic heterogeneities
• Mechanical disorder of sticky-sphere glasses. II. Thermo-mechanical inannealability
• Impact of elastic heterogeneity on the propagation of vibrations at finite temperatures in glasses
• Extracting the properties of quasilocalized modes in computer glasses: Long-range continuum fields, contour integrals and boundary effects
• Anharmonic properties of vibrational excitations in amorphous solids
• Density of States below the First Sound Mode in 3D Glasses
• Relationship between two-level systems and quasi-localized normal modes in glasses
• A unified quantifier of mechanical disorder in solids
• Variability of mesoscopic mechanical disorder in disordered solids
• Internally-stressed and positionally-disordered minimal complexes yield glasslike nonphononic excitations
• Analytical prediction of logarithmic Rayleigh scattering in amorphous solids from tensorial heterogeneous elasticity with power-law disorder
• Sound damping in frictionless granular materials: The interplay between configurational disorder and inelasticity
• Novel elastic instability of amorphous solids in finite spatial dimensions
• Properties of stable ensembles of Euclidean random matrices
• Structural and mechanical characteristics of sphere packings near the jamming transition: From fully amorphous to quasi-ordered structures
• A self-consistent current response theory of jamming and vibrational modes in low-temperature amorphous solids
• Phonon transport properties of particulate physical gels
• Universal Density of Low Frequency States in Silica Glass at Finite Temperatures
• Sound Attenuation in Glasses
• Singularities in Hessian element distributions of amorphous media
• Unified study of viscoelasticity and sound damping in hard and soft amorphous solids
• Vibrational density of states of amorphous solids with long-ranged power-law correlated disorder in elasticity
• Thermal Conductivity of Glass-Forming Liquids
• Structural, mechanical, and vibrational properties of particulate physical gels