The temperature dependence of the thermal conductivity of amorphous solids is markedly different from that of their crystalline counterparts, but exhibits universal behaviour. Sound attenuation is believed to be related to this universal behaviour. Recent computer simulations demonstrated that in the harmonic approximation sound attenuation $Γ$ obeys quartic, Rayleigh scattering scaling for small wavevectors $k$ and quadratic scaling for wavevectors above the Ioffe-Regel limit. However, simulations and experiments do not provide a clear picture of what to expect at finite temperatures where anharmonic effects become relevant. Here we study sound attenuation at finite temperatures for model glasses of various stability, from unstable glasses that exhibit rapid aging to glasses whose stability is equal to those created in laboratory experiments. We find several scaling laws depending on the temperature and stability of the glass. First, we find the large wavevector quadratic scaling to be unchanged at all temperatures. Second, we find that at small wavectors $Γ\sim k^{1.5}$ for an aging glass, but $Γ\sim k^2$ when the glass does not age on the timescale of the calculation. For our most stable glass, we find that $Γ\sim k^2$ at small wavevectors, then a crossover to Rayleigh scattering scaling $Γ\sim k^4$, followed by another crossover to the quadratic scaling at large wavevectors. Our computational observation of this quadratic behavior reconciles simulation, theory and experiment, and will advance the understanding of the temperature dependence of thermal conductivity of glasses.
Understanding the difference between universal low-temperature properties of amorphous and crystalline solids requires an explanation of the stronger damping of long-wavelength phonons in amorphous solids. A longstanding sound attenuation scenario, resulting from a combination of experiments, theories, and simulations, leads to a quartic scaling of sound attenuation with the wavevector, which is commonly attributed to Rayleigh scattering of the sound. Modern computer simulations offer conflicting conclusions regarding the validity of this picture. We simulate glasses with an unprecedentedly br…
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 $Γ(k)$ 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 $k_\dagger$, where phonons are …
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 $Γ(ω)$ in the low-frequency limit ($ω\!\to\!0$), 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, $Γ(ω)\!\sim\!γ\,ω^{d+1}$, where $γ\!=\!γ(V_{\rm c})$ quantifies the coarse-grained spatial fluctuations of elastic moduli, involving a c…
Structured metamaterials are at the core of extensive research, promising for acoustic and thermal engineering. Nevertheless, the computational cost required for correctly simulating large systems imposes to use a continuous model to describe the effective behavior without knowing the atomistic details. Crucially, a correct description needs to describe both the extrinsic interface-induced and the intrinsic atomic scale-originated phonon scattering, especially when the component material is made of glass, a highly dissipative material in which wave attenuation is strongly dependent on frequenc…
Glasses feature universally low-frequency excess vibrational modes beyond Debye prediction, which could help rationalize, e.g., the glasses' unusual temperature dependence of thermal properties compared to crystalline solids. The way the density of states of these low-frequency excess modes $D(ω)$ depends on the frequency $ω$ has been debated for decades. Recent simulation studies of 3D glasses suggest that $D(ω)$ scales universally with $ω^4$ in a low-frequency regime below the first sound mode. However, no simulation study has ever probed as low frequencies as possible to test directly wheth…
Sound attenuation in low temperature amorphous solids originates from their disordered structure. However, its detailed mechanism is still being debated. Here we analyze sound attenuation starting directly from the microscopic equations of motion. We derive an exact expression for the zero-temperature sound damping coefficient. We verify that the sound damping coefficients calculated from our expression agree very well with results from independent simulations of sound attenuation. The small wavevector analysis of our expression shows that sound attenuation is primarily determined by the non-a…
On the ratio between longitudinal and transverse Ioffe-Regel frequencies in glasses
School of Physics, State Key Laboratory of Opto-Electronic Information Acquisition and Protection Technology, Anhui University（安徽大学物理学院光电信息获取与保护技术国家重点实验室）
The paper presents a description of the sound wave absorption in glasses, from the lowest temperatures up to the glass transition, in terms of three compatible phenomenological models. Resonant tunneling, the rise of the relaxational tunneling to the tunneling plateau and the crossover to classical relaxation are universal features of glasses and are well described by the tunneling model and its extension to include soft vibrations and low barrier relaxations, the soft potential model. Its further extension to non-universal features at higher temperatures is the very flexible Gilroy-Phillips m…
In this paper, we derive a dispersion relation for sound waves in viscous and heat conducting fluids. In particular this dispersion (i.e. variation of speed of sound with frequency) is shown to be of second order of magnitude, w.r.t. Knudsen numbers, as in the Stokes [2] case, corresponding to non-conductive fluid (Prandtl number P r = $\infty$). This formula completes the classical attenuation relation called Stokes-Kirchhoff. We represent in a simplified manner the Kirchhoff approach to derive this attenuation [1], starting from the 3D compressible Navier-stokes system. The classical Stokes-…
The goal of this study is to contribute to the physics underlying the material properties of suspensions that exhibit shear thickening through the ultrasonic characterization of suspensions of cornstarch in a density-matched solution. Ultrasonic measurements at frequencies in the range of 4 to 8 MHz of the speed of sound and the frequency-dependent attenuation properties are reported for concentrations of cornstarch in a density-matched aqueous (cesium chloride brine) suspension, ranging up to 40% cornstarch. The speed of sound is found to range from 1483 +/- 10 m/s in pure brine to 1765 +/- 9…
In low-temperature glasses, the sound velocity changes as the logarithmic function of temperature below $10$K: $[c(T) - c(T_0)]/c(T_0) = \mathcal{C}\ln(T/T_0)$. With increasing temperature starting from $T=0$K, the sound velocity does not increase monotonically, but reaches a maximum at a few Kelvin and decreases at higher temperatures. Tunneling-two-level-system (TTLS) model explained the $\ln T$ dependence of sound velocity shift. In TTLS model the slope ratio of $\ln T$ dependence of sound velocity shift between lower temperature increasing regime (resonance regime) and higher temperature d…
We present a theoretical derivation of acoustic phonon damping in amorphous solids based on the nonaffine response formalism for the viscoelasticity of amorphous solids. The analytical theory takes into account the nonaffine displacements in transverse waves and is able to predict both the ubiquitous low-energy diffusive damping $\sim k^{2}$, as well as a novel contribution to the Rayleigh damping $\sim k^{4}$ at higher wavevectors and the crossover between the two regimes observed experimentally. The coefficient of the diffusive term is proportional to the microscopic viscous (Langevin-type) …
Some aspects of how sound waves travel through disordered solids are still unclear. Recent work has characterized a feature of disordered solids which seems to influence vibrational excitations at the mesoscales, local elastic heterogeneity. Sound waves propagation has been demonstrated to be strongly affected by inhomogeneous mechanical features of the materials which add to the standard anharmonic couplings, amounting to extremely complex transport properties at finite temperatures. Here, we address these issues for the case of a simple atomic glass former, by Molecular Dynamics computer sim…
We present theoretical investigation on the high-frequency collective dynamics in liquids and glasses at microscopic length scales and terahertz frequency region based on the mode-coupling theory for ideal liquid-glass transition. We focus on recently investigated issues from inelastic-X-ray-scattering and computer-simulation studies for dynamic structure factors and longitudinal and transversal current spectra: the anomalous dispersion of the high-frequency sound velocity and the nature of the low-frequency excitation called the boson peak. It will be discussed how the sound mode interferes w…
Connectedness and applied stress strongly affect elasticity in solids. In various amorphous solids, mechanical stability can be lost either by reducing connectedness or by increasing pressure. We present an effective medium theory of elasticity that extends previous approaches by incorporating the effect of compression, of amplitude $e$, allowing one to describe quantitative features of sound propagation, transport, the boson peak, and elastic moduli near the elastic instability occurring at a compression $e_c$. The theory disentangles several frequencies characterizing the vibrational spectru…
Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency $ω$ as $ω^4$ in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows $D_\text{exc}(ω)\sim ω^2 $ …
Soft, quasilocalized excitations (QLEs) are known to generically emerge in a broad class of disordered solids, and to govern many facets of the physics of glasses, from wave attenuation to plastic instabilities. In view of this key role of QLEs, shedding light upon several open questions in glass physics depends on the availability of computational tools that allow to study QLEs' statistical mechanics. The latter is a formidable task since harmonic analyses are typically contaminated by hybridizations of QLEs with phononic excitations at low frequencies, obscuring a clear picture of QLEs' abun…
We construct a linear response theory of applying shear deformations from boundary walls in the film geometry in Kubo's theoretical scheme. Our method is applicable to any solids and fluids. For glasses, we assume quasi-equilibrium around a fixed inherent state. Then, we obtain linear-response expressions for any variables including the stress and the particle displacements, even though the glass interior is elastically inhomogeneous. In particular, the shear modulus can be expressed in terms of the correlations between the interior stress and the forces from the walls. It can also be expresse…
We report an experimental and theoretical investigation of the frequency-dependent effective mass, $\tilde{M}(ω)$, of loose granular particles which occupy a rigid cavity to a given filling fraction, the remaining volume being air of differing humidities. This allow us to study the mechanisms of elastic response and attenuation of acoustic modes in granular media. We demonstrate that this is a sensitive and direct way to measure those properties of the granular medium that are the cause of the changes in acoustic properties of structures containing grain-filled cavities. Specifically, we apply…
Amorphous materials exhibit peculiar mechanical and vibrational properties, including non-affine elastic responses and excess vibrational states, i.e., the so-called boson peak. For polymer glasses, these properties are considered to be affected by the bending rigidity of the constituent polymer chains. In our recent work [Tomoshige, et al., Sci. Rep. 9 19514 (2019)], we have revealed simple relationships between the variations of vibrational properties and the global elastic properties: the response of the boson peak scales only with that of the global shear modulus. This observation suggests…
Soft quasilocalized modes (QLMs) are universally featured by structural glasses quenched from a melt, and are supposedly involved in a number of glassy anomalies such as the low temperature scaling of their thermal conductivity and specific heat, and sound attenuation at intermediate frequencies. In computer glasses, QLMs may assume the form of harmonic vibrational modes under a narrow set of circumstances, however direct access to their full distribution over frequency is hindered by hybridizations of QLMs with other low-frequency modes (e.g.~phonons). Previous studies to overcome this issue …
Rapid cooling of liquids below a certain temperature range can result in a transition to glassy states. The traditional understanding of glasses includes their thermodynamic metastability with respect to crystals. However, here we present specific examples of interactions that eliminate the possibilities of crystalline and quasicrystalline phases, while creating mechanically stable amorphous glasses down to absolute zero temperature. We show that this can be accomplished by introducing a new ideal state of matter called a "perfect glass." A perfect glass represents a soft-interaction analog of…
Recent numerical studies on glassy systems provide evidences for a population of non-Goldstone modes (NGMs) in the low-frequency spectrum of the vibrational density of states $D(ω)$. Similarly to Goldstone modes (GMs), i. e., phonons in solids, NGMs are soft low-energy excitations. However, differently from GMs, NGMs are localized excitations. Here we first show that the parental temperature $T^*$ modifies the GM/NGM ratio in $D(ω)$. In particular, the phonon attenuation is reflected in a parental temperature dependency of the exponent $s(T^*)$ in the low-frequency power law $D(ω) \sim ω^{s(T^…
