Emergence of crystal-like atomic dynamics in glasses at the nanometer scale

Heterogeneous attenuation of sound waves in three-dimensional amorphous solids

Sound waves are attenuated as they propagate in amorphous materials. We investigate the mechanism driving sound attenuation in the Rayleigh scattering regime by resolving the dynamics of an excited phonon in time and space via numerical simulations. We find sound attenuation is spatiotemporally heterogeneous. It starts in localized regions, which identify soft regions within the material and correlate with low-frequency vibrational modes. As time progresses, the regions where sound is primarily attenuated invade the system via an apparent diffusive process.

Properties of stable ensembles of Euclidean random matrices

We study the spectrum of a system of coupled disordered harmonic oscillators in the thermodynamic limit. This Euclidean random matrix ensemble has been suggested as a model for the low temperature vibrational properties of glass. Exact numerical diagonalization is performed in three and two spatial dimensions, which is accompanied by a detailed finite size analysis. It reveals a low-frequency regime of sound waves that are damped by Rayleigh scattering. At large frequencies localized modes exist. In between, the central peak in the vibrational density of states is well described by Wigner's semicircle law for not too large disorder, as is expected for simple random matrix systems. We compare our results with predictions from two recent self-consistent field theories.

Vibrational Phenomena in Glasses at Low Temperatures Captured by Field Theory of Disordered Harmonic Oscillators

We investigate the vibrational properties of topologically disordered materials by analytically studying particles that harmonically oscillate around random positions. Exploiting classical field theory in the thermodynamic limit at T=0, we build up a self-consistent model by analyzing the Hessian utilizing Euclidean random matrix theory. In accordance with earlier findings [T. S. Grigera et al.J. Stat. Mech. (2011) P02015.JSMTC61742-546810.1088/1742-5468/2011/02/P02015], we take nonplanar diagrams into account to correctly address multiple local scattering events. By doing so, we end up with a first principles theory that can predict the main anomalies of athermal disordered materials, including the boson peak, sound softening, and Rayleigh damping of sound. In the vibrational density of states, the sound modes lead to Debye's law for small frequencies. Additionally, an excess appears in the density of states starting as ω^{4} in the low frequency limit, which is attributed to (quasi-) localized modes.

Unifying Description of the Vibrational Anomalies of Amorphous Materials

The vibrational density of states D(ω) of solids controls their thermal and transport properties. In crystals, the low-frequency modes are extended phonons distributed in frequency according to Debye's law, D(ω)∝ω^{2}. In amorphous solids, phonons are damped, and at low frequency D(ω) comprises extended modes in excess over Debye's prediction, leading to the so-called boson peak in D(ω)/ω^{2} at ω_{bp}, and quasilocalized ones. Here we show that boson peak and phonon attenuation in the Rayleigh scattering regime are related, as suggested by correlated fluctuating elasticity theory, and that amorphous materials can be described as homogeneous isotropic elastic media punctuated by quasilocalized modes acting as elastic heterogeneities. Our numerical results resolve the conflict between theoretical approaches attributing amorphous solids' vibrational anomalies to elastic disorder and localized defects.

Sound damping in soft particle packings: the interplay between configurational disorder and inelasticity

We numerically investigate sound damping in disordered two-dimensional soft particle packings. We simulate evolution of standing waves of particle displacements and analyze time correlation functions of particle velocities and power spectra. We control the strength of inelastic interactions between the particles in contact to show how the inelasticity affects anomalous sound characteristics of disordered systems: Increasing the strength of inelastic interactions, we find that (i) sound softening vanishes and (ii) attenuation coefficients exhibit a transition from the Rayleigh law to quadratic growth. We also report (iii) how the Ioffe-Regel limit frequencies depend on the strength of inelasticity as useful information for experiments and applications of the sound in disordered media. Our findings suggest that sound damping in soft particle packings is determined by the interplay between elastic heterogeneities and inelasticity.

Key role of retardation and non-locality in sound propagation in amorphous solids as evidenced by a projection formalism

We investigate acoustic propagation in amorphous solids by constructing a projection formalism based on separating atomic vibrations into two, "phonon" (P) and "non-phonon" (NP), subspaces corresponding to large and small wavelengths. For a pairwise interaction model, we show the existence of a "natural" separation lengthscale, determined by structural disorder, for which the isolated P subspace presents the acoustic properties of a nearly homogenous (Debye-like) elastic continuum, while the NP one encapsulates all small scale non-affinity effects. The NP eigenstates then play the role of dynamical scatterers for the phonons. However, at variance with a conjecture of defect theories, their spectra present a finite low frequency gap, which turns out to lie around the Boson peak frequency, and only a small fraction of them are highly localized. We then show that small scale disorder effects can be rigorously reduced to the existence, in the Navier-like wave equation of the continuum, of a generalized elasticity tensor, which is not only retarded, since scatterers are dynamical, but also non-local. The full neglect of both retardation and non-locality suffices to account for most of the corrections to Born macroscopic moduli. However, these two features are responsible for sound speed dispersion and have quite a significant effect on the magnitude of sound attenuation. Although it remains open how they impact the asymptotic, large wavelength scaling of sound damping, our findings rule out the possibility of representing an amorphous solid by an inhomogeneous elastic continuum with the standard (i.e., local and static) elastic moduli.

Sound attenuation in finite-temperature stable glasses

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 wavevectors Γ∼k^1.5 for an aging glass, but Γ∼k² when the glass does not age on the timescale of the calculation. For our most stable glass, we find that Γ∼k² at small wavevectors, then a crossover to Rayleigh scattering scaling Γ∼k⁴, 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.

Sound attenuation in stable glasses

Understanding the difference between the universal low-temperature properties of amorphous and crystalline solids requires an explanation for 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 the Rayleigh scattering of sound. Modern computer simulations offer conflicting conclusions regarding the validity of this picture. We simulate glasses with an unprecedentedly broad range of stabilities to perform the first microscopic analysis of sound damping in model glass formers across a range of experimentally relevant preparation protocols. We present convincing evidence that quartic scaling is recovered for small wavevectors irrespective of the glass's stability. With increasing stability, the wavevector where the quartic scaling begins increases by approximately a factor of three and the sound attenuation decreases by over an order of magnitude. Our results uncover an intimate connection between glass stability and sound damping.

Fluctuating Elasticity Fails to Capture Anomalous Sound Scattering in Amorphous Solids

The fluctuating elasticity (FE) model, introduced phenomenologically and developed by Schirmacher [J. Non-Cryst. Solids 357, 518 (2011)JNCSBJ0022-309310.1016/j.jnoncrysol.2010.07.052], is today the only theoretical framework available to analyze low-temperature elastic acoustic scattering in glasses. Its existing formulations, which neglect the tensorial nature of elasticity and exclude long-range disorder correlations, predict that the acoustic damping coefficients obey the standard Rayleigh scaling law: Γ∼k^{d+1}, with k the acoustic wave vector, in dimension d. However, recent numerical data, supported by the analysis of existing experimental results, show that Γ does not obey this scaling law but Γ∼-k^{d+1}lnk. Here we analyze in detail how a fully tensorial FE model can be constructed as a long wavelength approximation of the elastic response of the discrete, atomistic, problem. We show that, although it incorporates all long-range correlations, it fails to capture the observed damping in two respects: (i) it misses the anomalous scaling, and predicts the standard Rayleigh law; (ii) it grossly underestimates the amplitude of scattering by about 2 orders of magnitude. This brings clear evidence that the small scale nonaffine displacement fields, although not simply reducible to local defects, play a crucial role in acoustic wave scattering and hence cannot be ignored.

Damping of vibrational excitations in glasses at terahertz frequency: The case of 3-methylpentane

We report a compared analysis of inelastic X ray scattering (IXS) and of low frequency Raman data of glassy 3-methylpentane. The IXS spectra have been analysed allowing for the existence of two distinct excitations at each scattering wavevector obtaining a consistent interpretation of the spectra. In particular, this procedure allows us to interpret the linewidth of the modes in terms of a simple model which relates them to the width of the first sharp diffraction peak in the static structure factor. In this model, the width of the modes arises from the blurring of the dispersion curves which increases approaching the boundary of the first pseudo-Brillouin zone. The position of the boson peak contribution to the density of vibrational states derived from the Raman scattering measurements is in agreement with the interpretation of the two excitations in terms of a longitudinal mode and a transverse mode, the latter being a result of the mixed character of the transverse modes away from the center of the pseudo-Brillouin zone.

Anomalous phonon scattering and elastic correlations in amorphous solids

A major issue in materials science is why glasses present low-temperature thermal and vibrational properties that sharply differ from those of crystals. In particular, long-wavelength phonons are considerably more damped in glasses, yet it remains unclear how structural disorder at atomic scales affects such a macroscopic phenomenon. A plausible explanation is that phonons are scattered by local elastic heterogeneities that are essentially uncorrelated in space, a scenario known as Rayleigh scattering, which predicts that the damping of acoustic phonons scales with wavenumber k as k^d+1 (in dimension d). Here we demonstrate that phonon damping scales instead as - k^d+1 ln k, with this logarithmic enhancement originating from long-range spatial correlations of elastic disorder caused by similar stress correlations. Our work suggests that the presence of long-range spatial correlations of local stress and elasticity may well be the crucial feature that distinguishes amorphous solids from crystals.

Impact of pressure on plastic yield in amorphous solids with open structure

Plasticity in amorphous silica is unusual: The yield stress decreases with hydrostatic pressure, in contrast to the Mohr-Coulomb response commonly found in more compact materials such as bulk metallic glasses. To better understand this response, we have carried out molecular dynamics simulations of plastic response in a model glass with open structure. The simulations reproduce the anomalous dependence of yield stress with pressure and also correctly predict that the plastic response turns to normal once the material has been fully compacted. We also show that the overall shape of the yield surface is consistent with a quadratic behavior predicted assuming local buckling of the structure, a point of view that fits well into the present understanding of the deformation mechanisms of amorphous silica. The results also confirm that free volume is an adequate internal variable for a continuum scale description of the plastic response of amorphous silica. Finally, we also investigate the long-range correlations between rearrangement events. We find that strong intermittency is observed when the structure remains open, while compaction results in more homogeneous rearrangements. These findings are in agreement with recent results on the effect of compression on the middle range order in silicate glasses and also suggest that the well-known volume recovery of densified silica at relatively low temperatures is in fact a form of aging.

Structural heterogeneities at the origin of acoustic and transport anomalies in glycerol glass-former

By means of large scale molecular dynamics simulations, we explore mesoscopic properties of prototypical glycerol glass-former above and below the glass transition. The model used, in excellent agreement with various experimental techniques, permits to carefully study the structure and the vibrational dynamics. We find that a medium range order is present in glycerol glass-former and arises from hydrogen bond network extension. The characteristic size of the structural heterogeneities is related to the anomalous properties of acoustic vibrations (Rayleigh scattering, "mode softening," and Boson Peak) in the glassy state. Finally the characteristic size of these heterogeneities, nearly constant in temperature, is also connected to the cross-over between structural relaxation and diffusion in liquid glycerol.

Evaluation of x-ray Brillouin scattering data

Making use of the classical second-moment sum rule, it is possible to convert a series of constant-Q x-ray Brillouin scattering scans (Q momentum transfer) into a series of constant frequency scans over the measured Q range. The method is applied to literature results for the longitudinal phonon dispersion in several glass formers. The constant frequency scans are well fitted in terms of a Q-independent phonon damping depending exclusively on the frequency, in agreement with two recent theories of the boson peak. The method allows us to link the x-ray Brillouin scattering to the diffuse Umklapp scattering from the boson peak vibrations at higher momentum transfer on an absolute intensity scale.

Acoustic excitations and elastic heterogeneities in disordered solids

In the recent years, much attention has been devoted to the inhomogeneous nature of the mechanical response at the nanoscale in disordered solids. Clearly, the elastic heterogeneities that have been characterized in this context are expected to strongly affect the nature of the sound waves which, in contrast to the case of perfect crystals, cannot be completely rationalized in terms of phonons. Building on previous work on a toy model showing an amorphization transition, we investigate the relationship between sound waves and elastic heterogeneities in a unified framework by continuously interpolating from the perfect crystal, through increasingly defective phases, to fully developed glasses. We provide strong evidence of a direct correlation between sound wave features and the extent of the heterogeneous mechanical response at the nanoscale.

Anharmonic damping of terahertz acoustic waves in a network glass and its effect on the density of vibrational states

We report the observation, by means of high-resolution inelastic x-ray scattering, of an unusually large temperature dependence of the sound attenuation of a network glass at terahertz frequency, an unprecedentedly observed phenomenon. The anharmonicity can be ascribed to the interaction between the propagating acoustic wave and the bath of thermal vibrations. At low temperatures the sound attenuation follows a Rayleigh-Gans scattering law. As the temperature is increased the anharmonic process sets in, resulting in an almost quadratic frequency dependence of the damping in the entire frequency range. We show that the temperature variation of the sound damping accounts quantitatively for the temperature dependence of the density of vibrational states.

Structural evolution and medium range order in permanently densified vitreous SiO2

Positron annihilation lifetime spectroscopy is employed to measure the size of the interstitial void spaces characterizing the structure of a set of permanently densified SiO2 glasses. The average volume of the voids is markedly affected by the densification process and linearly shrinks by almost an order of magnitude after a relative density variation of 22%. In addition, x-ray diffraction shows that this change of density does not modify appreciably the short range order, which remains organized in SiO4 tetrahedra. These results strongly suggest a porous medium description for v-SiO2 glasses where the compressibility and the medium range order are dominated by the density variation of the voids volume up to densities close to that of α-quartz.

Avalanches mediate crystallization in a hard-sphere glass

By molecular-dynamics simulations, we have studied the devitrification (or crystallization) of aged hard-sphere glasses. First, we find that the dynamics of the particles are intermittent: Quiescent periods, when the particles simply "rattle" in their nearest-neighbor cages, are interrupted by abrupt "avalanches," where a subset of particles undergo large rearrangements. Second, we find that crystallization is associated with these avalanches but that the connection is not straightforward. The amount of crystal in the system increases during an avalanche, but most of the particles that become crystalline are different from those involved in the avalanche. Third, the occurrence of the avalanches is a largely stochastic process. Randomizing the velocities of the particles at any time during the simulation leads to a different subsequent series of avalanches. The spatial distribution of avalanching particles appears random, although correlations are found among avalanche initiation events. By contrast, we find that crystallization tends to take place in regions that already show incipient local order.