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

Moriel, Avraham; Kapteijns, Geert; Rainone, Corrado; Zylberg, Jacques; Lerner, Edan; Bouchbinder, Eran

doi:10.1063/1.5111192

Cited by 69 publications

(74 citation statements)

References 59 publications

(164 reference statements)

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“…for longitudinal current, L. Here, v j (t) is the velocity of particle j at time t, k = | k|,k = k/| k| with k the wavevector. Previous studies demonstrated either explicitly 31,32 or implicitly 45 that there are finite size effects in the calculations of sound attenuation within the harmonic approximation. We find the finite-size effects persist for finite temperatures, especially at low temperatures.…”

Section: Simulation Detailsmentioning

confidence: 99%

“…Recently, large-scale computer simulations confirmed Rayleigh scattering scaling of sound attenuation in the harmonic approximation at small wavevectors and quadratic scaling at large wavevectors [30][31][32] . It is not expected that the quadratic small wavevector scaling could be captured in the harmonic approximation since this scaling is attributed to anharmonic effects.…”

Section: Introductionmentioning

confidence: 98%

“…It is not expected that the quadratic small wavevector scaling could be captured in the harmonic approximation since this scaling is attributed to anharmonic effects. Between the small wavevector quartic and large wavevector quadratic regime a possible crossover k 4 ln(k) regime has been identified in simulations [29][30][31][32][33] , but this crossover arXiv:2004.00700v1 [cond-mat.soft] 1 Apr 2020 region shrinks with increasing glass stability 32 . To observe Rayleigh scattering scaling in simulations researchers have to utilize very large systems 30 or examine very stable glasses 32 .…”

Section: Introductionmentioning

confidence: 99%

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Sound attenuation in stable glasses

et al. 2019

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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 ∼ k 1.5 for an aging glass, but Γ ∼ k 2 when the glass does not age on the timescale of the calculation. For our most stable glass, we find that Γ ∼ k 2 at small wavevectors, then a crossover to Rayleigh scattering scaling Γ ∼ 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.

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Section: Simulation Detailsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Sound attenuation in stable glasses

et al. 2019

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“…It is precisely this population of soft QLMs, and their interaction with phonons, that is thought to influence various unexplained universal phenomena that are specific to structural glasses [20][21][22]26]. Furthermore, a subset of QLMs were shown to represent the carriers of plasticity in externally-loaded glasses [30,31,39], and might be key in determining relaxation patterns in supercooled liquids [32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear quasilocalized excitations in glasses: True representatives of soft spots

2020

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Structural glasses formed by quenching a melt possess a population of soft quasilocalized excitations -often called 'soft spots' -that are believed to play a key role in various thermodynamic, transport and mechanical phenomena. Under a narrow set of circumstances, quasilocalized excitations assume the form of vibrational (normal) modes, that are readily obtained by a harmonic analysis of the multi-dimensional potential energy. In general, however, direct access to the population of quasilocalized modes via harmonic analysis is hindered by hybridizations with other low-energy excitations, e.g. phonons. In this series of papers we re-introduce and investigate the statistical-mechanical properties of a class of low-energy quasilocalized modes -coined here nonlinear quasilocalized excitations (NQEs) -that are defined via an anharmonic (nonlinear) analysis of the potential energy landscape of a glass, and do not hybridize with other low-energy excitations. In this first paper, we review the theoretical framework that embeds a micromechanical definition of NQEs. We demonstrate how harmonic quasilocalized modes hybridize with other soft excitations, whereas NQEs properly represent soft spots without hybridization. We show that NQEs' energies converge to the energies of the softest, non-hybridized harmonic quasilocalized modes, cementing their status as true representatives of soft spots in structural glasses. Finally, we perform a statistical analysis of the mechanical properties of NQEs, which results in a prediction for the distribution of potential energy barriers that surround typical inherent states of structural glasses, as well as a prediction for the distribution of local strain thresholds to plastic instability. arXiv:1912.10930v1 [cond-mat.soft]

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“…Due to the small size of the simulation box, it is not possible to obtain diffusivity at small ω using the method of Allen and Feldman. Additionally, it has been recently observed that there are finite size effects in calculations of vibrational modes from the Hessian matrix 33,34,38 , which may result in calculated thermal diffusivity d AF (ω) that does not correspond to the thermodynamic limit.…”

Section: Energy Transportmentioning

confidence: 99%

Energy transport in glasses

2020

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The temperature dependence of the thermal conductivity is linked to the nature of the energy transport at a frequency ω, which is quantified by thermal diffusivity d(ω). Here we study d(ω) for a poorly annealed glass and a highly stable glass prepared using the swap Monte Carlo algorithm. To calculate d(ω), we excite wave packets and find that the energy moves diffusively for high frequencies up to a maximum frequency, beyond which the energy stays localized. At intermediate frequencies, we find a linear increase of the square of the width of the wave packet with time, which allows for a robust calculation of d(ω), but the wave packet is no longer well described by a Gaussian as for high frequencies.In this intermediate regime, there is a transition from a nearly frequency independent thermal diffusivity at high frequencies to d(ω) ∼ ω −4 at low frequencies. For low frequencies the sound waves are responsible for energy transport and the energy moves ballistically. The low frequency behavior can be predicted using sound attenuation coefficients.The thermal conductivity of amorphous solids is vastly different than that of their crystalline counterparts. The existence of several common features in the temperature dependence of the thermal conductivity of amorphous solids indicates a common origin 1-8 . At temperatures below ∼ 1K the thermal conductivity grows as T 2 compared to T 3 growth for crystalline solids. This quadratic growth of the thermal conductivity with temperature is generally attributed to two-level tunneling states 3,5,7,9-11 , although alternative explanations exist 12-14 . Around T ≈ 10K a plateau develops in the thermal conductivity and there is a nearly linear rise in the thermal conductivity after the plateau.The temperature dependence of the thermal conductivity κ can be analyzed in terms of frequency dependent thermal diffusivity d(ω), which quantifies how fast a wave packet, narrowly peaked around a frequency ω, propagates [15][16][17][18] . At low temperatures, only the low frequency modes are excited, and only the low frequency thermal diffusivity significantly contributes to the thermal conductivity. The most prevalent theories attribute the low frequency thermal diffusivity to two-level states, which provide the dominant contribution below 1K, and to thermal transport due to sound waves 19,20 . By considering the sound waves as a phonon gas, Debye argued that there is a contribution to d(ω) given by v(ω) (ω)/3 where v(ω) is the speed of sound and (ω) is the mean free path 21 . It is often assumed, and confirmed in recent simulations, that sound attenuation obeys Rayleigh scaling, and thus the contribution due to sound waves behaves as d s (ω) ∼ ω −422-24 . Several researchers demonstrated that the thermal conductivity can be accurately described for temperatures at and below the low temperature plateau by combining the contributions to d(ω) due to two level systems and due to sound waves 19,20,25,26 .At room temperature, where all vibrational modes are excited, the average mean free path...

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

Cited by 69 publications

References 59 publications

Sound attenuation in stable glasses

Sound attenuation in stable glasses

Nonlinear quasilocalized excitations in glasses: True representatives of soft spots

Energy transport in glasses

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