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Register a new userA continuum model reproducing the multiple frequency crossovers in acoustic attenuation in glasses
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Structured metamaterials are at the core of extensive research, promising for thermal and acoustic engineering. However, the computational cost required for correctly simulating large systems imposes to use continuous modeling, able to grasp the physics at play without entering in the atomistic details. Crucially, a correct description needs to describe both the extrinsic interface-induced and the intrinsic atomic scale-originated phonon scattering. This latter becomes considerably important when the metamaterial is made out of a glass, which is intrinsically highly dissipative and with a wave attenuation strongly dependent on frequency and temperature. In amorphous systems, the effective acoustic attenuation triggered by multiple mechanisms is now well characterized and exhibits a nontrivial frequency dependence with a double crossover of power laws. Here we propose a continuum mechanical model for a viscoelastic medium, able to bridge atomic and macroscopic scales in amorphous materials and reproduce well the phonon attenuation from GHz to THz with a ${omega}^2-{omega}^4-{omega}^2$ dependency, including the influence of temperature.
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The sound attenuation in the THz region is studied down to T=16 K in glassy glycerol by inelastic x-ray scattering. At striking variance with the decrease found below 100 K in the GHz data, the attenuation in the THz range does not show any T dependence. This result i) indicates the presence of two different attenuation mechanisms, active respectively in the high and low frequency limits; ii) demonstrates the non-dynamic origin of the attenuation of THz sound waves, and confirms a similar conclusion obtained in SiO2 glass by molecular dynamics; and iii) supports the low frequency attenuation mechanism proposed by Fabian and Allen (Phys.Rev.Lett. 82, 1478 (1999)).
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 $Gamma$ 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 $Gamma sim k^{1.5}$ for an aging glass, but $Gamma sim k^2$ when the glass does not age on the timescale of the calculation. For our most stable glass, we find that $Gamma sim k^2$ at small wavevectors, then a crossover to Rayleigh scattering scaling $Gamma sim k^4$, 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.
Experimental results on the density of states and on the acoustic modes of glasses in the THz region are compared to the predictions of two categories of models. A recent one, solely based on an elastic instability, does not account for most observations. Good agreement without adjustable parameters is obtained with models including the existence of non-acoustic vibrational modes at THz frequency, providing in many cases a comprehensive picture for a range of glass anomalies.
A theory for the vibrational dynamics in disordered solids [W. Schirmacher, Europhys. Lett. {bf 73}, 892 (2006)], based on the random spatial variation of the shear modulus, has been applied to determine the wavevector ($k$) dependence of the Brillouin peak position ($Omega_k)$ and width ($Gamma_k$), as well as the density of vibrational states ($g(omega)$), in disordered systems. As a result, we give a firm theoretical ground to the ubiquitous $k^2$ dependence of $Gamma_k$ observed in glasses. Moreover, we derive a quantitative relation between the excess of the density of states (the boson peak) and $Gamma_k$, two quantities that were not considered related before. The successful comparison of this relation with the outcome of experiments and numerical simulations gives further support to the theory.
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 $k_dagger$, where phonons are no longer quantized into bands. For $k!<!k_dagger$, finite-size effects dominate $Gamma(k)$, which is quantitatively described by a theory of disordered phonon bands. For $k!>!k_dagger$, 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 ($k_0!>k_dagger$ 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.
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