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Register a new userFrustration and sound attenuation in structural glasses
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Three classes of harmonic disorder systems (Lennard-Jones like glasses, percolators above threshold, and spring disordered lattices) have been numerically investigated in order to clarify the effect of different types of disorder on the mechanism of high frequency sound attenuation. We introduce the concept of frustration in structural glasses as a measure of the internal stress, and find a strong correlation between the degree of frustration and the exponent alpha that characterizes the momentum dependence of the sound attenuation $Gamma(Q)$$simeq$$Q^alpha$. In particular, alpha decreases from about d+1 in low-frustration systems (where d is the spectral dimension), to about 2 for high frustration systems like the realistic glasses examined.
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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 $Gamma$ 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.
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 dynamic structure factor, S(Q,w), of vitreous silica, has been measured by inelastic X-ray scattering in the exchanged wavevector (Q) region Q=4-16.5 nm-1 and up to energies hw=115 meV in the Stokes side. The unprecedented statistical accuracy in such an extended energy range allows to accurately determine the longitudinal current spectra, and the energies of the vibrational excitations. The simultaneous observation of two excitations in the acoustic region, and the persistence of propagating sound waves up to Q values comparable with the (pseudo-)Brillouin zone edge, allow to observe a positive dispersion in the generalized sound velocity that, around Q=5 nm-1, varies from 6500 to 9000 m/s: this phenomenon was never experimentally observed in a glass.
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 and verify that it agrees with results of earlier sound attenuation simulations. The small wavevector analysis of this expression shows that sound attenuation is primarily determined by the non-affine displacements contribution to the wave propagation coefficient coming from the frequency shell of the sound wave.
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