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Register a new userEvidence of anomalous dispersion of the generalized sound velocity in glasses
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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.
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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.
Glass sound velocity shift was observed to be longarithmically temperature dependent in both relaxation and resonance regimes: $Delta c/c=mathcal{C}ln T$. It does not monotonically increase with temperature from $T=0$K, but to reach a maximum around a few Kelvin. Different from tunneling-two-level-system (TTLS) which gives the slope ratio between relaxation and resonance regimes $mathcal{C}^{rm rel }:mathcal{C}^{rm res }=-frac{1}{2}:1$, we develop a generic coupled block model to give $mathcal{C}^{rm rel }:mathcal{C}^{rm res }=-1:1$, which agrees well with the majority of experimental measurements. We use electric dipole-dipole interaction to carry out a similar behavior for glass dielectric constant shift $Delta epsilon/epsilon=mathcal{C}ln T$. The slope ratio between relaxation and resonance regimes is $mathcal{C}^{rm rel}:mathcal{C}^{rm res}=1:-1$ which agrees with dielectric measurements quite well. By developing a renormalization procedure for non-elastic stress-stress and dielectric susceptibilities, we prove these universalities essentially come from $1/r^3$ long range interactions, independent of materials microscopic properties.
We comment on three incorrect claims in the paper by Fomin et al (arXiv:1507.06094) concerning the generalized hydrodynamic methodology and positive sound dispersion in fluids.
The paper presents a description of the sound wave absorption in glasses, from the lowest temperatures up to the glass transition, in terms of two 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 extension of the tunneling model 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 model, which allows to determine the barrier density of the energy landscape of the specific glass from the frequency and temperature dependence of the sound wave absorption in the classical relaxation domain. To apply it properly at elevated temperatures, one needs its formulation in terms of the shear compliance. As one approaches the glass transition, universality sets in again with an exponential rise of the barrier density reflecting the frozen fast Kohlrausch t^beta-tail (in time t, with beta close to 1/2) of the viscous flow at the glass temperature. The validity of the scheme is checked for literature data of several glasses and polymers with and without secondary relaxation peaks. The frozen Kohlrausch tail of the mechanical relaxation shows no indication of the strongly temperature-dependent excess wing observed in dielectric data of molecular glasses with hydrogen bonds. Instead, the mechanical relaxation data indicate an energy landscape describable with a frozen temperature-independent barrier density for any glass.
The dielectric anomalies of window-type glasses at low temperatures ($T<$ 1 K) are rather successfully explained by the two-level systems (2LS) tunneling model (TM). However, the magnetic effects discovered in the multisilicate glasses in recent times cite{ref1}-cite{ref3}, and also some older data from mixed (SiO$_2$)$_{1-x}$(K$_2$O)$_x$ and (SiO$_2$)$_{1-x}$(Na$_2$O)$_x$ glasses cite{ref4}, indicate the need for a suitable generalization of the 2LS TM. We show that, not only for the magnetic effects cite{ref3,ref5} but also for the mixed glasses in the absence of a field, the right extension of the 2LS TM is provided by the (anomalous) multilevel tunneling systems approach proposed by one of us. It appears that new 2LS develop via dilution near the hull of the SiO$_4$-percolating clusters in the mixed glasses.
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