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Register a new userAnomalous Sound Velocity and Dielectric Shift in Glass: a Renormalization Technique for Mechanical and Dielectric Susceptibilities from Generic Coupled Block Model
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Di Zhou
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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.
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In low-temperature glasses, the sound velocity changes as the logarithmic function of temperature below $10$K: $[c(T) - c(T_0)]/c(T_0) = mathcal{C}ln(T/T_0)$. With increasing temperature starting from $T=0$K, the sound velocity does not increase monotonically, but reaches a maximum at a few Kelvin and decreases at higher temperatures. Tunneling-two-level-system (TTLS) model explained the $ln T$ dependence of sound velocity shift. In TTLS model the slope ratio of $ln T$ dependence of sound velocity shift between lower temperature increasing regime (resonance regime) and higher temperature decreasing regime (relaxation regime) is $mathcal{C}^{rm res }:mathcal{C}^{rm rel }=1:-frac{1}{2}$. In this paper we develop the generic coupled block model to prove the slope ratio of sound velocity shift between two regimes is $mathcal{C}^{rm res }:mathcal{C}^{rm rel }=1:-1$ rather than $1:-frac{1}{2}$, which agrees with the majority of the measurements. The dielectric constant shift in low-temperature glasses, $[epsilon_r(T)-epsilon_r(T_0)]/epsilon_r(T_0)$, has a similar logarithmic temperature dependence below $10$K: $[epsilon(T)-epsilon(T_0)]/epsilon(T_0) = mathcal{C}ln(T/T_0)$. In TTLS model the slope ratio of dielectric constant shift between resonance and relaxation regimes is $mathcal{C}^{rm res}:mathcal{C}^{rm rel}=-1:frac{1}{2}$. In this paper we apply the electric dipole-dipole interaction, to prove that the slope ratio between two regimes is $mathcal{C}^{rm res}:mathcal{C}^{rm rel} = -1:1$ rather than $-1:frac{1}{2}$. Our result agrees with the dielectric constant measurements. By developing a real space renormalization technique for glass non-elastic and dielectric susceptibilities, we show that these universal properties essentially come from the $1/r^3$ long range interactions, independent of the materials microscopic properties.
We propose a microscopic model to study the avalanche problem of insulating glass deformed by external static uniform strain below $T=60$K. We use three-dimensional real-space renormalization procedure to carry out the glass mechanical susceptibility at macroscopic length scale. We prove the existence of irreversible stress drops in amorphous materials, corresponding to the steep positive-negative transitions in glass mechanical susceptibility. We also obtain the strain directions in which the glass system is brittle. The irreversible stress drops in glass essentially come from non-elastic stress-stress interaction which is generated by virtual phonon exchange process.
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.
In this work we provide a thorough examination of the nonlinear dielectric properties of a succinonitrile-glutaronitrile mixture, representing one of the rare example of a plastic crystal with fragile glassy dynamics. The detected alteration of the complex dielectric permittivity under high fields can be explained considering the heterogeneous nature of glassy dynamics and a field-induced variation of entropy. While the first mechanism was also found in structural glass formers, the latter effect seems to be typical for plastic crystals. Morover, the third harmonic component of the dielectric susceptibility is reported, revealing a spectral shape as predicted for cooperative molecular dynamics. In accord with the fragile nature of the glass transition in this plastic crystal, we deduce a relatively strong temperature dependence of the number of correlated molecules, in contrast to the much weaker temperature dependence in plastic-crystalline cyclo-octanol, whose glass transition is of strong nature.
The glassy dynamics of plastic-crystalline cyclo-octanol and ortho-carborane, where only the molecular reorientational degrees of freedom freeze without long-range order, is investigated by nonlinear dielectric spectroscopy. Marked differences to canonical glass formers show up: While molecular cooperativity governs the glassy freezing, it leads to a much weaker slowing down of molecular dynamics than in supercooled liquids. Moreover, the observed nonlinear effects cannot be explained with the same heterogeneity scenario recently applied to canonical glass formers. This supports ideas that molecular relaxation in plastic crystals may be intrinsically non-exponential. Finally, no nonlinear effects were detected for the secondary processes in cyclo-octanol.
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