Interaction of Sound Waves with Thermal Phonons in Dielectric Crystals

Intermittent rearrangements accompanying thermal fluctuations distinguish glasses from crystals

Glasses exhibit vibrational and thermal properties that are markedly different from those of crystals. While recent works have advanced our understanding of vibrational excitations in glasses in the harmonic approximation limit, efforts in understanding finite-temperature anharmonic processes have been limited. In crystals, phonon-phonon coupling provides an extremely efficient mechanism for anharmonic decay that is also important in glasses. By using extensive molecular dynamics simulation of model atomic systems, here we first describe, both numerically and analytically, the anharmonic couplings in the crystal and the glass by focusing on the temperature dependence of the associated decay rates. Next, we show that an additional anharmonic channel of different origin emerges in the amorphous case, which induces unconventional intermittent rearrangements of particles. We have found that thermal vibrations in glasses trigger transitions among numerous different local minima of the energy landscape, which, however, are located within the same wide (meta)basin. These processes generate motions that are different from both diffusive and out-of-equilibrium aging dynamics. We suggest that (i) the observed intermittent rearrangements accompanying thermal fluctuations are crucial features distinguishing glasses from crystals and (ii) they can be considered as relics of the liquid state that survive the complete dynamic arrest taking place at the glass transition temperature.

Dissipation induced by phonon elastic scattering in crystals

We demonstrate that the phonon elastic scattering leads to a dominant dissipation in crystals at low temperature. The two-level systems (TLSs) should be responsible for the elastic scattering, whereas the dissipation induced by static-point defects (SPDs) can not be neglected. One purpose of this work is to show how the energy splitting distribution of the TLS ensemble affects the dissipation. Besides, this article displays the proportion of phonon-TLS elastic scattering to total phonon dissipation. The coupling coefficient of phonon-SPD scattering and the constant P₀ of the TLS distribution are important that we estimate their magnitudes in this paper. Our results is useful to understand the phonon dissipation mechanism, and give some clues to improve the performance of mechanical resonators, apply the desired defects, or reveal the atom configuration in lattice structure of disordered crystals.

Quality Factor Measurements of Various Types of Quartz Crystal Resonators Operating Near 4 K

Quartz crystal resonators can exhibit huge quality factors (in excess of 1 billion) at liquid-helium temperature. However, they must satisfy a set of conditions to meet this high level of performance. With the help of experimentation, the main conditions are identified, such as the material quality, the energy trapping due to the vibrational mode structure, as well as the corresponding influence of the support mechanism and the effects of the electrodes.

Second Harmonic Generation of Nanoscale Phonon Wave Packets

Phonons are often regarded as delocalized quasiparticles with certain energy and momentum. The anharmonic interaction of phonons determines macroscopic properties of the solid, such as thermal expansion or thermal conductivity, and a detailed understanding becomes increasingly important for functional nanostructures. Although phonon-phonon scattering processes depicted in simple wave-vector diagrams are the basis of theories describing these macroscopic phenomena, experiments directly accessing these coupling channels are scarce. We synthesize monochromatic acoustic phonon wave packets with only a few cycles to introduce nonlinear phononics as the acoustic counterpart to nonlinear optics. Control of the wave vector, bandwidth, and consequently spatial extent of the phonon wave packets allows us to observe nonlinear phonon interaction, in particular, second harmonic generation, in real time by wave-vector-sensitive Brillouin scattering with x-rays and optical photons.

Lifetime of high-order thickness resonances of thin silicon membranes

Femtosecond laser pulses are used to excite and probe high-order longitudinal thickness resonances at a frequency of ∼270 GHz in suspended Si membranes with thickness ranging from 0.4 to 15 μm. The measured acoustic lifetime scales linearly with the membrane thickness and is shown to be controlled by the surface specularity which correlates with roughness characterized by atomic force microscopy. Observed Q-factor values up to 2400 at room temperature result from the existence of a local maximum of the material Q in the sub-THz range. However, surface specularity would need to be improved over measured values of ∼0.5 in order to achieve high Q values in nanoscale devices. The results support the validity of the diffuse boundary scattering model in analyzing thermal transport in thin Si membranes.

Intrinsic to extrinsic phonon lifetime transition in a GaAs-AlAs superlattice

We have measured the lifetimes of two zone-center longitudinal acoustic phonon modes, at 320 and 640 GHz, in a 14 nm GaAs/2 nm AlAs superlattice structure. By comparing measurements at 296 and 79 K we separate the intrinsic contribution to phonon lifetime determined by phonon-phonon scattering from the extrinsic contribution due to defects and interface roughness. At 296 K, the 320 GHz phonon lifetime has approximately equal contributions from intrinsic and extrinsic scattering, whilst at 640 GHz it is dominated by extrinsic effects. These measurements are compared with intrinsic and extrinsic scattering rates in the superlattice obtained from first-principles lattice dynamics calculations. The calculated room-temperature intrinsic lifetime of longitudinal phonons at 320 GHz is in agreement with the experimentally measured value of 0.9 ns. The model correctly predicts the transition from predominantly intrinsic to predominantly extrinsic scattering; however the predicted transition occurs at higher frequencies. Our analysis indicates that the 'interfacial atomic disorder' model is not entirely adequate and that the observed frequency dependence of the extrinsic scattering rate is likely to be determined by a finite correlation length of interface roughness.

Interaction of collinear and noncollinear phonons in anharmonic scattering processes and their role in ultrasound absorption of fast quasi-transverse modes in cubic crystals

The absorption of fast quasi-transverse modes during anharmonic scattering processes in cubic crystals with positive (Ge, Si, diamond and InSb) or negative (KCl and CaF(2)) anisotropies of the second-order elastic moduli is studied. Mechanisms underlying the relaxation of the fast quasi-transverse mode by two fast (the FFF mechanism) or two slow (the FSS) modes are discussed in the long-wavelength approximation. Angular dependences of the ultrasound absorption for the FFF, FSS and Landau-Rumer relaxation mechanisms are analyzed in terms of the anisotropic continuum model. The full absorption of the fast quasi-transverse mode is determined. The problem of the scattering of collinear and noncollinear phonons in cubic crystals and their role in the ultrasound absorption of the fast quasi-transverse modes is considered. It is shown that the FFF and FSS relaxation mechanisms are due to the cubic anisotropy of the crystals, leading to the interaction between noncollinear phonons. In crystals with a considerable anisotropy of the elastic energy (InSb and KCl), the total contribution of the FFF and FSS relaxation mechanisms to the full absorption is one to two orders of magnitude larger than the contribution from the Landau-Rumer mechanism, depending on the direction. Much of the dominance of the former relaxation mechanisms over the Landau-Rumer mechanism is explained by second-order elastic moduli. The role of the Landau-Rumer mechanism in ultrasound absorption may be considerable in cubic crystals with a smaller anisotropy of the elastic energy. It is demonstrated that when anharmonic scattering processes play the dominant role, the inclusion of one of the relaxation mechanisms (the Landau-Rumer mechanism or the FFF or FSS mechanisms of relaxation) is insufficient for the quantitative description of the anisotropy of the full absorption of the fast quasi-transverse modes in cubic crystals.

Ultrasonic properties near 50 K of the quasi-one-dimensional conductors A(0.30)MoO(3) (A = K, Rb) and Rb(0.30)(Mo(1-x)V(x))O(3)

The charge density wave (CDW) nonlinear conductivity of the blue bronzes A(0.30)MoO(3) (A = K, Rb) shows two different regimes depending on the temperature: a strongly damped CDW motion above ∼50 K and a CDW motion with almost no damping below ∼50 K. In a search for an elastic signature of this CDW behaviour, we performed ultrasonic measurements on A(0.30)MoO(3) single crystals in the temperature range 4-300 K. In Rb(0.30)MoO(3), at T∼50 K, upon cooling, a large increase of the sound velocity for the longitudinal mode measured along the [Formula: see text], [102] and b directions is observed. The ultrasonic attenuation coefficient shows an increase down to 50 K followed by a plateau. Similar results are found in K(0.30)MoO(3). In V-doped samples, Rb(0.30)(Mo(1-x)V(x))O(3) (x = 0.4%) the anomaly broadens and is shifted towards higher temperatures. The results are discussed in relation to the changes in the CDW rigidity, disorder and dielectric response. A scenario based on a glass transition for the CDW superstructure is proposed.

Anharmonic processes of scattering and absorption of slow quasi-transverse modes in cubic crystals with positive and negative anisotropies of second-order elastic moduli

The quasi-transverse ultrasound absorption during anharmonic processes of the scattering in cubic crystals with positive (Ge, Si, diamond and InSb) and negative (KCl and NaCl) anisotropies of the second-order elastic moduli is studied. Mechanisms underlying the relaxation of the slow quasi-transverse mode by two slow (the SSS mechanism) or two fast (the SFF) modes are discussed in the long-wavelength approximation. Angular dependences of the ultrasound absorption for the SSS, SFF and Landau-Rumer relaxation mechanisms are analyzed in terms of the anisotropic continuum model. The full absorption of the slow quasi-transverse mode is determined. It is shown that the SSS and SFF relaxation mechanisms are due to the cubic anisotropy of the crystals, leading to the interaction between noncollinear phonons. Two most important cases-the wavevectors of phonons are in the cube face plane or the diagonal planes-are considered. In crystals with a considerable anisotropy of the elastic energy (Ge, Si, InSb, KCl and NaCl) the total contribution of the SSS and SFF relaxation mechanisms to the full absorption is either several times or one to two orders of magnitude larger than the contribution from the Landau-Rumer mechanism depending on the direction. Much of the dominance of the former relaxation mechanisms over the Landau-Rumer mechanism is explained by second-order elastic moduli.