Generation of higher acoustic harmonics at a flat rough interface between two solids

The results of experimental studies of the influence of a static pressure applied to a flat rough interface between two solids on its nonlinear elastic properties are presented. The studies were performed by the spectral method on the basis of an analysis of the efficiency of generation of higher acoustic harmonics, which arise upon the reflection of a longitudinal elastic wave of finite amplitude from the boundary and the passage through it. A nonmonotonic dependence of the amplitudes of acoustic harmonics on the value of the external reversible static pressure applied to the interface was revealed: pronounced amplitude maxima for the amplitudes of the second and third harmonics were observed with a decrease in the external static pressure. It was also found that the amplitudes of the second, third, and fourth acoustic harmonics increase with a decrease in the external static pressure (in comparison with their values at the same pressure values during its increase). The experimentally determined power dependence of the higher acoustic harmonics on the amplitude of the first acoustic harmonic significantly differed from the classical indices for these harmonics. The influence of the external pressure on the values of the nonlinear second- and third-order elastic parameters was analyzed. The experimental results were analyzed on the basis of nonclassical acoustic nonlinearity.     

粗糙接触界面超声非线性效应的概率模型

提出描述粗糙接触界面超声非线性效应的概率模型,利用分段均匀概率函数描述粗糙接触界面劲度系数变化,结合表面粗糙峰的几何分布特征,得到界面粗糙度和两侧表面相对运动对声波的非线性调制作用。实验观测了铝合金材料的粗糙接触界面的高次谐波现象和阈值现象,进一步分析了归一化非线性参数与界面加载压力、粗糙度之间的关系。实验测量结果与概率模型的理论预测一致,证明了该模型的正确性,为利用超声非线性效应评价粗糙接触界面提供了理论依据。     

Linear and nonlinear Biot waves in a noncohesive granular medium slab: transfer function, self-action, second harmonic generation

Experimental results are reported on second harmonic generation and self-action in a noncohesive granular medium supporting wave energy propagation both in the solid frame and in the saturating fluid. The acoustic transfer function of the probed granular slab can be separated into two main frequency regions: a low frequency region where the wave propagation is controlled by the solid skeleton elastic properties, and a higher frequency region where the behavior is dominantly due to the air saturating the beads. Experimental results agree well with a recently developed nonlinear Biot wave model applied to granular media. The linear transfer function, second harmonic generation, and self-action effect are studied as a function of bead diameter, compaction step, excitation amplitude, and frequency. This parametric study allows one to isolate different propagation regimes involving a range of described and interpreted linear and nonlinear processes that are encountered in granular media experiments. In particular, a theoretical interpretation is proposed for the observed strong self-action effect.     

Determination of elastic properties of Si/Ge superlattices and Si1-xGex films from surface acoustic modes by Brillouin scattering

Surface acoustic waves (SAW) have been measured by means of Brillouin scattering (BS) both as a function of k×h and the direction of k in the sample plane (k is the wavevector of the surface acoustic mode and h the thickness of the film). The velocity of the Rayleigh wave on sufficiently thick films (h > 4000 Å) has been experimentally found to ve uneffected by the elastic properties of the substrate material. Thus the directional dependence of the hypersonic surface wave is completely determined by the elastic properties of the layer material alone and reflects its crystallographic symmetry. The SL's can be treated as media with effective elastic constants because the wavelength of the thermally excited Rayleigh wave is much longer than the SL period. Furthermore, the angular dispersion of the SAW can be used to calculate the elastic constants of each film separately.     

Influence of the surrounding pressure on acoustic properties of slightly compressible porous media permeated with air-filled bubbles

The effective wave velocity, attenuation, and nonlinear properties of slightly compressible porous media permeated with air-filled bubbles are studied numerically by employing the nonlinear Hooke’s law for different surrounding pressures. Numerical simulations show that the acoustic properties of porous media are greatly affected by the surrounding pressure if the shear modulus of the elastic medium is very small due to the fact that the acoustic wave propagation in porous media are strongly influenced by the nonlinear oscillation of bubbles; moreover, the oscillation of a bubble depends on the equilibrium bubble radius, which is affected by the surrounding pressures. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 4, pp. 490–496. The text was submitted by the authors in English.     

Dispersion and Attenuation of Surface Acoustic Waves of Various Polarizations on a Stress-Free Randomly Rough Surface of Solid

An approach to obtaining the dispersion equation of surface acoustic waves (SAWs) on a stress-free, randomly rough surface of an anisotropic elastic medium is suggested. The problem is solved in the approximation of a weakly rough surface using Green′s function technique. The dispersion and attenuation of sagittally and shear horizontally (SH) polarized SAWs are investigated both analytically and numerically for a three-dimensionally (3D) and a two-dimensionally (2D) rough surface of an isotropic medium. The results for 2D roughness are shown to be contained in the more general expressions for the 3D case, and the connection between the results for the 3D and the 2D cases is pointed out. Dispersion relations are derived for SAWs of both polarizations propagating in an arbitrary direction along a 2D rough surface. The SAW attenuation mechanisms are investigated at various incidence angles. It is concluded that all three mechanisms (viz. scattering into bulk transverse, longitudinal, and Rayleigh surface acoustic waves) are involved for the Rayleigh and SH polarized SAWs at certain incidence angles, whereas at the other angles only some of the mechanisms are. The criterion for the existence of SH polarized SAWs on a rough surface is considered. A possible increase of the SAW phase velocity on a rough surface compared with that for a flat boundary is discussed. In the limit λ a (where a is the roughness correlation length) simple explicit expressions for the phase velocities of Rayleigh and SH polarized SAWs are derived. A comparison of the results obtained herein with those of other workers is presented.     

Interaction of a Surface Acoustic Wave with a Two-dimensional Electron Gas

When a surface acoustic wave （SAW） propagates on the surface of a GaAs semiconductor, coupling between electrons in the two-dimensional electron gas beneath the interface and the elastic host crystal through piezoelectric interaction will attenuate the SAW. The coupling coemcient is ~alculated for the SAW propagating along an arbitrary direction. It is found that the coupling strength is strongly dependent on the propagating direction. When the SAW propagates along the [011] direction, the coupling becomes quite weak.     

Effects of surface roughness on surface acoustic wave propagation in semiconductor materials

The effect of surface roughness on adhesion and tribological properties of films and interfaces is of key importance. Therefore, it is of utmost importance to be able to measure this quantity and to predict the effects that different roughness levels may cause. Roughness affects the propagation of surface acoustic waves on a material but there is little useful quantitative data on the topic. This work investigates the dispersive effect of roughness on surface acoustic wavepackets (30-200 MHz frequency range) for different degrees of nanometer roughness on silicon (0 0 1) and (1 1 1) surfaces, we show that the roughness-induced frequency dispersion effect is significant, and that although available theories agree qualitatively with the results, the theory is not adequate to predict the real SAW dispersion. These experimental results have considerable implications for design of SAW devices, for accuracy of Brillouin spectroscopy measurements, and for possible applications to non-destructive testing of materials. Previously unknown dispersive effects on anisotropic crystal surfaces are also demonstrated.     

Interaction of a Surface Acoustic Wave with a Two-dimensional Electron Gas

When a surface acoustic wave (SAW) propagates on the surface of a GaAs semiconductor, coupling between electrons in the two-dimensional electron gas beneath the interface and the elastic host crystal through piezoelectric interaction will attenuate the SAW. The coupling coefficient is calculated for the SAW propagating along an arbitrary direction. It is found that the coupling strength is strongly dependent on the propagating direction. When the SAW propagates along the [011] direction, the coupling becomes quite weak.     

由于表面粗糙引起的激光声表面波色散的实验和理论研究

表面粗糙是材料制造过程中必有的副产物, 粗糙表面会引起其中传播的声表面波的速度发生变化. 在利用激光声表面波对材料性质进行评估时, 常用宽带的激光声表面波速度频散特性对材料性质进行反演. 为了研究表面粗糙度是否能作为反演的特征参数之一, 本文建立了激光在表面粗糙样品中激发声表面波、聚偏氟乙烯换能器宽带接收声表面波的实验装置来研究不同粗糙度表面对声表面波速度的影响; 理论上建立了激光在粗糙表面中激发声表面波的计算模型, 利用有限元法得到声表面波的时域特征, 并进一步得到声表面波的速度色散曲线, 理论结果和实验结果能很好地拟合. 这为利用激光声表面波对表面粗糙的评估提供理论和实验依据. 关键词： 表面粗糙 激光声表面波 速度色散 聚偏氟乙烯传感器 有限元法     

Nonlinear surface acoustic waves: silicon strength in phonon-focusing directions

The anisotropy of the elastic properties of single-crystal silicon manifests itself in features of both the linear and nonlinear surface acoustic wave (SAW) propagation. Directions showing the phonon-focusing effect and strong nonlinearity were employed in contact-free and notch-free laser-based fracture experiments, yielding the intrinsic strength of silicon. The critical tensile stress values vary between 2.5 GPa and 7 GPa for the different crystallographic planes and directions of SAW propagation investigated.     

Nonlinear surface acoustic waves: realization of solitary pulses and fracture

A laser-based technique for the contact-free generation and detection of strongly nonlinear surface acoustic wave (SAW) pulses with amplitudes limited by the materials strength has been developed. The effects of nonlinear propagation of short elastic surface pulses with finite strength in isotropic solids, such as fused quartz, anisotropic solids, such as silicon, and dispersive media were investigated. Solitary surface wave propagation was observed in layered structures for normal and anomalous dispersion. In addition, a SAW-based method for evaluating the critical fracture stress of anisotropic brittle solids, such as single crystal silicon, is introduced.     

The self-induced transparency for the surface acoustic wave

The theory of the self-induced transparency is constructed for the surface acoustic wave which is propagated on the interface with two elastic media when two-level systems are present. The expressions for the surface acoustic nonlinear wave (soliton) were obtained.     

Acoustic scattering by a three-dimensional elastic object near a rough surface

The ensemble-averaged field scattered by a smooth, bounded, elastic object near a penetrable surface with small-scale random roughness is formulated. The formulation consists of combining a perturbative solution for modeling propagation through the rough surface with a transition (T-) matrix solution for scattering by the object near a planar surface. All media bounding the rough surface are assumed to be fluids. By applying the results to a spherical steel shell buried within a rough sediment bottom, it is demonstrated that the ensemble-averaged "incoherent" intensity backscattered by buried objects illuminated with shallow-grazing-angle acoustic sources can be well enhanced at high frequencies over field predictions based on scattering models where all environmental surfaces are planar. However, this intensity must compete with the incoherent intensity scattered back from the interface itself, which can defeat detection attempts. The averaged "coherent" component of the field maintains the strong evanescent spectral decay exhibited by flat interface predictions of shallow-angle measurements but with small deviations. Nevertheless, bistatic calculations of the coherent field suggest useful strategies for improving long-range detection and identification of buried objects.     

Recursive Green functions technique applied to the propagation of elastic waves in layered media

Guided by similarities between electronic and classical waves, a numerical code based on a formalism proven to be very effective in condensed matter physics has been developed, aiming to describe the propagation of elastic waves in stratified media (e.g. seismic signals). This so-called recursive Green function technique is frequently used to describe electronic conductance in mesoscopic systems. It follows a space-discretization of the elastic wave equation in frequency domain, leading to a direct correspondence with electronic waves travelling across atomic lattice sites. An inverse Fourier transform simulates the measured acoustic response in time domain. The method is numerically stable and computationally efficient. Moreover, the main advantage of this technique is the possibility of accounting for lateral inhomogeneities in the acoustic potentials, thereby allowing the treatment of interface roughness between layers.     

Generalization of the Fresnel law to the case of a pressure-wave-induced displacement of the interface between acoustic media

The problem of interaction between a nonsteady-state pressure wave and a moving interface between acoustic media is analyzed and solved for the first time with allowance for a finite displacement of the interface induced by the wave. An analytic solution is obtained using a nonlinear time transformation method. Expressions are obtained for the law of motion of the interface, and for the reflected and transmitted waves as a function of the time profile of the incident wave and the acoustic characteristics of the media. Zh. Tekh. Fiz. 69, 114–115 (April 1999)     

Nonlinear wave processes in porous waterlike media containing a system of capillaries partially filled with a viscous liquid

A nonlinear dynamic state equation of waterlike porous material that contains a system of cylindrical capillaries partially filled with viscous liquid was received. It is shown that an acoustic nonlinearity of such media contains the relaxation elastic and inelastic components due to the nonlinear dependence of the capillary and viscous pressure in fluid on the capillary diameter. For the medium, theoretical study of such nonlinear phenomena as generation of the second harmonic and a difference frequency wave, self-demodulation of high-frequency pulses as well as the change in the propagation velocity and absorption coefficient of a test wave being under an action of static loading have been carried out. The frequency dependences of medium nonlinearity parameters for these processes were determined.     

Scattering of time-harmonic elastic waves by an elastic inclusion with quadratic nonlinearity

This paper considers the scattering of a plane, time-harmonic wave by an inclusion with heterogeneous nonlinear elastic properties embedded in an otherwise homogeneous linear elastic solid. When the inclusion and the surrounding matrix are both isotropic, the scattered second harmonic fields are obtained in terms of the Green's function of the surrounding medium. It is found that the second harmonic fields depend on two independent acoustic nonlinearity parameters related to the third order elastic constants. Solutions are also obtained when these two acoustic nonlinearity parameters are given as spatially random functions. An inverse procedure is developed to obtain the statistics of these two random functions from the measured forward and backscattered second harmonic fields.     

纳米接触过程中黏着规律的变化

本文应用大规模分子动力学方法, 模拟了两种具有不同粗糙形貌的、刚性球形探头与弹性平面基体之间的纳米尺度接触, 计算了探头与基体之间的拉离力和黏着功, 研究了接触过程中界面黏着力随载荷的变化规律, 分析了接触界面原子的法向应力分布. 研究发现, 原子级光滑接触的黏着力随着载荷的增大而线性增大, 而原子级粗糙接触的黏着力-载荷曲线分为以不同斜率增长的两个阶段. 相比于原子级光滑探头, 原子级粗糙探头与基体之间具有较小的拉离力和黏着功, 却在接触过程中形成了较大的黏着力. 因此, 拉离力和黏着功不能表征出纳米接触过程中原子吸引作用对界面法向力的贡献大小.