Measurement of material nonlinearity using surface acoustic wave parametric interaction and laser ultrasonics

A dual frequency mixing technique has been developed for measuring velocity changes caused by material nonlinearity. The technique is based on the parametric interaction between two surface acoustic waves (SAWs): The low frequency pump SAW generated by a transducer and the high frequency probe SAW generated and detected using laser ultrasonics. The pump SAW stresses the material under the probe SAW. The stress (typically <5 MPa) is controlled by varying the timing between the pump and probe waves. The nonlinear interaction is measured as a phase modulation of the probe SAW and equated to a velocity change. The velocity-stress relationship is used as a measure of material nonlinearity. Experiments were conducted to observe the pump-probe interaction by changing the pump frequency and compare the nonlinear response of aluminum and fused silica. Experiments showed these two materials had opposite nonlinear responses, consistent with previously published data. The technique could be applied to life-time predictions of engineered components by measuring changes in nonlinear response caused by fatigue.     

Solitary surface acoustic waves and bulk solitons in nanosecond and picosecond laser ultrasonics

Recent achievements of nonlinear acoustics concerning the realization of solitons and solitary waves in crystals and their surfaces attained by nanosecond and picosecond laser ultrasonics are discussed and compared. The corresponding pump-probe setups are described, which allow an all-optical contact-free excitation and detection of short strain pulses in the broad frequency range between 10 MHz and about 300 GHz. The formation of solitons in the propagating longitudinal strain pulses is investigated for nonlinear media with intrinsic lattice-based dispersion. The excitation of solitary surface acoustic waves is realized by a geometric film-based dispersion effect. Future developments and potential applications of nonlinear nanosecond and picosecond ultrasonics are discussed.     

Measurement of the elastic properties of evaporated C60 films by surface acoustic waves

Surface Acoustic Wave (SAW) pulses were excited in C₆₀ films deposited on quartz and silicon substrates using pulses from excimer lasers with wavelengths of 248 nm and 308 nm for excitation. An optical beam-deflection technique and polymer electret transducers were utilized to detect the propagation of the SAW pulse with high spatial and temporal resolution, allowing an accuracy of better than 0.1% for SAW velocity measurements. With this technique the frequency dependence of the SAW velocity was determined for a number of fullerite films and density, as well as elastic bulk properties of the films were derived by a theoretical analysis of the dispersion effect.     

Evolution of acoustic waves in microinhomogeneous media with quadratic elastic nonlinearity and relaxation

A nonlinear wave equation for the velocity “relaxator” is derived in the framework of the rheological model and the corresponding equation of state of a microinhomogeneous medium containing viscoelastic defects with quadratic nonlinear elasticity. The equation is qualitatively analyzed, and numerical solutions to it are presented for a stationary symmetric shock wave and the evolution of initially harmonic waves.     

Nanoscale self-organization using standing surface acoustic waves

The diffusion of an adatom on a substrate submitted to a standing surface acoustic wave is theoretically studied. By performing large scale molecular dynamic simulations, we show that the wave dynamically structures the substrate by encouraging the presence of the adatom in the vicinity of the maximum displacements of the substrate. Using an analytical model, we explain this feature introducing an effective potential induced by the wave. Applied in an atomic deposition experiment, this dynamic structuring process should govern the nucleation sites distribution opening the route to accurately control the self-organization process at the nanoscale.     

Angular and frequency dependence of light diffracted by surface acoustic waves

The intensity of light diffracted by surface acoustic waves is described by its spectrum, which contains all the harmonics of the acoustic frequency. A formulation is given, mainly for the first harmonic angular dependence, taking into account most of the experimental parameters. Calculated results are compared with experimental data. Optimum conditions for detection are given for a wide range of frequencies.     

Study of surface and bulk acoustic phonon excitations in superlattices using picosecond ultrasonics

We have performed picosecond ultrasonic studies on the surface and bulk acoustic phonons in amorphous Mo/Si superlattices. Localized surface modes within the first, second, and sixth frequency gaps of the zone-folded phonons are observed. A selection rule derived from symmetry considerations provides new understanding of why certain modes are seen and not the others. The excitation strengths and detailed spectral features of these lines are studied, and the results are well explained by an elastic-continuum theory. It is found that the line shapes are significantly modified by the presence of bulk modes near the zone center.     

Diagnostics of elastic properties of a planar interface between two rough media using surface acoustic waves

The results of experimental studies on the nonlinear elastic properties of a planar interface between two media are presented—an optically polished glass substrate and flat samples with different degrees of roughness. The nonlinear elastic properties of the interfaces between two media were investigated by the spectral method using surface acoustic waves (SAWs). The effect of external pressure applied to the interface on the efficiency of the generation of the second SAW harmonic was studied. Using the measured amplitudes of the first and second harmonics of the SAW that passes along the interface, the second-order nonlinear acoustic parameter was calculated as a function of the external pressure applied to the sample at a fixed amplitude of a probing wave. It was revealed that the nonlinear parameter of the SAW is a nonmonotonic function of the pressure at the boundary. The results were analyzed on the basis of an elastic contact nonlinearity, and it is concluded that these results can be used in nondestructive testing for roughness and waviness of surfaces of flat solids.     

Investigation of surface acoustic waves in laser shock peened metals

Laser shock peening is a well-known method for extending the fatigue life of metal components by introducing near-surface compressive residual stress. The surface acoustic waves (SAWs) are dispersive when the near-surface properties of materials are changed. So the near-surface properties (such as the thickness of hardened layers, elastic properties, residual stresses, etc.) can be analyzed by the phase velocity dispersion. To study the propagation of SAWs in metal samples after peening, a more reasonable experimental method of broadband excitation and reception is introduced. The ultrasonic signals are excited by laser and received by polyvinylindene fluoride (PVDF) transducer. The SAW signals in aluminum alloy materials with different impact times by laser shock peening are detected. Signal spectrum and phase velocity dispersion curves of SAWs are analyzed. Moreover, reasons for dispersion are discussed.     

High-performance modeling acoustic and elastic waves using the parallel Dichotomy Algorithm

A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant elliptic operator and different right-hand sides via the integral Laguerre transform. It is proposed to solve difference equations by the conjugate gradient method for acoustic equations and by the GMRES(k) method for modeling elastic waves. A preconditioning operator was the Laplace operator that is inverted using the variable separation method. The novelty of the proposed algorithm is using the Dichotomy Algorithm [26], which was designed for solving a series of tridiagonal systems of linear equations, in the context of the preconditioning operator inversion. Via considering analytical solutions, it is shown that modeling wave processes for long instants of time requires high-resolution meshes. The proposed parallel fine-mesh algorithm enabled to solve real application seismic problems in acceptable time and with high accuracy. By solving model problems, it is demonstrated that the considered parallel algorithm possesses high performance and efficiency over a wide range of the number of processors (from 2 to 8192).     

Optical method for measuring the coupling constant of surface acoustic waves

The coupling constant of common or thin-layered-piezoelectric interdigital transducers for surface acoustic waves up to the highest frequencies can be determined in an optical way with reproducibility better than 3%. Being a nondestructive and noncontact method one can apply it in the technological process for fabricating uniform piezoelectric layered transducers.     

Exfoliation of metal-organic framework nanosheets using surface acoustic waves

Two-dimensional (2D) metal–organic framework (MOF) nanosheets have recently received extensive attention due to their ultra-thin thickness, large specific surface area, chemical and functional designability. In this study, an unconventional method using surface acoustic wave (SAW) technology is proposed to exfoliate large quantities and uniform layers of 2D MOF-Zn₂(bim)₄ nanosheets in a microfluidic system. We successfully demonstrated that the thickness of 2D MOF is effectively and accurately controlled by optimizing the SAW parameters. The mechanisms for the efficient exfoliation of 2D MOF nanosheets is attributed to both the electric and acoustic fields generated by the SAWs in the liquid. The electric field ionizes the methanol to produce H⁺ ions, which intercalate Zn₂(bim)₄ sheets and weaken the interlayer bonding, and the strong shear force generated by SAWs separates the MOF sheets. A yield of 66% for monolayer MOFs with a maximum size of 3.5 μm is achieved under the combined effect of electric and acoustic fields. This fast, low-energy exfoliation platform has the potential to provide a simple and scalable microfluidic exfoliation method for production of large-area and quantities of 2D MOFs.     

The explicit secular equation for surface acoustic waves in monoclinic elastic crystals

The secular equation for surface acoustic waves propagating on a monoclinic elastic half-space is derived in a direct manner, using the method of first integrals. Although the motion is at first assumed to correspond to generalized plane strain, the analysis shows that only two components of the mechanical displacement and of the tractions on planes parallel to the free surface are nonzero. Using the Stroh formalism, a system of two second order differential equations is found for the remaining tractions. The secular equation is then obtained as a quartic for the squared wave speed. This explicit equation is consistent with that found in the orthorhombic case. The speed of subsonic surface waves is then computed for 12 specific monoclinic crystals.     

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.     

A two-dimensional analysis of surface acoustic waves in finite elastic plates with eigensolutions

It is generally known that surface acoustic waves, or Rayleigh waves, have different mode shapes in infinite plates. To be precise, there are both exponentially decaying and growing components in plates appearing in pairs, representing symmetric and antisymmentric modes in a plate. As the plate thickness increases, the combined modes will approach the Rayleigh mode in a semi-infinite solid, exhibiting surface acoustic wave deformation and velocity. In this study, the two-dimensional theory for surface acoustic waves in finite plates is extended to include the exponentially growing modes in the expansion function. With these extra equations, we study the surface acoustic waves in a plate with different thickness to examine the coupling of the exponentially decaying and growing modes. It is found that for small thickness, the two groups of waves are strongly coupled, showing the significance of including the effect of thickness in analysis. As the thickness increases to certain values, such as more than five wavelengths, the exponentially decaying modes alone will be able to predict vibrations of surface acoustic wave modes accurately, thus simplifying the equations and solutions significantly. Supported by Qianjiang River Fund established by Zhejiang Provincial Government and Ningbo University and administered by Ningbo University and the National Natural Science Foundation of China (Grant No. 10572065)     

Investigation of solid/solid interface waves with laser ultrasonics

A new method for detection of the soild/soild interface wave with laser ultrasonics is introduced in this paper. Based on the interaction between the acoustic wave and the probe laser beam of an interferometer in a transparent solid, the Stoneley waves propagated along the quartz/steel interface are detected successfully. The dispersion properties of Leaky Rayleigh wave are studied when the boundary conditions are described by interface spring mode. The Leaky Rayleigh wave at Plexiglas/aluminum interface is also detected and the experimental results are in good agreement with the theoretical results. It shows that the interface wave should be a powerful technique for evaluation of the interface properties.     

Generation and detection of acoustic solitons in crystalline slabs by laser ultrasonics

Acoustic solitons have been recently observed in different systems (Si, Sapphire, MgO, alpha-quartz). Such acoustic waves could lead to sub-picosecond acoustic pulses. In this paper, we report on the formation of acoustic solitons in a GaAs crystalline slab. A short picosecond acoustic pulse is generated by absorption of a femtosecond laser pulse in an aluminum thin film deposited on one side of the slab. This strain pulse travels through the sample up to the opposite side where it is detected by a time delayed laser pulse reflected by an aluminum transducer. We use interferometric detection to measure independently the real and imaginary parts of the relative change in optical reflectivity induced by the acoustic pulse. We find that, at low temperature and with a laser pump pulse energy of 10 nJ, an acoustic soliton clearly separates from the acoustic pulse in GaAs slab. The soliton shape is compared with numerical simulations for different excitation conditions. From the very unique properties of solitons, we infer a soliton pulse duration of about 2.3 ps which corresponds to a spatial extent of only 12 nm.     

Measurement of the acoustic nonlinearity parameter in 1-alkanols

We present a harmonic generation method based on a pitch-catch experimental setup and the calculation of the corresponding nonlinear parameter in 1-alkanols, from methanol to 1-decanol. By focusing a 14 MHz ultrasonic toneburst through a spherical quartz lens in these alcohols, a second harmonic is produced and measured as a function of distance by a 28 MHz piezoelectric transducer placed near the focus. By extracting the point where the second harmonic power is at a maximum in each liquid, the corresponding nonlinear parameter is then computed with a model developed by Germain et al. The preliminary results from this experiment are in reasonable agreement with the values found in the literature for primary alcohols and support the idea that the nonlinear parameter is dependent on the chain structure.