Rayleigh waves

Based upon a piezoelectric 1-3-composite material, air-bome ultrasonic probes for frequencies up to 2 MHz were developped. These probes are characterized by a bandwidth larger than 50 % as well as a signal-to-noise ratio higher than 100 dB. Applications are the thickness measurement of thin powder layers, the inspection of sandwich structures, the detection of surface near cracks in metals or ceramics by generation/reception of Rayleigh waves and the inspection of plates by Lamb waves. 

Fig. 2 shows the CFRP-sandwich specimen and the transducer mounted on the scanner. Fig. 23 presents a C-scan of the specimen as first interesting result. Only the defects visible from the outside are indicated. The distance between transducer and specimen was smaller than the focal length, so that the angle of incidence at the edge of the sound beam converts the longitudinal waves to Rayleigh-waves in the specimen. These waves provide a very sharp image of the surface. This method opens the possibility for a non-contact acoustic microscope. 

Fig. 9 Generation and detection of Rayleigh waves at a green ceramic sample...

SASW-result (dispersion curve) showing Rayleigh Wave speed as a function of wavelength (depth)... 

The Rayleigh wave speed of sound Cr is determined by the equation ... 

F 6. (a) Distortion of a square lattice in a plane containing the surface normal and the propagation direction of the Rayleigh wave. (After Ref. 14.). (b) Relative amplitudes of the vertical and longitudinal displacements of the Rayleigh wave as a function of penetration depth into the... 

The first successful measurement of surface phonons by means of inelastic He scattering was performed in Gottingen in 1980. By using a highly monochromatic He beam (Av/t 1%) Brusdeylins et al. were able to measure the dispersion of the Rayleigh wave of the LiF(001) crystal surfae. In earlier attempts the inelastic events could not be resolved satisfactorily due to the low beam monochromaticity. In Fig. 10a we show a typical TOF spectrum. 

Fig. 11. Measured decrease of inelastic scattered He intensity (Rayleigh wave) from Pt(l 11) with increasing momentum transfer.

A dramatic hybridization splitting around the crossing between the dispersionless adlayer mode and the substrate Rayleigh wave (and a less dramatic one around the crossing with the co = CiQg line - due to the Van Hove singularity in the projected bulk phonon density of states). 

Experimental data of Gibson and Sibener appears to confirm qualitatively these predictions at least for monolayers. The phonon linewidths were broadened around T up to half of the Brillouin zone. The hybridization splitting could not be resolved, but an increase of the inelastic transition probability centered around the crossing with the Rayleigh wave and extending up to 3/4 of the zone has been observed and attributed to a resonance between the adatom and substrate modes. 

Figure 26 shows the dispersion curve of the Kr monolayer obtained from a large number of spectra like those in Fig. 25. The hybridization splitting around the crossing with the substrate Rayleigh wave (solid line) is clearly observed. Also the predicted tiny frequency upshift close to the T point due to the coupling to the substrate vibrations is seen. The observed linewidth broadening is also shown in Fig. 26. As a measure of the broadening, the quantity Ae = [( ) — with dE the FWHM of the major loss feature...

It is noteworthy that the phonon anomaly, due to the dynamical coupling between substrate Rayleigh wave and adlayer mode, is likewise present in the bi- and even the trilayer films. It is only the Q range of the anomaly which... 

It will become very clear by the end of this book that in a great deal of acoustic microscopy of materials the contrast is dominated by Rayleigh waves excited in the surface of the specimen (Briggs 1985). A summary of the properties of Rayleigh waves will be given in Table 6.2, and their role in the contrast will be introduced in 7.2.1. What all that means in terms of acoustic pictures will be... 

Fig. 6.2. Rayleigh wave displacement velocity components as a function of depth from the surface, measured in Rayleigh wavelengths (a) longitudinal and shear components (eqns (6.44), (6.45), (6.51), and (6.52)) (b) components parallel and perpendicular to the surface (eqns (6.59) and (6.60)). The curves have been normalized to give the shear component at the surface a value of unity. The Poisson ratio o = 0.17, corresponding to fused silica, was used to calculate the curve.

Figure 6.2(a), which was calculated using the results to be derived here, shows the amplitudes of the longitudinal and shear components of a Rayleigh wave in fused silica, and their exponential decay below the surface. 

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