Rayleigh contrast

In contrast to the method based on Rayleigh scattering, the procedure based on Mie scattering theory (a) is not restricted to small particles, (b) chemical absorption may be considered, (c) and lastly, it can be extended to permit the use of a nonlinear... 

In contrast, reduction of Cr(Vt) in solution, followed by precipitation of hydrated Cr jOj, produces fractionation in that follows a Rayleigh process (Fig. 9). When plotted as a... 

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... 

The term in the curly brackets describes the response at x due to the excitation at x, transmitted by the Rayleigh wave mechanism it can therefore be thought of as a kind of Green function. The results described by eqns (7.33) and (7.34) are central to the theory of the contrast from cracks and interfaces that will be presented in Chapter 12. 

Anyone who has successfully used a microscope to image properties to which it is sensitive will sooner or later find himself wanting to be able to measure those properties with the spatial resolution which that microscope affords. Since an acoustic microscope images the elastic properties of a specimen, it must be possible to use it to measure elastic properties both as a measurement technique in its own right and also in order to interpret quantitatively the contrast in images. It emerged from contrast theory that the form of V(z) could be calculated from the reflectance function of a specimen, and also that the periodicity and decay of oscillations in V(z) can be directly related to the velocity and attenuation of Rayleigh waves. Both of these observations can be inverted in order to deduce elastic properties from measured V(z). 

Fig. 9.13. Quantitative analysis of the contrast from a white spot lesion in human tooth enamel (i) micrograph, 370 MHz (ii) V(z) curves of selected points along the line in the micrograph (iii) Rayleigh velocity and attenuation calculated from V(z) measured at each of the points on the line in (i) (Peck et al. 1989).

There is one picture in which plastic deformation seems undoubtedly to have been captured (Ishikawa et al. 1989). Figure 11.13 shows a specimen of an Fe-3%Si alloy that has been deformed. Every precaution was taken to eliminate spurious sources of contrast for example, the specimen was carefully repolished after deformation to avoid any topographical contrast due to bowing in or out of the surface around a stress concentrator as a result of deformation under plane stress. So the contrast seems indubitably to be due to interaction of Rayleigh waves with regions of plastic deformation. 

The experimental observation that Rayleigh wave scattering plays a dominant role in the contrast suggests that the reflection coefficient should be separated into the geometrical and Rayleigh parts in the way described in 7.2.1 ... 

Starting from a crack that is small compared with a wavelength, the effect on V z) when the lens is directly over the crack initially increases with crack depth. The chief information about the crack depth lies in the phase there is a weak resonance when the crack depth is comparable with the Rayleigh wavelength, and beyond that the contrast tends to become independent of the crack... 

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