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The first edition of Acoustic Microscopy ended with a chapter emphasizing the need to understand the contrast in terms of the variation of signal with defocus, V(z). This is a fundamental concept in the contrast from surfaces of stiff materials, and is dominated by excitation of Rayleigh waves in the surface of the sample. The second edition contains a major new chapter on acoustically excited probe microscopy, which changes everything. In ultrasonic force microscopy there is no V(z), no defocus, and no Rayleigh waves. Instead the contrast is dominated by the non‐linear mechanical contact between the tip of an atomic force microscope and the surface of the sample, with its underlying elastic nanostructure.

When the boundary condition is homogeneous, one may think that there is no data at the boundary and that there is no need of boundary estimates in the maximal estimates. This is reminiscent of the case of weakly dissipative symmetric IBVP, and is compatible with the failure of the K.-L. condition at some elliptic boundary frequencies. This chapter constructs a weakly dissipative symmetrizer under appropriate assumptions. This context is the realm of surface waves of finite energy. A paradigm is the Rayleigh waves in linear elasticity.

A good way to start to appreciate what acoustic microscopy can do for you is to look at examples which show unique contrast from the elastic structure of the sample. In glass matrix composites such as borosilicate with silicon carbide fibres, there is contrast between the fibre and the matrix, and also from cracks in the matrix and at the interface between fibre and matrix. A phase of crystobalite is visible where the matrix has devitrified. Samples of granordiorite rock containing plagioclase, biotite, and quartz can be seen, together with boundaries of misorientation which occurred to accommodate strain during the geological processes of deformation of the rock. The composite and rock samples show fringes arising from the Rayleigh waves which are a recurrent motif in acoustic microscopy of stiff materials. Hydroxyapatite, the principal crystalline mineral constituent of bone, can be seen in living cells, with the distinctive contrast arising from the elastic properties and structure of the sample.

Hybrid modes exist as a consequence of acoustic and optical waves having to satisfy the boundary conditions at an interface or at a surface. The author begins the description of hybrid modes in nanostructures with an account of modes in a non-polar, free-standing slab. This chapter includes long-wavelength assumption decouples acoustic and optical modes; isotropy decouples LO and TO modes; s and p modes; acoustic hybrid modes: Love waves, Lamb waves, guided modes, Rayleigh waves; the boundary condition u = 0 for optical modes; the sTO mode; double hybrid: LO and pTO modes; and energy normalization.