The discussion of experimental methods has been deferred until this point, because relevant background material was covered in Chapters 2 and 3. The usual experimental objectives are to determine one or both of the following quantities: 1. The elastic constants or, equivalently, the ultrasonic velocities; and 2. The dissipation or loss. The second property is known by several names, often depending on the method of measurement – ultrasonic attenuation, internal friction, logarithmic decrement, inverse Q, etc. Many different experimental techniques have been developed over the years, and there are various ways to categorize them. One possible approach is to divide the different methods into continuous wave techniques, in which a standing wave resonance is set up in the specimen, and pulse methods in which a short pulse of ultrasound is sent through the specimen, sometimes called the pulse-echo technique. However, when considering the problems of sample preparation and orientation, transducers, and corrections for non-ideal experimental configurations, it seems better to divide the methods into: 1. plane-wave propagation methods; and 2. methods not based on the plane-wave approximation.

In the discussion to follow, a few seminal papers will be cited, but the emphasis will be on modern techniques. It is not possible to cite the many, many scientists who have contributed to the development of the present-day methods.

Plane-Wave Propagation Methods

The plane-wave propagation methods are divided naturally into pulse techniques and continuous wave (resonance) techniques. After a short discussion of common problems, the pulse and resonance methods will be discussed separately below.

Figure 4.1 shows a typical sample-transducer arrangement used in the planewave propagation methods. Configurations with a single transducer, the same one being used for transmitting and receiving, are also used. The specimen is prepared with flat and parallel end faces. The transducers, which convert electrical voltages to mechanical displacements and vice-versa, are usually specially oriented cuts of piezoelectric materials and are commercially available. Single-crystal quartz, PZT, and lithium niobate are common transducer materials. Polyvinylidene fluoride (PVDF) piezoelectric film transducers have also been used [68].

The present chapter will serve as an overview of the material to be presented in the rest of the book. While it is hoped that the material will prove useful to all those involved in or interested in the use of ultrasound as a probe of condensed matter, a special effort is made to present the material in sufficient detail so as to be helpful to dedicated, upper-level undergraduate students and beginning graduate students. Scientists from several different disciplines are nowadays finding ultrasonic spectroscopy a useful tool, thus a strong background in solid-state physics, statistical physics, and quantum mechanics is not assumed of the readers. Brief background material is presented as needed. Several monographs have contributed to the advancement of ultrasonic spectroscopy, among them References [1, 2, 3]. The author is deeply indebted to those who have helped develop the field of ultrasonic studies of materials.

Chapter 2 deals with classical elasticity; the solid is treated as a continuum. The continuum approximation is valid for virtually all ultrasonic experiments. The present treatment of elasticity is more extensive than is usually found in books on ultrasonic techniques, but this more extensive treatment seems important if the researcher is to understand the widest implications of her/his ultrasonic research. Basic physical parameters in this chapter are stress (a two-index tensor), strain (a two-index tensor), and elastic constants (a four-index tensor, which by Hooke's Law connects stress and strain). Thus, many indices and sums over these indices appear frequently. For pedagogical reasons, it was decided not to use the elegant Einstein summation convention. For those new to the field, it seems better to write out the sums explicitly. The relation of elastic constants to thermodynamic potentials is derived. The condensed (Voigt) notation for stress, strain, and elastic constants is explained in detail. Coordinate transformations are treated. The form of the elastic constant matrix for each of the seven crystal systems is derived, as well as the form for the icosahedral quasicrystal.