Ever-decreasing rugby balls

Imaging Phonons
November 5, 1999

Every undergraduate taking a course in condensed-matter physics learns about phonons. The two key properties that students grasp of phonons are their dispersion and their quantum nature. This book is about neither, though each is mentioned when relevant. Rather it is about another property that arises from the crystalline nature of solids, namely the anisotropy of their propagation.

The author is a self-avowed experimentalist, though the book is not short on theory. The basic experimental arrangement behind many of the results presented in the book is to heat a spot on one side of a crystal and to detect the heat arriving at another spot on the other side. There are many ways to supply the heat to the first spot. There are also many ways to detect the arrival of the phonons, but a common theme is to deposit lithographically on the opposite surface of the crystal a design with two contact pads connected by a small area of material whose resistance (or possibly superconductivity) will be affected by the arrival of a heat pulse.

Typical experimental arrangements might have excitation and detection spots each of size 10-20µm, with a separation between the faces of the crystal of 10-20mm, giving an angular

resolution of 10-3radians, or about 0.06°. This is the key parameter for the core phenomena described in Imaging Phonons : by scanning the source of excitation in phonon experiments, it is possible to image the phonon propagation and to measure the anisotropy of the radiation in intensity and velocity.

A fundamental concept in visualising this is the slowness surface. It is constructed by finding the phase velocity at a given angular velocity w for each direction of the wave-vector k, and then plotting in 3D the surface of k/w.

For most people the slowness surface is less intuitive than the velocity surface. If you throw a stone into a pond, the circular waves that radiate from the point of impact form a velocity surface. If you look closely you will see small wavelets travelling through the

overall wave: this is because waves on water are dispersive; and the velocity of the overall wave packet is known as the group velocity. You can imagine that if the propagation

velocity were different in different directions, then the velocity surface would not be spherical, but might bulge out in certain directions. This happens for light propagation in bire- fringent crystals such as calcite, where the velocity surface has the shape of a rugby ball. The phenomena with phonons are even richer.

I believe that this book will find a wider readership than the phonon physics community. It is emphatically written at the graduate level, and would be suitable only for very specialised undergraduate courses. But there is an enormous amount of research that does not go under the label of phonon physics for which Imaging Phonons will provide a definitive textbook. Since the thrust of the book is on propagation in anisotropic media, and not on the quantum or dispersive properties of phonons, it is applicable to the propagation of non-dispersive continuous and pulsed waves in anisotropic solids. Not since the two-volume Acoustic Fields and Waves in Solids by B. A. Auld have they received such authoritative treatment.

Imaging Phonons will be of relevance to applications as diverse as non-destructive testing of composites and single-crystal alloys, acoustic microscopy of semiconductors and opto-electronic materials, and surface Brillouin spectroscopy of crystalline layers and coatings. The author has produced a masterpiece.

Andrew Briggs is professor in materials, University of Oxford.

Imaging Phonons: Acoustic Wave Propagation in Solids

Author - James P. Wolfe
ISBN - 0 521 62061 9
Publisher - Cambridge University Press
Price - £65.00
Pages - 411

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