Imaging Phonons: Acoustic Wave Propagation in Solids

428 Pages·2005·51.25 MB·English

by  James P. Wolfe

Drop a pebble in a pond and the results are quite predictable: circular waves flow
from the point of impact. Hit a point on a crystalline solid, however, and the
expanding waves are highly nonspherical; the elasticity of a crystal is anisotropic.
This book provides a fresh look at the vibrational properties of crystalline
solids, elucidated by new imaging techniques. From the megahertz vibrations of
ultrasound to the near-terahertz vibrations associated with heat, the underlying
elastic anisotropy of the crystal asserts itself. Phonons — the elementary packets of
heat — display unique patterns of "caustics" such as the one for CaF shown on
2
the front cover (see Chapter 4).
Written from the viewpoint of an experimentalist, the text contains both the
basic theory of wave propagation in solids and its experimental applications.
Imaging techniques are described that provide graphic insights into the topics of
phonon focusing, lattice dynamics, and ultrasound propagation. Scattering of
phonons from interfaces, superlattices, defects, and electrons are treated in detail.
The book includes many striking and original illustrations.
This book will be of interest to graduates and researchers in condensed
matter physics, materials science, and acoustics.

Imaging Phonons
to Kathy
Imaging Phonons
Acoustic Wave Propagation in Solids
JAMES P. WOLFE
University of Illinois at
Urb ana-Champaign
CAMBRIDGE
UNIVERSITY PRESS
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo
Cambridge University Press
The Edinburgh Building, Cambridge CB2 2RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521620611
©James P. Wolfe 1998
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.
First published 1998
This digitally printed first paperback version 2005
A catalogue record for this publication is available from the British Library
Library of Congress Cataloguing in Publication data
Wolfe, J. P. (James Philip), 1943-
Imaging phonons : acoustic wave propagation in solids / James P.
Wolfe.
p. cm.
Includes bibliographical references.
ISBN 0-521-62061-9
1. Waves. 2. Solids. 3. Acoustic surface waves. 4. Phonons.
5. Imaging systems. I. Title.
QC176.8.W3W65 1998
530.4'16-dc21 97-36117
CIP
ISBN-13 978-0-521-62061-1 hardback
ISBN-10 0-521-62061-9 hardback
ISBN-13 978-0-521-02208-8 paperback
ISBN-10 0-521-02208-8 paperback
Contents
Preface ix
Prologue - Anisotropic heat flow in crystals 1
A. Historical overview 1
B. Central themes of this book 6
C. Acknowledgements 7
1 Ballistic heat pulses and phonon imaging - A first look 10
2 Phonon focusing 21
A. Acoustic waves in an anisotropic medium 23
B. Phonons 29
C. Mathematical basis for phonon focusing 36
i) Stresses and strains 36
ii) The elasticity tensor 40
iii) The wave equation 41
iv) Slowness surface 43
v) Group velocity and energy propagation 46
vi) Ballistic heat flux 51
3 Generation and detection of phonons - Experimental aspects 60
A. Tools of the trade 61
B. Phonon detection 70
i) Superconducting bolometers 71
ii) Superconducting tunnel junctions 73
a) Fabrication of tunnel junctions for phonon imaging 76
b) Frequency selectivity of tunnel junctions 78
c) Scannable tunnel-junction detector 79
VI CONTENTS
C. Phonon generation 80
i) Phonon emission by a heated metal overlayer 81
ii) Example of an optically excited metal-film radiator 83
iii) Bubbles in the bath 86
4 Focusing in cubic crystals 91
A. Introduction - Eigenvalues and eigenvectors for 91
general symmetry
B. Application to cubic crystals 92
C. Phonon focusing in cubic crystals 97
i) Negative-A regime 99
ii) Positive-A regime 105
D. Origins of the phonon caustics 116
E. Summation 120
5 Acoustic symmetry and piezoelectricity 122
A. Degeneracy and the slowness surface 122
B. Tetragonal crystals 124
C. Hexagonal and lower symmetries 130
D. Piezoelectricity 135
E. Acoustic symmetry 142
6 Lattice dynamics 146
A. Linear chain 147
B. Vibrations of Bravais lattices 149
C. Ionic and covalent crystals - A look at more realistic models 158
D. Constant-frequency surfaces 162
7 Imaging of dispersive phonons 166
A. Early experiments 169
B. Dispersive phonon imaging in InSb 172
i) Velocity dispersion 174
ii) Angular dispersion 176
C. Comparison to lattice-dynamics models 178
D. First-order spatial dispersion 182
8 Phonon dynamics 189
A. The simple harmonic oscillator 189
B. The linear chain - Creation and annihilation of phonons 193
C. Phonons in three dimensions 196
D. Phonon scattering from isotopic defects 197
E. Anisotropy in mass-defect scattering 205
F. Phonon-phonon scattering 208
CONTENTS Vll
9 Bulk scattering of phonons - Experiments 213
A. Phonon scattering and thermal conduction 213
B. Nonequilibrium phonons and the color temperature 216
C. Elastic scattering of phonons in silicon 217
D. Phonon scattering from impurities in GaAs 226
E. Scattering from dislocations in LiF - A phonon polarizer 232
10 Quasidiffusion and the phonon source 244
A. Qualitative description of quasidiffusion 245
B. Improved models of anharmonic phonon decay 248
C. Observation of quasidiffusion in Si 251
D. Quantitative description of quasidiffusion 252
E. Localized phonon source at high excitation density 258
F. A phonon hot spot? 258
G. Origin of the localized phonon source in Si 261
H. Extension to other semiconductors 268
I. Return of the bubble 269
J. Prospectus 271
11 Phonon scattering at interfaces 275
A. The Kapitza problem 275
B. Solid/solid interfaces 279
C. Acoustic-mismatch model 280
i) Isotropic solids 281
ii) Anisotropic solids 288
D. Emission of phonons from a planar source 289
E. Model for the Kapitza anomaly in the helium/solid case 293
12 Refraction and reflection at solid/solid interfaces - Experiment 299
A. Phonon refraction at a solid/solid interface 299
B. Critical-cone channeling at a loosely bonded surface 305
C. Phonon reflection imaging 309
D. Internal interfaces 314
i) Phonon transmission through superlattices 314
ii) Ferroelectric domain boundaries - Another perfect
match 324
13 Imaging ultrasound in solids 332
A. Phonons versus ultrasound 333
B. Ultrasonic-flux imaging 335
C. Internal diffraction 337
D. Applications of ultrasonic-flux imaging 342
E. Acoustic wavefront imaging 345
F. Acoustic imaging in composite materials 349