Phonons: Theory and Experiments II: Experiments and Interpretation of Experimental Results

288 Pages·1986·6.308 MB·English

by  Dr. Peter Brüesch (auth.)

65 Springer Series in Solid-State Sciences
Edited by Peter Fulde
Springer Series in Solid-State Sciences
Editors: M. Cardona P. Fulde K. von Klitzing H.-J. Queisser
40 Semiconductor Physics An Introduction 56 Spin Fluctuations in Itinerant Electron
3rd Edition By K. Seeger Magnetism By T. Moriya
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61 Localization, Interaction, and
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Transport Phenomena
45 Electronic Properties of Doped Semiconductors Editors: B. Kramer, G. Bergmann.
By B. I. Shklovskii and A. L. Efros and Y. Bruynseraede
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64 Symmetries in Physics, Group Theory
49 Organic Molecular Aggregates, Electronic Applied to Physical Problems
Excitation and Interaction Processes By W. Ludwig and G. Falter
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65 Phonons: Theory and Experiments II
50 Multiple Diffraction of X-Rays in Crystals Experiments and Interpretation of
By Shih-Lin Chang Experimental Results By P. Briiesch
51 Phonon Scattering in Condensed Matter 66 Phonons: Theory and Experiments III
Editors: W. Eisenmenger, K. Laflmann. Phenomena Related with Phonons
and S. D6ttinger By P. Briicsch
52 Superconductivity in Magnetic and Exotic 67 Two-Dimensional Systems: Physics
Materials and New Devices
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53 Two-Dimensional Systems, Heterostructures, 68 Phonon Scattering in Condensed Matter V
and Superiattices Editors: A.C. Anderson and J. P. Wolfe
Editors: G. Bauer, F. Kuchar, and H. Heinrich
69 Nonlinearity in Condensed Matter
54 Magnetic Excitations and Fluctuations Editors: A. R. Bishop, D. K. Campbell,
Editors: S. Lovesey, U. Balucani, F. Borsa, P. Kumar and S. E. Trullinger
and V. Tognetti
70 From Hamiltonians to Phase Diagrams
55 The Theory of Magnetism II The Electronic and Statistical-Mechanical
Thermodynamics and Statistical Mechanics Theory of sp-Bonded Metals and Alloys
By D.C. Mattis By J. Hafner
Volumes 1-39 are listed on the back inside cover
Peter Briiesch
Phonons: Theory
and Experiments II
Experiments and Interpretation
of Experimental Results
With a Chapter by W. Buhrer
With 123 Figures
Springer-Verlag Berlin Heidelberg New York
London Paris Tokyo
Dr. Peter Briiesch
Brown Boveri Research Center, CH-5045 Baden-Oiittwil, and
Ecole Poly technique Federale de Lausanne, CH-1015 Lausanne, Switzerland
Series Editors:
Professor Dr., Dr. h. c. Manuel Cardona
Professor Dr., Dr. h. c. Peter Fulde
Professor Dr. Klaus von Klitzing
Professor Dr. Hans-Joachim Queisser
Max-Planck-Institut fur Festki:irperforschung, Heisenbergstrasse 1
0-7000 Stuttgart 80. Fed. Rep. of Germany
ISBN 978-3-642-52265-9 ISBN 978-3-642-52263-5 (eBook)
DOI 10.1007/978-3-642-52263-5
Library of Congress Cataloging-in-Publication Data. Briiesch, Peter, 1934-. Phonons, theory and experi
ments. (Springer series in solid-state scicnces ; 34, 65) Includes bibliographical references and index.
Contents; Lattice dynamics and models of interatomic forces. 1. Phonons. I. Title. II. Series. III. Series;
Springer series in solid-state sciences; 34, etc. QC176.8.P5B78 1982 530.4'1 81·21424
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© Springer-Verlag Berlin Heidelberg 1986
Softcover reprint of the hardcover I st edition 1986
The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a
specific statement, that such names are, exempt from the relevant protective laws and regulations and
therefore free for general use.
2153/3150-543210
Dedicated to my wife
and my family
Preface
The first part of this three-volume treatment, Phonons: Theory and Exper
iments I, has been devoted to the basic concepts of the physics of phonons
and to a study of models of interatomic forces. The present second volume,
Phonons: Theory and Experiments II, contains a thorough study of experi
mental techniques and the interpretation of experimental results. In a third
volume we shall treat a number of phenomena which are directly related to
lattice dynamics.
The aim of this treatment is to bridge the gap between theory and ex
periment. Both experimental aspects and theoretical concepts necessary for
an interpretation of experimental data are discussed. An attempt has been
made to present the descriptive as well as the analytical aspects of the top
ics. Although emphasis is placed on the experimental and theoretical study
of the dynamics of atoms in solids, most chapters also contain a general in
troduction to the specific subject. The text is addressed to experimentalists
and theoreticians working in the vast field of dynamical properties of solids.
It will also prove useful to graduate students starting research in this or
related fields.
The choice of the topics treated was partly determined by the author's
own activity in these areas. This is particularly the case for the chapters
dealing with infrared, Raman and inelastic neutron spectroscopy, as well as
for some newer developments such as the optical spectroscopy of thin films
and adsorbates.
I am very grateful to my colleague W. Biihrer who wrote Chapter 6
about "Inelastic Neutron Spectroscopy".
The author is indebted to BBC Brown, Boveri & Company Limited,
Baden, Switzerland, for giving him the opportunity to carry out this work.
The BBC Research Center provided the scientific atmosphere necessary to
accomplish this goal. As in the first volume, several chapters of this second
volume grew out of lectures the author gave at the "Ecole Polyt echnique
Federale de Lausanne" (EPFL) during the years 1975-1986 for graduate
students in experimental physics in their last year of study. I am grateful
to BBC and to the EPFL for giving me the chance to prepare parts of this
book by lecturing.
The entire manuscript was strongly influenced by the detailed criticism
and valuable suggestions of my colleagues Drs. Th. Baumann, J. Bernasconi,
E. Cartier, T. Hibma, P. Pfluger, W.R. Schneider, H.J. Wiesmann and H.R.
Zeller from the Brown Boveri Research Center, and by Dr. W. Biihrer from
VII
the lnstitut fiir Reaktortechnik ETHZ in Wiirenlingen, Switzerland. My
debt to them is indeed great. I am also grateful to Professor Ph. Choquard
from EPFL for many interesting discussions in Lausanne.
I wish to express very grateful thanks to Mrs. M. Zamfirescu from BBC
Research Center for the very skilful drawing of over 100 figures; without her
immense work the goal of presenting a well-illustrated book could not have
been accomplished. The author is also indebted to the late Mrs. E. Knotz,
to Mrs. N. Bingham and to Mrs. E. Martens for their never-ending patience
in typing the manuscript, and to W. Foditsch and P. Unternahrer for pho
tographing some of the figures. Finally, I am grateful to Professor P. Fulde
for valuable suggestions and to Dr. H. Lotsch, Springer-Verlag, for good co
operation.
Baden, June 1986 Peter Briiesch
VIII
Contents
1. Introduction .................................................. 1
1.1 General Remarks ........................................... 1
1.2 Infrared Spectroscopy ...................................... 3
1.3 Raman Spectroscopy ....................................... 4
1.4 Brillouin Spectroscopy. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Interactions of X-Rays with Phonons ....................... 5
1.6 Inelastic Neutron Scattering ................................ 5
1.7 Other Techniques .......................................... 6
2. Infrared Spectroscopy ....................................... 8
2.1 Experimental Techniques............................... .... 8
2.1.1 Grating Spectrometers ............................... 8
2.1.2 Fourier Interferometers. . . . . . . . . .. . .. .. . . .. . . . . . . . . . . . 9
2.2 Dielectric Properties: Classical Treatment ................... 12
2.2.1 Reflectivity, Transmission, Absorptivity
and Optical Constants ............................... 12
2.2.2 Examples of Reflectivity and Transmission Spectra ... 15
2.2.3 Evaluation of £"(w) from a Kramers-Kronig Analysis
of the Reflectivity .................................... 20
2.2.4 Direct Determination of £"(w) from Experimental Data 23
2.2.5 £"(w) from a Model Fit to the Observed Reflectivity... 24
2.2.6 Kramers-Kronig Relations and Sum Rules ............ 28
2.2.7 Polaritons and Propagation of Light in Crystals ...... 30
2.3 Quantum-Mechanical Treatment of the Dielectric Constant.. 34
2.3.1 Qualitative Discussion ............................... 34
2.3.2 Relation Between £"2(W) and Transition Probabilities. . 40
2.3.3 Interaction of a Charged Oscillating Particle
with the Radiation Field............................. 41
2.3.4 Quantum Mechanical Formulation
of the Dipole Moment of the Crystal. . . . . . . . . . . . . . . . . . 43
2.3.5 One-Phonon Absorption ....... . . . . . . . . . . . . . . . . . . . . . . . 48
2.3.6 Two-Phonon Processes Due to the Second-Order
Dipole Moment Mechanism .......................... 51
2.3.7 Two-Phonon Processes Due to Anharmonic Coupling. 58
2.4 Problems................................................... 61
2.4.1 Dielectric Constant of Diatomic Cubic Crystals ....... 61
IX
2.4.2 Conductivity Sum Rule for Lattice Vibrations ........ 63
2.4.3 Second-Order Dipole Moment ........................ 63
3. Raman Spectroscopy ......................................... 65
3.1 Experimental Techniques ................................... 66
3.1.1 Raman-Scattering Apparatus ........... " . . . . . . . . . . . . 66
3.1.2 Scattering Configurations ............................ 67
3.2 Classical Theory ............................................ 70
3.2.1 Basic Model ......................................... 70
3.2.2 The Polarizability Tensor ............................ 74
3.2.3 Raman Active and Raman Inactive Modes:
Simple Molecules ..................................... 78
3.2.4 Raman Active and Raman Inactive Modes:
Simple Crystals ...................................... 81
3.3 Quantum Theory ........................................... 85
3.3.1 Qualitative Discussion ............................... 85
3.3.2 The Intensity of the Scattered Light .................. 91
3.3.3 Placzek's Approximation............................. 97
3.3.4 Raman Intensities Based on Placzek's Theory ........ 99
3.3.5 Raman Scattering by Phonon-Polaritons .............. 101
3.4 Problems ................................................... 103
3.4.1 Polarizability a(R) of Diatomic Molecules ............ 103
3.4.2 Decomposition of the Scattering Tensor into Its
Isotropic, Symmetric, and Antisymmetric Parts....... 104
3.4.3 Scattering by a Charged Oscillating Particle .......... 105
4. Brillouin Spectroscopy ....................................... 106
4.1 Experimental Techniques ................................... 106
4.2 Kinematics and Origin of Brillouin Scattering ............... 109
4.3 Strain Dependence of Dielectric Constant ................... 111
4.4 Intensities of Brillouin Components ......................... 115
4.5 Problems ................................................... 121
4.5.1 Doppler Effect and Brillouin Frequency Shifts ........ 121
4.5.2 Strain Dependence of coo Under the Effect
of Hydrostatic Pressure for Alkali Halides. . . . . . . . . . . .. 121
4.5.3 Brillouin Intensities for Isotropic Solids and Liquids 122
5. Interaction of X-Rays with Phonons ........................ 123
5.1 The Static Approximation .................................. 124
5.2 Experimental Technique .................................... 126
5.3 Interaction Mechanism ...................................... 128
5.4 Scattering by a Perfectly Ordered Crystal ................... 131
5.5 Thermal Diffuse Scattering for a Bravais Crystal ............ 136
x
5.6 Thermal Scattering for a Crystal with Basis. . . . . . . . . . . . . . . .. 141
5.7 The Debye-Waller Factor................................... 142
5.8 Problems ................................................... 146
5.8.1 Compton Scattering....... ........................... 146
5.8.2 Atomic Scattering Factor ............................. 146
5.8.3 Debye-Waller Factor for a Cubic Bravais Crystal ...... 146
5.8.4 Correlation Function.... ........ ...... ............... 147
6. Inelastic Neutron Scattering (By W. Biihrer) ..... ........... 149
6.1 Basic Properties ............................................ 150
6.1.1 Cross Section ........................................ 150
6.1.2 Coherent and Incoherent Scattering .................. 154
6.2 Phonon Dispersion-Relation Measurements.... .............. 155
6.2.1 Coherent Scattering Cross Section .................... 155
6.2.2 Selection Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 159
6.2.3 Experimental: Triple Axis Spectrometer.... . . . . . . . . . .. 160
6.2.4 Examples............................................. 163
6.3 Phonon Density of States Measurements .................... 170
6.3.1 Incoherent Scattering Cross Section .................. 170
6.3.2 Examples ............................................ 171
7. Other Techniques ............................................. 174
7.1 Ultrasonic Methods......................... ...... ........ .. 174
7.1.1 Experimental Techniques. ............... ............. 175
7.1.2 Ultrasonic Attenuation
Due to Phonon-Phonon Interactions .................. 178
7.2 Inelastic Electron Tunneling Spectroscopy................... 181
7.2.1 Experimental Techniques......... .................... 183
7.2.2 The Inelastic Electron Current ....................... 184
7.2.3 Some Selected Examples of lETS ..................... 186
7.3 Point Contact Spectroscopy... . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 188
7.3.1 Experimental Techniques. ........ ....... ...... .. ..... 190
7.3.2 Qualitative Discussion of Point-Contact Spectra ...... 192
7.4 Spectroscopy of Surface Phonons, Thin Films
and Adsorbates ............................................. 196
7.4.1 Acoustical and Optical Surface Phonons .............. 196
7.4.2 Electron Energy Loss Spectroscopy................ ... 199
7.4.3 Inelastic Molecular Beam Scattering. ........ ......... 202
7.4.4 Optical Studies of Surface Modes ..................... 205
7.4.5 Infrared Reflection Absorption Spectroscopy.......... 207
Appendices ....................................................... 210
A. Michelson Interferometer ..................................... 210
B. Classical Optics .............................................. 211
XI