Principles of Magnetic Resonance

407 Pages·1978·8.27 MB·English

by  Professor Charles P. Slichter PhD (auth.)

1 Springer Series in Solid-State Sciences
Edited by Peter Fulde
Springer Series in Solid-State Sciences
Editors: M. Cardona P. Fulde H.-J. Queisser
Volume 1 Principles of Magnetic Resonance 2nd Edition
By C. P. Slichter
Volume 2 Introduction to Solid-State Theory
By O. Madelung
Volume 3 Dynamical Scattering of X-Rays in Crystals
By Z. G. Pinsker
Volume 4 Inelastic Electron Tunneling Spectroscopy
Editor: T. Wolfram
c.
P. Slichter
Principles of
Magnetic Resonance
Second Revised and Expanded Edition
W ith 115 Figures
Springer-Verlag Berlin Heidelberg GmbH 1978
Professor Charles P. Slichter, PhO
Department of Physics, University of Illinois at Urbana-Champaign
Urbana, IL 61801, USA
Editors:
Professor Or. Manuel Cardona
Professor Or. Peter Fulde
Professor Or. Hans-J oachim Queisser
Max-Planck-Institut für Festkörperforschung
Büsnauer Strasse 171, D-7000 Stuttgart 80, Fed. Rep. of Germany
The original edition Principles oJ Magnetic Resonallce with Examples Jrom Solid State
Physics was published in 1963 by Harper & Row Publishers, New York, Evanston,
and London.
ISBN 978-3-662-12786-5 ISBN 978-3-662-12784-1 (eBook)
DOI 10.1007/978-3-662-12784-1
Library of Congress Cataloging in Publication Data. Slichter. Charles P. Principles of magnetic resonance.
(Springer series in solid-state sciences: v. I) Bibliography: p. lncludes index. I. Nuclear magnetic resonance.
I. Title. 11. Series. QC762.S55 1978 538'.3 77-25373
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© by Springer-Verlag Berlin Heidelberg 1978
Originally published by Springer-Verlag Berlin Heidelberg New York in 1978.
Softcover reprint of the hardcover 2nd edition 1978
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Preface
It is a source of great pleasure to help launch the new Springer Series in
Solid-State Sciences. Some years aga I wrote my book, Principles of Magnetic
Resonance. I have been eager to publish a new book concerned with spin
temperature, double resonance, and spin-flip line narrowing, topics basic to
important trends in present-day magnetic resonance which were not treated
in my earlier book. Invitations to lecture in Osaka, Japan, in Leuven, Belgium,
and Lausanne, Switzerland, had provided occasion to prepare first drafts of
the new topics and to get student feedback. My plans were changed, however,
when I learned that Principles of M agnetic Resonance was no longer available.
Dr. Lotsch, Physics Editor of Springer-Verlag, and I decided it made sense to
combine the new book with a modified old one, thereby continuing to
make available a complete text in basic magnetic resonance written with a
philosophy of presenting a thorough treatment of a small number of concepts
which are key to large areas of magnetic res on an ce. In addition to adding three
new chapters, I have added new material to the original chapters, have added
two new appendices-one on the use of Bloch equations to describe rate
processes, the other on the effect of diffusion on spin echoes-and have
augmented the collection of homework problems.
U rbana, Illinois
January 1978 Charles P. Slichter
Contents
1. Elements of Resonance
1.1 Introduction . . . . . . . . . . . . . . 1
1.2 Simple Resonance Theory . . . . . . . . . . . 2
1.3 Absorption of Energy and Spin-Lattice Relaxation 4
2. Basic Theory
2.1 Motion of Isolated Spins-Classical Treatment .... 11
2.2 Quantum Mechanical Description of Spin in a Static Field 13
2.3 Equations of Motion of the Expectation Value 18
2.4 Effect of Alternating Magnetic Fields . . . . . . . . . 20
2.5 Exponential Operators . . . . . . . . . . . . . . . 26
2.6 Quantum Mechanical Treatment of a Rotating Magnetic Field 30
2.7 Bloch Equations . . . . . . . . . . . . 32
2.8 Solution of the Bloch Equations for Low H 1 . . . • • . •• 34
2.9 Spin Echoes . . . . . . . . . . . . . . . . . . . . .. 38
2.10 Relationship Between Transient and Steady-State Response of
a System and of the Real and Imaginary Parts of the Sus-
ceptibility . . . . . . . . . . . . . . . . 43
2.11 Atomic Theory of Absorption and Dispersion . . . . . .. 50
3. Magnetic Dipolar Broadening of Rigid Lattices
3.1 Introduction 56
3.2 Basic Interaction .......... 57
3.3 Method of Moments . . . . . . . . . 62
3.4 Example of the Use of Second Moments 71
4. Magnetic Interactions of N uclei with Electrons
4.1 Introduction ............ 77
4.2 Experimental Facts About Chemical Shifts 78
4.3 Quenching of Orbital Motion . . 78
4.4 Formal Theory of Chemical Shifts 82
4.5 Computation of Current Density 86
4.6 Electron Spin Interaction . . . . 100
4.7 Knight Shift ......... 106
4.8 Second-Order Spin Effects-Indirect Nuclear Coupling 121
VIII Contents
5. Spin-Lattice Relaxation and Motional Narrowing of Resonance Lines
5.1 Introduction ................... 137
5.2 Relaxation of a System Described by a Spin Temperature 138
5.3 Relaxation of Nuclei in a Metal . . . . . 144
5.4 Density Matrix-General Equations . . . 150
5.5 Density Matrix-An Introductory Example 158
5.6 Bloch-Wangsness-Redfield Theory 167
5.7 Example of Redfield Theory . . . 174
5.8 Effect of Applied Alternating Fields 183
6. Spin Temperature in Magnetism and in Magnetic Resonance
6.1 Introduction .................. 188
6.2 A Prediction from the Bloch Equations . . . . . . . 188
6.3 The Concept of Spin Temperature in the Laboratory Frame in
the Absence of Alternating Magnetic Fields 190
6.4 Adiabatic and Sudden Changes ...... 192
6.5 Magnetic Resonance and Saturation . . . . 200
6.6 Redfield Theory Neglecting Lattice Coupling 204
6.6.1 Adiabatic Demagnetization in the Rotating Frame 204
6.6.2 Sudden Pulsing . . . . . . . . . . . . . 207
6.7 The Approach to Equilibrium for Weak H 1 208
6.8 Conditions for Validity of the Redfield Hypothesis 210
6.9 Spin-Lattice Effects ....... 211
6.10 Spin Locking, T and Slow Motion . . . . . . 214
1p,
7. Double Resonance
7.1 Why Do Double Resonance? . . . . . . . . . . . . . . 217
7.2 Basic Elements of the Overhauser-Pound Family of Double
Resonance .. . . . . . . . . . . . . . . . 217
7.3 Energy Levels and Transitions of a Model System. 219
7.4 The Overhauser Effect . . . . . . . . . . . 223
7.5 Polarization by F orbidden Transitions . . . . 227
7.6 Electron-Nuclear Double Resonance (ENDOR) 229
7.7 Bloembergen's Three-Level Maser . . . . . . 232
7.8 A Potpouri of Other Ingenious Double Resonance Schemes 233
7.9 The Problem of Sensitivity 236
7.10 Hahn's Ingenious Concept .... 238
7.11 The Quantum Description .... 240
7.12 The Mixing Cycle and Its Equations 244
7.13 Energy and Entropy . . . . . . . 249
8. Advanced Concepts in Pulsed Magnetic Resonance
8.1 Introduction ...... 252
8.2 The Carr-Purcell Sequence ....... 252
Contents IX
8.3 The Phase Alternation and Meiboom-Gill Methods 254
8.4 The Relation of Spin-Flip Narrowing to Motional Narrowing 256
8.5 The Formal Description of Spin-Flip Narrowing 259
8.6 Observation of the Spin-Flip Narrowing 267
8.7 Real Pulses and Sequences 272
8.7.1 Avoiding a z-Axis Rotation 273
8.7.2 N onideality of Pulses 273
9. Electric Quadrupole Effects
9.1 Introduction .................... . 275
9.2 Quadrupole Hamiltonian-Part 1 275
9.3 Clebsch-Gordan Coefficients, Irreducible Tensor Operators,
and the Wigner-Eckart Theorem . . . . 279
9.4 Quadrupole Hamiltonian-Part 2 . . . 285
9.5 Examples at Strong and Weak Magnetic Fields 288
9.6 Computation of Field Gradients . . . . . . . 291
10. Electron Spin Resonance
10.1 Introduction . . . . . . . . . . . . . . . . . . 294
10.2 Example of Spin-Orbit Coupling and Crystalline Fields 296
10.3 Hyperfine Structure 308
10.4 Vk Center. . . . . . . . . . . . . . . . . . . . 315
11. Summary 339
Problems
Chapter 2 341
Chapter 3 344
Chapter 4 345
Chapter 5 348
Chapter 6 349
Chapter 7 351
Chapter 8 352
Chapter 9 353
Chapter 10 . 354
Appendixes
Appendix A: A Theorem About Exponential Operators . . . . . 357
Appendix B: Some Further Expressions for the Susceptibility . . . 358
Appendix C: Derivation ofthe Correlation Function for a Field that
±h
Jumps Randomly Between o . . . . 362
Appendix D: A Theorem from Perturbation Theory . 364
Appendix E: The High Temperature Approximation. 368
X Contents
Appendix F: The Effects of Changing the Precession Frequency-
Using NMR to Study Rate Phenomena . . . 371
Appendix G: Diffusion in an Inhomogeneous Magnetic Field . . . 377
Selected Bibliography 383
References 390
Author Index 393
Subject Index 394