Table Of ContentNMR Basic Principles and Progress 11
Grundlagen und Fortschritte
Editors: P. Diehl E. Fluck R. Kosfeld
Editorial Board: S. Forsan S. Fujiwara
R. K. Harris C. L. Khetrapal
E. Lippmaa G. J. Martin A. Pines
F. H. A. Rummens B. L. Shapiro
M. Mehring
H ighResolution
N M R Spectroscopy
in Solids
With 104 Figures
Springer-Verlag
Berlin Heidelberg New York 1976
Professor Dr. Michael Mehring
Universitat Dortmund, Institut fur Physik
Baroper StrliBe, D-4600 Dortmund 50
ISBN-13: 978-3-642-96334-6 e-ISBN-13: 978-3-642-96332-2
DOl: 10.1007/978-3-642-96332-2
Library of Congress Cataloging in Publication Data. Mehring, Michael, 1937 - High resolution
NMR in solids. (NMR, basic principles and progress; v. 11) Bibliography: p. 1. Nuclear magnetic
resonance spectroscopy. I. Title. II. Series. QC490.N2 vol. 11 [QC762] 538'.3 76-10680
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© by Springer-Verlag Berlin· Heidelberg 1976.
Softcover reprint of the hardcover I st edition 1976
The use of registered names, trademarks, etc. in this publication does not imply, even in the
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Editorial
Since the Series "NMR-Basic Principles and Progress" was founded in 1969
it has dealt primarily with the theoretical and physical aspects of the methods. Today
nuclear-magnetic resonancespectroscopy has become one of the principal techniques
of the chemist and is finding increasing use in the fields of Biology, Pharmacy,
Medicine, and Criminology. The growing significance of applied spectroscopy has
earned it a correspondingly important place for the future in this Series. With the
aim of achieving a balanced representation of theoretical and practical problems
and results, the present Editors have asked several world-renowned scientists in the
field of NMR-spectroscopy to join an International Editorial Board.
The international nature of this Board will facilitate closer contact among
research groups and .authors throughout the world, making it possible to follow
comprehensively the developments in pure and applied NMR-spectroscopy. On this
basis, the readers of the Series will be assured of up-to-date contributions not only
of current significance, but of long-term value as well.
Prof. E. Fluck Prof. P. Diehl Prof. R. Kosfeld 1976
Preface
Manipulation and Dilution
Tools for Ruling Abundant Species
"NMR is dead" was the slogan heard in the late 1960s at least among physicists,
until John S. Waugh and his co-workers initiated a series of new NMR experiments,
which employed the coherent modulation of interactions by strong radiofrequency
fields. A wealth of new phenomena was observed, which are summarized in the
introduction for the convenience of the unbiased reader, whereas Section 2 collects
the basic spin interactions observed in solids.
Line-narrowing effects in dipolar coupled solids by the application of multiple
pulse experiments are extensively discussed in Section 3. Numerous extensions of the
basic Waugh, Huber, and Haeberlen experiment have been developed by different
groups and have been applied to the nuclei IH, 9Be, 19F, 27Al, 31p, 63CU in solids.
Application of this technique to a variety of systems is still in progress and should
reveal interesting insights into weak spin interactions in solids.
It was soon realized that rare spins could be used as monitors for molecular
fields in the solid state; however, rare spin observation is difficult because of the
small signal-to-noise ratio. Pines, Gibby, and Waugh introduced a new concept of
cross-polarization, based on ideas of Hahn and co-workers, which allows the
detection ofrare spins with increased sensitivity. The dynamics involved are treated
in detail. Other sections merely list results obtained by the techniques described
and demonstrate their usefulness in the investigation of dynamical problems in molec
ular and solid state physics.
Prerequisite to reading this monograph is some familiarity with the fundamental
book by A. Abragam and M. Goldman. Additional reading of the review article
written by U. Haeberlen is highly recommended.
I have tried very hard to cover the whole current literature in this growing field;
however, I am aware that I have certainly missed important contributions. Of those
who suffer from this, I herewith beg pardon.
Among my friends and colleagues I am particularly indebted, for their patient
criticisms, discussions and comments to O. Kanert, A. Pines and J. S. Waugh. Among
these my friend A. Pines has encouraged and excited me continuously and I have
benefited tremendously from this ingenious restlessness. I gratefully acknowledge
the kind hospitality of J. S. Waugh during my stay at the Massachusetts Institute of
Technology during 1969-1971, where I learned about these fascinating experiments.
This monograph would certainly not have been written without the help of my
friend and colleague O. Kanert, who took most of the administrative burden off my
shoulders during the time of writing.
I am very much obliged to my co-workers, who have supported me tremendously
with the preparation of the manuscript. Several drawings had to be specially computed
VIII
and material had to be prepared. Special thanks are due to J. Becker, H. Raber,
G. Sinning, D. Suwelack and E. Wolff. There are numerous scientists from whose
discussion I have benefited greatly in the past, among these I am particularly indebted
to R. G. Griffin, R. W. Vaughan and especially to U. Haeberlen, who kindly let me
have the manuscript of his review article prior to publication.
I also gratefully acknowledge the patience and endurance of Miss A. Gassner,
who typed the manuscript in several versions, and of Mrs. A. SchrOder and Mrs. L.
Sinning who have drawn and photographed most of the figures.
Finally I want to apologize to my wife Sabine and the children for spoiling
many sunny weekends by working on this monograph. Their patience and under
standing are gratefully acknowledged here.
The editors of this series have contributed much to the final layout of this
volume and their continuous interest and support are highly appreciated.
Dortmund, June 21,1976 M. Mehring
Table of Contents
1. Introduction ......................................... .
2. Nuclear Spin Interactions in Solids. . . . . . . . . . . . . . . . . . . . . . . . . . .. 6
2.1 Basic Nuclear Spin Interactions in Solids .................... , 6
2.2 Spin Interactions in High Magnetic Fields .. . . . . . . . . . . . . . . . . .. 11
2.3 Transformation Properties of Spin Interactions in Real Space . . . . . .. 15
2.4 Powder Spectrum Line Shapes ........................... 21
2.5 Specimen Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 24
2.6 Rapid Anisotropic Molecular Rotation ..................... , 28
2.7 Line Shapes in the Presence of Molecular Reorientation . . . . . . . . . .. 30
3. Multiple-Pulse NMR Experiments ............................ 40
3.1 Idealized Multiple-Pulse Sequences. . . . . . . . . . . . . . . . . . . . . . . .. 48
3.2 The Four-Pulse Sequence (WHH4) ........................ 55
3.3 Coherent Averaging Theory ............................. 65
3.4 Application of Coherent Averaging Theory to Multiple-Pulse Sequences 70
3.5 Arbitrary Rotations in Multiple-Pulse Experiments . . . . . . . . . . . . .. 76
3.6 Second Averaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83
3.7 The Influence of Pulse Imperfection on Multiple-Pulse Experiments ... 88
3.8 Resolution of Multiple-Pulse Experiments .................... 101
3.9 Magic Angle Rotating Frame Line Narrowing Experiments ......... 107
4. Double Resonance Experiments ............................. 112
4.1 Basic Principles of Double Resonance Experiments .............. 113
4.2 Cross-Polarization of Dilute Spins ......................... 127
4.3 Cross-Polarization Dynamics ............................. 135
4.4 Spin Decoupling Dynamics .............................. 153
5. Magnetic Shielding Tensor ................................. 167
5.1 Ramsey's Formula ................................... 168
5.2 Approximate Calculations of the Shielding Tensor .............. 168
5.3 Proton Shielding Tensors ............................... 170
5.4 19F Shielding Tensors ................................. 174
5.5 l3C Shielding Tensors ................................. 183
5.6 Other Shielding Tensors . . . . . . . . . . . . . . . . . . . . ............ 189
6. Spin-Lattice Relaxation in Line Narrowing Experiments ............. 192
6.1 Spin-Lattice Relaxation in Multiple-Pulse Experiments ........... 192
6.2 Application of Multiple-Pulse Experiments to the Investigation of
Spin-Lattice Relaxation ................................ 201
x
6.3 Spin-Lattice Relaxation in Dilute Spin Systems ................ 208
7. Appendix ............................................ 213
A. Irreducible Tensor Representation of Spin Interactions ........... 213
B. Rotations ......................................... 218
C. Contribution of Non-Secular Shielding Tensor Elements to the Resonance
Shift ............................................ 221
D. Bloch Siegert Shift ................................... 225
E. General Line Shape Theory ............................. 227
References ............................................. 236
List of Editors
Managing Editors
Professor Dr. Peter Diehl, Physikalisches Institut der Universitat Basel, Klingel
bergstr. 82, CH-4056 Basel
Professor Dr. Ekkehard Fluck, Institut fUr Anorganische Chemie der Universitat
Stuttgart, Pfaffenwaldring 55, D-7000 Stuttgart 80
Professor Dr. Robert Kosfeld, Institut fur Physikalische Chemie der Rhein.-Westf.
Technischen Hochschule Aachen, Tempelgraben 59, D-5100 Aachen
Editorial Board
Professor Sture Forsen, Department of Physical Chemistry, Chemical Centre,
University of Lund, P.O.B. 740, S-22007 Lund
Professor Dr. Shizuo Fujiwara, Department of Chemistry, Faculty of Science,
The University of Tokyo, Bunkyo-Ku, Tokyo, Japan
Dr. R. K. Harris, School of Chemical Sciences, The University of East Anglia,
Norwich NR4 7TJ, Great Britain
Professor C. L. Khetrapal, Raman Research Institute, Bangalore -560006, India
Professor E. Lippmaa, Department of Physics, Institute of CybernetiCS Academy of
Sciences of the Estonian SSR, Lenini puiestee 10, Tallinn 200001, USSR
Professor G. J. Martin, Chimie Organique Physique, Universite de Nantes, UER de
Chimie, 38, Bd. Michelet, F-44 Nantes, B.P. 1044
Professor A. Pines, Department of Chemistry, University of California, Berkeley,
CA 94720, USA
Professor Franz H. A. Rummens, Department of Chemistry, University of Regina,
Regina, Saskatschewan S4S OA2, Canada
Professor Dr. Bernard L. Shapiro, Department of Chemistry, Texas A and M
University, College Station, TX 77843, USA
1. Introduction
Spin engineering has brought about a wealth of techniques to overcome the natural line
broadening mechanisms in solids, such as dipole-dipole and quadrupole interactions. We
are going to review in this monograph the different techniques involved and we shall
discuss the results obtained. For the convenience of the unbiased reader let us fIrst
take a look at some representative results.
As is well known to the chemist, the NMR spectrum of a liquid consists of numer
ous sharp lines typically with less than 1 Hz linewidth, due to magnetic field inhomo
geneities or spin relaxation [1]. In order to supply a reference to this concept of "High
Resolution NMR", Fig. 1.1 displays as a representative example the spectrum of ethyl
alcohol [2]. Neither manipulation nor dilution is indicated in order to obtain the NMR
spectrum of this compound in the liquid state. It may be obtained in a rather standard
fashion by taking simply the NMR spectrum of the liquid sample. However, also high
resolution NMR spectroscopists like to manipulate on their spectra as is demonstrated
CH3 -CH2 -OH
OH 1 ppm
CH2
________ J. ______________ ____ _
~~ ""~
Fig. 1.1. Highly resolved proton spectrum of ethanol using spin decoupling. Top: While recording
the methyl group line, irradiation was performed on the methylene resonance. Bottom: While
recording the methylene group line, irradiation was performed on the methyl group resonance [2]
