Principles of Magnetic Resonance (3rd Enlarged and Updated Edition)

339 Pages·1996·89.254 MB·English

by  Charles P. Slichter

Conversion ofGaussian to 51 Units
Fundamental Gaussian SI Ratio·
quantity
SI
Symbol Units Symbol Units
Gaussian
Magnetization 4,M G M Aim 10)/41(
Permeabilityof - , - J.lo",4IlX 10-7 Wb/Am 4l1:xlO-'
freespace
Anisotropy K erg/emJ K JIm) 10-1
Exchange ,A erg/em A Jim 10-)
Gyromagneticratio (S·Oe)-1 Y (s-A/ml-l 411'/10J
-
Gilbertparameter • - • I
Parameter Defining Units Defining Units Ratio·
(ormula formula
Magneticflekl H IH-dl.4IfNI/1O De JH,-dl=NI Aim IOJ/4J11'
strength
Magneticinduction •B B_H+41tM G B=1JJ.H+M) WblmJ 10-·
Flux .-fB·dA M, .~fB.dA Wb 10-'
Energyproduct BH/8lf.=-MHfl crgfcm' BHf1.=:>JloMHfl Jim' 10-1
Demagnetizatjon N H.__NM - H.=-NM - 1/4/f
factor
,.K - -
Volume l-dM/dH ,.=dM/dH 4K
susexptibility
Permeability P Jl-dB/dH - lJ.=dB/dH - 411X10-7
-1+4n:X =JlJI+K) -Po
Anisotropyfield H, Hr-2K/M De Hr=2KIJloM Aim 10'/411:
Stabilityfactor Q Q_H./4rtM - Q=H.IM - 1
Wallenergy • lJ_4j.!AK ergfcm2 a=4VA'K J/m2 10-3
density
Characteristic I l_a/4nM2 om l=alpoM2 m 10-2
length
Y~ ~a.=1~
Wallmobility P~ Po-w· - - cm/s·Oe m2/s·A 4nxlO-l
« K • K
,
m meter second A Ampere 0, Oersted G Gauss
cm centimeter N numberofturns J Joule Wb Weber M, Maxwell
• To obtain values in 51 units multiply value in Gaussian units by therespective ratio
The effect of Ul",U-1 for various U's and for a = X,Y,Z. The bottom line applies
for spin! only
1. I, 1,
U
ei91% 1% I,oos8-/~sin8 I~ cos 8+1, sin 8
ei(Jly /%cos8+I~sin8 I, /~ cos8-/% sin 8
ei91~ /% cos 8 -I, sin 8 1,0058+1% sin 8 I,
e-i(JI~S~ 1. c05(8/2) 1, 000(812) 1,
+1,(25, 5;0(812))\ ••- 1.(25, ';0(p/2))
.
,
'.'
Useful relations for unitary operators U. (U is a function of I, or S, or I and S)
Uj,(J,5lf,U,5W-' = Uf,U,5jU-'Uf,U,5)U-'
Uexp[i/U,S)IU-1 = exp(iUI(J,S}U-lj
.
""1'",
For spin!: ccMi.·(I~B,~;,1=·c.os(8/2) . - f ,- -, ,
sin (I~9) = 2l~ sin (8/2)
12 - 1 "a~:z:y:;\''''' :~ ,..,
"'-'I -"
1%111 = t/~ I'.
: lL.DltliI.cyclic permutations
1, 1% = -'"27zr->',_.. ..
,. .
..
"
;,
... :1 ','
.
,
- ..
,
,
.
.
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1
Springer Series in Solid-State Sciences
EditedbyPelerFuldc
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Springer Series in Solid-State Sciences P. Slichter
Editors: M. Cardona P. Fuldc K. von Klitzing H.·J. Queisscr
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Preface to the Third Edition
The first edition of Ihis book was wrilten in 1961 when I was Morris Loeb
LeclUrer in Physics 31 Harvard. In the preface I wrote: "TIle problem faced by
a beginner today is enonnous. If he attempts to read a current aniele. he oftcn
finds that the first paragraph refers to an earlierpaperon which the whole article
is based. and with which the authornaturally assumes familiarity. That reference
in turn is based on another, so the hapless student finds himself in a seemingly
endless retrcat.
I have felt that graduate siudems or others beginning research in magnetic
resonance needed a book which really went into the details ofca1culUlions, yet
was aimed al the beginner rather than the expert."
The original gool was to treat only those topics that are essential to an
understanding of the literature. Thus the goal was to be selective rather than
comprehensive. With thepassageoftime, importantnewconceptswere becoming
SO all-pervasive that Ifelt the need to add them. That led to the second edition,
which Dr. Latsch, Physics EditorofSpringer~Verlag,encouraged metowriteand
which helped launch the SpringerSeries in Solid-StateSciences. Now, ten years
later, that book (and its 1980revised printing) is no longeravailable. Meanwhile,
workers in magnetic resonance havecontinued to develop startling new insights.
There are new topics which are so important that they must be included in a
book that is intended to be an intrOductory text. The original course was one
semester - the book had more topics than I taught in that amount of time. The
new edition clearly would need a full year.
Throughout the history of this book, I have considered it as a textbook.
Thus the aim was to explain in a rigorous but physical manner concepts which
are essential for the student of magnetic resonance. Rather than giving an ex
haustive treatment of anyone topic, my intention has been to help prepare a
student to read the literature on that topic. The main additions include an en
largement and modest rewrite of the topic ofdouble resonance, explanations of
one- and two-dimensional Fourier tmnsfonn methods, of coherence transfer, of
multiple quantum coherence, and ofimportant topics related to dipolar coupling
that underlie the method of spin-flip line narrowing. In the earlier editions, the
chapteron the density matrix focused almost exclusively on its use in analyzing
relaxation processes. The new edition explains its use in analyzing the effect of
rf fields.
v
The first edition ofthis book came oot shortly after the publication of Ana
Contents
tole Abragam's classic-to-be Principles ofNuclear Magnetic Resonance. There
were not many other books on the market Today there are many books on mag
netic resonance, a large fraction written by some of the most illustrious founders
ofthe field and practitioners ofthe art. The styles ofthese books are as varied as
the scientific styles of their authors. As I have explored these marvellous books,
I have been struck by the opportunity that exists today to get the flavor of the
scientific thought of these great scientists.
When I wrote the first edition ofthis book at Harvard, Ihad noduties other
than preparing and giving the lectures. The third edition has been written on
1. Elements ofResonance .........................•.......... 1
evenings and weekends while I tried to carry on my nonnal activities. It would
1.1 Introduction ...................................•..•. 1
not have been possible without theexpert,dedicated. andalwayscheerful support
1.2 Simple Resonance Theory ........................• _••. 2
of my secretary, Ann Wells. Her association with the book has been long, since
1.3 Absorption of Energy and Spin-Lanice Relaxation . 4
she helped type the original edition. I am also grateful for the help of Jamie
Froman in the final stages.
2. Basic Theory . 11
2.1 Motion of Isolated Spins-Classical Treattnent . II
Urbana, Illinois
2.2 Quantum Mechanical Description ofSpin in a Static Field 13
June 1989 Charles P. SUchter
2.3 Equations of Motion ofthe Expectation Value . 17
2.4 Effect of Alternating Magnetic Fields . 20
2.5 Exponential Operators . 25
2.6 Quantum Mechanical Treatment of a Rotating Magnetic Field 29
2.7 Bloch Equations . 33
2.8 Solution of the Bloch Equations for Low HI . 35
2.9 Spin Echoes . 39
2.10 Quantum Mechanical Treatment of the Spin Echo . 46
2.11 Relationship Between Transient and Steady-State Response
of a System and of the Real and Imaginary Parts
of the Susceptipility . 51
2.12 Atomic Theory of Absorption and Dispersion ........•.•.. 59
3. Magnetic Dipolar Broadening ofRigid Lattices ........•.... 65
3.1 Introduction ............................••.•.. 65
3.2 Basic Interaction ........................•..•....... 66
3.3 Method of Moments ......................•..•..•... 71
3.4 Example of the Use of Second Moments .......•.•...... 80
4. Magnetic Interactions ofNuclei with Electrons ........•..•.••.. 87
4.1 Introduction ...............................••••.••.. 87
4.2 Experimental Facts About Chemical Shifts ......•..•..... 88
4.3 Quenching of Orbital Motion 89
4.4 Fonnal Theory of Chemical Shifts 92
4.5 Computation of Current Density ......•.............. 96
4.6 Electron Spin Interaction ............•..........•..•... 108
4.7 Knight Shift ..........................•..•,......... 113
VI
VII
4.8 Single Crystal Spectra . 127
4.9 Second-Order Spin Effects-Indirect Nuclear Coupling 131 7.8 Bloembergen's Three-Level Maser ......••.••••.....•... 269
7.9 The Problem ofSensitivity ................•....•...... 270
S. Spin-Lattice Relaxalion and Motional Narrowing 7.10 Cross-Relaxation Double Resonance ................•... 271
ofResonance Lines . 145 7:11 The B1oembe'1len-Somkin E<periment ......•.••.•••••... 275
5.1 Introduction . 145 7.12 Hahn's Ingenious Concept ................•..•..•..•... 277
5.2 Relaxation of a System Described by a Spin Temperature . 146 7.13 The Quantum Description ................•..•..•..•... 279
5.3 Relaxation of Nuclei in a Metal . 151 7.14 The Mixing Cycle and Its Equations ..........•.•_ . 283
5.4 Density Matrix-General Equations . 157 7.15 Energy and Entropy . 287
5.5 The Rotating Coordinate Transfonnation .....•..•..•..... 165 7.16 The Effects of Spin-Lattice Relaxation . 289
5.6 Spin Echoes Using the Density Matrix . 169 7.17 The Pines-Gibby-Waugh Method of Cross Polarization . 293
5.7 The Response to a 6-Function . 174 7.18 Spin-Coherence Double Resonance-Introduction . 295
5.8 The Response to a 1f/2 Pulse: FourierTransfonn NMR . 179 7.19 A Model System- An Elemen!ary Experiment:
5.9 The Density Matrix of aTwo-Level System . 186 The S-Aip-Only Echo ...........................•.... 296
5.10 Density Matrix- An Introductory Example . 190 7.20 Spin Decoupling . 303
5.11 Bloch-Wangsness-Redfield Theory .............•........ 199 7.21 Spin Echo Double Resonance . 311
5.12 Example of Redfield Theory . 206 7.22 Two-Dimensional FT Spectra-The Basic Concept . 319
5.13 Effect ofApplied Ahemaling Fields . 215 7.23 Two-Dimensional FT Spectra-Line Shapes . 324
7.24 Formal lbeoretical Apparatus I- The Time Development
6. Spin Temperature in Magnetism liInd in Magnetic Resonance 219 of the Density Matrix _ . 325
6.1 Introduction _ _ _ . 219 7.25 Coherence Transfer _ _ 331
6.2 A Predicrion from the Bloch Equations _ _.. 220 7.26 Fonnal Theoretical Apparatus II- The Product Operator
6.3 The Concept ofSpin Temperature in the Laboratory Frame Method . 344
in the Absence of Ahemating Magnetic Fields . 221 7.27 The Jeener Shift Correlation (COSY) Experiment _ 350
6.4 Adiabatic and Sudden Changes . 223 7.28 Magnetic Resonance Imaging . 357
6.5 Magnetic Resonance and Saturation . 231
6.6 Redfield Theory Neglecting Lattice Coupling . 234
6.6.1 Adiabatic Demagnetization in the Rotating Frame 235 8. Advanced Concepts in Pulsed Magnetic Resonance 367
6.6.2 Sudden Pulsing . 237 8.1 Introduction . 367
6.7 The Approach to Equilibrium for Weak HI . 239 8.2 The Carr-Purcell Sequence . 367
6.8 Conditions for Validity of the Redfield Hypothesis . 241 8.3 The Phase Alternation and Meiboom-Gill Methods . 369
6.9 Spin-Lattice Effects _.....................•... 242 8.4 Refocusing Dipolar Coupling . 371
6.10 Spin Locking, Tl". and Slow Motion ................•... 244 8.5 Solid Echoes . 371
8.6 The Jeener-Broekaert Sequence for Creating Dipolar Order 380
7. Double Resonance _ . 247 8.7 The Magic Angle in the Rotating Frame-
7.1 What Is Double Resonance and Why Do It? . 247 The Lee-Goldburg Experiment . 384
7.2 Basic Elements of the Overhauser-Pound Family 8.8 Magic Echoes . 388
of Double Resonance . 248 8.9 Magic Angle Spinning . 392
7.3 Energy Levels and Transitions ofa Model System . 250 8.10 The Relation ofSpin-Flip Narrowing to Motional Narrowing 406
7.4 The Overhauser Effect ............................•... 254 8.11 The Fonnal Description ofSpin·Flip Narrowing . 409
7.5 The Overhauser Effect in Liquids: The Nuclear 8.12 Observation of the Spin-Flip Narrowing . 416
Overhauser Effect . 257 8.13 Real Pulses and Sequences .......................•.... 421
7.6 Polarization by Forbidden Transitions: The Solid Effect . 264 8.13.1 Avoiding a z-Axis Rotation ..............•.•.... 421
7.7 Electron-Nuclear Double Resonance (ENDOR) . 266 8.13.2 Nonideality of Pulses . 422
8.14 Analysis of and More Uses for Pulse Sequence .....••.... 423
VIII
IX
9. Multiple Quantum Coherence . 43I
G. Diffusion in an Inhomogeneous Magnetic Field , . 597
9.1 Introduction _ . 43I
H. The Equivalence ofThree Quantum Mechanics Problems _ . 601
9.2 The Feasibility ofGenerating Multiple Quantum Coherence- !-
Powder Patterns _ . 605
Frequency Selective Pumping . 434
J. lime-Dependent Hamiltonians _ . 616
9.3 Nonselective Excitation _ . 444
K. Correction Tenns in Average HamiltOnian Theory-
9.3.1 The Need for Nonselective Excitation . 444
The Magnus Expansion _•••.... 623
9.3.2 Generating Multiple Quantum Coherence . 445
9.3.3 Evolution, Mixing, and Detection of Multiple
Selected Bibliography .............•.•.•,.••..•..•..•..•..•.... 629
Quantum Coherence . 449
9.3.4 Three or More Spins . 455 References .
, 639
9.3.5 Selecting the Signal ofaParticularOrderofCoherence 463
9.4 High Orders of Coherence . 470 Author Index ...............................................
647
9.4.1 Generating a Desired Order of Coherence . 47I
9.4.2 Mixing to Detect High Orders of Coherence . 480 Subjed Index ...............................................
651
10. Electric Quadrupole Effects ...... .......................... 485
10.1 Introduction 485
10.2 Quadrupole Hamiltonian- Pan J •••......••••.•......••• 486
10.3 Clebsch-Gordan Coefficients, Irreducible Tensor Operators,
and the Wigner-Eckart Theorem 489
10.4 Quadrupole Hamiltonian- Part 2 494
10.5 Examples at Strong and Weak Magnetic Fields 497
10.6 Computation of Field Gradienls ,............ 500
11, Electron Spin Resonance .,.,.,.. ,,.,.. ,.,.... ,....,...,.. ,. 503
11,1 Introduction , ,............................. 503
11.2 Example of Spin-Orbit Coupling and Crystalline Fields ., .., 505
11.3 Hyperfine Structure 516
11.4 Electron Spin Echoes , _..... 524
11.5 V", Center .................•....•..•................ 533
1.2. Summary .........••....•..•.•••....•.••.......•..•..... 555
Problems 557
Appendixes . 579
A. A Theorem About Exponential Operators ............••..... 579
B. Some Further Expressions for the Susceptibility ........•.,... 580
C. Derivation of the Correlation Function for a Field
That Jumps Randomly Between ±ho , . 584
D. A Theorem from Perturbation Theory ...............••..... 585
E. The High Temperature Approximation ................•_.... 589
F. The Effects ofChanging the Precession Frequency-
Using NMR to Study Rate Phenomena . 592
x
XI
•