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Relaxation in Magnetic Resonance - 1st Edition - ISBN: 9780125614504, 9780323151825

Relaxation in Magnetic Resonance

1st Edition

Dielectric and Mossbauer Applications

Editor: Charles P. Jr. Poole
eBook ISBN: 9780323151825
Imprint: Academic Press
Published Date: 1st January 1971
Page Count: 408
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Relaxation in Magnetic Resonance contains a series of lecture notes for a special topics course at the University of South Carolina in 1967. This book contains 21 chapters that summarize the main theoretical formulations and experimental results of magnetic resonance relaxation phenomena in several physical systems. This text deals first with the various methods in determining the relaxation behavior of the macroscopic spin system, such as Bloch equations, saturation methods, and transient resonant absorption. The subsequent chapters discuss the homogeneous and inhomogeneous resonant lines in solids and liquids and the significance of the Kubo-Tomita and Redfield theories in magnetic resonance. This book then considers the background research on electron spin resonance and relaxation in ionic solids. The concluding chapters explore the acoustic absorption coefficient and dielectric constant calculation; the relaxation processes in paramagnetic substance; and the characteristics of Mössbauer spectra and their application in magnetic relaxation. This book will be useful to both graduate students embarking upon thesis problems in relaxation and more advanced workers who seek an overall summary of the status of the field, as well as to physicists and chemists.

Table of Contents



1. Introduction

2. The Bloch Equations

2.1. Introduction

2.2. Static Case

2.3. Dynamic Case

2.4. Modified Bloch Equations

2.5. Summary


3. Saturation Methods for Determining Relaxation Times

3.1. Introduction

3.2. Basic Formulas

3.3. Determination of T1 and T2

3.4. High Resolution NMR

3.5. Dispersion

3.6. Measurement of H1

3.7. Concluding Remarks


4. Transient Resonant Absorption

4.1. Introduction

4.2. Pulse Experiments

4.3. Spin-Echoes

4.4. Measuring T2 by Spin-Echo Method A

4.5. Measuring T2 by Spin-Echo Method B

4.6. Stimulated Spin-Echo Method

4.7. Measuring T1 by Free Precession Decay

4.8. Spin Diffusion

4.9. Adiabatic Fast Passage

4.10. Pulse Saturation

4.11. Fourier Transforms and Lineshapes

4.12. Concluding Remarks


5. Line Broadening in Solids

5.1. Introduction

5.2. Homogeneous and Inhomogeneous Lines

5.3. The Dipolar and Exchange Hamiltonians

5.4. The Method of Moments

5.5. Exchange Narrowing

5.6. The 10/3 Effect

5.7. Dipolar Coupled Pairs

5.8. Anisotropy Broadening

5.9. Hyperfine and Quadrupolar Broadening

5.10. Dysonian Line Shape

5.11. Concluding Remarks


6. Relaxation in Liquids

6.1. Introduction

6.2. Spontaneous Emission

6.3. Brownian Motion

6.4. Perturbation Theory

6.5. Magnetic Field Perturbations

6.6. The Dipolar Interaction

6.7. Relaxation of Nuclei through Chemical Shielding, Quadrupole Moments, and Paramagnetic Impurities

6.8. Anisotropie g-Factors

6.9. Anisotropie Hyperfine Interactions

6.10. Zero Field Splittings

6.11. Spin-Rotational Interaction and Electric Field Fluctuations

6.12. Exchange Interactions

6.13. Inter- and Intramolecular Relaxation

6.14. Conclusion


7. The Kubo-Tomita Theory

7.1. Introduction

7.2. Density Matrix

7.3. The Relaxation Function

7.4. Moments of Spectral Lines

7.5. Motional Narrowing

7.6. Dipolar Broadening

7.7. Concluding Remarks


8. The Redfield Theories

8.1. Introduction

8.2. Theory of Bloembergen, Purcell, and Pound

8.3. Entropy Changes

8.4. Redfield's Modified Bloch Equations

8.5. The Hamiltonian Equations of Motion

8.6. Presence of Two Spin Species

8.7. Overall Graphical Results

8.8. Modulation Effects and Experimental Confirmation

8.9. Rotary Saturation

8.10. Redfield's General Relaxation Theory


9. Inhomogeneously Broadened Lines

9.1. Introduction

9.2. Homogeneous Broadening

9.3. Inhomogeneous Broadening

9.4. The Lineshape

9.5. Gaussian Envelope of Lorentzian Spin Packets

9.6. The T2* Method for Determining T1

9.7. Portis' Four Cases

9.8. Discussion


10. Spin—Lattice Relaxation in Ionic Solids

10.1. Introduction

10.2. The Jahn-Teller Effect

10.3. The Hamiltonian Terms

10.4. The Orbit-Lattice Interaction

10.5. Calculation of Direct Process for Ti3+

10.6. Calculation of Raman Process for Ti3+

10.7. Concluding Remarks


11. Orbach Processes in Rare Earths

11.1. Introduction

11.2. Rare Earth Ions

11.3. Orbach Relaxation Processes

11.4. Crystal Field Potential

11.5. Orbit-Lattice Interaction

11.6. One Phonon Relaxation in a Non-Kramers' Salt

11.7. One Phonon Relaxation in a Kramers' Salt

11.8. Two Phonon Processes

11.9. Two Phonon Relaxation in Non-Kramers' Salts

11.10. Two Phonon Processes in Kramers' Salts

11.11. Internal Fields

11.12. Conclusions


12. Phonon Bottleneck

12.1. Introduction

12.2. Relaxation Rates

12.3. Hot Phonon Interactions

12.4. Hot Phonon Rate Equations

12.5. Rate Equation Solutions with Zero Applied Power

12.6. Rate Equation Solution with Constant Applied Power

12.7. Orbach and Raman Processes

12.8. Phonon Transport

12.9. Lattice Modes

12.10. Role of Lattice Defects

12.11. Inverted Spin System

12.12. Discussion


13. Cross Relaxation

13.1. Introduction

13.2. Experiments with Lithium Floride

13.3. The Frequency Distribution Function

13.4. Cross Relaxation Rate Processes

13.5. Intermediate Relaxation

13.6. Relaxing Hyperfine Components

13.7. Homogeneous and Inhomogeneous Broadening

13.8. Cross-Maser Effects

13.9. Grant's Theory of Cross Relaxation

13.10. Concluding Remarks


14. Exchange Reservoir

14.1. Introduction

14.2. The Néel Temperature

14.3. The Exchange Interaction

14.4. Zeeman and Exchange Specific Heats

14.5. Energy Transfer Coefficients

14.6. Correlation Effects

14.7. Relaxation below the Curie Temperature

14.8. Pairs of Coupled Spins

14.9. Conclusion


15. Diffusion

15.1. Introduction

15.2. Fundamental Diffusion Relations

15.3. The Diffusion Differential Equation

15.4. Correlation Times

15.5. Rotational and Translational Correlation Times

15.6. Random Processes

15.7. Spin Diffusion in Inhomogeneously Broadened Lines

15.8. Diffusion to Paramagnetic Impurities

15.9. Conduction Electrons in Metals

15.10. Conclusions


16. Ultrasonic Resonance

16.1. Introduction

16.2. Absorption of Sound

16.3. Evaluation of Acoustic Absorption Coefficient

16.4. Phenomenological Hamiltonian

16.5. Indirect Method for Measuring Acoustic Saturation

16.6. Direct Method for Measuring Acoustic Saturation

16.7. Acoustic Paramagnetic Resonance of Nuclei

16.8. Instrumentation

16.9. Discussion


17. High Resolution Nuclear Magnetic Resonance

17.1. Introduction

17.2. Bloch Equations

17.3. Short Relaxation Times

17.4. Long Relaxation Times

17.5. Pulse Methods


18. Paramagnetic Relaxation

18.1. Introduction

18.2. Thermodynamic Background

18.3. Magnetic Susceptibility

18.4. Static Susceptibility

18.5. Dynamic Susceptibility

18.6. Populations of Energy Levels

18.7. Response to Radiofrequency Fields

18.8. Complex Dynamic Susceptibility

18.9. Conclusions


19. The Mössbauer Effect

19.1. Introduction

19.2. The Mössbauer Resonance

19.3. Electron Spin Resonance

19.4. Nuclear Magnetic Resonance

19.5. Core Polarization

19.6. The Hyperfine Interaction

19.7. Relaxation Effects

19.8. Double Resonance Experiments

19.9. Conclusions


20. Dielectric Relaxation

20.1. Introduction

20.2. Debye-Type Theories

20.3. The Local Field

20.4. Types of Polarizability

20.5. Dipolar Polarizability

20.6. Relaxation

20.7. Debye Relaxation

20.8. The Cole-Cole Plot

20.9. Relaxation in Gases

20.10. Relaxation in Liquids

20.11. Relaxation in Solids

20.12. Permanent Dipoles

20.13. Ionic Lattices

20.14. Application of the Kubo Formalism

20.15. Conclusions


21. Experimental Determination of Dielectric Constants

21.1. Introduction

21.2. Capacitor Equivalent Circuit

21.3. Bridge Method

21.4. Resonance Method

21.5. Heterodyne Beat Method

21.6. Microwave Dielectric Constants

21.7. Microwave Measurements

21.8. Microwave Cavity Method

21.9. Conclusions



Author Index

Subject Index


No. of pages:
© Academic Press 1971
1st January 1971
Academic Press
eBook ISBN:

About the Editor

Charles P. Jr. Poole

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