Ultrasonic Methods in Solid State Physics

Ultrasonic Methods in Solid State Physics is devoted to studies of energy loss and velocity of ultrasonic waves which have a bearing on present-day problems in solid-state physics. The discussion is particularly concerned with the type of investigation that can be carried out in the megacycle range of frequencies from a few megacycles to kilomegacycles; it deals almost entirely with short-duration pulse methods rather than with standing-wave methods. The book opens with a chapter on a classical treatment of wave propagation in solids. This is followed by separate chapters on methods and techniques of ultrasonic pulse echo measurements, and the physics of ultrasonically measurable properties of solids. It is hoped that this book will provide the reader with the special background necessary to read critically the many research papers and special articles concerned with the use of ultrasonic methods in solid state physics. The book is intended to help the person beginning work in this field. At the same time, it will also be useful to those actively involved in such work. An attempt has been made to provide a fairly general and unified treatment suitable for graduate students and others without extensive experience.

Preface

Introduction

Chapter 1. Propagation of Stress Waves in Solids

1. Introduction

2. Stress, Strain, and Displacement Relations

3. Equations of Motion and Solutions

4. Propagation Directions and Velocities

5. Energy and Energy Flux

6. Scattering Relations

7. Orientation Dependence of Stress Waves in Single Crystals

8. Explicit Expressions for Fractional Velocity Change as Function of Misorientation for Several Crystal Systems

9. Some Numerical Results for Misorientation Effects in Cubic Crystals

10. Energy Flux Associated with Stress Waves

11. Stress Waves in Piezoelectric Crystals

12. Nonlinear or Anharmonic Effects

Chapter 2. Measurement of Attenuation and Velocity by Pulse Methods

13. The Pulse Echo Method

14. Definitions of the Attenuation α, of the Decrement δ, and of the Dissipation Q

15. Methods of Measuring Attenuation

16. Coupling with Two Transducers (through Transmission)

17. Coupling Losses

18. Velocity Measurements

19. Systems for Velocity Measurements

20. Measurement Losses

21. Diffraction Losses

22. Nonparallelism and Wedging Effects

23. Effects of Wedging of Elastic Properties

24. The Spectrum Analyzer and Its Uses

25. Specific Application of the Spectrum Analyzer: Factors Affecting the Spectrum

26. Attenuation Equipment Considerations

27. Velocity Equipment Considerations

28. Microwave Ultrasonic Equipment

Chapter 3. Causes of Losses and Associated Velocity Changes

29. Introduction to Loss Interactions

I. Scattering

30. Statement of the Problem

31. Scattering Cross Section and Attenuation

32. Calculation of Scattering Cross Sections

33. Numerical Calculations of Scattering Cross Sections

34. Multiple Scattering and Scattering Density

II. Thermoelastic Effects

35. Physical Description of the Effect

36. Phenomenological Analysis

37. Attenuation and Velocity Changes Due to the Thermoelastic Effect

38. Calculations for Cubic and Hexagonal Crystals

III. Dislocation Damping

39. Description of the Model for Dislocation Damping

40. Equations of Motion and Solutions

41. Attenuation and Velocity

42. Distribution of Dislocation Loop Lengths

43. Strain Amplitude Effects

44. Thermal Effects in Dislocation Damping

45. Anomalous Ultrasonic Velocity Effects Associated with Dislocation Behavior

46. The Generation of Harmonics in Crystalline Solids Due to Dislocations

47. Some Selected Experimental Results

48. Bordoni Peaks

49. The Kink Model of Dislocation Damping

IV. Magnetoelastic Interactions

50. Stress Wave Interaction with Magnetic Domain Walls: Experimental Results

51. Outline of an Analytical Approach to Domain Wall Motion

52. Interaction of Spin Waves and Ultrasonic Waves in Ferromagnetic Crystals

53. Experimental Observations concerning Spin Waves and Ultrasonic Waves

V. Stress Wave Interaction with Conduction Electrons in Metals

54. Conditions for Interaction

55. More Complete Classical Interpretation

56. Quantum-Mechanical Interpretation

57. Influence of Magnetic Field

58. Application to Fermi Surface Study

59. Application to Superconductivity Study

VI. Ultrasonic Stress Wave Interaction with Thermal Waves: Phonon-Phonon Interaction

60. Description of the Problem

61. Experimental Situation

62. Theoretical Situation and Calculation of Attenuation

VII. Stress Wave Interactions with Nuclear Spin Systems

63. Preliminary Remarks

64. Conditions for Interaction

65. The Ultrasonic Attenuation Coefficient

66. Coupling through the Dynamic Electric Quadrupole Moment

VIII. Stress Wave Interaction with Electron Spins of Paramagnetic Centers

67. Stress Waves and Electron Spin Level Transitions

IX. Stress Waves and Electrical Phenomena in Piezoelectric Crystals

68. Wave Propagation in Piezoelectric Semiconductors

69. Light-Sensitive Ultrasonic Attenuation in CdS

70. Ultrasonic Amplification in CdS

X. Acoustoelectric Effect in Semiconductors

71. General Description

Appendix A. Elastic Constants of Trigonal Crystals (Al2O3)

Appendix B. Fractional Velocity Changes and Eigenvectors Associated with Section 8

Appendix C. Sample Preparation, Transducer and Bond Considerations

Appendix D. Some Useful Physical Constants for Various Crystalline Solids

Appendix E. Automatic Attenuation Measurement System

Appendix F. Automatic Time Measurement System

Appendix G. Evaluation of Coefficients in Scattering Cross Section for Transverse Waves

Appendix H. Numerical Computation of Normalized Cross Sections yN

Appendix I. Method of the Boltzmann Transport Equation

Appendix J. Quantum-Mechanical Treatment of Attenuation by the Three Phonon Process

References

Author Index

Subject Index