Anelastic Relaxation In Crystalline Solids

Anelastic Relaxation in Crystalline Solids provides an overview of anelasticity in crystals. This book discusses the various physical and chemical phenomena in crystalline solids. Comprised of 20 chapters, this volume begins with a discussion on the formal theory of anelasticity, and then explores the anelastic behavior, which is a manifestation of internal relaxation process. This text lays the groundwork for the formal theory by introducing the postulates. Other chapters explore the different dynamical methods that are frequently used in studying anelasticity. The reader is then introduced to the physical origin of anelastic relaxation process in terms of atomic model. This text also discusses the various types of point defects in crystals, including elementary point defects, composite defects, and self-interstitial defects. The final chapter provides relevant information on the various frequency ranges used in the study. This book is intended for crystallographers, mechanical engineers, metallurgical engineers, solid-state physicists, materials scientists, and researchers.

Preface

Acknowledgments

Chapter 1 Characterization of Anelastic Behavior

1.1 The Meaning of Anelasticity

1.2 Quasi-Static Response Functions

1.3 The Primary Dynamic Response Functions

1.4 Additional Dynamic Response Functions

1.5 Resonant Systems with Large External Inertia

1.6 Wave Propagation Methods

1.7 Summary of Results for Various Dynamic Experiments

Problems

General References

Chapter 2 Relations among the Response Functions: The Boltzmann Superposition Principle

2.1 Statement of the Boltzmann Superposition Principle

2.2 Relations between the Creep and Stress Relaxation Functions

2.3 Relations between Quasi-Static and Dynamic Properties

2.4 Interrelation of the Dynamic Properties

2.5 Summary of Relations among Response Functions

Problems

General References

Chapter 3 Mechanical Models and Discrete Spectra

3.1 Differential Stress-Strain Equations and the Construction of Models

3.2 The Voigt and Maxwell Models

3.3 Three Parameter Models; the Standard Anelastic Solid

3.4 Dynamic Properties of the Standard Anelastic Solid

3.5 Dynamic Properties of the Standard Anelastic Solid as Functions of Temperature

3.6 Multiple Relaxations; Discrete Spectra

3.7 Obtaining the Spectrum from a Response Function

Problems

General References

Chapter 4 Continuous Spectra

4.1 Continuous Relaxation Spectra at Constant Stress and Constant Strain

4.2 Relations between the Two Relaxation Spectra

4.3 Direct Methods for the Calculation of Spectra

4.4 Approximate Relations among Response Functions

4.5 Indirect or Empirical Methods for the Determination of Spectra

4.6 Remarks on the Use of Direct and Indirect Methods

4.7 Restrictions on the Form of Distribution Functions for Thermally Activated Processes

4.8 Temperature Dependence of the Gaussian Distribution Parameter

4.9 Dynamic Properties as Functions of Temperature

Problems

General References

Chapter 5 Internal Variables and the Thermodynamic Basis for Relaxation Spectra

5.1 Case of a Single Internal Variable

5.2 Case of a Set of Coupled Internal Variables

5.3 Thermodynamic Considerations

5.4 Relaxation Spectra under Different Conditions

Problems

General References

Chapter 6 Anisotropic Elasticity and Anelasticity

6.1 Stress, Strain, and Hooke's Law

6.2 The Characteristic Elastic Constants

6.3 Use of Symmetrized Stresses and Strains

6.4 The "Practical" Moduli

6.5 Transition from Elasticity to Anelasticity

6.6 Thermodynamic Considerations

Problems

General References

Chapter 7 Point Defects and Atom Movements

7.1 Types of Point Defects in Crystals

7.2 Defects in Equilibrium

7.3 Kinetics of Atom or Defect Migration

7.4 General Remarks Applicable to Both Formation and Activation of Defects

7.5 Diffusion

7.6 Nonequilibrium Defects

Problems

General References

Chapter 8 Theory of Point-Defect Relaxations

8.1 Crystal and Defect Symmetry

8.2 Concept of an "Elastic Dipole"

8.3 Thermodynamics of Relaxation of Elastic Dipoles under Uniaxial Stress

8.4 Some Examples in Cubic Crystals

8.5 Generalization of the Thermodynamic Theory: The Selection Rules

8.6 Generalization of the Thermodynamic Theory: Expressions for the Relaxation Magnitudes

8.7 Information Obtainable from Lattice Parameters

8.8 Kinetics of Point-Defect Relaxations: An Example

8.9 Kinetics of Point-Defect Relaxations: General Theory

8.10 Limitations of the Simple Theory

Problems

General References

Chapter 9 The Snoek Relaxation

9.1 Theory of the Snoek Relaxation

9.2 Experimental Investigations of the Snoek Relaxation

9.3 Applications of the Snoek Relaxation

Problems

Chapter 10 The Zener Relaxation

10.1 Zener's Pair Reorientation Theory

10.2 Results for Dilute Alloys

10.3 The Zener Relaxation in Concentrated Alloys

10.4 Theory of the Zener Relaxation in Concentrated Alloys

10.5 Applications of the Zener Relaxation

Problems

Chapter 11 Other Point-Defect Relaxations

11.1 Substitutionals and Vacancies

11.2 Interstitials

11.3 Defect Pairs Containing a Vacancy

11.4 Interstitial Impurity (i-i) Pairs and Higher Clusters

11.5 Interstitial-Substitutional (i-s) Pairs

11.6 Defects in Various Other Crystals

Problem

Chapter 12 Dislocations and Crystal Boundaries

12.1 Definitions, Geometry, and Energetics of Dislocations

12.2 Motion of Dislocations

12.3 Interaction of Dislocations with Other Imperfections

12.4 Grain Boundaries

Problems

General References

Chapter 13 Dislocation Relaxations

13.1 Description of the Bordoni Peak in fee Metals

13.2 Theories of the Bordoni Relaxation

13.3 Other Low-Temperature Peaks in fee Metals

13.4 Relaxation Peaks in bec and hep Metals

13.5 Peaks in Ionic and Covalent Crystals

13.6 The Snoek-Koster (Cold Work) Relaxation in bec Metals

Problem

General References

Chapter 14 Further Dislocation Effects

14.1 The Vibrating-String Model and Dislocation Resonance

14.2 Experimental Observations concerning ϕi

14.3 Theory of the Amplitude-Dependent Damping ϕh

14.4 Experimental Studies of Amplitude-Dependent Damping

Problems

General References

Chapter 15 Boundary Relaxation Processes and Internal Friction at High Temperatures

15.1 Formal Theory of Relaxation by Grain-Boundary Sliding

15.2 Experimental Studies of the Grain-Boundary Relaxation

15.3 Studies of the Macroscopic Sliding of Boundaries

15.4 Mechanism of the Grain-Boundary Relaxation

15.5 Twin-Boundary Relaxation

15.6 The High-Temperature Background

Problems

General References

Chapter 16 Relaxations Associated with Phase Transformations

16.1 Theory of Relaxation near a Lambda Transition

16.2 Examples of Relaxation near a Lambda Transition

16.3 Relaxation in Two-Phase Mixtures

Problems

General References

Chapter 17 Thermoelastic Relaxation and the Interaction of Acoustic Waves with Lattice Vibrations

17.1 Thermoelastic Coupling as a Source of Anelasticity

17.2 Thermal Relaxation under Inhomogeneous Deformation

17.3 Transverse Thermal Currents

17.4 Longitudinal Thermal Currents

17.5 Intercrystalline Thermal Currents

17.6 Interaction of Ultrasonic Waves with Lattice Vibrations: Theory

17.7 Interaction of Ultrasonic Waves with Lattice Vibrations: Experiments

Problems

General References

Chapter 18 Magnetoelastic Relaxations and Hysteresis Damping of Ferromagnetic Materials

18.1 Background Review

18.2 Macroeddy Currents

18.3 Microeddy Currents

18.4 Magnetomechanical Hysteresis Damping

18.5 Magnetoelastic Relaxation and Directional Order

Problems

General References

Chapter 19 Electronic Relaxation and Related Phenomena

19.1 Interaction of Ultrasonic Waves with Electrons in Metals

19.2 Interaction of Ultrasonic Waves with Electrons in Semiconductors

19.3 Relaxations Attributed to Bound Electrons

Problem

General References

Chapter 20 Experimental Methods

20.1 Quasi-Static Methods

20.2 Subresonance Methods

20.3 Resonance Methods

20.4 High-Frequency Wave Propagation Methods

General References

Appendix A Resonant Systems with Distributed Inertia

Appendix B The Kronig-Kramers Relations

Appendix C Relation between Relaxation and Resonance Behavior

Appendix D Torsion-Flexure Coupling

Appendix E Wave Propagation in Arbitrary Directions

Appendix F Mechanical Vibration Formulas

Torsional and Longitudinal Vibrations

Flexural Vibrations

General References

Appendix G Computed Response Functions for the Gaussian Distribution

References

Author Index

Subject Index