Anelastic Relaxation In Crystalline Solids

PrefaceAcknowledgmentsChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ProblemsChapter 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 ProblemsChapter 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 ProblemChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 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 ReferencesChapter 20 Experimental Methods 20.1 Quasi-Static Methods 20.2 Subresonance Methods 20.3 Resonance Methods 20.4 High-Frequency Wave Propagation Methods General ReferencesAppendix A Resonant Systems with Distributed InertiaAppendix B The Kronig-Kramers RelationsAppendix C Relation between Relaxation and Resonance BehaviorAppendix D Torsion-Flexure CouplingAppendix E Wave Propagation in Arbitrary DirectionsAppendix F Mechanical Vibration Formulas Torsional and Longitudinal Vibrations Flexural Vibrations General ReferencesAppendix G Computed Response Functions for the Gaussian DistributionReferencesAuthor IndexSubject Index