Applied Superconductivity, Metallurgy, and Physics of Titanium Alloys

I: Metallurgy.- 1. Equilibrium and Nonequilibrium Phases.- 1.1 Equilibrium Phases.- 1.1.1 Electron/Atom Ratio Systematics.- 1.1.2 Electronic Structure and Phase Stability.- 1.2 ?-Titanium Alloys.- 1.3 ?-Titanium Alloys.- 1.4 Binary Titanium-Transition-Metal Alloys.- 1.4.1 Further Classification Schemes for Titanium-Alloy Phases.- 1.4.2 The Ti-Cr System.- 1.4.3 The Ti-Nb System.- 1.5 Multicomponent Titanium-Transition-Metal Alloys.- 1.5.1 Titanium-Base Multicomponent Alloys in General.- 1.5.2 The Ti-Zr-Nb System.- 1.6 Nonequilibrium Phases.- 1.6.1 The Martensitic and Athermal ?-Phases in Quenched Titanium-Transition-Metal Alloys.- 1.6.2 The Quenching Process.- 1.6.3 Stability Limit of the ?-Phase in Titanium-Transition- Metal Alloys.- 1.7 Formation and Structures of the Martensitic Phases.- 1.7.1 Morphology of Martensites.- 1.7.2 Structure of the Martensites.- 1.7.3 Crystallographic, Thermodynamic, and Acoustic Aspects of the Martensitic Transformation.- 1.8 Occurrence and Structure of the Quenched w-Phase.- 1.9 Summary—The Occurrence of the Martensitic and co-Phases in Quenched Titanium-Niobium Alloys.- 2. Aging and Deformation.- 2.1 The Aging of Quenched ?-Titanium Alloys.- 2.2 The Athermal and Isothermal ?-Phases.- 2.2.1 Athermal ?-Phase.- 2.2.2 Isothermal ?-Phase.- 2.3 ?-Phase Separation.- 2.3.1 Occurrence of the Reaction.- 2.3.2 Ti-Cr.- 2.3.3 Ti-Mo.- 2.3.4 Ti-Nb.- 2.3.5 Thermodynamics of the Phase-Separation Reaction.- 2.4 ?-Phase Precipitation from ?-Titanium Alloys.- 2.4.1 Direct Precipitation.- 2.4.2 Precipitation from the ?’ + ?-Phase.- 2.4.3 Precipitation from the ? + ?-Phase.- 2.5 Down-Quenching and Up-Quenching—?-Reversion.- 2.6 Effects of Third Element Additions on Precipitation in Quenched-and-Aged Titanium-Transition-Metal Alloys.- 2.6.1 The Ternary ? + ?Phase Regime.- 2.6.2 The Ternary ?’ + ?-Phase Regime.- 2.7 ?-Phase Immiscibility.- 2.8 Effects of Cold Deformation on the Microstructures of Quenched ?-Titanium Alloys.- 2.8.1 Low- and High-Level Deformation Microstructures.- 2.8.2 Further Studies of Cold Rolling.- 2.8.3 Swaging.- 2.8.4 Flattening.- 2.8.5 Wire Drawing.- 2.8.6 Summary.- 2.9 Influence of Stress, Strain, and Interstitial-Element Additions on the Transformation Kinetics of Quenched ?-Titanium Alloys.- 2.10 Influence of Stress on the Transformation.- 2.11 Influence of Heavy Plastic Deformation.- 2.11.1 Influence of Heavy Deformation on the Kinetics of Precipitation.- 2.11.2 Influence of Aging on the Fibrous Cell Structure.- 2.12 The Influence of Interstitial-Element Additions.- 2.13 Summary—The Occurrence of Isothermal ?- and Equilibrium ?-Phases in Deformed and/or Aged Titanium-Niobium Alloys.- 2.13.1 The Isothermal ?-Phase.- 2.13.2 The Equilibrium ?-Phase.- 3. Mechanical Properties.- 1. HARDNESS.- 3.1 The Hardness Test.- 3.2 Hardness of Quenched Titanium-Transition-Metal Alloys.- 3.3 Hardness of Aged Titanium-Niobium Alloys.- 3.4 Influence of Third-Element Additions on the Hardnesses of Unalloyed Titanium and Titanium-Niobium Alloys.- 3.5 Hardness of Ternary and Quaternary Transition-Metal Alloys.- 3.6 Theoretical Relationships Between Hardness and Strength.- 3.7 Application of the Marsh formula to the Determination of the Yield Strength of a Wire.- 3.8 Normal and Anomalous Tensile Properties of Superconductors.- 2. ANOMALOUS MECHANICAL PROPERTIES.- 3.9 Anomalous Tensile and Related Properties.- 3.10 Acoustic Emission from Copper and Titanium-Niobium.- 3.11 Mechanical Fatigue of Composite Conductors.- 3.12 Thermomechanical Heating.- 3. NORMAL MECHANICAL PROPERTIES OF TITANIUM-NIOBIUM ALLOYS AND COMPOSITE CONDUCTORS.- 3.13 Young’s Modulus of Titanium-Niobium Superconductors.- 3.14 Hardness and Modulus of Titanium-Niobium Superconductors.- 3.15 Hardness, Modulus, and Yield Strength in Titanium-Niobium Superconductors.- 3.16 Tensile Strengths of Titanium-Alloy Superconductors.- 3.17 Tensile Properties of Titanium-Niobium Technical Superconducting Alloys.- 3.18 Strengths of Titanium-Niobium-Base Multicomponent Alloys.- 3.19 Modulus and Strength of Composite Superconductors.- 3.20 Determination of the Tensile Properties of Composites.- 3.21 Strengthening Principles in Alloys and Composite Conductors.- 3.22 Strengthening of Alloys.- 3.23 Strengthening of Composite Conductors.- 3.24 Workability of Titanium-Alloy Superconductors.- II: Physics.- 4. Dynamic Elastic Modulus.- 4.1 Determination of Dynamic Moduli.- 4.1.1 Definitions and Interrelationships.- 4.1.2 Terminology.- 4.1.3 Long-Wavelength Measurement Techniques.- 4.2 Ultrasonic (MHz) Methods in Elastic Modulus Measurement.- 4.2.1 Cubic Monocrystals.- 4.2.2 The Isotropic Solid.- 4.2.3 The Anisotropic Solid.- 4.3 Calculation of Polycrystalline Elastic Moduli from the Mono- crystalline Compliance Moduli and Stiffness Moduli (i.e., the Elastic Constants).- 4.3.1 The VRH Approximation.- 4.3.2 The VRHG Approximation—The Debye Temperature.- 4.4 The Elastic Moduli of Titanium-Transition-Metal Alloys.- 4.5 Systematic Variation of Elastic Moduli with Composition and Microstructure in Titanium-Transition-Metal Alloys.- 4.5.1 The ?-Isomorphous Alloys Ti-V, Ti-Nb, and Ti-Mo.- 4.5.2 The ?-Eutectoid Alloys: Ti-Cr, Ti-Mn, Ti-Fe, Ti-Co, and Ti-Ni.- 4.6 The Dynamic Modulus of Titanium-Niobium.- 4.7 The Dynamic Moduli of Composite Superconductors.- 5. Electrical Resistivity.- 5.1 Electrical Resistivity of Titanium-Alloy Superconductors.- 5.2 Resistometrically Monitored Transformation and Aging.- 5.3 The Resistivity of Alloys—Composition Dependence.- 5.3.1 Simple Models of Alloy Resistivity.- 5.3.2 Residual Resistivities of Binary Transition-Metal Alloys.- 5.3.3 Relative Scattering Strengths of Simple-Metal and Transition-Metal Solutes in Ti.- 5.4 The Resistivity of Alloys—Temperature Dependence.- 5.4.1 Dilute Alloys at Low Temperatures.- 5.4.2 Ti-Alloy Resistivity at Moderate-to-High Temperatures.- 5.4.3 Ti-Alloy Resistivity at Moderate to Low Temperatures— Gross Features.- 5.5 Anomalous Resistivity Concentration Dependence and Temperature Dependence in Titanium-Base Alloys.- 5.5.1 Anomalous Concentration Dependence.- 5.5.2 Negative Temperature Dependence.- 5.6 Three Case Studies of Negative dp/dT.- 5.6.1 Negative dp/dT in Ti-V and Ti-Mo.- 5.6.2 Negative dp/dT in Ti-Cr.- 5.7 Mechanisms of Anomalous Resistivity Temperature Dependence.- 5.7.1 Impurity-Scattering Mechanisms.- 5.7.2 Ideal- (i.e., Phonon-) Scattering Mechanisms.- 5.7.3 Anomalous dp/dT in Strong-Scattering Disordered Binary Alloys.- 5.8 Magnetoresistivity in Normal Metals.- 6. Thermal Conductivity.- 6.1 Thermal Conductivity in Insulators and Normal Metals.- 6.2 Insulators.- 6.2.1 Intrinsic Lattice Conductivity.- 6.2.2 Influence of Impurities.- 6.2.3 Influence of Grain Boundaries and Lattice Disorder.- 6.3 Conductors.- 6.3.1 Relative Magnitudes of Insulator and Conductor Conductivity.- 6.3.2 The Electronic Component.- 6.3.3 The Lattice Component—Thermal Conductivity under Phonon-Electron and Phonon-Impurity Scattering.- 6.4 Thermal Conductivity of Alloys.- 6.4.1 Influence of Solute Concentration.- 6.4.2 Separation of the Electronic and Lattice Components.- 6.5 Thermal Conductivity Data.- 6.6 Thermal Conductivity in a Magnetic Field.- 6.7 Superconductors.- 6.7.1 The Electronic Thermal Conducitivity of Superconductors, Kes.- 6.7.2 The Phonon Thermal Conductivity of Superconductors, Kgs.- 6.8 The Mixed State.- 6.8.1 General Conclusion.- 6.9 Transition-Metal-Alloy Superconductors.- 6.9.1 Normal-State Electronic Resistivity.- 6.9.2 Normal-State Lattice Resistivity.- 6.9.3 Superconducting State.- 6.10 Thermal Transport in Titanium-Niobium Alloys.- 6.10.1 Thermal Conductivity of Ti-Nb.- 6.10.2 Thermal Diffusivity of Ti-Nb.- 6.11 Thermal Resistance of Superconductor/Normal Interfaces.- 6.11.1 Occurrence of the Thermal-Boundary Effect—Kapitza Resistance.- 6.11.2 Kapitza Resistance of the Cu/Ti-Nb Interface.- 6.11.3 Temperature Drop at the Cu/Ti-Nb Interface in a Composite Conductor—A Simple Model Calculation.- 7. Magnetic Susceptibility.- 7.1 Introduction.- 7.1.1 Magnetic Susceptibilities of Solids.- 7.1.2 The Role of Magnetic Susceptibility in Ti-Alloy Physics.- 7.2 Components of the Total Magnetic Susceptibility of Transition Metals and Their Alloys.- 7.3 Pauli Paramagnetic Susceptibility.- 7.3.1 Many-Body Effects in Pauli Paramagnetism.- 7.3.2 Many-Body Effects in Electronic Specific Heat.- 7.3.3 Calorimetrically Determined xP.- 7.4 Landau Diamagnetism.- 7.5 Ion-Core Diamagnetism.- 7.6 Orbital Paramegnetism.- 7.7 Magnetic Susceptibilities of Some Pure Transition Elements.- 7.8 Susceptibility Composition Dependences in Binary Transition- Metal Alloys.- 7.8.1 Total Magnetic Susceptibility.- 7.8.2 Pauli Paramagnetism.- 7.8.3 Orbital Paramagnetism.- 7.9 Susceptibility Temperature Dependences of Pure Transition Elements.- 7.10 Curie-Weiss Paramagnetism in Titanium-Transition-Metal Alloys.- 7.10.1 Dilute Alloys.- 7.10.2 Concentrated Ti-Mn Alloys.- 7.11 Susceptibility Temperature Dependence in Concentrated Titanium-Base Alloys—Case Studies of Ti-Al, Ti-V, and Ti-Mo.- 7.11.1 ?-Phase Alloys.- 7.11.2 ?-Phase Alloys.- 7.12 Concentration, Microstructure, and Temperature Dependences of Magnetic Susceptibility—A Case Study of Titanium- Vanadium.- 7.12.1 Concentration and Microstructure Dependence.- 7.12.2 Anomalous Temperature Dependence.- 7.13 Magnetic Susceptibility as a Function of Microstructure in Titanium-Base Alloys.- 7.13.1 Quenched Ti-TM Alloys.- 7.13.2 Magnetic Susceptibility of ?-Phase.- 7.14 Magnetic Studies of Precipitation and Aging in Titanium- Transition-Metal Alloys.- 7.14.1 The Aging Process in the ? + ?-Field.- 7.14.2 Properties of a “Saturation-Aged” ? + ?-Phase Ti-TM Alloy.- 8. Low-Temperature Specific Heat.- 8.1 Low-Temperature Specific Heat of Solids.- 8.1.1 Specific Heat of Insulators.- 8.1.2 Low-Temperature Specific Heat of Metals.- 8.1.3 Interrelationships Between y and ?D.- 8.2 Composition and Microstructure Dependence of Low- Temperature Specific Heat in Titanium Transition-Metal Alloys.- 8.2.1 General Description.- 8.2.2 Low-Temperature Specific Heats of Ti-V, Ti-Mo, and Ti- Fe.- 8.2.3 Normal-State Low-Temperature Specific Heat of Ti-Nb.- 8.3 Low-Temperature Specific Heats of Superconductors.- 8.3.1 Experimental Observations.- 8.3.2 Lattice Specific Heat in the Normal and Superconducting States.- 8.4 The Superconductive Electronic Specific Heat.- 8.4.1 The Gorter-Casimir Two-Fluid Relationships.- 8.4.2 The Exponential Form.- 8.4.3 The Full BCS Electronic Specific Heat.- 8.4.4 The Electronic Specific Heat at Tc—Height of the Specific Heat Jump, ?C.- 8.5 The Electron-Phonon Coupling Strength.- 8.5.1 Coupling Strength and the Temperature-Ratio Tc/ ?D.- 8.5.2 Coupling Strength and the Deviation Function, D(t).- 8.6 Relative Height of the Specific Heat Jump at Tc as a Function of Coupling Strength.- 8.6.1 Jump Height in Terms of the Deviation Function.- 8.6.2 Jump Height in Terms of Tc/ ?D.- 8.7 Empirical Determination of the Electron-Phonon Coupling Constant—A Case Study of Ti-Mo Alloys.- 8.7.1 Electron-Phonon Enhancement of the Density-of-States— Theoretical.- 8.7.2 Electron-Phonon Effects—Semiempirical.- 8.7.3 Electron-Phonon Effects—Empirical Method for an Alloy Series.- 9. Low-Temperature Thermal Expansion.- 9.1 Thermal Expansion of Insulators and Metals.- 9.1.1 Harmonicity and Anharmonicity in Thermal Expansion.- 9.1.2 Development of the Subject.- 9.1.3 The Electronic, Magnetic, and Other Contributions to Low- Temperature Thermal Expansion.- 9.1.4 Literature Sources—Plan of the Chapter.- 9.2 Thermal Expansion of Insulators.- 9.2.1 Thermodynamics of the Debye Isotropic Continuum.- 9.2.2 Lattice-Dynamical Approach.- 9.3 Thermal Expansion of Metals.- 9.3.1 The Electronic Expansion Coefficient.- 9.3.2 The Free-Electron Expansion Coefficient.- 9.3.3 Relative Linear Expansion at Low Temperatures.- 9.3.4 Further Calculations of the Electronic Thermal Expansion Coefficient—Departures from the Free Electron Model.- 9.4 Thermal Expansion of Magnetic Solids.- 9.5 Thermal Dilatometry.- 9.5.1 Introduction.- 9.5.2 Interference Methods.- 9.5.3 Resonance Methods.- 9.5.4 Push-Rod, Optical-Lever, SQUID, and Capacitive Techniques.- 9.6 Thermal Expansions of Selected Metals and Alloys.- 9.6.1 Thermal Expansion of Cu.- 9.6.2 Thermal Expansion of Al.- 9.6.3 Thermal Expansion of Ti.- 9.6.4 Thermal Expansions of Some Selected Technical Alloys.- 9.6.5 Estimation of Thermal Expansion (Contraction) Curves.- 9.7 Thermal Expansion of Superconductors.- 9.7.1 Thermal Expansion Through the Superconducting Transition.- 9.7.2 Phenomenological Thermodynamic Relationships.- 9.7.3 Thermal Expansion At and Below Tc.- 9.7.4 Normal-State Thermal Expansions of Ti-Nb and Ti-Zr-Nb.- 9.8 Thermal Expansion of Metallic and Nonmetallic Composites.- 9.8.1 Parallel Strips.- 9.8.2 Isotropic Solid-State Dispersion.- 9.8.3 Granular Compacts.- 9.8.4 Fiber-Reinforced Composites.- III: The Superconducting Transition.- 10. Calorimetric Studies of the Superconducting Transition and the Mixed State.- 10.1 The Calorimetrically Determined Transition Temperature.- 10.2 Calorimetric Studies of Tc as a Function of Composition- Related Microstructure—General Descriptions.- 10.2.1 Tc in the Martensitic Alloys.- 10.2.2 Tc in the ? + ?-Phase Alloys.- 10.2.3 Tc and Other Properties of ?-Ti-Mo.- 10.3 Calorimetrically Determined Superconducting Transitions in Quenched Low-Concentration ?m-Phase Ti-TM Alloys.- 10.3.1 Typical Results.- 10.3.2 Atypical Results—Ti-Mn.- 10.3.3 Distributed Calorimetrie Transitions.- 10.4 Transition Temperatures of Unstable bcc Alloys—A Case Study of Titanium-Molybdenum.- 10.4.1 The Tc of bcc-Ti.- 10.4.2 The Tc of Dilute bcc Ti-Mo Alloys.- 10.5 Influence of Aging on the Transition Temperatures of Titanium-Transition Metal Alloys.- 10.5.1 Magnetic Susceptibility and Electronic Specific Heat.- 10.5.2 The Transition Temperature.- 10.5.3 Verification of the Properties of ?-Ti-Mo(10.3 at.%).- 10.6 Low-Temperature Specific-Heat in the Mixed State.- 10.6.1 The Electronic Specific Heat.- 10.6.2 Height of the Specific Heat Jump.- 10.7 Influence of Deformation Itself, and Deformation- or Solute- Induced Phase Transformations on the Superconducting Transition.- 10.7.1 Deformation of Pure Elements.- 10.7.2 Deformation-Induced Transformation in Ti-TM Alloys.- 10.7.3 Solute-Induced Transformation in Ti-TM Alloys.- 10.8 Analysis of the Rounded Zero-Field Calorimetrie Superconducting Transition.- 10.8.1 The Transition Temperature Distribution Function.- 10.8.2 Outline of a Two-Component Model.- 10.8.3 Application of the Two-Component Model.- 10.9 Rounded Calorimetrie Transitions into the Mixed State.- 10.9.1 General Principles.- 10.9.2 Deformation Structure and the Mixed State.- 10.9.3 Calorimetrie Studies of ?GL Modulation.- 11. The Superconductive Proximity Effect.- 11.1 Introduction.- 11.1.1 Terminology.- 11.1.2 Coherence Length and Literature Survey.- 11.1.3 Measuring Techniques.- 11.1.4 Influence of the Underlay er on Tsn.- 11.2 Selection of Couples.- 11.3 Experimental Materials and Techniques.- 11.4 Theoretical Considerations—Cooper’s Model.- 11.5 The Theory of de Gennes.- 11.5.1 Thick Films in Which Dn,s » ?n,s.- 11.5.2 Thin Superconductive Film on a Massive Normal Under- layer.- 11.5.3 Thin Films—The Cooper Limit (D « ?).- 11.6 The Theory of de Gennes and Werthamer.- 11.6.1 Formulations of the Theory.- 11.6.2 Proximity Effect Against Normal Metals.- 11.6.3 Proximity Effect Against Magnetic Metals.- 11.7 The Evolution of Proximity-Effect Research.- (a) Supercurrent Tunnelling.- (b) Proximity Effect in Modulated Structures.- (c) Low-Temperature Specific Heat in the Study of Proximity Effect.- 11.8 Low-Temperature Specific Heats of Proximity Effect Couples.- 11.8.1 Theory of the Specific Heat and Its Discontinuity at Tc.- 11.8.2 Experimental Studies of Specific Heat in the Proximity Effect Regime.- 11.9 Proximity Effects in ? + ?-Phase Transition-Metal Alloys—A Case Study of Ti-Mo(10.3 at.%).- 11.9.1 Experimental Results—General.- 11.9.2 Experimental Results—Ti-Mo(10.3 at.%).- 11.9.3 Data Analysis—Ti-Mo(10.3 at.%) Aged 880h/350°C.- 11.9.4 Conclusion.- 12. The Superconducting Transition Temperature.- 12.1 The BCS Weak-Coupling Result.- 12.2 Strong-Coupling Theory.- 12.3 The Cardinal Determiner of the Transition Temperature.- 12.4 Transition Temperature Systematics in Crystalline and Amorphous Transition-Metal Alloys.- 12.4.1 Transition Temperatures of bcc Transition-Metal Alloys.- 12.4.2 Superconductivity in Crystalline and Amorphous Transition-Metal Alloys.- 12.5 Transition Temperatures of Titanium-Niobium-Base Alloy Superconductors— Some Experimental Results.- 12.5.1 Transition Temperature of Ti-Nb.- 12.5.2 Simple Metal Additions to Ti-Nb.- 12.5.3 Substitutes for Titanium in Ti-Nb Alloys.- 12.5.4 Substitutes for Niobium in Ti-Nb Alloys.- 12.5.5 Substitutes for both Ti and Nb in Ti-Nb Alloys.- IV: The Mixed State.- 13. Magnetic Properties of Superconductors.- 13.1 Development of the Classical Models.- 13.2 Type-I and Type-II Superconductors.- 13.3 The London Penetration Depth, ?L.- 13.4 Extension of London Theory.- 13.4.1 The Coherence Length, ?.- 13.4.2 The Penetration Depth, ?.- 13.5 Parameters of the Ginzburg-Landau (G-L) Theory.- 13.5.1 Penetration Depths and Coherence Lengths.- 13.5.2 The Ginzburg-Landau Parameters, ?GL.- 13.5.3 Clean and Dirty Limits of ?GL in Type-II Superconductors.- 13.6 The Thermodynamic Critical Field, Hc.- 13.6.1 Thermodynamic Relationships.- 13.6.2 The BCS “Thermodynamic” Critical Field.- 13.7 The Lower Critical Field, Hc1—Onset of the Mixed State.- 13.8 The Upper Critical Field, Hc2—Onset of the Normal State.- 13.8.1 Microscopy Theory.- 13.8.2 Thermodynamic Relationships.- 13.9 The Surface Sheath Critical Field, Hc3.- 14. The Mixed State.- 14.1 Temperature Dependences of the Critical Fields.- 14.1.1 Early Experimental Studies of Hc1(T).- 14.1.2 Early Semiempirical Studies of Hc2(T).- 14.2 Foundations of the Ginzburg-Landau-Abrikosov-Gor’kov (GLAG) Theory of the Mixed State.- 14.2.1 The Ginzburg-Landau Parameter and Its Response to Alloying.- 14.2.2 Structure of the Flux Lattice.- 14.3 Dirtiness and Irreversibility in Type-II Superconductors.- 14.3.1 The Ginzburg-Landau-Gor’kov Impurity Parameter, ?0/l.- 14.3.2 Irreversible Alloy Superconductors.- 14.4 The Full Ginzburg-Landau-Gor’kov-Bardeen-Cooper- Schrieffer Relationships.- 14.5 Evolution of Nonparamagnetic Post-GLAG Theories of the Upper Critical Field Temperature Dependences.- 14.5.1 Symbols for the Upper Critical Fields.- 14.5.2 Development of the Maki Dirty-Limit Equations.- 14.5.3 Magnetic and Calorimetric Determinations of ?1(t).- 14.5.4 Magnetic and Calorimetric Determinations of ?2(t).- 14.5.5 Final Developments in Nonparamagnetic Mixed-State Theory.- 14.6 Evaluation of the Nonparamagnetic Upper Critical Field.- 14.6.1 Evaluation of Hc2 in Terms of Normal-State Properties.- 14.6.2 Evaluation of Hc2 in Terms of Superconductive-State Properties.- 14.7 Evaluation of the Thermodynamic Critical Field.- 14.7.1 Hc0 in Terms of Measurable Parameters.- 14.7.2 A Case Study with Ti-Nb.- 14.8 Evaluation of the Maki Lower Critical Field.- 14.8.1 Hcl0 in Terms of Measurable Parameters.- 14.8.2 Validity of Nonparamagentic Maki Theory as a Descriptor of Hc1 in Intermediate-?GL Alloys—A Case Study of Ti- Doped Nb.- 15. The Paramagnetic Mixed State.- 15.1 Pauli Paramagnetic Limitation.- 15.2 Mechanisms for the Relief of Pauli Paramagnetic Limitation.- 15.2.1 Early Observations.- 15.2.2 Thermodynamic Model for the SOS Relief of PPL.- 15.2.3 Mechanistic Interpretation of the SOS/PPL Effects.- 15.3 Calorimetric Evidence for the Paramagnetic Mixed State.- 15.4 The Spin-Paramagnetic Theories of Maki and of Werthamer, Helfand, and Hohenberg.- 15.5.1 The Theories of Maki.- 15.4.2 The Theory of Werthamer, Helfand, and Hohenberg (WHH).- 15.4.3 The Conjoint Theories of Maki and WHH.- 15.5 The Maki Result.- 15.5.1 Pauli Paramagnetic Limitation (PPL).- 15.5.2 Spin-Orbit Scattering (SOS).- 15.5.3 The Maki Mixed State ?i(t) and Hc2(t) Relationships.- 15.5.4 An Application of Maki Theory.- 15.6 The Werthamer, Helfand, and Hohenberg (WHH) Result.- 15.6.1 Essential Parameters and Formalisms of WHH Theory.- 15.6.2 The Order of the Transition at Hc2.- 15.6.3 Early Applications of WHH Theory.- 15.6.4 Experimental Spin-Orbit Relaxation Time, ?so.- 15.6.5 Influence of Atomic Number on the Spin-Orbit-Scattering Frequency, ?so.- 15.7 Application of the Coupled Results of Maki and WHH.- 15.7.1 Interrelationships Between the Maki and WHH Theories.- 15.7.2 Applications of the Coupled Maki-WHH Theories.- 15.8 The Breakdown of Simple WHH Theory—Consideration of Many-Body Effects and Spin-Orbit-Scattering Frequency.- 15.8.1 The Influence of Many-Body Interaction on the Clogston Limiting Field.- 15.8.2 Spin-Orbit Scattering Frequency.- 15.9 Conclusion—Summary of Essential Factors Controlling the Magnitude of the Upper Critical Field.- 16. The Critical State.- 16.1 Reversible and Irreversible Type-II Superconductors.- 16.2 The Critical State.- 16.2.1 Introduction.- 16.2.2 Thermodynamic Equilibrium in the Critical State.- 16.2.3 The Elementary Pinning Force, fp.- 16.2.4 Introduction of the Maxwellian Supercurrent.- 16.3 Critical State Models.- 16.4 The Bean Model of the Critical State.- 16.4.1 Basic Phenomenological Equations of the Model.- 16.4.2 Cylinder Magnetization in the Bean Model.- 16.5 Models for the Pinned Critical State.- 16.6 Applications of the Critical State Models to Tube and Coil Magnetization.- 16.6.1 Tube and Coil Magnetization Studies—A General Introduction.- 16.6.2 The Tube-Magnetization Experiments of Kim et al.- 16.6.3 Relationship Between the 47?M versus H and B versus H Diagrams.- 16.7 Relationship Between Applied Field and Induction in Irreversible (i.e., Hard) Type-II Superconductors.- 16.7.1 Relationship Between B and H at the Surface.- 16.7.2 Relationship Between the Field Gradients in the Interior.- 16.7.3 Relationship Between µeq0 and µeq.- 16.8 The Role of HC1 in Critical State Theory.- 16.9 Experimental Studies of Induction Profiles in the Critical State.- 16.9.1 Induction Profile Scanning.- 16.9.2 Field Modulation Methods.- 17. The Upper Critical Field.- 17.1 The Nonparamagnetic Critical Fields.- 17.1.1 Temperature Dependences of the Critical Fields.- 17.1.2 Evaluation of the Zero-K Upper Critical Field.- 17.2 The Paramagnetically Limited Upper Critical Field and Its Temperature Dependence.- 17.2.1 Influence of Normal-State Pauli Paramagnetism.- 17.2.2 Further Developments of Mixed-State Theory.- 17.2.3 Influence of Electron-Phonon and Electron-Electron Interaction on the Paramagnetic Limit, Hp0.- 17.2.4 Summary of Recent Advances in WHH Theory.- 17.3 Fundamental Determiners of the Upper Critical Field—Pros pects for Raising Hc2.- 17.3.1 Prospects for Raising H*c20.- 17.3.2 Prospects for Raising Hp0CL.- 17.3.3 Prospects for Raising Hp0.- 17.3.4 Prospects for Raising Hc20 above Hc20min.- 17.4 Influence of Metallurgical and Physical Variables on the Measured Upper Critical Field.- 17.4.1 Cold Deformation.- 17.4.2 Aging.- 17.4.3 Influence of Temperature.- 17.5 Measurement of the Upper Critical Field.- 17.5.1 Transition Criteria.- 17.5.2 Measurement Current Density and Other Considerations.- 17.6 Upper Critical Fields of Titanium-Niobium-Base Alloy Super-conductors—Some Experimental Results.- 17.6.1 Upper Critical Field of Ti-Nb.- 17.6.2 Simple-Metal Additions to Ti-Nb.- 17.6.3 Substitutes for Ti in Ti-Nb Alloys.- 17.6.4 Substitutes for Nb in Ti-Nb Alloys.- 17.6.5 Substitutes for Both Ti and Nb in Ti-Nb Alloys.- 18. Flux in Motion under the Influence of a Field Gradient.- 18.1 Classes of Flux Motion.- 18.1.1 Flux Creep.- 18.1.2 Flux Flow.- 18.1.3 Flux Jumping.- 18.1.4 Summary.- 18.2 Physical Analogs of the Dynamic Mixed State.- 18.2.1 Mechanical and Thermal Analogs.- 18.2.2 An Electrical Transport Analog.- 18.3 Electromagnetism of the Dynamic Mixed State.- 18.3.1 The Magnetic Driving Force.- 18.3.2 The Lorentz Driving Force.- 18.3.3 Electromotive Force and Power Dissipation Associated with Flux Motion.- 18.4 The Tube Magnetization Experiment in Flux Dynamics Studies.- 18.5 Flux Creep.- 18.5.1 Experimental Observations—Temperature Dependence of the Critical State.- 18.5.2 Experimental Observations—Time-Dependence of Critical State Decay.- 18.6 The Thermal Activation Theory of Flux Creep.- 18.6.1 Development of the Theory.- 18.6.2 Temperature Dependence of the Critical Parameter, ?c(T).- 18.6.3 Commentary on Anderson’s Theory.- 18.7 Current-Voltage Relationships in the Creep State.- 18.8 Time Dependence of the Critical State.- 18.9 Relatively Recent Magnetic Studies of Flux Creep.- 18.9.1 Determination of Pinning Energy.- 18.9.2 Evidence for Flux Clustering.- 18.10 Flux Creep as Magnetic Diffusion.- 18.10.1 Atomic Diffusion.- 18.10.2 Magnetic Diffusion.- 18.11 Phenomenological Investigation of Electromagnetic Diffusion.- 18.11.1 The Basic Equations.- 18.11.2 Application of the Electromagnetic Diffusion Equations to the Measurement of Creep Resistivity.- 18.12 Magnetic Studies of Flux Flow.- 18.12.1 The Flow Viscosity Coefficient.- 18.12.2 Experimental Design for Viscosity Coefficient Measurement.- 18.12.3 Analysis of the Flux-Flow Equations.- 18.12.4 Flux-Flow Viscosity in Weakly-Pinned Alloys—A Case Study of Annealed Ti-Nb and Zr-Nb Alloys.- 18.12.5 Conclusion—Relationship Between Pinning Strength and the Dynamics of Flux Motion.- 18.13 Flow Resistivities and Critical Current Densities of Annealed Ti-Nb(75 at.%) and Zr-Nb(75 at.%) Alloys.- 18.13.1 Flow Resistivity.- 18.13.2 Critical Current Density.- 18.13.3 Corollary.- 18.14 Magnetic Studies of Flux Jumping.- 18.14.1 The Use of Tube and Cylinder Magnetization Techniques.- 18.14.2 The Experiments of Wipf and Lubell.- 18.14.3 The Experiments of Kroeger.- 18.14.4 The Experiments of Gandolfo.- 18.15 Magnetic Instability in Tube Magnetization.- 18.15.1 Incomplete and Full Flux Jumping—Historical Background and Present Status.- 18.15.2 Intrinsic Stability Considerations.- 18.16 Upper Shielding Limit of Full Critical State Stability, Hfi—The Lower Bound of the Incomplete Flux-Jump Regime.- 18.17 Upper Bound of the Incomplete Flux-Jump Regime, Hfj— The Threshold of Runaway Instability.- 18.18 The Concept of “Limited Instability”.- 18.19 Insights into Superconductor Stabilization Derived from Flux-Jump Studies.- 18.19.1 The Stability Cycle.- 18.19.2 Stability and Degradation.- 19. Magnetization and Critical Current Density.- 19.1 Principles of Magnetic Critical Current Density Measurement.- 19.2 Static Tube Magnetization.- 19.3 Saturation-Magnetization Reversal.- 19.4 Harmonic Analysis.- 19.5 Static Field Profile Analysis.- 19.6 Dynamic Field Profile Analysis.- 19.7 Torque Magnetometry.- 19.8 Vibrating-Sample Magnetometry.- 19.8.1 Adaptation of the Magnetization-Reversal Technique.- 19.8.2 Measurement of Critical Current Density Anisotropy.- References.- Symbols and Abbreviations.- Index of Plotted and Tabulated Data.