Applied Superconductivity, Metallurgy, and Physics of Titanium Alloys: Fundamentals Alloy Superconductors: Their Metallurgical, Physical, and Magnetic

ISBN-13: 9781461292418 / Angielski / Miękka / 2011 / 854 str.

E. W. Collings

Opis

Scope and Purpose Although conductors based on the Al5 intermetallic compound Nb Sn 3 possess desirable high-field superconducting properties, manufacturing and handling difficulties, coupled with the tendency of their critical current densities to degrade rapidly under stress, have generally restricted their use to fairly straightforward, usually small-scale solenoidal-magnet applica- tions. Likewise the Al5 compound VGa, which has a wider critical strain 3 window than NbSn but a uniformly lower upper critical field, has not 3 entered widespread service. Strain has been found to have no measurable influence on either the critical fields or the critical current densities of compound superconductors with BI and Cl5 crystal structures, but as yet they are still in the research and development stages. On the other hand, conductors using the binary alloy Ti-Nb or multi component alloys based on it, because of their relative ease of manufacture, excellent mechanical properties, and relatively low strain sensitivities, are now being pressed into service in numerous large-scale devices. Such conductors are being wound into magnets for use in energy storage, energy conversion (i. e., generators and motors), and high-energy particle detectors and beam-handling magnets. of cold-rolled or drawn Ti-Nb-alloy wire for superconducting The use magnet applications was first proposed in 1961. During the ensuing ten years, while progress was being made in the development of Cu-clad filamentary-Ti-Nb-alloy conductors, Ti-Nb and other Ti-base binary transi- tion-metal (TM) alloys were being employed as model systems in the fundamental study of type-II superconductivity.

Spis treści

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.