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Superconductivity of Transition Metals E.H. Brandt

Superconductivity of Transition Metals By E.H. Brandt

Superconductivity of Transition Metals by E.H. Brandt


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Summary

This is a major shortcoming since most physicists working in the field of superconduc tivity are mainly concerned with specific materials and subsequently often need to know more about the interplay of superconductivity and material prop erties.

Superconductivity of Transition Metals Summary

Superconductivity of Transition Metals: Their Alloys and Compounds by E.H. Brandt

This book should fill a gap which has existed in the literature on supercon ductivity. There have been a number of excellent textbooks available on the phenomenon of superconductivity, which describe in detail the variety of ef fects connected with it and the mathematical techniques to deal with them properly. However, until now there has not been a textbook available in English which concentrates on the mate~ial aspects of superconductivity. This is a major shortcoming since most physicists working in the field of superconduc tivity are mainly concerned with specific materials and subsequently often need to know more about the interplay of superconductivity and material prop erties. On the other hand, people working in the field know that a competent and well-written book by S. V. Vonsovsky, V. A. Izyumov, and E. Z. Kurmaev has been available in Russian. It presents a thorough discussion of superconducting transition-metal alloys and compounds. This volume is a translation of an updated version of the Russian edition. The translation was done by A. P. Zavarnitsyn of the authors' institution and by Dr. E. H. Brandt of the Max-Planck-Institut fur Metallforschung in Stuttgart. The master manuscript was ably typed by Mrs. C. Pendl. I would like to take this opportunity to thank each of them. I sincerely hope that the book will turn out to be useful to physicists working in the field of superconductivity as well as to nonspecialists and interested graduate students.

Table of Contents

1. Introduction.- 1.1 The Distribution of Superconductors Among the Elements of the Periodic Table, Their Alloys and Compounds.- 1.1.1 Superconductivity in Pure Elements.- 1.1.2 Superconductivity in Alloys.- 1.1.3 Superconductivity in Chemical Compounds.- 1.1.4 Outlook.- 1.2 Survey of Theoretical Concepts.- 1.2.1 The Fundamentals of the BCS Theory.- 1.2.2 The Role of the Coulomb Interaction.- 1.2.3 The Effects of Retardation in the Electron-Phonon Interaction.- 1.2.4 The Electron-Phonon Coupling Constant.- 1.2.5 The Peculiarities of the Transition Metals.- 1.2.6 Superconductivity and Magnetism.- 2. The Theory of Strong Coupling Superconductors.- 2.1 Perturbation Theory for Green's Functions.- 2.1.1 The Gor'kov-Nambu Matrix Formalism.- 2.1.2 Perturbation Theory.- 2.1.3 The Momentum Representation.- 2.1.4 Lower-Order Graphs for ?.- 2.2 Eliashberg Equations for the Electron Green's Function.- 2.2.1 Formulation of the Equations and Summation over Frequencies.- 2.2.2 Calculation of the Phonon Part ?ph(p,?).- 2.2.3 Calculation of the Coulomb Part ?c (p,?)).- 2.2.4 Basic Equations for a Superconductor.- 2.2.5 Dispersion Relations.- 2.3 The Superconducting Transition Temperature.- 2.3.1 Linearized Eliashberg's Equations.- 2.3.2 Weak Coupling.- 2.3.3 Intermediate Coupling.- 2.3.4 Strong Coupling.- 2.3.5 Contribution of Low-Frequency Modes.- 2.4 Calculations of the Electron-Phonon Coupling Constant ?.- 2.4.1 Green's Function of Phonons.- 2.4.2 Expression of ? in Terms of the Phonon Green's Function.- 2.4.3 The McMillan Representation.- 2.4.4 The Hopfield Representation for a Transition Metal.- 3. Superconductivity and Magnetism.- 3.1 Conditions for the Occurrence of Superconductivity in a Ferromagnetic Metal.- 3.1.1 Four-Dimensional Matrix Formalism.- 3.1.2 Wick's Theorem.- 3.1.3 Perturbation Theory.- 3.1.4 Matrix Structure of Green's Functions.- 3.1.5 Superconducting Transition Temperature of a Ferromagnetic Metal.- 3.2 Superconductivity in Dilute Ferromagnetic Alloys.- 3.2.1 The Problem of the Coexistence of Superconductivity and Magnetic Ordering.- 3.2.2 Equations Including Dynamic Effects.- 3.2.3 Quasi-Static Approximation.- 3.3 The Coexistence of Superconductivity and Helical Magnetic Ordering.- 3.3.1 The Anderson-Suhl Hypothesis.- 3.3.2 Equations for the Electron Green's Function in the Weak-Coupling Approximation.- 3.3.3 Analysis of the Free Energy.- 3.4 Magnetic Ordering in Superconducting Rare-Earth Compounds.- 3.4.1 Superconductivity and Antiferromagnetism.- 3.4.2 Superconductivity and Ferromagnetism.- 3.4.3 Phenomenological Theory of Magnetic Ordering in Superconductors.- 3.4.4 Magnetic Fluctuations and Superconductivity.- 3.4.5 Critical Behaviour of Magnetic Superconductors.- 3.5 Magnetic Impurities in Superconductors.- 3.5.1 The Abri kosov-Gor'kov Theory.- 3.5.2 The Crystalline Field Effects.- 3.6 The Kondo Effect in Superconductors.- 3.6.1 The Equation for the Scattering Amplitude.- 3.6.2 Impurity States Within the Energy Gap.- 3.6.3 The Lowering of the Superconducting Transition Temperature by Magnetic Impurities.- 3.6.4 Comparison with Experiment.- 3.7 Nonmagnetic Localized States in Superconducting Alloys.- 3.7.1 Anderson's Model.- 3.7.2 The Energy Gap and the Order Parameter.- 3.7.3 Suppression of the Superconducting Transition.- 3.8 Localized Spin Fluctuations in Superconducting Alloys.- 3.8.1 The Anomalous Behaviour of a Number of Alloys with Nonmagnetic Impurities.- 3.8.2 Theoretical Study of the Effect of LSF on Tc.- 3.8.3 Alloys Based on Transition Metals.- 3.9 Spin Fluctuations in Pure Transition Metals.- 3.9.1 Itinerant Spin Fluctuations of a Nonferromagnetic Metal (Paramagnons).- 3.9.2 Virtual-Paramagnon Creation and Superconductivity.- 3.9.3 Comparison with Experiment.- 4. Superconductivity in Transition Metals.- 4.1 The Principal Parameters of Superconducting Metals.- 4.1.1 The Superconducting Transition Temperature.- 4.1.2 The Energy Gap.- 4.1.3 Empirical Correlations Between Tc and Physical Properties of Transition Metals.- 4.1.4 The Pressure Dependence of Tc.- 4.1.5 Superconductivity in Thin Films.- 4.2 The Electron Structure of Transition Metals.- 4.2.1 Theoretical Band Structure Calculations.- 4.2.2 The Fermi Surface.- 4.2.3 X-Ray and Optical Spectra.- 4.2.4 Contributions of the Partial Density of States to N(O).- 4.3 Lattice Dynamics of Transition Metals.- 4.4 The Electron-Phonon Interaction and Tc in Transition Metals.- 4.4.1 Analysis of Empirical Values of ?.- 4.4.2 The Contribution of Electron and Lattice Factors to the Quantity x.- 4.5 Calculating the Electron-Phonon Interaction Constant from First Principle.- 4.5.1 Gaspari and Gyorffy's Representation for .- 4.5.2 Calculation of N(O) for Transition Metals.- 4.5.3 Calculation of the Pressure Dependence of Tc.- 5. Superconductivity in Transition-Metal Alloys.- 5.1 Types of Solid Solutions and Conditions of Their Formation.- 5.1.1 Conditions for the Formation of Solid Solutions.- 5.1.2 Types of Solid Solutions and Phase Diagrams.- 5.2 The Superconducting Transition Temperature of Alloys.- 5.2.1 Types of Concentration Dependences of Tc.- 5.2.2 Binary Alloys.- 5.2.3 The Influence of Pressure on the Tc of Alloys.- 5.3 The Empirical Correlations Between Tc and the Electron and Lattice Properties of Solid Solutions.- 5.3.1 Matthias' Rule.- 5.3.2 The Rigid-Band Approximation.- 5.3.3 The Relation of Tc to the Lattice Instability.- 5.4 Miedema's Empirical Method of Describing Concentration Dependences of the Properties of Metals.- 5.5 Theoretical Analysis of the Concentration Dependence of Tc in Alloys.- 5.5.1 The Alloy Model.- 5.5.2 The CPA Method.- 5.5.3 The Superconducting Transition Temperature.- 6. Compounds with A-15 Structure.- 6.1 Physical Properties.- 6.1.1 The Crystal Structure.- 6.1.2 Superconducting Transition Temperature of Pure Compounds and Their Alloys.- 6.1.3 The Electron Concentration Dependence of Electronic Heat Capacity and Magnetic Susceptibility.- 6.1.4 The Temperature Dependence of the Susceptibility, the Knight Shift and X-Ray and Optical Spectra.- 6.1.5 Structural Transformation.- 6.1.6 Acoustic Properties.- 6.1.7 The Phonon Density of States.- 6.1.8 Effect of Pressure on the Superconducting Transition Temperature.- 6.2 Band Structure.- 6.2.1 The Clogston-Jaccarino Model.- 6.2.2 The Noninteracting Chains Model.- 6.2.3 Electron Structure in the Presence of Interchain Interaction.- 6.2.4 Band Structure Calculations from First Principles.- 6.3 Investigation into Theoretical Models.- 6.3.1 The Weger-Labbe-Friedel Model.- 6.3.2 The Cohen-Cody-Halloran Model.- 6.3.3 Gor'kov's Model I.- 6.3.4 Gor'kov's Model II.- 6.3.5 The Birman-Lee-Williamson Model.- 6.3.6 Bhatt's Model.- 6.4 Analysis of the Electron-Phonon Interaction and Tc.- 6.4.1 Experimental Data on the Electron-Phonon Coupling Constant ?.- 6.4.2 Analysis of ? and Tc.- 6.4.3 Pairing of Electrons via Acoustic Plasmons.- 6.5 The Theory of Structural Transition in A-15 Compounds.- 6.5.1 The Character of the Phase Transition.- 6.5.2 The Noolandi and Sham Theory [6.280].- 6.5.3 Effect of Pressure on Structural Phase Transition.- 6.5.4 Structural Transition as a Result of a Peierls Instability in Chains.- 6.5.5 A Comparison of Different Theories of Martensitic Transformations.- 7. Other Compounds Based on Transition Metals.- 7.1 Intermetallics.- 7.1.1 Laves Phases.- 7.1.2 Compounds with CsCl (B-2) Structure.- 7.1.3 ? Phases and Compounds with ?-Mn (A-12) Structure.- 7.1.4 C-40 Structure Compounds.- 7.2 Compounds with NaCl Structure.- 7.2.1 Crystal Chemistry.- 7.2.2 Superconductivity.- 7.2.3 Band Structure.- 7.2.4 Phonon Spectra.- 7.2.5 Electron-Phonon Interactions.- 7.3 Compounds of Palladium with Hydrogen and Deuterium.- 7.3.1 The Superconductivity of PdH and PdD and the Reverse Isotopic Effect.- 7.3.2 The Mechanisms of Superconductivity in Pd Hydrides.- 7.3.3 Other Systems Based on Palladium.- 7.4 Sesquicarbides and Ternary Borides.- 7.4.1 Crystal Chemistry.- 7.4.2 Superconductivity.- 7.5 Chalcogenides.- 7.5.1 Sulphides.- 7.5.2 Chevrel Phases.- 7.5.3 Oxides.- 8. High Temperature Superconductors and Lattice Instability of Compounds.- 8.1 Comparison of Superconductivity in Various Crystal Structures.- 8.1.1 Symmetry.- 8.1.2 Crystallochemistry.- 8.1.3 Stoichiometry.- 8.1.4 Alloying.- 8.1.5 Electron Concentration.- 8.2 Types of Lattice Instability.- 8.2.1 Structural Transition.- 8.2.2 Virtual Structural Transition.- 8.2.3 Softening of Long-Wave Lattice Moduli with Decreasi ng Temperature.- 8.2.4 Softening of Short-Wave Phonons.- 8.2.5 The Coexistence of Different Structural Phases in the Vicinity of a Given Composition.- 8.3 Phase Transition in 0n Structures from the Point of View of Symmetry Theory.- 8.3.1 Characteristics of the Phase Transitions.- 8.3.2 Construction of the Mechanical Representation and Analysis of Phonon Modes at the Point ?.- 8.3.3 Seeking the Group of the New Phase.- 8.3.4 Discussion of Results.- 8.4 Correlation Between High Tc and Lattice Instability.- 9. Radiation Effects on Superconductors.- 9.1 Radiation Resistance of Superconducting Materials.- 9.1.1 Compounds with A-15 Structure.- 9.1.2 Disordered Alloys of Transition Metals.- 9.1.3 Laves Phases.- 9.1.4 Chevrel Phases.- 9.1.5 Carbides and Nitrides of Transition Metals.- 9.2 Structural Investigations of Radiation Defects.- 9.2.1 Lattice Parameter Measurements.- 9.2.2 Determination of the Degree of Long-Range Order.- 9.2.3 Investigation by Small-Angle Scattering of Neutrons.- 9.2.4 Electron-Microscopic Investigations.- 9.2.5 Channelling of ? Particles.- 9.2.6 The Moessbauer Effect.- 9.3 Physical Properties of Irradiated Superconducting Materials.- 9.3.1 Magnetic Susceptibility.- 9.3.2 Heat Capacity.- 9.3.3 The Velocity of Sound.- 9.3.4 Inelastic and Elastic Scattering of Neutrons.- 9.3.5 Resistivity.- 9.3.6 The Temperature Coefficient of the Upper Critical Field.- 9.4 Theoretical Models for the Degradation of Superconducti ng Properties.- 9.4.1 Variations of the Electron-Phonon Interaction.- 9.4.2 Smearing of the Peak in the Density of Electron States.- 9.4.3 Radiation Defects in the Cluster Approximation.- References.

Additional information

NLS9783642618215
9783642618215
3642618219
Superconductivity of Transition Metals: Their Alloys and Compounds by E.H. Brandt
New
Paperback
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
2011-10-12
512
N/A
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