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E-book
Author Economou, E. N., 1940-

Title The physics of solids : essentials and beyond / Eleftherios N. Economou
Published Heidelberg ; Berlin : Springer-Verlag, ©2010

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Description 1 online resource (xix, 865 pages) : illustrations
Series Graduate texts in physics
Graduate texts in physics.
Contents Note continued: 3.1.8. Liquid Crystals -- 3.1.9. Self-Assembled Soft Matter -- 3.1.10. Artificial Structures -- 3.1.11. Clusters and Other Finite Systems -- 3.2. Bonding Types and Resulting Properties -- 3.2.1. Simple Metals -- 3.2.2. Transition Metals and Rare Earths -- 3.2.3. Covalent Solids -- 3.2.4. Ionic Solids -- 3.2.5. Van der Waals Bonded Solids -- 3.2.6. Hydrogen Bonded Solids -- 3.3. Short Introduction to Crystal Structures -- 3.3.1. Some Basic Definitions -- 3.3.2. Unit and Primitive Cells of Some Commonly Occurring 3-D Crystal Structures -- 3.3.3. Systems and Types of 3D Bravais Lattices -- 3.3.4. Crystal Planes and Miller Indices -- 3.4. Bloch Theorem, Reciprocal Lattice, Bragg Planes, and Brillouin Zones -- 3.4.1. Bloch Theorem -- 3.4.2. Reciprocal Lattice -- 3.4.3. Bragg Planes -- 3.4.4. Brillouin Zones -- 3.5. Key Points -- 3.6. Questions and Problems -- pt. II Two Simple Models for Solids -- 4. Jellium Model and Metals I: Equilibrium Properties -- 4.1. Introduction -- 4.2. Electronic Eigenfunctions, Eigenenergies, Number of States -- 4.3. Kinetic and Potential Energy, Pressures, and Elastic Moduli -- 4.4. Acoustic Waves are the Ionic Eigenoscillations in the JM -- 4.5. Thermodynamic Quantities -- 4.5.1. General Formulas -- 4.5.2. Specific Heat, Cv -- 4.5.3. Bulk Thermal Expansion Coefficient -- 4.6. Key Points -- 4.7. Problems -- 5. Jellium Model and Metals II: Response to External Perturbations -- 5.1. Response to Electric Field -- 5.2. Dielectric Function -- 5.3. Static Electrical Conductivity -- 5.4. Phonon Contribution to Resistivity -- 5.5. Response in the Presence of a Static Uniform Magnetic Field -- 5.5.1. Magnetic Resonances -- 5.5.2. Hall Effect and Magnetoresistance -- 5.5.3. Magnetic Susceptibility, Xm -- 5.6. Thermoelectric Response -- 5.7. Key Points -- 5.8. Problems
Note continued: 6. Solids as Supergiant Molecules: LCAO -- 6.1. Diversion: The Coupled Pendulums Model -- 6.2. Introductory Remarks Regarding the LCAO Method -- 6.3. Single Band One-Dimensional Elemental "Metal" -- 6.4. One-Dimensional Ionic "Solid" -- 6.5. One-Dimensional Molecular "Solid" -- 6.6. Diversion: Eigenoscillations in One-Dimensional "solid" with two Atoms Per Primitive Cell -- 6.7. One-Dimensional Elemental Sp1 "Semiconductor" -- 6.8. One-Dimensional Compound Sp1 "Semiconductor" -- 6.9. Key Points -- 6.10. Problems -- 7. Semiconductors and Other Tetravalent Solids -- 7.1. Lattice Structures: A Reminder -- 7.2. Band Edges and Gap -- 7.3. Differences Between the 1-D and the 3-D Case and Energy Diagrams -- 7.4. Metals, Semiconductors, and Ionic Insulators -- 7.5. Holes -- 7.6. Effective Masses and DOS -- 7.7. Dielectric Function and Optical Absorption -- 7.8. Effective Hamiltonian -- 7.9. Impurity Levels -- 7.9.1. Impurity Levels: The General Picture -- 7.9.2. Impurity Levels: Doping -- 7.10. Concentration of Electrons and Holes at Temperature T -- 7.10.1. Intrinsic case -- 7.10.2. Extrinsic case -- 7.11. Band Structure and Electronic DOS -- 7.12. Eigenfrequencies, Phononic DOS, and Dielectric Function -- 7.13. Key Points -- 7.14. Problems -- 8. Beyond the Jellium and the LCAO: An Outline -- 8.1. Introductory Remarks -- 8.2. Four Basic Approximations -- 8.3. Density Functional Theory -- 8.4. Outline of an Advanced Scheme for Calculating the Properties of Solids -- 8.5. Beyond the Four Basic Approximations -- 8.5.1. Periodicity Broken or Absent -- 8.5.2. Electron-Electron Correlations, Quasi-Particles, Magnetic Phases, and Superconductivity -- 8.5.3. Electron-Phonon Interactions, Transport Properties, Superconductivity, and Polarons
Note continued: 8.5.4. Phonon-Phonon Interactions, Thermal Expansion, Melting, Structural Phase Transitions, Solitons, Breathers -- 8.5.5. Disorder and Many Body Effects in Coexistence -- 8.5.6. Quantum Informaties and Solid State Systems -- 8.6. Key Points -- 8.7. Problems -- pt. III More About Periodicity & its Consequences -- 9. Crystal Structure and Ionic Vibrations -- 9.1. Experimental Determination of Crystal Structures -- 9.2. Determination of the Frequency vs. Wavevector -- 9.3. Theoretical Calculation of the Phonon Dispersion Relation -- 9.4. Debye-Waller Factor and the Inelastic Cross-Section -- 9.5. Key Points -- 9.6. Problems -- 10. Electrons in Periodic Media. The Role of Magnetic Field -- 10.1. Introduction -- 10.2. Dispersion Relations, Surfaces of Constant Energy, and DOS: A Reminder -- 10.3. Effective Hamiltonian and Semiclassical Approximation -- 10.4. Semiclassical Trajectories in the Presence of a Magnetic Field -- 10.5. Two Simple but Elucidating TB Models -- 10.6. Cyclotron Resonance and the de Haas-van Alphen Effect -- 10.7. Hall Effect and Magnetoresistance -- 10.8. Key Points -- 10.9. Problems -- 11. Methods for Calculating the Band Structure -- 11.1. Introductory Remarks -- 11.2. Ionic and Total Pseudopotentials -- 11.3. Schrodinger Equation, Plane Wave Expansion, and Bloch's Theorem -- 11.4. Plane Waves and Perturbation Theory -- 11.5. Muffin-Tin Potential -- 11.6. Schrodinger Equation and the Augmented Plane Wave (APW) Method -- 11.7. Schrodinger Equation and the Korringa-Kohn-Rostoker (KKR) Method -- 11.8. k p Method of Band Structure Calculations -- 11.9. Key Points -- 11.10. Problems -- 12. Pseudopotentials in Action -- 12.1. One-Dimensional Case -- 12.2. Two-Dimensional Square Lattice -- 12.2.1. Spaghetti Diagrams -- 12.2.2. Fermi Lines -- 12.3. Harrison's Construction
Note continued: 12.4. Second-Order Correction to the Total JM Energy -- 12.5. Ionic Interactions in Real Space -- 12.6. Phononic Dispersions in Metals -- 12.7. Scattering by Phonons, Mean Free Path, and the Dimensionales Constant & lambda; in Metals -- 12.8. Key Points -- 12.9. Problems -- pt. IV Materials -- 13. Simple Metals and Semiconductors Revisited -- 13.1. Band Structure and Fermi Surfaces of Simple Metals -- 13.1.1. Alkali Metals -- 13.1.2. Alkaline Earths: Be, Mg, Ca, Sr, Ba, and Ra -- 13.1.3. Trivalent Metals -- 13.1.4. Tetravalent Metals -- 13.2. Band Structure of Semiconductors -- 13.3. Jones Zone and the Disappearance of the Fermi Surface -- 13.4. Mechanical Properties of Semiconductors -- 13.5. Magnetic Susceptibility of Semiconductors -- 13.6. Optical and Transport Properties of Semiconductors -- 13.6.1. Excitons -- 13.6.2. Conductivity and Mobility in Semiconductors -- 13.7. Silicon Dioxide (SiO2) -- 13.8. Graphite and Graphene -- 13.9. Organic semiconductors -- 13.10. Key Points -- 13.11. Questions and Problems -- 14. Closed-Shell Solids -- 14.1. Van Der Waals Solids -- 14.2. Ionic Compounds I: Types and Crystal Structures -- 14.3. Ionic Compounds II: Mechanical Properties -- 14.4. Ionic Compounds III: Optical Properties -- 14.5. Key Points -- 14.6. Problems -- 15. Transition Metals and Compounds -- 15.1. Experimental Data for the Transition Metals -- 15.2. Calculations I: APW or KKR -- 15.3. Calculations II: LCAO -- 15.4. Calculations III: The Simple Friedel Model -- 15.5. Compounds of Transition Elements, I: Perovskites -- 15.6. Compounds of Transition Elements, II: High Tc Superconducting Materials -- 15.7. Compounds of Transition Metals, III: Oxides, etc. -- 15.8. Key Points -- 15.9. Problems -- 16. Artificial Periodic Structures -- 16.1. Semiconductor Superlattices
Note continued: 16.2. Photonic Crystals: An Overview -- 16.3. Photonic Crystals: Theoretical Considerations -- 16.4. Phononic Crystals -- 16.5. Left-Handed Metamaterials (LHMs) -- 16.6. Designing, Fabricating, and Measuring LHMs -- 16.7. Key Points -- 16.8. Problems -- pt. V Deviations from Periodicity -- 17. Surfaces and Interfaces -- 17.1. Surface Preparation -- 17.2. Relaxation and Reconstruction -- 17.3. Surface States -- 17.4. Work Function -- 17.5. Measuring the Work Function -- 17.6. p -- n Homojunction in Equilibrium -- 17.7. p -- n Homojunction Under an External Voltage V -- 17.8. Some Applications of Interfaces -- 17.9. Key Points -- 17.10. Problems -- 18. Disordered and Other Nonperiodic Solids -- 18.1. Introductory Remarks -- 18.2. Alloys and the Hume-Rothery Rule -- 18.3. Glasses and other Amorphous Systems -- 18.4. Distribution and Correlation Functions -- 18.5. Quasi-Crystals -- 18.6. Electron Transport and Quantum Interference -- 18.7. Band Structure, Static Disorder, and Localization -- 18.7.1. 3D Case -- 18.7.2. 2D Case -- 18.7.3. 1D and quasi 1D Systems -- 18.8. Calculation Techniques -- 18.8.1. Coherent Potential Approximation -- 18.8.2. Weak Localization due to Quantum Interference -- 18.8.3. Scaling Approach -- 18.8.4. Quasi-One-Dimensional Systems and Scaling -- 18.8.5. Potential Well Analogy -- 18.9. Quantum Hall Effect -- 18.10. Key Points -- 18.11. Problems -- 19. Finite Systems -- 19.1. Introduction -- 19.2. Metallic Clusters -- 19.3. Fullerenes -- 19.4. C60-Based Solids -- 19.5. Carbon Nanotubes -- 19.6. Other Clusters -- 19.7. Quantum Dots -- 19.7.1. Overview -- 19.7.2. Optical Transitions -- 19.7.3. QDs and Coulomb Blockade -- 19.8. Key Points -- 19.9. Problems -- pt. VI Correlated Systems -- 20. Magnetic Materials, I: Phenomenology
Note continued: 20.1. Which Property Characterizes These Materials? -- 20.2. Experimental Data for Ferromagnets -- 20.2.1. Saturation Magnetization vs Temperature for Simple Ferromagnets -- 20.2.2. Magnetic Susceptibility of Simple Ferromagnet for T> Te -- 20.2.3. Saturation Magnetization vs Temperature for Ferrimagnets -- 20.2.4. Magnetic Susceptibility of Ferrimagnets vs Temperature (T> Tc) -- 20.3. Experimental Data for Antiferromagnets -- 20.3.1. Determination of the Antiferromagnetic Ordered Structure -- 20.3.2. Magnetic Susceptibility vs Temperature -- 20.4. Materials -- 20.4.1. Simple Ferromagnetic Materials -- 20.4.2. Ferrimagnetic Materials -- 20.4.3. Antiferromagnetic Materials -- 20.5. Thermodynamic Relations -- 20.5.1. Thermodynamic Potentials -- 20.5.2. Mean Field Approximation (Landau's Approach) -- 20.5.3. Why are Magnetic Domains Formed? -- 20.5.4. How Thick is the Bloch Wall? -- 20.5.5. Examples of Magnetic Domains -- 20.5.6. Thermodynamics of Antiferrmagnets -- 20.6. Spintronics -- 20.7. Key Points -- 20.8. Problems -- 21. Magnetic Materials II: Microscopic View -- 21.1. Introduction -- 21.2. Jellium model and el-el Coulomb Repulsion -- 21.2.1. Is There Ferromagnetic Order in the JM? -- 21.2.2. Magnetic Susceptibility Within the JM in the Presence of Electron-Electron Interactions -- 21.2.3. Is There Antiferromagnetic Order in the JM? -- 21.3. Hubbard Model -- 21.4. Heisenberg Model -- 21.4.1. Hamiltonian -- 21.4.2. Mean Field Approximation -- 21.4.3. Ferromagnetic Case, (Jij> 0) and its spin waves -- 21.4.4. AF Case -- 21.5. Key Points -- 21.6. Problems -- 22. Superconductivity, I: Phenomenology -- 22.1. Materials -- 22.2. Properties of Superconductors -- 22.2.1. Zero DC Resistivity -- 22.2.2. Expulsion of the Magnetic Field B from the Interior of a Superconductor
Note continued: 22.2.3. Critical Value of the Magnetic Field Beyond Which Superconductivity Disappears -- 22.2.4. Specific Heat and Other Thermodynamic Quantities -- 22.2.5. Response to Microwave or Far Infrared EM Radiation -- 22.2.6. Ultrasound Attenuation -- 22.2.7. Tunneling Current in Metal/Insulator/Superconductor Junctions -- 22.2.8. Temperature Dependence of the Superconduting Gap -- 22.2.9. Isotope Effect -- 22.2.10. Relaxation Times for Nuclear Spin -- 22.2.11. Thermoelectric Coefficients -- 22.3. Thermodynamic Relations -- 22.4. London Equation -- 22.5. Pippard's Generalization -- 22.6. Ginzburg-Landau Theory -- 22.7. Quantization of the Magnetic Flux -- 22.8. Key Points -- 22.9. Problems -- 23. Superconductivity, II: Microscopic Theory -- 23.1. Electron-Electron Indirect Attraction -- 23.2. Cooper Pairs -- 23.3. Comments -- 23.4. Corrected Binding Energy and the Critical Temperature -- 23.5. Further Corrections to the Formula for Tc -- 23.6. Bardeen-Cooper-Schrieffer (BCS) Theory -- 23.7. Thermodynamic Quantities -- 23.8. Response to Electromagnetic Fields -- 23.9. Towards Material-Specific Calculations of Superconducting Quantities -- 23.10. Josephson Effects and SQUID -- 23.11. Key Points -- 23.12. Problems -- pt. VII Appendices -- A. Elements of Electrodynamics of Continuous Media -- A.1. Field Vectors, Potentials, and Maxwell's Equations -- A.2. Relations Among the Fields -- B. Elements of Quantum Mechanics -- B.1. General Formalism -- B.2. Bra and Ket Notation -- B.3. Spherically Symmetric Potentials -- B.4. Perturbation Results -- B.5. Interaction of Matter with an External Electromagnetic Field -- C. Elements of Thermodynamics and Statistical Mechanics -- C.1. Thermodynamic Relations -- C.2. Basic Relations of Statistical Mechanics -- C.3. Non-Interacting Particles
Note continued: C.3.1. Non-Interacting Electrons -- C.3.2. Phonons -- D. Dielectric Function, E(k, & omega;): Formulas and Uses -- D.1. Uses -- D.2. Expressions for E(k, & omega;) within the JM -- D.3. Phenomenological Expressions for the Dielectric Function -- E. Waves in Continuous Elastic Media -- E.1. Strains -- E.2. Equations of Motion -- E.3. Connecting Stress and Strain -- E.4. Elastic Wave Equation -- F. Method LCAO Applied to Molecules -- F.1. Formulation of the LCAO Method -- F.2. Some Important Examples -- F.2.1. Covalent Diatomic Molecule -- F.2.2. Ionic Diatomic Molecule -- F.3. Hybridization of Atomic Orbitals -- F.3.1. sp1 Hybrid Atomic Orbitals -- F.3.2. sp2 Hybrid Atomic Orbitals -- F.3.3. sp3 Hybrid Atomic Orbitals -- G. Boltzmann's Equation -- H. Tables
Summary This textbook emphasizes a few fundamental principles and extracts from them a wealth of information. This approach also unifies an enormous and diverse subject which seems to consist of too many disjoint pieces. The book starts with the absolute minimum of formal tools, emphasizes the basic principles, and employs physical reasoning (" a little thinking and imagination" to quote R. Feynman) to obtain results. Continuous comparison with experimental data leads naturally to a gradual refinement of the concepts and to more sophisticated methods. After the initial overview with an emphasis on the physical concepts and the derivation of results by dimensional analysis, The Physics of Solids deals with the Jellium Model (JM) and the Linear Combination of Atomic Orbitals (LCAO) approaches to solids and introduces the basic concepts and information regarding metals and semiconductors. The remainder, constituting enrichment and elective material, re-examines the model under more realistic assumptions as well as new, more advanced subjects. While prerequisites include quantum mechanics, electromagnetism, and statistical physics, appendices summarizing these subjects are included to make the book more self-contained. The basic text is enhanced with worked problems, copious illustrations, chapter-end exercises and summaries. The approach, which emphasizes the underlying physical concepts, unifies to some extent a subject that can seem too diverse and consisting of too many disjoint pieces, requires from students less memorizing of facts and formalisms but more thinking
Bibliography Includes bibliographical references and index
Notes English
Print version record
Subject Solid state physics.
Physique.
Solid state physics
Festkörperphysik
Form Electronic book
LC no. 2009929022
ISBN 9783642020698
3642020690
9783642020681
3642020682