Chapter 1: Crystal Structure 1 Periodic Arrays of Atoms 3 Lattice Translation Vectors 4 Basis and the Crystal Structure 5 Primitive Lattice Cell 6 Fundamental Types of Lattices 6 Two-Dimensional Lattice Types 8 Three-Dimensional Lattice Types 9 Index Systems for Crystal Planes 11 Simple Crystal Structures 13 Sodium Chloride Structure 13 Cesium Chloride Structure 14 Hexagonal Close-Packed Structure (hcp) 15 Diamond Structure 16 Cubic Zinc Sulfide Structure 17 Direct Imaging of Atomic Structure 18 Nonideal Crystal Structures 18 Random Stacking and Polytypism 19 Crystal Structure Data 19 Summary 22 Problems 22 Chapter 2: Wave Diffraction And The Reciprocal Lattice 25 Diffraction of Waves by Crystals 27 The Bragg Law 27 Scattered Wave Amplitude 28 Fourier Analysis 29 Reciprocal Lattice Vectors 31 Diffraction Conditions 32 Laue Equations 34 Brillouin Zones 35 Reciprocal Lattice to sc Lattice 36 Reciprocal Lattice to bcc Lattice 38 Reciprocal Lattice to fcc Lattice 39 Fourier Analysis of the Basis 41 Structure Factor of the bcc Lattice 42 Structure Factor of the fcc Lattice 42 Atomic Form Factor 43 Summary 45 Problems 45 Chapter 3: Crystal Binding And Elastic Constants 49 Crystals of Inert Gases 51 Van der Waals–London Interaction 55 Repulsive Interaction 58 Equilibrium Lattice Constants 60 Cohesive Energy 61 Ionic Crystals 62 Electrostatic or Madelung Energy 62 Evaluation of the Madelung Constant 66 Covalent Crystals 69 Metals 71 Hydrogen Bonds 72 Atomic Radii 72 Ionic Crystal Radii 74 Analysis of Elastic Strains 75 Dilation 77 Stress Components 77 Elastic Compliance and Stiffness Constants 79 Elastic Energy Density 79 Elastic Stiffness Constants of Cubic Crystals 80 Bulk Modulus and Compressibility 82 Elastic Waves in Cubic Crystals 82 Waves in the [100] Direction 83 Waves in the [110] Direction 84 Summary 87 Problems 87 Chapter 4: phonons I. Crystal vibrations 91 Vibrations of Crystals with Monatomic Basis 93 First Brillouin Zone 95 Group Velocity 96 Long Wavelength Limit 96 Derivation of Force Constants from Experiment 96 Two Atoms per Primitive Basis 97 Quantization of Elastic Waves 101 Phonon Momentum 102 Inelastic Scattering by Phonons 102 Summary 104 Problems 104 Chapter 5: phonons 11. Thermal properties 107 Phonon Heat Capacity 109 Planck Distribution 109 Normal Mode Enumeration 110 Density of States in One Dimension 110 Density of States in Three Dimensions 113 Debye Model for Density of States 114 Debye T3 Law 116 Einstein Model of the Density of States 116 General Result for D( ) 119 Anharmonic Crystal Interactions 121 Thermal Expansion 122 Thermal Conductivity 123 Thermal Resistivity of Phonon Gas 125 Umklapp Processes 127 Imperfections 128 Problems 130 Chapter 6: Free Electron Fermi Gas 133 Energy Levels in One Dimension 136 Effect of Temperature on the FermiDirac Distribution 138 Free Electron Gas in Three Dimensions 139 Heat Capacity of the Electron Gas 143 Experimental Heat Capacity of Metals 147 Heavy Fermions 149 Electrical Conductivity and Ohm’s Law 149 Experimental Electrical Resistivity of Metals 150 Umklapp Scattering 153 Motion in Magnetic Fields 154 Hall Effect 155 Thermal Conductivity of Metals 158 Ratio of Thermal to Electrical Conductivity 158 Problems 159 Chapter 7: Energy Bands 163 Nearly Free Electron Model 166 Origin of the Energy Gap 167 Magnitude of the Energy Gap 169 Bloch Functions 169 Kronig-Penney Model 170 Wave Equation of Electron in a Periodic Potential 171 Restatement of the Bloch Theorem 175 Crystal Momentum of an Electron 175 Solution of the Central Equation 176 Kronig-Penney Model in Reciprocal Space 176 Empty Lattice Approximation 178 Approximate Solution Near a Zone Boundary 179 Number of Orbitals in a Band 182 Metals and Insulators 183 Summary 184 Problems 184 Chapter 8: Semiconductor Crystals 187 Band Gap 189 Equations of Motion 193 Physical Derivation of 195 Holes 196 Effective Mass 199 Physical Interpretation of the Effective Mass 200 Effective Masses in Semiconductors 202 Silicon and Germanium 204 Intrinsic Carrier Concentration 207 Intrinsic Mobility 210 Impurity Conductivity 211 Donor States 211 Acceptor States 213 Thermal Ionization of Donors and Acceptors 215 Thermoelectric Effects 216 Semimetals 217 Superlattices 218 Bloch Oscillator 219 Zener Tunneling 219 Summary 219 Problems 220 Chapter 9: Fermi Surfaces And Metals 223 Reduced Zone Scheme 225 Periodic Zone Scheme 227 Construction of Fermi Surfaces 228 Nearly Free Electrons 230 Electron Orbits, Hole Orbits, and Open Orbits 232 Calculation of Energy Bands 234 Tight Binding Method for Energy Bands 234 Wigner-Seitz Method 238 Cohesive Energy 239 Pseudopotential Methods 241 Experimental Methods in Fermi Surface Studies 244 Quantization of Orbits in a Magnetic Field 244 De Haas-van Alphen Effect 246 Extremal Orbits 250 Fermi Surface of Copper 251 Magnetic Breakdown 253 Summary 254 Problems 254 Chapter 10: Superconductivity 259 Experimental Survey 261 Occurrence of Superconductivity 262 Destruction of Superconductivity by Magnetic Fields 264 Meissner Effect 264 Heat Capacity 266 Energy Gap 268 Microwave and Infrared Properties 270 Isotope Effect 271 Theoretical Survey 272 Thermodynamics of the Superconducting Transition 272 London Equation 275 Coherence Length 278 BCS Theory of Superconductivity 279 BCS Ground State 280 Flux Quantization in a Superconducting Ring 281 Duration of Persistent Currents 284 Type II Superconductors 285 Vortex State 286 Estimation of Hc1 and Hc2 286 Single Particle Tunneling 289 Josephson Superconductor Tunneling 291 Dc Josephson Effect 291 Ac Josephson Effect 292 Macroscopic Quantum Interference 294 High-Temperature Superconductors 295 Summary 296 Problems 296 Reference 298 Chapter 11: Diamagnetism And Paramagnetism 299 Langevin Diamagnetism Equation 301 Quantum Theory of Diamagnetism of Mononuclear Systems 303 Paramagnetism 304 Quantum Theory of Paramagnetism 304 Rare Earth Ions 307 Hund Rules 308 Iron Group Ions 309 Crystal Field Splitting 309 Quenching of the Orbital Angular Momentum 310 Spectroscopic Splitting Factor 313 Van Vleck Temperature-Independent Paramagnetism 313 Cooling by Isentropic Demagnetization 314 Nuclear Demagnetization 316 Paramagnetic Susceptibility of Conduction Electrons 317 Summary 319 Problems 320 Chapter 12: Ferromagnetism And Antiferromagnetism 323 Ferromagnetic Order 325 Curie Point and the Exchange Integral 325 Temperature Dependence of the Saturation Magnetization 328 Saturation Magnetization at Absolute Zero 330 Magnons 332 Quantization of Spin Waves 335 Thermal Excitation of Magnons 336 Neutron Magnetic Scattering 337 Ferrimagnetic Order 338 Curie Temperature and Susceptibility of Ferrimagnets 340 Iron Garnets 341 Antiferromagnetic Order 342 Susceptibility Below the Néel Temperature 345 Antiferromagnetic Magnons 346 Ferromagnetic Domains 348 Anisotropy Energy 350 Transition Region Between Domains 351 Origin of Domains 353 Coercivity and Hysteresis 354 Single-Domain Particles 356 Geomagnetism and Biomagnetism 357 Magnetic Force Microscopy 357 Summary 359 Problems 359 Chapter 13: Magnetic Resonance 363 Nuclear Magnetic Resonance 365 Equations of Motion 368 Line Width 372 Motional Narrowing 373 Hyperfine Splitting 375 Examples: Paramagnetic Point Defects 377 F Centers in Alkali Halides 378 Donor Atoms in Silicon 378 Knight Shift 379 Nuclear Quadrupole Resonance 381 Ferromagnetic Resonance 381 Shape Effects in FMR 382 Spin Wave Resonance 384 Antiferromagnetic Resonance 385 Electron Paramagnetic Resonance 388 Exchange Narrowing 388 Zero-field Splitting 388 Principle of Maser Action 388 Three-Level Maser 390 Lasers 391 Summary 392 Problems 393 Chapter 14: Dielectrics And Ferroelectrics 395 Maxwell Equations 397 Polarization 397 Macroscopic Electric Field 398 Depolarization Field, E1 400 Local Electric Field at an Atom 402 Lorentz Field, E2 404 Field of Dipoles Inside Cavity, E3 404 Dielectric Constant and Polarizability 405 Electronic Polarizability 406 Classical Theory of Electronic Polarizability 408 Structural Phase Transitions 409 Ferroelectric Crystals 409 Classification of Ferroelectric Crystals 411 Displacive Transitions 413 Soft Optical Phonons 415 Landau Theory of the Phase Transition 416 Second-Order Transition 417 First-Order Transition 419 Antiferroelectricity 421 Ferroelectric Domains 421 Piezoelectricity 423 Summary 424 Problems 425 Chapter 15: Plasmons, Polaritons, And Polarons 429 Dielectric Function of the Electron Gas 431 Definitions of the Dielectric Function 431 Plasma Optics 432 Dispersion Relation for Electromagnetic Waves 433 Transverse Optical Modes in a Plasma 434 Transparency of Metals in the Ultraviolet 434 Longitudinal Plasma Oscillations 434 Plasmons 437 Electrostatic Screening 439 Screened Coulomb Potential 442 Pseudopotential Component U(0) 443 Mott Metal-Insulator Transition 443 Screening and Phonons in Metals 445 Polaritons 446 LST Relation 450 Electron-Electron Interaction 453 Fermi Liquid 453 Electron-Electron Collisions 453 Electron-Phonon Interaction: Polarons 456 Peierls Instability of Linear Metals 458 Summary 460 Problems 460 Chapter 16: Optical Processes And Excitons 465 Optical Reflectance 467 Kramers-Kronig Relations 468 Mathematical Note 470 Example: Conductivity of Collisionless Electron Gas 471 Electronic Interband Transitions 472 Excitons 473 Frenkel Excitons 475 Alkali Halides 478 Molecular Crystals 478 Weakly Bound (Mott-Wannier) Excitons 479 Exciton Condensation into Electron-Hole Drops (EHD) 479 Raman Effect in Crystals 482 Electron Spectroscopy with X-Rays 485 Energy Loss of Fast Particles in a Solid 486 Summary 487 Problems 488 Chapter 17: Surface And Interface Physics 491 Reconstruction and Relaxation 493 Surface Crystallography 494 Reflection High-Energy Electron Diffraction 497 Surface Electronic Structure 498 Work Function 498 Thermionic Emission 499 Surface States 499 Tangential Surface Transport 501 Magnetoresistance in a Two-Dimensional Channel 502 Integral Quantized Hall Effect (IQHE) 503 IQHE in Real Systems 504 Fractional Quantized Hall Effect (FQHE) 507 p-n Junctions 507 Rectification 508 Solar Cells and Photovoltaic Detectors 510 Schottky Barrier 510 Heterostructures 511 n-N Heterojunction 512 Semiconductor Lasers 514 Light-Emitting Diodes 515 Problems 517 Chapter 18: Nanostructures 521 Imaging Techniques for Nanostructures 525 Electron Microscopy 526 Optical Microscopy 527 Scanning Tunneling Microscopy 529 Atomic Force Microscopy 532 Electronic Structure of 1D Systems 534 One-dimensional (1D) Subbands 534 Spectroscopy of Van Hove Singularities 535 1D Metals—Coulomb Interactions and Lattice Couplings 537 Electrical Transport in 1D 539 Conductance Quantization and the Landauer Formula 539 Two Barriers in Series-Resonant Tunneling 542 Incoherent Addition and Ohm’s Law 544 Localization 545 Voltage Probes and the Büttiker-Landauer Formalism 546 Electronic Structure of 0D Systems 551 Quantized Energy Levels 551 Semiconductor Nanocrystals 551 Metallic Dots 553 Discrete Charge States 555 Electrical Transport in 0D 557 Coulomb Oscillations 557 Spin, Mott Insulators, and the Kondo Effect 560 Cooper Pairing in Superconducting Dots 562 Vibrational and Thermal Properties 563 Quantized Vibrational Modes 563 Transverse Vibrations 565 Heat Capacity and Thermal Transport 567 Summary 568 Problems 568 Chapter 19: Noncrystalline Solids 573 Diffraction Pattern 575 Monatomic Amorphous Materials 576 Radial Distribution Function 577 Structure of Vitreous Silica, SiO2 578 Glasses 581 Viscosity and the Hopping Rate 582 Amorphous Ferromagnets 583 Amorphous Semiconductors 585 Low Energy Excitations in Amorphous Solids 586 Heat Capacity Calculation 586 Thermal Conductivity 587 Fiber Optics 589 Rayleigh Attenuation 590 Problems 590 Chapter 20: Point Defects 593 Lattice Vacancies 595 Diffusion 598 Metals 601 Color Centers 602 F Centers 602 Other Centers in Alkali Halides 603 Problems 605 Chapter 21: Dislocations 607 Shear Strength of Single Crystals 609 Slip 610 Dislocations 611 Burgers Vectors 614 Stress Fields of Dislocations 615 Low-angle Grain Boundaries 617 Dislocation Densities 620 Dislocation Multiplication and Slip 621 Strength of Alloys 623 Dislocations and Crystal Growth 625 Whiskers 626 Hardness of Materials 627 Problems 628 Chapter 22: Alloys 631 General Considerations 633 Substitutional Solid Solutions— Hume-Rothery Rules 636 Order-Disorder Transformation 639 Elementary Theory of Order 641 Phase Diagrams 644 Eutectics 644 Transition Metal Alloys 646 Electrical Conductivity 648 Kondo Effect 649 Problems 652 Appendix A: Temperature Dependence Of The Reflection Lines 653 Appendix B: Ewald Calculation Of Lattice Sums 656 Ewald-Kornfeld Method for Lattice Sums for Dipole Arrays 659 Appendix C: Quantization Of Elastic Waves: Phonons 660 Phonon Coordinates 661 Creation and Annihilation Operators 663 Appendix D: Fermi-Dirac Distribution Function 664 Appendix E: Derivation Of The Dk/Dt Equation 667 Appendix F: Boltzmann Transport Equation 668 Particle Diffusion 669 Classical Distribution 670 Fermi-Dirac Distribution 671 Electrical Conductivity 673 Appendix G: Vector Potential, Field Momentum, And Gauge Transformations 673 Lagrangian Equations of Motion 674 Derivation of the Hamiltonian 675 Field Momentum 675 Gauge Transformation 676 Gauge in the London Equation 677 Appendix H: Cooper Pairs 677 Appendix I: Ginzburg-Landau Equation 679 Appendix J: Electron-Phonon Collisions 683 Index 687