Chapter 1: Crystal Structure 1
Periodic Array 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 23
Diffraction of Waves by Crystals 25
Bragg Law 25
Scattered Wave Amplitude 26
Fourier Analysis 27
Reciprocal Lattice Vectors 29
Diffraction Conditions 30
Laue Equations 32
Brillouin Zones 33
Reciprocal Lattice to sc Lattice 34
Reciprocal Lattice to bcc Lattice 36
Reciprocal Lattice to fcc Lattice 37
Fourier Analysis of the Basis 39
Structure Factor of the bcc Lattice 40
Structure factor of the fcc Lattice 40
Atomic Form Factor 41
Summary 43
Problems 43
Chapter 3: Crystal Binding and Elastic Constants 47
Crystals of Inert Gases 49
Van der Waals—London Interaction 53
Repulsive Interaction 56
Equilibrium Lattice Constants 58
Cohesive Energy 59
Ionic Crystals 60
Electrostatic or Madelung Energy 60
Evaluation of the Madelung Constant 64
Covalent Crystals 67
Metals 69
Hydrogen Bonds 70
Atomic Radii 70
Ionic Crystal Radii 72
Analysis of Elastic Strains 73
Dilation 75
Stress Components 75
Elastic Compliance and Stiffness Constants 77
Elastic Energy Density 77
Elastic Stiffness Constants of Cubic Crystals 78
Bulk Modulus and Compressibility 80
Elastic Waves in Cubic Crstals 80
Waves in the [100] Direction 81
Waves in the [110] Direction 82
Summary 85
Problems 85
Chapter 4: Phonons I. Crystal Vibrations 89
Vibrations of Crystals with Monatomic Basis 91
First Brillouin Zone 93
Group Velocity 94
Long Wavelength Limit 94
Derivation of Force Constants from Experiment 94
Two Atoms per Primitive Basis 95
Quantization of Elastic Waves 99
Phonon Momentum 100
Inelastic Scattering by Phonons 100
Summary 102
Problems 102
Chapter 5: Phonons 11. Thermal Properties 105
Phonon Heat Capacity 107
Planck Distribution 107
Normal Mode Enumeration 108
Density of States in One Dimension 108
Density of States in Three Dimensions 111
Debye Model for Density of States 112
Debye T3 Law 114
Einstein Model of the Density of States 114
General Result for D(w) 117
Anharmonic Crystal Interactions 119
Thermal Expansion 120
Thermal Conductivity 121
Thermal Resistivity of Phonon Gas 123
Umklapp Processes 125
Imperfecions 126
Problems 128
Chapter 6: Free Electron Fermi Gas 131
Energy Levels in One Dimension 134
Effect of Temperature on the Fermi-Dirac Distribution 136
Free Electron Gas in Three Dimensions 137
Heat Capacity of the Electron Gas 141
Experimental Heat Capacity of Metals 145
Heavy Fermions 147
Electrical Conductivity and Ohm’s Law 147
Experimental Electrical Resistivity of Metals 148
Umklapp Scattering 151
Motion in Magnetic Fields 152
Hall Effect 153
Thermal Conductivity of Metals 156
Ratio of Thermal to Electrical Conductivity 156
Problems 157
Chapter 7: Energy Bands 161
Nearly Free Electron Model 164
Origin of the Energy Gap 165
Magnitude of the Energy Gap 167
Bloch Functions 167
Kronig-Penney Model 168
Wave Equation of Electron in a Periodic Potential 169
Restatement of the Bloch Theorem 173
Crystal Momentum of an Electron 173
Solution of the Central Equation 174
Kronig-Penney Model in Reciprocal Space 174
Empty Lattice Approximation 176
Approximate Solution Near a Zone Boundary 177
Number of Orbitals in a Band 180
Metals and Insulators 181
Summary 182
Problems 182
Chapter 8: Semiconductor Crystals 185
Band Gap 187
Equations of Motion 191
Physical Derivation of ?k? = F 193
Holes 194
Effective Mass 197
Physical Interpretation of the Effective Mass 198
Effective Masses in Semiconductors 200
Silicon and Germanium 202
Intrinsic Carrier Concentration 205
Intrinsic Mobility 208
Impurity Conductivity 209
Donor States 209
Acceptor States 211
Thermal Ionization of Donors and Acceptors 213
Thermoelectric Effects 214
Semimetals 215
Superlattices 216
Bloch Oscillator 217
Zener Tunneling 217
Summary 217
Problems 218
Chapter 9: Fermi Surfaces and Metals 221
Reduced Zone Scheme 223
Periodic Zone Scheme 225
Construction of Fermi Surfaces 226
Nearly Free Electrons 228
Electron Orbits, Hole Orbits, and Open Orbits 230
Calculation of Energy Bands 232
Tight Binding Method of Energy Bands 232
Wigner-Seitz Method 236
Cohesive Energy 237
Pseudopotential Methods 239
Experimental Methods in Fermi Surface Studies 242
Quantization of Orbits in a Magnetic Field 242
De Haas-van Alphen Effect 244
Extremal Orbits 248
Fermi Surface of Copper 249
Magnetic Breakdown 251
Summary 252
Problems 252
Chapter 10: Superconductivity 257
Experimental Survey 259
Occurrence of Superconductivity 260
Destruction of Superconductivity of Magnetic Fields 262
Meissner Effect 262
Heat Capacity 264
Energy Gap 266
Microwave and Infrared Properties 268
Isotope Effect 269
Theoretical Survey 270
Thermodynamics of the Superconducting Transition 270
London Equation 273
Coherence Length 276
BCS Theory of Superconductivity 277
BCS Ground State 278
Flux Quantization in a Superconducting Ring 279
Duration of Persistent Currents 282
Type II Superconductors 283
Vortex State 284
Estimation of Hc1 and Hc2 284
Single Particle Tunneling 287
Josephson Superconductor Tunneling 289
Dc Josephson Effect 289
Ac Josephson Effect 290
Macroscopic Quantum Interference 292
High-Temperature Superconductors 293
Summary 294
Problems 294
Reference 296
Chapter 11: Diamagnetism and Paramagnetism 297
Langevin Diamagnetism Equation 299
Quantum Theory of Diamagnetism of
Mononuclear Systems 301
Paramagnetism 302
Quantum Theory of Paramagnetism 302
Rare Earth Ions 305
Hund Rules 306
Iron Group Ions 307
Crystal Field Splitting 307
Quenching of the Orbital Angular Momentum 308
Spectroscopic Splitting Factor 311
Van Vleck Temperature-Independent Paramagnetism 311
Cooling by Isentropic Demagnetization 312
Nuclear Demagnetization 314
Paramagnetic Susceptibility of Conduction Electrons 315
Summary 317
Problems 318
Chapter 12: Ferromagnetism and Antiferromagnetism 321
Ferromagnetic Order 323
Curie Point and the Exchange Integral 323
Temperature Dependence of the Saturation Magnetization 326
Saturation Magnetization at Absolute Zero 328
Magnons 330
Quantization of Spin Waves 333
Thermal Excitation of Magnons 334
Neutron Magnetic Scattering 335
Ferrimagnetic Order 336
Curie Temperature and Susceptibility of Ferrimagnets 338
Iron Garnets 339
Antiferromagnetic Order 340
Susceptibility Below the Neel Temperature 343
Antiferromagnetic Magnons 344
Ferromagnetic Domains 346
Anisotropy Energy 348
Transition Region between Domains 349
Origin of Domains 351
Coercivity and Hysteresis 352
Single Domain Particles 354
Geomagnetism and Biomagnetism 355
Magnetic Force Microscopy 355
Summary 356
Problems 357
Chapter 13: Magnetic Resonance 361
Nuclear Magnetic Resonance 363
Equations of Motion 366
Line Width 370
Motional Narrowing 371
Hyperfine Splitting 373
Examples: Paramagnetic Point Defects 375
F Centers in Alkali Halides 376
Donor Atoms in Silicon 376
Knight Shift 377
Nuclear Quadrupole Resonance 379
Ferromagnetic Resonance 379
Shape Effects in FMR 380
Spin Wave Resonance 382
Antiferromagnetic Resonance 383
Electron Paramagnetic Resonance 386
Exchange Narrowing 386
Zero-field Splitting 386
Principle of Maser Action 386
Three-Level Maser 388
Lasers 389
Summary 390
Problems 391
Chapter 14: Plasmons, Polaritons, and Polarons 393
Dielectric Function of the Electron Gas 395
Definitions of the Dielectric Function 395
Plasma Optics 396
Dispersion Relation for Electromagnetic Waves 397
Transverse Optical Modes in a Plasma 398
Transparency of Metals in the Ultraviolet 398
Longitudinal Plasma Oscillations 398
Plasmons 401
Electrostatic Screening 403
Screened Coulomb Potential 406
Pseudopotential Component U(0) 407
Mott Metal-Insulator Transition 407
Screening and Phonons in Metals 409
Polaritons 410
LST Relation 414
Electron-Electron Interaction 417
Fermi Liquid 417
Electron-Electron Collisions 417
Electron-Phonon Interaction: Polarons 420
Peierls Instability of Linear Metals 422
Summary 424
Problems 424
Chapter 15: Optical Processes and Excitons 427
Optical Reflectance 429
Kramers-Kronig Relations 430
Mathematical Note 432
Example: Conductivity of collisionless Electron Gas 433
Electronic Interband Transitions 434
Excitons 435
Frenkel Excitons 437
Alkali Halides 440
Molecular Crystals 440
Weakly Bound (Mott-Wannier) Excitons 441
Exciton Condensation into Electron-Hole Drops (EHD) 441
Raman Effects in Crystals 444
Electron Spectroscopy with X-Rays 447
Energy Loss of Fast Particles in a Solid 448
Summary 449
Problems 450
Chapter 16: Dielectrics And Ferroelectrics 453
Maxwell Equations 455
Polarization 455
Macroscopic Electric Field 456
Depolarization Field, E1 458
Local Electric Field at an Atom 460
Lorentz Field, E2 462
Field of Dipoles Inside Cavity, E3 462
Dielectric Constant and Polarizability 463
Electronic Polarizability 464
Classical Theory of Electronic Polarizability 466
Structural Phase Transitions 467
Ferroelectric Crystals 467
Classification of Ferroelectric Crystals 469
Displacive Transitions 471
Soft Optical Phonons 473
Landau Theory of the Phase Transition 474
Second-Order Transition 475
First-Order Transition 477
Antiferroelectricity 479
Ferroelectric Domains 479
Piezoelectricity 481
Summary 482
Problems 483
Chapter 17: Surface and Interface Physics 487
Reconstruction and Relaxation 489
Surface Crystallography 490
Reflection High-Energy Electron Diffraction 493
Surface Electronic Structure 494
Work Function 494
Thermionic Emission 495
Surface States 495
Tangential Surface Transport 497
Magnetoresistance in a Two-Dimensional Channel 498
Integral Quantized Hall Effect (IQHE) 499
IQHE in Real Systems 500
Fractional Quantized Hall Effect (FQHE) 503
p-n Junctions 503
Rectification 504
Solar Cells and Photovoltaic Detectors 506
Schottky Barrier 506
Heterostructures 507
n-N Heterojunction 508
Semiconductor Lasers 510
Light-Emitting Diodes 511
Problems 513
Chapter 18: Nanostructures 515
Imaging Techniques for Nanostructures 519
Electron Microscopy 520
Optical Microscopy 521
Scanning Tunneling Microscopy 523
Atomic Force Microscopy 526
Electronic Structure of 1D Systems 528
One-Dimensional Subbands 528
Spectroscopy of Van Hove Singularities 529
1D Metals — Coluomb Interactions and Lattice Copulings 531
Electrical Transport in 1D 533
Conductance Quantization and the Landauer Formula 533
Two Barriers in Series-resonant Tunneling 536
Incoherent Addition and Ohm’s Law 538
Localization 539
Voltage Probes and the Buttiker-Landauer
Formalism 540
Electronic Structure of 0D Systems 545
Quantized Energy Levels 545
Semiconductor Nanocrystals 545
Metallic Dots 547
Discrete Charge States 549
Electrical Transport in 0D 551
Coulomb Oscillations 551
Spin, Mott Insulators, and the Kondo Effect 554
Cooper Pairing in Superconducting Dots 556
Vibrational and Thermal Properties of Nanostructures 557
Quantized Vibrational Modes 557
Transverse Vibrations 559
Heat Capacity and Thermal Transport 561
Summary 562
Problems 562
Chapter 19: Noncrystalline Solids 565
Diffraction Pattern 567
Monatomic Amorphous Materials 568
Radial Distribution Function 569
Structure of Vitreous Silica, SiO2 570
Glasses 573
Viscosity and the Hopping Rate 574
Amorphous Ferromagnets 575
Amorphous Semiconductors 577
Low Energy Excitations in Amorphous Solids 578
Heat Capacity Calculation 578
Thermal Conductivity 579
Fiber Optics 581
Rayleigh Attenuation 582
Problems 582
Chapter 20: Point Defects 583
Lattice Vacancies 585
Diffusion 588
Metals 591
Color Centers 592
F Centers 592
Other Centers in Alkali Halides 593
Problems 595
Chapter 21: Dislocations 597
Shear Strength of Single Crystals 599
Slip 600
Dislocations 601
Burgers Vectors 604
Stress Fields of Dislocations 605
Low-angle Grain Boundaries 607
Dislocation Densities 610
Dislocation Multiplication and Slip 611
Strength of Alloys 613
Dislocations and Crystal Growth 615
Whiskers 616
Hardness of Materials 617
Problems 618
Chapter 22: Alloys 619
General Considerations 621
Substitutional Solid Solutions—Hume-Rothery Rules 624
Order-Disorder Transformation 627
Elementary Theory of Order 629
Phase Diagrams 632
Eutectics 632
Transition Metal Alloys 634
Electrical Conductivity 636
Kondo Effect 637
Problems 640
Appendix A: Temperature Dependence of the Reflection Lines 641
Appendix B: Ewald Calculation of Lattice Sums 644
Ewald-Kornfeld Method for Lattice Sums for Dipole Arrays 647
Appendix C: Quantization of Elastic Waves: Phonons 648
Phonon Coordinates 649
Creation and Annihilation Operators 651
Appendix D: Fermi-Dirac Distribution Function 652
Appendix E: Derivation of the dk/dt Equation 655
Appendix F: Boltzmann Transport Equation 656
Particle Diffusion 657
Classical Distribution 658
Fermi-Dirac Distribution 659
Electrical Conductivity 661
Appendix G: Vector Potential, Field Momentum, and Gauge Transformations 661
Lagrangian Equations of Motion 662
Derivation of the Hamiltonian 663
Field Momentum 663
Gauge Transformation 664
Gauge in the London Equation 665
Appendix H: Cooper Pairs 665
Appendix I: Ginzburg-Landau Equation 667
Appendix J: Electron-Phonon Collisions 671
Index 675
