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
