Section 1.1, Introduction, page 3
Section 1.1.1, Why are Solids Crystalline?, page 4
Section 1.2, Two-Dimensional Lattices, page 6
Section 1.2.1, Bravais Lattices, page 6
Section 1.2.2, Enumeration of Two-Dimensional Bravais Lattices, page 7
Section 1.2.3, Lattices with Bases, page 7
Section 1.2.4, Primitive Cells, page 9
Section 1.2.5, Wigner--Seitz Cells, page 10
Section 1.3, Symmetries, page 11
Section 1.3.1, The Space Group, page 11
Section 1.3.2, Translation and Point Groups, page 11
Problems, page 13
References, page 15
Section 2.1, Introduction, page 17
Section 2.1.1, Distribution Among Elements, page 17
Section 2.2, Monatomic Lattices, page 20
Section 2.2.1, The Simple Cubic Lattice, page 20
Section 2.2.2, The Face-Centered Cubic Lattice, page 20
Section 2.2.3, The Body-Centered Cubic Lattice, page 21
Section 2.2.4, The Hexagonal Lattice, page 22
Section 2.2.5, The Hexagonal Close-Packed Lattice, page 23
Section 2.2.6, The Diamond Lattice, page 24
Section 2.3, Compounds , page 24
Section 2.3.1, Rocksalt---Sodium Chloride, page 25
Section 2.3.2, Cesium Chloride, page 26
Section 2.3.3, Fluorite---Calcium Fluoride, page 26
Section 2.3.4, Zincblende---Zinc Sulfide, page 26
Section 2.3.5, Wurtzite---Zinc Oxide, page 28
Section 2.3.6, Perovskite---Calcium Titanate , page 28
Section 2.4, Classification of Lattices by Symmetry, page 28
Section 2.4.1, Fourteen Bravais Lattices and Seven Crystal Systems, page 30
Section 2.5, Symmetries of Lattices with Bases, page 32
Section 2.5.1, Thirty-Two Crystallographic Point Groups, page 32
Section 2.5.2, Two Hundred Thirty Distinct Lattices, page 36
Section 2.6, Some Macroscopic Implications of Microscopic Symmetries, page 37
Section 2.6.1, Pyroelectricity, page 37
Section 2.6.2, Piezoelectricity, page 37
Section 2.6.3, Optical Activity, page 38
Problems, page 38
References, page 41
Section 3.1, Introduction, page 43
Section 3.2, Theory of Scattering from Crystals, page 44
Section 3.2.1, Lattice Sums, page 47
Section 3.2.2, Reciprocal Lattice, page 48
Section 3.2.3, Miller Indices, page 51
Section 3.2.4, Scattering from a Lattice with a Basis, page 52
Section 3.3, Experimental Methods, page 54
Section 3.3.1, Laue Method, page 55
Section 3.3.2, Rotating Crystal Method, page 56
Section 3.3.3, Powder Method, page 58
Section 3.4, Further Features of Scattering Experiments, page 59
Section 3.4.1, Interaction of X-Rays with Matter, page 60
Section 3.4.2, Production of X-Rays, page 60
Section 3.4.3, Neutrons, page 61
Section 3.4.4, Electrons, page 61
Section 3.4.5, Deciphering Complex Structures, page 63
Section 3.4.6, Accuracy of Structure Determinations, page 64
Problems, page 65
References, page 67
Section 4.1, Introduction, page 69
Section 4.2, Geometry of Interfaces, page 69
Section 4.2.1, Coherent and Commensurate Interfaces, page 70
Section 4.2.2, Stacking Period and Interplanar Spacing, page 71
Section 4.2.3, Other Topics in Surface Structure, page 73
Section 4.3, Experimental Observation and Creation of Surfaces, page 73
Section 4.3.1, Low-Energy Electron Diffraction (LEED), page 74
Section 4.3.2, Reflection High-Energy Electron Diffraction (RHEED), page 75
Section 4.3.3, Molecular Beam Epitaxy (MBE), page 76
Section 4.3.4, Field Ion Microscopy (FIM), page 77
Section 4.3.5, Scanning Tunneling Microscopy (STM), page 77
Section 4.3.6, Atomic Force Microscopy (AFM), page 82
Section 4.3.7, High Resolution Electron Microscopy (HREM), page 82
Problems, page 82
References, page 85
Section 5.1, Introduction, page 87
Section 5.2, Alloys, page 87
Section 5.2.1, Equilibrium Structures, page 87
Section 5.2.2, Phase Diagrams, page 89
Section 5.2.3, Superlattices, page 90
Section 5.2.4, Phase Separation, page 91
Section 5.2.5, Nonequilibrium Structures in Alloys, page 94
Section 5.2.6, Dynamics of Phase Separation, page 95
Section 5.3, Simulations, page 97
Section 5.3.1, Monte Carlo, page 97
Section 5.3.2, Molecular Dynamics, page 98
Section 5.4, Liquids, page 99
Section 5.4.1, Correlation Functions, page 99
Section 5.4.2, Extended X-Ray Absorption Fine Structure (EXAFS), page 101
Section 5.4.3, Calculating Correlation Functions, page 103
Section 5.5, Glasses, page 103
Section 5.6, Liquid Crystals, page 107
Section 5.6.1, Nematics, Cholesterics, and Smectics, page 108
Section 5.6.2, Liquid Crystal Order Parameter, page 109
Section 5.7, Polymers, page 110
Section 5.7.1, Ideal Radius of Gyration, page 111
Section 5.8, Quasicrystals, page 115
Section 5.8.1, One-Dimensional Quasicrystal, page 116
Section 5.8.2, Two-Dimensional Quasicrystals---Penrose Tiles, page 121
Section 5.8.3, Experimental Observations, page 124
Section 5.8.4, Fullerenes, page 124
Problems, page 125
References, page 129
Section 6.1, Introduction, page 135
Section 6.2, The Basic Hamiltonian, page 137
Section 6.3, Densities of States, page 139
Section 6.3.1, Definition of Density of States ${D, page {140}
Section 6.3.2, Results for Free Electrons, page 141
Section 6.4, Statistical Mechanics of Noninteracting Electrons, page 143
Section 6.5, Sommerfeld Expansion, page 146
Section 6.5.1, Specific Heat of Noninteracting Electrons at Low Temperatures , page 149
Problems, page 150
References, page 153
Section 7.1, Introduction, page 155
Section 7.2, Translational Symmetry---Bloch's Theorem, page 155
Section 7.2.1, Van Hove Singularities, page 160
Section 7.2.2, Fourier Analysis of Bloch's Theorem, page 163
Section 7.2.3, Kronig--Penney Model, page 166
Section 7.3, Rotational Symmetry---Group Representations, page 169
Section 7.3.1, Classes and Characters, page 175
Section 7.3.2, Consequences of point group symmetries for Schr\"odinger's equation, page 178
Problems, page 181
References, page 184
Section 8.1, Introduction, page 185
Section 8.2, Nearly Free Electrons, page 185
Section 8.2.1, Degenerate Perturbation Theory, page 187
Section 8.3, Brillouin Zones, page 189
Section 8.3.1, Nearly Free Electron Fermi Surfaces, page 191
Section 8.4, Tightly Bound Electrons, page 194
Section 8.4.1, Wannier Functions, page 194
Section 8.4.2, Tight Binding Model, page 197
Problems, page 199
References, page 202
Section 9.1, Introduction, page 203
Section 9.2, Hartree and Hartree--Fock Equations, page 204
Section 9.2.1, Variational Principle, page 205
Section 9.2.2, Hartree--Fock Equations, page 205
Section 9.2.3, Numerical Implementation, page 209
Section 9.2.4, Hartree--Fock Equations for Jellium, page 212
Section 9.3, Density Functional Theory, page 214
Section 9.3.1, Thomas--Fermi Theory, page 216
Section 9.3.2, Kohn--Sham Equations, page 218
Section 9.4, Stability of Matter, page 220
Problems, page 223
References, page 226
Section 10.1, Introduction, page 229
Section 10.2, Numerical Methods, page 230
Section 10.2.1, Pseudopotentials and Orthogonalized Planes Waves (OPW), page 230
Section 10.2.2, Linear Combination of Atomic Orbitals (LCAO), page 235
Section 10.2.3, Plane Waves, page 237
Section 10.2.4, Linear Augmented Plane Waves (LAPW), page 240
Section 10.2.5, Linearized Muffin Tin Orbitals (LMTO), page 243
Section 10.3, Definition of Metals, Insulators, and Semiconductors, page 246
Section 10.4, Brief Survey of the Periodic Table, page 248
Section 10.4.1, Noble Gases, page 248
Section 10.4.2, Nearly Free Electron Metals, page 250
Section 10.4.3, Semiconductors, page 252
Section 10.4.4, Transition Metals, page 252
Section 10.4.5, Rare Earths, page 252
Problems, page 254
References, page 258
Section 11.1, Introduction, page 263
Section 11.1.1, Radii of Atoms, page 263
Section 11.2, Noble Gases, page 265
Section 11.3, Ionic Crystals, page 269
Section 11.3.1, Ewald Sums, page 270
Section 11.4, Metals, page 272
Section 11.4.1, Use of Pseudopotentials, page 275
Section 11.5, Band Structure Energy, page 276
Section 11.5.1, Peierls Distortion, page 277
Section 11.5.2, Structural Phase Transitions, page 279
Section 11.6, Hydrogen-Bonded Solids, page 280
Section 11.7, Cohesive Energy from Band Calculations, page 280
Section 11.8, Classical Potentials, page 282
Problems, page 283
References, page 285
Section 12.1, Introduction, page 287
Section 12.2, General Theory of Linear Elasticity , page 287
Section 12.2.1, Solids of Cubic Symmetry, page 289
Section 12.2.2, Isotropic Solids, page 290
Section 12.3, Other Constitutive Laws, page 295
Section 12.3.1, Liquid Crystals, page 295
Section 12.3.2, Rubber, page 298
Section 12.3.3, Composite and Granular Materials, page 301
Problems, page 301
References, page 303
Section 13.1, Introduction, page 305
Section 13.2, Vibrations of a Classical Lattice, page 305
Section 13.2.1, Normal Modes, page 307
Section 13.2.2, Lattice with a Basis, page 309
Section 13.3, Vibrations of a Quantum--Mechanical Lattice, page 313
Section 13.3.1, Phonon Specific Heat, page 317
Section 13.3.2, Einstein and Debye Models, page 321
Section 13.3.3, Thermal Expansion, page 324
Section 13.4, Inelastic Scattering from Phonons, page 326
Section 13.4.1, Neutron Scattering, page 327
Section 13.4.2, Formal Theory of Neutron Scattering, page 329
Section 13.4.3, Averaging Exponentials, page 333
Section 13.4.4, Evaluation of Structure Factor, page 335
Section 13.4.5, Kohn Anomalies, page 336
Section 13.5, The M\"ossbauer Effect, page 336
Problems, page 339
References, page 340
Section 14.1, Introduction, page 343
Section 14.2, Dislocations, page 345
Section 14.2.1, Experimental Observations of Dislocations, page 347
Section 14.2.2, Force to Move a Dislocation, page 350
Section 14.2.3, One-Dimensional Dislocations: Frenkel--Kontorova Model, page 350
Section 14.3, Two-Dimensional Dislocations and Hexatic Phases, page 353
Section 14.3.1, Impossibility of Crystalline Order in Two Dimensions, page 353
Section 14.3.2, Orientational Order, page 355
Section 14.3.3, Kosterlitz--Thouless--Berezinskii Transition, page 356
Section 14.4, Cracks, page 363
Section 14.4.1, Fracture of a Strip, page 363
Section 14.4.2, Stresses Around an Elliptical Hole, page 366
Section 14.4.3, Stress Intensity Factor, page 368
Section 14.4.4, Atomic Aspects of Fracture, page 368
Problems, page 370
References, page 373
Section 15.1, Introduction, page 375
Section 15.2, Newtonian Fluids, page 375
Section 15.2.1, Euler's Equation, page 375
Section 15.2.2, Navier--Stokes Equation, page 377
Section 15.3, Polymeric Solutions, page 378
Section 15.4, Plasticity, page 385
Section 15.5, Superfluid $^4$He, page 389
Section 15.5.1, Two-Fluid Hydrodynamics, page 392
Section 15.5.2, Second Sound, page 393
Section 15.5.3, Origin of Superfluidity, page 395
Section 15.5.4, Lagrangian Theory of Wave Function, page 400
Section 15.5.5, Superfluid 3He, page 403
Problems, page 404
References, page 408
Section 16.1, Introduction, page 413
Section 16.1.1, Drude Model, page 413
Section 16.2, Semiclassical Electron Dynamics, page 415
Section 16.2.1, Bloch Oscillations, page 416
Section 16.2.2, k . P Method, page 417
Section 16.2.3, Effective Mass, page 419
Section 16.3, Noninteracting Electrons in an Electric Field, page 419
Section 16.3.1, Zener Tunneling, page 422
Section 16.4, Semiclassical Equations from Wave Packets, page 425
Section 16.4.1, Formal Dynamics of Wave Packets, page 425
Section 16.5, Quantizing Semiclassical Dynamics, page 430
Section 16.5.1, Wannier--Stark Ladders, page 432
Section 16.5.2, de Haas--van Alphen Effect, page 432
Section 16.5.3, Experimental Measurements of Fermi Surfaces, page 434
Problems, page 437
References, page 440
Section 17.1, Introduction, page 443
Section 17.2, Boltzmann Equation, page 443
Section 17.2.1, Boltzmann Equation, page 445
Section 17.2.2, Relaxation Time Approximation, page 446
Section 17.2.3, Relation to Rate of Production of Entropy, page 448
Section 17.3, Transport Symmetries, page 449
Section 17.3.1, Onsager Relations, page 450
Section 17.4, Thermoelectric Phenomena, page 451
Section 17.4.1, Electrical Current, page 451
Section 17.4.2, Effective Mass and Holes, page 453
Section 17.4.3, Mixed Thermal and Electrical Gradients, page 454
Section 17.4.4, Wiedemann--Franz Law, page 455
Section 17.4.5, Thermopower---Seebeck Effect, page 456
Section 17.4.6, Peltier Effect, page 457
Section 17.4.7, Thomson Effect, page 457
Section 17.4.8, Hall Effect, page 459
Section 17.4.9, Magnetoresistance, page 461
Section 17.4.10, Giant Magnetoresistance, page 462
Section 17.5, Fermi Liquid Theory, page 462
Section 17.5.1, Basic Ideas, page 462
Section 17.5.2, Statistical Mechanics of Quasi-Particles, page 464
Section 17.5.3, Effective Mass, page 466
Section 17.5.4, Specific Heat, page 468
Section 17.5.5, Fermi Liquid Parameters, page 469
Section 17.5.6, Traveling Waves, page 470
Section 17.5.7, Comparison with Experiment in 3He, page 473
Problems, page 474
References, page 478
Section 18.1, Introduction, page 481
Section 18.2, Weak Scattering Theory of Conductivity, page 481
Section 18.2.1, General Formula for Relaxation Time, page 481
Section 18.2.2, Matthiessen's Rule, page 486
Section 18.2.3, Fluctuations, page 487
Section 18.3, Metal--Insulator Transitions, page 488
Section 18.3.1, Types of Impurities, page 488
Section 18.3.2, Impurity Scattering and Green's Functions , page 492
Section 18.3.3, Green's Functions, page 493
Section 18.3.4, Single Impurity, page 497
Section 18.4, Coherent Potential Approximation, page 499
Section 18.5, Localization, page 500
Section 18.5.1, Exact Results in One Dimension, page 501
Section 18.5.2, Scaling Theory of Localization, page 505
Section 18.5.3, Comparison with Experiment, page 509
Problems, page 510
References, page 514
Section 19.1, Introduction, page 517
Section 19.2, Metal Interfaces, page 518
Section 19.2.1, Work Functions, page 519
Section 19.2.2, Schottky Barrier, page 520
Section 19.2.3, Contact Potentials, page 522
Section 19.3, Semiconductors, page 524
Section 19.3.1, Pure Semiconductors, page 525
Section 19.3.2, Semiconductor in Equilibrium, page 528
Section 19.3.3, Intrinsic Semiconductor, page 530
Section 19.3.4, Extrinsic Semiconductor, page 531
Section 19.4, Diodes and Transistors, page 533
Section 19.4.1, Surface States, page 536
Section 19.4.2, Semiconductor Junctions, page 537
Section 19.4.3, Boltzmann Equation for Semiconductors, page 540
Section 19.4.4, Detailed Theory of Rectification, page 542
Section 19.4.5, Transistor, page 545
Section 19.5, Inversion Layers, page 548
Section 19.5.1, Heterostructures, page 548
Section 19.5.2, Quantum Point Contact, page 550
Section 19.5.3, Quantum Dot, page 553
Problems, page 556
References, page 557
Section 20.1, Introduction, page 561
Section 20.2, Maxwell's Equations, page 563
Section 20.2.1, Traveling Waves, page 565
Section 20.2.2, Mechanical Oscillators as Dielectric Function, page 566
Section 20.3, Kramers--Kronig Relations, page 568
Section 20.3.1, Application to Optical Experiments, page 570
Section 20.4, The Kubo--Greenwood Formula, page 573
Section 20.4.1, Born Approximation, page 573
Section 20.4.2, Susceptibility, page 577
Section 20.4.3, Many-Body Green Functions, page 578
Problems, page 578
References, page 581
Section 21.1, Introduction, page 583
Section 21.2, Cyclotron Resonance, page 583
Section 21.2.1, Electron Energy Surfaces, page 586
Section 21.3, Semiconductor Band Gaps, page 588
Section 21.3.1, Direct Transitions, page 588
Section 21.3.2, Indirect Transitions, page 589
Section 21.4, Excitons, page 591
Section 21.4.1, Mott--Wannier Excitons, page 591
Section 21.4.2, Frenkel Excitons, page 594
Section 21.4.3, Electron--Hole Liquid, page 595
Section 21.5, Optoelectronics, page 595
Section 21.5.1, Solar Cells, page 595
Section 21.5.2, Lasers, page 596
Problems, page 602
References, page 606
Section 22.1, Introduction, page 609
Section 22.2, Polarization, page 609
Section 22.2.1, Ferroelectrics, page 609
Section 22.2.2, Clausius--Mossotti Relation, page 611
Section 22.3, Optical Modes in Ionic Crystals, page 613
Section 22.3.1, Polaritons, page 616
Section 22.3.2, Polarons, page 618
Section 22.3.3, Experimental Observations of Polarons, page 623
Section 22.4, Point Defects and Color Centers, page 623
Section 22.4.1, Vacancies, page 624
Section 22.4.2, F Centers, page 625
Section 22.4.3, Electron Spin Resonance and Electron Nuclear Double Resonance, page 626
Section 22.4.4, Other Centers, page 628
Section 22.4.5, Franck--Condon Effect, page 628
Section 22.4.6, Urbach Tails, page 632
Problems, page 633
References, page 635
Section 23.1, Introduction, page 637
Section 23.1.1, Plasma Frequency, page 637
Section 23.2, Metals at Low Frequencies, page 640
Section 23.2.1, Anomalous Skin Effect, page 642
Section 23.3, Plasmons, page 643
Section 23.3.1, Experimental Observation of Plasmons, page 644
Section 23.4, Interband Transitions, page 646
Section 23.5, Brillouin and Raman Scattering, page 649
Section 23.5.1, Brillouin Scattering, page 650
Section 23.5.2, Raman Scattering, page 651
Section 23.5.3, Inelastic X-Ray Scattering, page 651
Section 23.6, Photoemission, page 651
Section 23.6.1, Measurement of Work Functions, page 651
Section 23.6.2, Angle-Resolved Photoemission, page 654
Section 23.6.3, Core-Level Photoemission and Charge-Transfer Insulators, page 658
Problems, page 664
References, page 667
Section 24.1, Introduction, page 671
Section 24.2, Three Views of Magnetism, page 671
Section 24.2.1, From Magnetic Moments, page 671
Section 24.2.2, From Conductivity, page 672
Section 24.2.3, From a Free Energy, page 673
Section 24.3, Magnetic Dipole Moments, page 675
Section 24.3.1, Spontaneous Magnetization of Ferromagnets, page 678
Section 24.3.2, Ferrimagnets, page 679
Section 24.3.3, Antiferromagnets, page 681
Section 24.4, Mean Field Theory and the Ising Model, page 682
Section 24.4.1, Domains , page 684
Section 24.4.2, Hysteresis, page 687
Section 24.5, Other Order--Disorder Transitions, page 688
Section 24.5.1, Alloy Superlattices, page 688
Section 24.5.2, Spin Glasses, page 691
Section 24.6, Critical Phenomena, page 691
Section 24.6.1, Landau Free Energy, page 692
Section 24.6.2, Scaling Theory, page 698
Problems, page 702
References, page 705
Section 25.1, Introduction, page 707
Section 25.2, Atomic Magnetism, page 709
Section 25.2.1, Hund's Rules, page 710
Section 25.2.2, Curie's Law, page 714
Section 25.3, Magnetism of the Free-Electron Gas, page 717
Section 25.3.1, Pauli Paramagnetism, page 718
Section 25.3.2, Landau Diamagnetism, page 719
Section 25.3.3, Aharonov--Bohm Effect, page 722
Section 25.4, Tightly Bound Electrons in Magnetic Fields, page 724
Section 25.5, Quantum Hall Effect, page 728
Section 25.5.1, Integer Quantum Hall Effect, page 728
Section 25.5.2, Fractional Quantum Hall Effect, page 733
Problems, page 739
References, page 742
Section 26.1, Introduction, page 745
Section 26.2, Origin of Ferromagnetism, page 745
Section 26.2.1, Heitler--London Calculation, page 745
Section 26.2.2, Spin Hamiltonian, page 750
Section 26.3, Heisenberg Model, page 750
Section 26.3.1, Indirect Exchange and Superexchange, page 752
Section 26.3.2, Ground State, page 753
Section 26.3.3, Spin Waves, page 753
Section 26.3.4, Spin Waves in Antiferromagnets, page 756
Section 26.3.5, Comparison with Experiment, page 759
Section 26.4, Ferromagnetism in Transition Metals, page 759
Section 26.4.1, Stoner Model, page 759
Section 26.4.2, Calculations Within Band Theory, page 761
Section 26.5, Kondo Effect, page 763
Section 26.5.1, Scaling Theory, page 768
Section 26.6, Hubbard Model, page 772
Section 26.6.1, Mean-Field Solution, page 773
Problems, page 776
References, page 779
Section 27.1, Introduction, page 783
Section 27.2, Phenomenology of Superconductivity, page 784
Section 27.2.1, Phenomenological Free Energy, page 785
Section 27.2.2, Thermodynamics of Superconductors, page 787
Section 27.2.3, Landau--Ginzburg Free Energy, page 788
Section 27.2.4, Type I and Type II Superconductors, page 789
Section 27.2.5, Flux Quantization, page 794
Section 27.2.6, The Josephson Effect, page 796
Section 27.2.7, Circuits with Josephson Junction Elements, page 798
Section 27.2.8, SQUIDS, page 799
Section 27.2.9, Origin of Josephson's Equations , page 800
Section 27.3, Microscopic Theory of Superconductivity, page 802
Section 27.3.1, Electron--Ion Interaction, page 803
Section 27.3.2, Formal Derivation, page 806
Section 27.3.3, Instability of the Normal State: Cooper Problem, page 808
Section 27.3.4, Self-Consistent Ground State, page 812
Section 27.3.5, Thermodynamics of Superconductors, page 817
Section 27.3.6, Superconductor in External Magnetic Field, page 820
Section 27.3.7, Derivation of Meissner Effect, page 824
Section 27.3.8, Comparison with Experiment, page 827
Section 27.3.9, High-Temperature Superconductors, page 828
Problems, page 833
References, page 837
Section A.1, One-Dimensional Sum, page 843
Section A.2, Area Under Peaks, page 843
Section A.3, Three-Dimensional Sum, page 844
Section A.4, Discrete Case, page 845
Section A.5, Convolution, page 846
Section A.6, Using the Fast Fourier Transform, page 846
References, page 848
Section B.1, Functionals and Functional Derivatives, page 849
Section B.2, Time-Independent Schroedinger Equation, page 850
Section B.3, Time-Dependent Schroedinger Equation, page 851
Section B.4, Method of Steepest Descent, page 852
References, page 852
Section C.1, Rules, page 853
Section C.1.1, States, page 853
Section C.1.2, Operators, page 853
Section C.1.3, Hamiltonians, page 854
Section C.2, Derivations, page 855
Section C.2.1, Bosons, page 855
Section C.2.2, Fermions, page 856