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CHAPTER 1: CRYSTAL STRUCTURE1

Periodic Array of Atoms3

Lattice Translation Vectors4

Basis and the Crystal Structure5

Primitive Lattice Cell6

Fundamental Types of Lattices6

Two-Dimensional Lattice Types8

Three-Dimensional Lattice Types9

Index Systems for Crystal Planes11

Simple Crystal Structures13

Sodium Chloride Structure13

Cesium Chloride Structure14

Hexagonal Close-Packed Structure (hcp)15

Diamond Structure16

Cubic Zinc Sulfide Structure17

Direct Imaging of Atomic Structure18

Nonideal Crystal Structures18

Random Stacking and Polytypism19

Crystal Structure Data19

Summary22

Problems22

CHAPTER 2: WAVE DIFFRACTION AND THE RECIPROCAL LATTICE23

Diffraction of Waves by Crystals25

Bragg Law25

Scattered Wave Amplitude26

Fourier Analysis27

Reciprocal Lattice Vectors29

Diffraction Conditions30

Laue Equations32

Brillouin Zones33

Reciprocal Lattice to sc Lattice34

Reciprocal Lattice to bcc Lattice36

Reciprocal Lattice to fcc Lattice37

Fourier Analysis of the Basis39

Structure Factor of the bcc Lattice40

Structure factor of the fcc Lattice40

Atomic Form Factor41

Summary43

Problems43

CHAPTER 3: CRYSTAL RINDING AND ELASTIC CONSTANTS47

Crystals of Inert Gases49

Van der Waals—London Interaction53

Repulsive Interaction56

Equilibrium Lattice Constants58

Cohesive Energy59

Ionic Crystals60

Electrostatic or Madelung Energy60

Evaluation of the Madelung Constant64

Covalent Crystals67

Metals69

Hydrogen Bonds70

Atomic Radii70

Ionic Crystal Radii72

Analysis of Elastic Strains73

Dilation75

Stress Components75

Elastic Compliance and Stiffness Constants77

Elastic Energy Density77

Elastic Stiffness Constants of Cubic Crystals78

Bulk Modulus and Compressibility80

Elastic Waves in Cubic Crstals80

Waves in the [100] Direction81

Waves in the [110] Direction82

Summary85

Problems85

CHAPTER 4: PHONONS I. CRYSTAL VIBRATIONS89

Vibrations of Crystals with Monatomic Basis91

First Brillouin Zone93

Group Velocity94

Long Wavelength Limit94

Derivation of Force Constants from Experiment94

Two Atoms per Primitive Basis95

Quantization of Elastic Waves99

Phonon Momentum100

Inelastic Scattering by Phonons100

Summary102

Problems102

CHAPTER 5: PHONONS 11. THERMAL PROPERTIES105

Phonon Heat Capacity107

Planck Distribution107

Normal Mode Enumeration108

Density of States in One Dimension108

Density of States in Three Dimensions111

Debye Model for Density of States112

Debye T3 Law114

Einstein Model of the Density of States114

General Result for D(w)117

Anharmonic Crystal Interactions119

Thermal Expansion120

Thermal Conductivity121

Thermal Resistivity of Phonon Gas123

Umklapp Processes125

Imperfecions126

Problems128

CHAPTER 6: FREE ELECTRON FERMI GAS131

Energy Levels in One Dimension134

Effect of Temperature on the FermiDirac Distribution136

Free Electron Gas in Three Dimensions137

Heat Capacity of the Electron Gas141

Experimental Heat Capacity of Metals145

Heavy Fermions147

Electrical Conductivity and Ohm's Law147

Experimental Electrical Resistivity of Metals148

Umklapp Scattering151

Motion in Magnetic Fields152

Hall Effect153

Thermal Conductivity of Metals156

Ratio of Thermal to Electrical Conductivity156

Problems157

CHAPTER 7: ENERGY BANDS161

Nearly Free Electron Model164

Origin of the Energy Gap165

Magnitude of the Energy Gap167

Bloch Functions167

Kronig-Penney Model168

Wave Equation of Electron in a Periodic Potential169

Restatement of the Bloch Theorem173

Ciystal Momentum of an Electron173

Solution of the Central Equation174

Kronig-Penney Model in Reciprocal Space174

Empty Lattice Approximation176

Approximate Solution Near a Zone Boundary177

Number of Orbitals in a Band180

Metals and Insulators181

Summary182

Problems182

CHAPTER 8: SEMICONDUCTOR CRYSTALS185

Band Gap187

Equations of Motion191

Physical Derivation of hk = F193

Holes194

Effective Mass197

Physical Interpretation of the Effective Mass198

Effective Masses in Semiconductors200

Silicon and Germanium202

Intrinsic Carrier Concentration205

Intrinsic Mobility208

Impurity Conductivity209

Donor States209

Acceptor States211

Thermal Ionization of Donors and Acceptors213

Thermoelectric Effects214

Semimetals215

Superlattices216

Bloch Oscillator217

Zener Tunneling217

Summary217

Problems218

CHAPTER 9: FERMI SURFACES AND METALS221

Reduced Zone Scheme223

Periodic Zone Scheme225

Construction of Fermi Surfaces226

Nearly Free Electrons228

Electron Orbits, Hole Orbits, and Open Orbits230

Calculation of Energy Bands232

Tight Binding Method of Energy Bands232

Wigner-Seitz Method236

Cohesive Energy237

Pseudopotential Methods239

Experimental Methods in Fermi Surface Studies242

Quantization of Orbits in a Magnetic Field242

De Haas-van Alphen Effect244

Extremal Orbits248

Fermi Surface of Copper249

Magnetic Breakdown251

Summary252

Problems252

CHAPTER 10: SUPERCONDUCTIVITY257

Experimental Survey259

Occurrence of Superconductivity260

Destruction of Superconductivity of Magnetic Fields262

Meissner Effect262

Heat Capacity264

Energy Gap266

Microwave and Infrared Properties268

Isotope Effect269

Theoretical Survey270

Thermodynamics of the Superconducting Transition270

London Equation273

Coherence Length276

BCS Theory of Superconductivity277

BCS Ground State278

Flux Quantization in a Superconducting Ring279

Duration of Persistent Currents282

Type II Superconductors283

Vortex State284

Estimation of Hcl and Hc2284

Single Particle Tunneling287

Josephson Superconductor Tunneling289

Dc Josephson Effect289

Ac Josephson Effect290

Macroscopic Quantum Interference292

High-Temperature Superconductors293

Summary294

Problems294

Reference296

CHAPTER 11: DIAMAGNETISM AND PARAMAGNETISM297

Langevin Diamagnetism Equation299

Quantum Theory of Diamagnetism of Mononuclear Systems301

Paramagnetism302

Quantum Theory of Paramagnetism302

Rare Earth Ions305

Hund Rules306

Iron Group Ions307

Crystal Field Splitting307

Quenching of the Orbital Angular Momentum308

Spectroscopic Splitting Factor311

Van Vleck Temperature-Independent Paramagnetism311

Cooling by Isentropic Demagnetization312

Nuclear Demagnetization314

Paramagnetic Susceptibility of Conduction Electrons315

Summary317

Problems318

CHAPTER 12: FERROMAGNETISM AND ANTIFERROMAGNETISM321

Ferromagnetic Order323

Curie Point and the Exchange Integral323

Temperature Dependence of the Saturation Magnetization326

Saturation Magnetization at Absolute Zero328

Magnons330

Quantization of Spin Waves333

Thermal Excitation of Magnons334

Neutron Magnetic Scattering335

Ferrimagnetic Order336

Curie Temperature and Susceptibility of Ferrimagnets338

Iron Garnets339

Antiferromagnetic Order340

Susceptibility Below the Neel Temperature343

Antiferromagnetic Magnons344

Ferromagnetic Domains346

Anisotropy Energy348

Transition Region between Domains349

Origin of Domains351

Coercivity and Hysteresis352

Single Domain Particles354

Geomagnetism and Biomagnetism355

Magnetic Force Microscopy355

Summary356

Problems357

CHAPTER 13: MAGNETIC RESONANCE361

Nuclear Magnetic Resonance363

Equations of Motion366

Line Width370

Motional Narrowing371

Hyperfine Splitting373

Examples: Paramagnetic Point Defects375

F Centers in Alkali Halides376

Donor Atoms in Silicon376

Knight Shift377

Nuclear Quadrupole Resonance379

Ferromagnetic Resonance379

Shape Effects in FMR380

Spin Wave Resonance382

Antiferromagnetic Resonance383

Electron Paramagnetic Resonance386

Exchange Narrowing386

Zero-field Splitting386

Principle of Maser Action386

Three-Level Maser388

Lasers389

Summary390

Problems391

CHAPTER 14: PLASMONS, POLARITONS, AND POLARONS393

Dielectric Function of the Electron Gas395

Definitions of the Dielectric Function395

Plasma Optics396

Dispersion Relation for Electromagnetic Waves397

Transverse Optical Modes in a Plasma398

Transparency of Metals in the Ultraviolet398

Longitudinal Plasma Oscillations398

Plasmons401

Electrostatic Screening403

Screened Coulomb Potential406

Pseudopotential Component U(0)407

Mott Metal-Insulator Transition407

Screening and Phonons in Metals409

Polaritons410

LST Relation414

Electron-Electron Interaction417

Fermi Liquid417

Electron-Electron Collisions417

Electron-Phonon Interaction: Polarons420

Peierls Instability of Linear Metals422

Summary424

Problems424

CHAPTER 15: OPTICAL PROCESSES AND EXCITONS427

Optical Reflectance429

Kramers-Kronig Relations430

Mathematical Note432

Example: Conductivity of collisionless Electron Gas433

Electronic Interband Transitions434

Excitons435

Frenkel Excitons437

Alkali Halides440

Molecular Crystals440

Weakly Bound (Mott-Wannier) Excitons441

Exciton Condensation into Electron-Hole Drops (EHD)441

Raman Effects in Crystals444

Electron Spectroscopy with X-Rays447

Energy Loss of Fast Particles in a Solid448

Summary449

Problems450

CHAPTER 16: DIELECTRICS AND FERROELECTRICS453

Maxwell Equations455

Polarization455

Macroscopic Electric Field456

Depolarization Field, E1458

Local Electric Field at an Atom460

Lorentz Field, E2462

Field of Dipoles Inside Cavity, E3462

Dielectric Constant and Polarizability463

Electronic Polarizability464

Classical Theory of Electronic Polarizability466

Structural Phase Transitions467

Ferroelectric Crystals467

Classification of Ferroelectric Crystals469

Displacive Transitions471

Soft Optical Phonons473

Landau Theory of the Phase Transition474

Second-Order Transition475

First-Order Transition477

Antiferroelectricity479

Ferroelectric Domains479

Piezoelectricity481

Summary482

Problems483

CHAPTER 17: SURFACE AND INTERFACE PHYSICS487

Reconstruction and Relaxation489

Surface Crystallography490

Reflection High-Energy Electron Diffraction493

Surface Electronic Structure494

Work Function494

Thermionic Emission495

Surface States495

Tangential Surface Transport497

Magnetoresistance in a Two-Dimensional Channel498

Integral Quantized Hall Effect (IQHE)499

IQHE in Real Systems500

Fractional Quantized Hall Effect (FQHE)503

p-n Junctions503

Rectification504

Solar Cells and Photovoltaic Detectors506

Schottky Barrier506

Heterostructures507

n-N Heterojunction508

Semiconductor Lasers510

Light-Emitting Diodes511

Problems513

CHAPTER 18: NANOSTRUCTURES515

Imaging Techniques for Nanostructures519

Electron Microscopy520

Optical Microscopy521

Scanning Tunneling Microscopy523

Atomic Force Microscopy526

Electronic Structure of 1D Systems528

One-Dimensional Subbands528

Spectroscopy of Van Hove Singularities529

ID Metals — Coluomb Interactions and Lattice Copulings531

Electrical Transport in 1D533

Conductance Quantization and the Landauer Formula533

Two Barriers in Series-resonant Tunneling536

Incoherent Addition and Ohm's Law538

Localization539

Voltage Probes and the Buttiker-Landauer Formalism540

Electronic Structure of 0D Systems545

Quantized Energy Levels545

Semiconductor Nanocrystals545

Metallic Dots547

Discrete Charge States549

Electrical Transport in 0D551

Coulomb Oscillations551

Spin, Mott Insulators, and the Kondo Effect554

Cooper Pairing in Superconducting Dots556

Vibrational and Thermal Properties of Nanostructures557

Quantized Vibrational Modes557

Transverse Vibrations559

Heat Capacity and Thermal Transport561

Summary562

Problems562

CHAPTER 19: NONCRYSTALLINE SOLIDS565

Diffraction Pattern567

Monatomic Amorphous Materials568

Radial Distribution Function569

Structure of Vitreous Silica, SiO2570

Glasses573

Viscosity and the Hopping Rate574

Amorphous Ferromagnets575

Amorphous Semiconductors577

Low Energy Excitations in Amorphous Solids578

Heat Capacity Calculation578

Thermal Conductivity579

Fiber Optics581

Rayleigh Attenuation582

Problems582

CHAPTER 20: POINT DEFECTS583

Lattice Vacancies585

Diffusion588

Metals591

Color Centers592

F Centers592

Other Centers in Alkali Halides593

Problems595

CHAPTER 21: DISLOCATIONS597

Shear Strength of Single Crystals599

Slip600

Dislocations601

Burgers Vectors604

Stress Fields of Dislocations605

Low-angle Grain Boundaries607

Dislocation Densities610

Dislocation Multiplication and Slip611

Strength of Alloys613

Dislocations and Crystal Growth615

Whiskers616

Hardness of Materials617

Problems618

CHAPTER 22: ALLOYS619

General Considerations621

Substitutional Solid Solutions—Hume-Rothery Rules624

Order-Disorder Transformation627

Elementary Theory of Order629

Phase Diagrams632

Eutectics632

Transition Metal Alloys634

Electrical Conductivity636

Kondo Effect637

Problems640

APPENDIX A: TEMPERATURE DEPENDENCE OF THE REFLECTION LINES641

APPENDIX B: EWALD CALCULATION OF LATTICE SUMS644

Ewald-Kornfeld Method for Lattice Sums for Dipole Arrays647

APPENDIX C: QUANTIZATION OF ELASTIC WAVES :PHONONS648

Phonon Coordinates649

Creation and Annihilation Operators651

APPENDIX D: FERMI-DIRAC DISTRIBUTION FUNCTION652

APPENDIX E: DERIVATION OF THE DK/DT EQUATION655

APPENDIX F: BOLTZMANN TRANSPORT EQUATION656

Particle Diffusion657

Classical Distribution658

Fermi-Dirac Distribution659

Electrical Conductivity661

APPENDIX G: VECTOR POTENTIAL, FIELD MOMENTUM,AND GAUGE TRANSFORMATIONS661

Lagrangian Equations of Motion662

Derivation of the Hamiltonian663

Field Momentum663

Gauge Transformation664

Gauge in the London Equation665

APPENDIX H: COOPER PAIRS665

APPENDIX I: GINZBURG-lANDAU EQUATION667

APPENDIX J: ELECTRON-PHONON COLLISIONS671

INDEX675