CHAPTER 1: CRYSTAL STRUCTURE

Periodic Array of Atoms

Lattice Translation Vectors

Basis and the Crystal Structure

Primitive Lattice Cell

Fundamental Types of Lattices

Two-Dimensional Lattice Types

Three-Dimensional Lattice Types

Index Systems for Crystal Planes

Simple Crystal Structures

Sodium Chloride Structure

Cesium Chloride Structure

Hexagonal Close-Packed Structure (hcp)

Diamond Structure

Cubic Zinc Sulfide Structure

Direct Imaging of Atomic Structure

Nonideal Crystal Structures

Random Stacking and Polytypism

Crystal Structure Data

Summary

Problems

CHAPTER 2: WAVE DIFFRACTION AND THE RECIPROCAL LATTICE

Diffraction of Waves by Crystals

Bragg Law

Scattered Wave Amplitude

Fourier Analysis

Reciprocal Lattice Vectors

Diffraction Conditions

Laue Equations

Brillouin Zones

Reciprocal Lattice to sc Lattice

Reciprocal Lattice to bcc Lattice

Reciprocal Lattice to fcc Lattice

Fourier Analysis of the Basis

Structure Factor of the bcc Lattice

Structure factor of the fcc Lattice

Atomic Form Factor

Summary

Problems

CHAPTER 3: CRYSTAL RINDING AND ELASTIC CONSTANTS

Crystals of Inert Gases

Van der Waals—London Interaction

Repulsive Interaction

Equilibrium Lattice Constants

Cohesive Energy

Ionic Crystals

Electrostatic or Madelung Energy

Evaluation of the Madelung Constant

Covalent Crystals

Metals

Hydrogen Bonds

Atomic Radii

Ionic Crystal Radii

Analysis of Elastic Strains

Dilation

Stress Components

Elastic Compliance and Stiffness Constants

Elastic Energy Density

Elastic Stiffness Constants of Cubic Crystals

Bulk Modulus and Compressibility

Elastic Waves in Cubic Crstals

Waves in the [100] Direction

Waves in the [110] Direction

Summary

Problems

CHAPTER 4: PHONONS I. CRYSTAL VIBRATIONS

Vibrations of Crystals with Monatomic Basis

First Brillouin Zone

Group Velocity

Long Wavelength Limit

Derivation of Force Constants from Experiment

Two Atoms per Primitive Basis

Quantization of Elastic Waves

Phonon Momentum

Inelastic Scattering by Phonons

Summary

Problems

CHAPTER 5: PHONONS 11. THERMAL PROPERTIES

Phonon Heat Capacity

Planck Distribution

Normal Mode Enumeration

Density of States in One Dimension

Density of States in Three Dimensions

Debye Model for Density of States

Debye T3 Law

Einstein Model of the Density of States

General Result for D(w)

Anharmonic Crystal Interactions

Thermal Expansion

Thermal Conductivity

Thermal Resistivity of Phonon Gas

Umklapp Processes

Imperfecions

Problems

CHAPTER 6: FREE ELECTRON FERMI GAS

Energy Levels in One Dimension

Effect of Temperature on the FermiDirac Distribution

Free Electron Gas in Three Dimensions

Heat Capacity of the Electron Gas

Experimental Heat Capacity of Metals

Heavy Fermions

Electrical Conductivity and Ohm's Law

Experimental Electrical Resistivity of Metals

Umklapp Scattering

Motion in Magnetic Fields

Hall Effect

Thermal Conductivity of Metals

Ratio of Thermal to Electrical Conductivity

Problems

CHAPTER 7: ENERGY BANDS

Nearly Free Electron Model

Origin of the Energy Gap

Magnitude of the Energy Gap

Bloch Functions

Kronig-Penney Model

Wave Equation of Electron in a Periodic Potential

Restatement of the Bloch Theorem

Ciystal Momentum of an Electron

Solution of the Central Equation

Kronig-Penney Model in Reciprocal Space

Empty Lattice Approximation

Approximate Solution Near a Zone Boundary

Number of Orbitals in a Band

Metals and Insulators

Summary

Problems

CHAPTER 8: SEMICONDUCTOR CRYSTALS

Band Gap

Equations of Motion

Physical Derivation of hk = F

Holes

Effective Mass

Physical Interpretation of the Effective Mass

Effective Masses in Semiconductors

Silicon and Germanium

Intrinsic Carrier Concentration

Intrinsic Mobility

Impurity Conductivity

Donor States

Acceptor States

Thermal Ionization of Donors and Acceptors

Thermoelectric Effects

Semimetals

Superlattices

Bloch Oscillator

Zener Tunneling

Summary

Problems

CHAPTER 9: FERMI SURFACES AND METALS

Reduced Zone Scheme

Periodic Zone Scheme

Construction of Fermi Surfaces

Nearly Free Electrons

Electron Orbits, Hole Orbits, and Open Orbits

Calculation of Energy Bands

Tight Binding Method of Energy Bands

Wigner-Seitz Method

Cohesive Energy

Pseudopotential Methods

Experimental Methods in Fermi Surface Studies

Quantization of Orbits in a Magnetic Field

De Haas-van Alphen Effect

Extremal Orbits

Fermi Surface of Copper

Magnetic Breakdown

Summary

Problems

CHAPTER 10: SUPERCONDUCTIVITY

Experimental Survey

Occurrence of Superconductivity

Destruction of Superconductivity of Magnetic Fields

Meissner Effect

Heat Capacity

Energy Gap

Microwave and Infrared Properties

Isotope Effect

Theoretical Survey

Thermodynamics of the Superconducting Transition

London Equation

Coherence Length

BCS Theory of Superconductivity

BCS Ground State

Flux Quantization in a Superconducting Ring

Duration of Persistent Currents

Type II Superconductors

Vortex State

Estimation of Hcl and Hc2

Single Particle Tunneling

Josephson Superconductor Tunneling

Dc Josephson Effect

Ac Josephson Effect

Macroscopic Quantum Interference

High-Temperature Superconductors

Summary

Problems

Reference

CHAPTER 11: DIAMAGNETISM AND PARAMAGNETISM

Langevin Diamagnetism Equation

Quantum Theory of Diamagnetism of Mononuclear Systems

Paramagnetism

Quantum Theory of Paramagnetism

Rare Earth Ions

Hund Rules

Iron Group Ions

Crystal Field Splitting

Quenching of the Orbital Angular Momentum

Spectroscopic Splitting Factor

Van Vleck Temperature-Independent Paramagnetism

Cooling by Isentropic Demagnetization

Nuclear Demagnetization

Paramagnetic Susceptibility of Conduction Electrons

Summary

Problems

CHAPTER 12: FERROMAGNETISM AND ANTIFERROMAGNETISM

Ferromagnetic Order

Curie Point and the Exchange Integral

Temperature Dependence of the Saturation Magnetization

Saturation Magnetization at Absolute Zero

Magnons

Quantization of Spin Waves

Thermal Excitation of Magnons

Neutron Magnetic Scattering

Ferrimagnetic Order

Curie Temperature and Susceptibility of Ferrimagnets

Iron Garnets

Antiferromagnetic Order

Susceptibility Below the Neel Temperature

Antiferromagnetic Magnons

Ferromagnetic Domains

Anisotropy Energy

Transition Region between Domains

Origin of Domains

Coercivity and Hysteresis

Single Domain Particles

Geomagnetism and Biomagnetism

Magnetic Force Microscopy

Summary

Problems

CHAPTER 13: MAGNETIC RESONANCE

Nuclear Magnetic Resonance

Equations of Motion

Line Width

Motional Narrowing

Hyperfine Splitting

Examples: Paramagnetic Point Defects

F Centers in Alkali Halides

Donor Atoms in Silicon

Knight Shift

Nuclear Quadrupole Resonance

Ferromagnetic Resonance

Shape Effects in FMR

Spin Wave Resonance

Antiferromagnetic Resonance

Electron Paramagnetic Resonance

Exchange Narrowing

Zero-field Splitting

Principle of Maser Action

Three-Level Maser

Lasers

Summary

Problems

CHAPTER 14: PLASMONS, POLARITONS, AND POLARONS

Dielectric Function of the Electron Gas

Definitions of the Dielectric Function

Plasma Optics

Dispersion Relation for Electromagnetic Waves

Transverse Optical Modes in a Plasma

Transparency of Metals in the Ultraviolet

Longitudinal Plasma Oscillations

Plasmons

Electrostatic Screening

Screened Coulomb Potential

Pseudopotential Component U(0)

Mott Metal-Insulator Transition

Screening and Phonons in Metals

Polaritons

LST Relation

Electron-Electron Interaction

Fermi Liquid

Electron-Electron Collisions

Electron-Phonon Interaction: Polarons

Peierls Instability of Linear Metals

Summary

Problems

CHAPTER 15: OPTICAL PROCESSES AND EXCITONS

Optical Reflectance

Kramers-Kronig Relations

Mathematical Note

Example: Conductivity of collisionless Electron Gas

Electronic Interband Transitions

Excitons

Frenkel Excitons

Alkali Halides

Molecular Crystals

Weakly Bound (Mott-Wannier) Excitons

Exciton Condensation into Electron-Hole Drops (EHD)

Raman Effects in Crystals

Electron Spectroscopy with X-Rays

Energy Loss of Fast Particles in a Solid

Summary

Problems

CHAPTER 16: DIELECTRICS AND FERROELECTRICS

Maxwell Equations

Polarization

Macroscopic Electric Field

Depolarization Field, E1

Local Electric Field at an Atom

Lorentz Field, E2

Field of Dipoles Inside Cavity, E3

Dielectric Constant and Polarizability

Electronic Polarizability

Classical Theory of Electronic Polarizability

Structural Phase Transitions

Ferroelectric Crystals

Classification of Ferroelectric Crystals

Displacive Transitions

Soft Optical Phonons

Landau Theory of the Phase Transition

Second-Order Transition

First-Order Transition

Antiferroelectricity

Ferroelectric Domains

Piezoelectricity

Summary

Problems

CHAPTER 17: SURFACE AND INTERFACE PHYSICS

Reconstruction and Relaxation

Surface Crystallography

Reflection High-Energy Electron Diffraction

Surface Electronic Structure

Work Function

Thermionic Emission

Surface States

Tangential Surface Transport

Magnetoresistance in a Two-Dimensional Channel

Integral Quantized Hall Effect (IQHE)

IQHE in Real Systems

Fractional Quantized Hall Effect (FQHE)

p-n Junctions

Rectification

Solar Cells and Photovoltaic Detectors

Schottky Barrier

Heterostructures

n-N Heterojunction

Semiconductor Lasers

Light-Emitting Diodes

Problems

CHAPTER 18: NANOSTRUCTURES

Imaging Techniques for Nanostructures

Electron Microscopy

Optical Microscopy

Scanning Tunneling Microscopy

Atomic Force Microscopy

Electronic Structure of 1D Systems

One-Dimensional Subbands

Spectroscopy of Van Hove Singularities

ID Metals — Coluomb Interactions and Lattice Copulings

Electrical Transport in 1D

Conductance Quantization and the Landauer Formula

Two Barriers in Series-resonant Tunneling

Incoherent Addition and Ohm's Law

Localization

Voltage Probes and the Buttiker-Landauer Formalism

Electronic Structure of 0D Systems

Quantized Energy Levels

Semiconductor Nanocrystals

Metallic Dots

Discrete Charge States

Electrical Transport in 0D

Coulomb Oscillations

Spin, Mott Insulators, and the Kondo Effect

Cooper Pairing in Superconducting Dots

Vibrational and Thermal Properties of Nanostructures

Quantized Vibrational Modes

Transverse Vibrations

Heat Capacity and Thermal Transport

Summary

Problems

CHAPTER 19: NONCRYSTALLINE SOLIDS

Diffraction Pattern

Monatomic Amorphous Materials

Radial Distribution Function

Structure of Vitreous Silica, SiO2

Glasses

Viscosity and the Hopping Rate

Amorphous Ferromagnets

Amorphous Semiconductors

Low Energy Excitations in Amorphous Solids

Heat Capacity Calculation

Thermal Conductivity

Fiber Optics

Rayleigh Attenuation

Problems

CHAPTER 20: POINT DEFECTS

Lattice Vacancies

Diffusion

Metals

Color Centers

F Centers

Other Centers in Alkali Halides

Problems

CHAPTER 21: DISLOCATIONS

Shear Strength of Single Crystals

Slip

Dislocations

Burgers Vectors

Stress Fields of Dislocations

Low-angle Grain Boundaries

Dislocation Densities

Dislocation Multiplication and Slip

Strength of Alloys

Dislocations and Crystal Growth

Whiskers

Hardness of Materials

Problems

CHAPTER 22: ALLOYS

General Considerations

Substitutional Solid Solutions—Hume-Rothery Rules

Order-Disorder Transformation

Elementary Theory of Order

Phase Diagrams

Eutectics

Transition Metal Alloys

Electrical Conductivity

Kondo Effect

Problems

APPENDIX A: TEMPERATURE DEPENDENCE OF THE REFLECTION LINES

APPENDIX B: EWALD CALCULATION OF LATTICE SUMS

Ewald-Kornfeld Method for Lattice Sums for Dipole Arrays

APPENDIX C: QUANTIZATION OF ELASTIC WAVES :PHONONS

Phonon Coordinates

Creation and Annihilation Operators

APPENDIX D: FERMI-DIRAC DISTRIBUTION FUNCTION

APPENDIX E: DERIVATION OF THE DK/DT EQUATION

APPENDIX F: BOLTZMANN TRANSPORT EQUATION

Particle Diffusion

Classical Distribution

Fermi-Dirac Distribution

Electrical Conductivity

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

Lagrangian Equations of Motion

Derivation of the Hamiltonian

Field Momentum

Gauge Transformation

Gauge in the London Equation

APPENDIX H: COOPER PAIRS

APPENDIX I: GINZBURG-lANDAU EQUATION

APPENDIX J: ELECTRON-PHONON COLLISIONS

INDEX