Solid State Physics: An Introduction to Theory

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Solid State Physics:

An Introduction to Theory
Copyright
Dedication
About the Author
Preface
1
Crystal Structure of Solids
	Close Packing of Atoms in Solids
	Crystal Lattice and Basis
	Periodicities in Crystalline Solids
		Structural Periodicity
			Translational Symmetry
			Near Neighbors
			Primitive Unit Cell
		Rotational Symmetry
			Space Group
			Allowed Rotations in a Crystal
	One-Dimensional Crystals
	Two-Dimensional Crystals
	Three-Dimensional Crystals
	Simple Crystal Structures
		Simple Cubic Structure
		Body-Centered Cubic Structure
		Face-Centered Cubic Structure
		Hexagonal Structure
		Hexagonal Close-packed Structure
	Miller Indices
	Other Structures
		Zinc Sulfide Structure
		Diamond Structure
		Wurtzite Structure
		Perovskite Structure
		High-Tc Superconductors
	Quasicrystals
	Suggested Reading
2
Crystal Structure in Reciprocal Space
	X-Ray Diffraction
		Braggs Law of X-Ray Diffraction
	Electron Diffraction
	Neutron Diffraction
	Laue Scattering Theory
	Reciprocal Lattice
		Periodicity of Electron Density
		Periodicity of Atomic Density
			Monatomic Linear Lattice
			Two-Dimensional Square Lattice
			Three-Dimensional Cubic Lattice
	Primitive Cell in Reciprocal Space
		Linear Monatomic Lattice
		Square Lattice
		sc Lattice
		fcc Crystal Structure
		Hexagonal Crystal Structure
	Importance of Reciprocal Space and BZs
		Bragg Reflection
		Significant Wave Vectors
		Construction of Reciprocal Lattice
	Atomic Scattering Factor
	Geometrical Structure Factor
		sc Crystal Structure
		fcc Crystal Structure
		bcc Crystal Structure
	References
	Suggested Reading
3
Approximations in the Study of Solids
	Separation of Ion-Core and Valence Electrons
	Rigid Ion-Core Approximation
	Self-Consistent Potential Approximation
	The Born-Oppenheimer Approximation
	One-Electron Approximation
	Electron Exchange and Correlation Interactions
		Electron Exchange Interactions
			Intra-Atomic Exchange Interactions
			Interatomic Exchange Interactions
				Direct Interatomic Exchange Interaction
				Indirect Interatomic Exchange Interaction
			Conduction Electron-Conduction Electron Exchange Interaction
		Electron Correlation Interactions
			Coulomb Correlations
			Parallel-Spin Correlations
			Antiparallel-Spin Correlations
	References
	Suggested Reading
4
Bonding in Solids
	Interactions Between Atoms
	Cohesive Energy
	Equilibrium Distance
	Bulk Modulus and Compressibility
	Inert Gas Crystals
		Equilibrium Lattice Constant
		Cohesive Energy of Inert Gas Crystals
		Bulk Modulus
	Ionic Bonding
		Ionic-Bond Energy
		Lattice Energy
		Difference Between Bond Energy, Cohesive Energy, and Lattice Energy
		Bulk Modulus of Ionic Crystals
		Exponential Repulsive Potential
		Calculation of the Madelung Constant
			First Method
			Second Method
			Madelung Constant for NaCl Structure
	Covalent Bond
	Mixed Bond
	Metallic Bond
	Hydrogen Bond
	Suggested Reading
5
Elastic Properties of Solids
	Strain Tensor
	Dilation
	Stress Tensor
	Elastic Constants of Solids
	Elastic Energy Density
	Elastic Constants in Cubic Solids
	Elastic Energy Density in Cubic Solids
	Bulk Modulus in Cubic Solids
	Elastic Waves in Cubic Solids
		Elastic Waves in the [100] Direction
		Elastic Waves in the [110] Direction
		Elastic Waves in the [111] Direction
	Isotropic Elasticity
	Experimental Measurement of Elastic Constants
	Suggested Reading
6
Lattice Vibrations-1
	Vibrations in a Homogeneous Elastic Medium
	Interatomic Potential in Solids
		Square-Well Potential
		Harmonic Interaction Potential
	Lattice Vibrations in a Discrete One-Dimensional Lattice
		Monatomic Linear Lattice
		Diatomic Linear Lattice
	Excitation of Ionic Lattice in Infrared Region
7
Lattice Vibrations-2
	Equation of Motion of the Lattice
		Restrictions on Atomic Force Constants
	Normal Coordinate Transformation
	Properties of Dynamical Matrix and Eigenvectors
	Quantization of Lattice Hamiltonian
	Simple Applications
		Linear Monatomic Lattice
		Linear Diatomic Lattice
		Simple Cubic Lattice
	Experimental Determination of Phonon Frequencies
		Neutron Diffraction Technique
			Time-of-Flight Method
			Constant Momentum Method
	References
	Suggested Reading
	Further Reading
8
Specific Heat of Solids
	Experimental Facts
	Thermodynamical Definition
	Phase Space
	Classical Theories of Lattice Specific Heat
		Free Atom Model
			One-Dimensional Solid
			Two-Dimensional Solid
			Three-Dimensional Solid
		Fixed Classical Harmonic Oscillator Model
			One-Dimensional Solid
			Three-Dimensional Solid
	Quantum Mechanical Theories
		Einstein Theory of Specific Heat
		Debye Theory of Specific Heat
			Linear Monatomic Lattice
			Two-Dimensional Lattice
			Three-Dimensional Lattice
	Effect of Electrons on Specific Heat
	Ideal Phonon Gas
	Interacting Phonon Gas
	Thermal Expansion of Solids
	Thermal Conductivity of Solids
		Thermal Conductivity for an Ideal Gas of Atoms
		Thermal Conductivity in Insulators and Dielectrics
		Thermal Conductivity of Metals
	Further Reading
9
Free-Electron Theory of Metals
	Free-Electron Approximation
	Three-Dimensional Free-Electron Gas
	Two-Dimensional Free-Electron Gas
	Cohesive Energy and Interatomic Spacing of Ideal Metal
	The Fermi-Dirac Distribution Function
	Specific Heat of Electron Gas
		One-Dimensional Free-Electron Gas
		Two-Dimensional Free-Electron Gas
		Three-Dimensional Free-Electron Gas
	Paramagnetic Susceptibility of Free-Electron Gas
		One-Dimensional Free-Electron Gas
		Two-Dimensional Free-Electron Gas
		Three-Dimensional Free-Electron Gas
	Classical Spin Susceptibility
	Reference
	Suggested Reading
10
Electrons in Electric and Magnetic Fields
	Equation of Motion
	Free Electrons in a Static Electric Field
	Free Electrons in a Static Magnetic Field
	Electrons in Static Electric and Magnetic Fields
	The Hall Effect in Metals
	Free Electrons in an Alternating Electric Field
	Quantum Mechanical Theory of Electrons in Static Electric and Magnetic Fields
	Quantum Hall Effect
		Two-Dimensional Electron System
		Classical Theory of Conductivity in a Magnetic Field
		Quantum Theory of a 2D Free-Electron Gas in a Magnetic Field
		Experimental Setup for QHE
			Silicon MOSFETs
			Semiconductor Heterojunctions
		Integral Quantum Hall Effect
		Fractional Quantum Hall Effect
	Wiedemann-Franz-Lorentz Law
	References
	Suggested Reading
11
Transport Phenomena
	Velocity Distribution Function
	Electric Current and Electrical Conductivity
		Electrostatic Interactions
		Collision Interactions
	Heat Current and Thermal Conductivity
	The Boltzmann Transport Equation
		Classical Formulation
		Quantum Formulation
	Linearization of Boltzmann Equation
	Electrical Conductivity
		Classical Theory
		Quantum Theory
	Thermal Conductivity
		Classical Theory
		Quantum Theory
	Hall Effect
	Mobility of Charge Carriers in Solids
	Suggested Reading
12
Energy Bands in Crystalline Solids
	Bloch Theorem
		One-Dimensional Solid
		Three-dimensional Solid
	The Kronig-Penney Model
	Nearly Free-Electron Theory
		Application to One-Dimensional Solid
	Different Energy Zone Schemes
		Extended Zone Scheme
		Periodic Zone Scheme
		Reduced Zone Scheme
	Tight-Binding Theory
		Linear Monatomic Lattice
		Two-Dimensional Square Lattice
		Three-Dimensional sc Lattice
	Orthogonalized Plane Wave (OPW) Method
	Augmented Plane Wave (APW) Method
	Dynamics of Electrons in Energy Bands
		Behavior of Electrons in Free-Electron Theory
		Behavior of Electrons in Tight-Binding Approximation
	Distinction Between Metals, Insulators, and Semiconductors
	References
	Suggested Reading
13
The Fermi Surfaces
	Constant Energy Surfaces
	The Fermi Surfaces
	The Fermi Surface in the Free-Electron Approximation
		Type I Fermi Surface
		Type II Fermi Surface
			Electron Orbits
		Type III Fermi Surface
	Harrisons Construction of the Fermi Surface
	Nearly Free-Electron Approximation
	The Actual Fermi Surfaces
		Monovalent Metals
		Polyvalent Metals
	Experimental Methods in Fermi Surface Studies
		de Haas-van Alphen Effect
		Cyclotron Resonance
	References
	Suggested Reading
	Further Reading
14
Semiconductors
	Intrinsic Semiconductors
	Extrinsic Semiconductors
		n-Type Semiconductors
		p-Type Semiconductors
	Ionization Energy of Impurity
	Carrier Mobility
	Theory of Intrinsic Semiconductors
		Concentration of Charge Carriers
	Model for Extrinsic Semiconductors
		n-Type Semiconductors
		p-Type Semiconductors
	Effect of Temperature on Carrier Density
	Temperature Dependence of Mobility
	The Hall Effect
	Electrical Conductivity in Semiconductors
		Intrinsic Semiconductors
		Extrinsic Semiconductors
	Nondegenerate Semiconductors
	Degenerate Semiconductors
	Compensated Semiconductors
	Suggested Reading
15
Dielectric Properties of Nonconducting Solids
	Nonpolar Solids
	Polar Solids
	Electric Dipole Moment
	Macroscopic Electric Field
	Potential due to an Electric Dipole
	Depolarization Field due to Cuboid
	Polarization
	Dielectric Matrix
	Experimental Measurement of Dielectric Constant
	Local Electric Field at an Atom
	Polarizability
	Polarization
	Types of Polarizabilities
	Variation of Polarizability With Frequency
	Orientational Polarizability
	Classical Theory of Electronic Polarizability
	Suggested Reading
16
Ferroelectric Solids
	Classification of Ferroelectric Solids
		Tartrate Group
		Dihydrophosphates and Arsenates
		Perovskite Structure
	Theories of Ferroelectricity
		Atomic Models
			Electric Dipole Theory
			Polarization Catastrophe
	Thermodynamics of Ferroelectric Solids
		Second-Order Transition in Ferroelectric Solids
		First-Order Transition in Ferroelectric Solids
	Ferroelectric Domains
	Suggested Reading
17
Optical Properties of Solids
	Plane Waves in a Nonconducting Medium
	Reflection and Refraction at a Plane Interface
		Kinematic Properties
		Dynamic Properties
			Electric Field Perpendicular to Plane of Incidence
	Electromagnetic Waves in a Conducting Medium
	Reflectivity From Metallic Solids
	Reflectivity and Conductivity
	Kramers-Kronig Relations
	Optical Models
		Drude Model
		Lorentz Model for Insulators
	Lyddane-Sachs-Teller Relation
	Suggested Reading
18
Magnetism
	Atomic Magnetic Dipole Moment
		Orbital Magnetic Moment
		Spin Magnetic Moment
		Nuclear Magnetic Moment
	Magnetization
	Magnetic Induction
	Potential Energy of Magnetic Dipole Moment
	Larmor Precession
	Quantum Theory of Diamagnetism
	Paramagnetism
		Classical Theory of Paramagnetism
		Quantum Theory of Paramagnetism
	Hunds Rule
		Applications of Hunds Rule
			Rare-Earth Group
			Iron Group
	Crystal Field Splitting
		Quenching of Orbital Angular Momentum
	Suggested Reading
19
Ferromagnetism
	Weiss Molecular Field Theory
	Classical Theory of Ferromagnetism
	Quantum Theory of Ferromagnetism
	Comparison of Weiss Theory With Experiment
	Heisenberg Theory of Ferromagnetism
	Spin Waves
		Bloch Theory of Spin Waves
		Magnons in Monatomic Linear Lattice
		Magnons in Square Lattice
		Magnons in sc Lattice
	Quantization of Spin Waves
	Thermal Excitation of Magnons
	Hysteresis Curve
	Suggested Reading
20
Antiferromagnetism and Ferrimagnetism
	Antiferromagnetism
		Two-Sublattice Model
			Susceptibility for TTN
			Susceptibility for TTN
		Spin Waves in Antiferromagnetism
			Linear Monatomic Lattice
			Square Lattice
	Ferrimagnetism
		Structure of Ferrites
		Two-Sublattice Model
	Reference
	Suggested Reading
21
Magnetic Resonance
	Nuclear Magnetic Moment
	Zeeman Effect
	Relaxation Phenomena
		Spin-Lattice Relaxation
		Spin-Spin Relaxation
	Equation of Motion
	Magnetic Resonance in the Absence of Relaxation Phenomena
	Bloch Equations
		Free Precession in Static Magnetic Field
	Magnetic Broadening of Resonance Lines
	Effect of Molecular Motion on Resonance
	Electron Spin Resonance
	Hyperfine Interactions
	Knight Shift
	Quadrupole Interactions in Magnetic Resonance
		Nuclear Quadrupole Resonance
	Ferromagnetic Resonance
	Spin Wave Resonance
	Antiferromagnetic Resonance
	Reference
	Suggested Reading
22
Superconductivity
	Experimental Survey
		Electrical Properties
		Magnetic Properties
		Thermal Properties
			Entropy
			Specific Heat
		Isotopic Effect
	Occurrence of Superconductivity
	Theoretical Aspects of Superconductivity
		Failure of Ohms Law in Superconductors
		London Theory
		Penetration Depth
		Coherence Length
		Destruction of Superconductivity by Magnetic Field
		Stabilization Energy
		Classification of Superconductors
		Persistent Currents
		Thermodynamics of Superconductors
			Entropy
				Alternate Proof
			Specific Heat
			First-Order and Second-Order Phase Transitions
		Bardeen-Cooper-Schrieffer (BCS) Theory
			Electron-Phonon Interactions
			Cooper Pairs
			Generalization of Cooper Pair Formation
			The Energy Gap
		Criterion for the Existence of Superconductivity
		Why Do Magnetic Impurities Lower Tc?
	Superconducting Quantum Tunneling
		Single-Electron Superconducting Tunneling
			MOM Tunneling Junction
			MOS Tunneling Junction
			SOS Tunneling Junction
		Josephson Tunneling
	High-Tc Superconductivity
		Chevrel Phases and Superconductivity
		Perovskite Superconductivity
		Cu-Oxide Superconductors
		A2BX4 Superconductors
		Quaternary Copper Oxides
		Bismates and Thallates
	References
	Suggested Reading
23
Defects in Crystalline Solids
	Point Defects in Solids
		Solid Solutions
			Types of Solid Solutions
		Types of Point Defects
			Substitutional Point Defects
			Vacancies
			Interstitial Point Defects
			The Frenkel Defects
			Color Centers
		Excitons
			Types of Excitons
				Frenkel Excitons
				Wannier-Mott Excitons
				Atomic and Molecular Excitons
		Statistical Distribution of Point Defects
			Substitutional Point Defects
			Interstitial Point Defects
			The Frenkel Defects
	Dislocations
		Plastic Deformation of Crystals
		Definition of Dislocation
		Force Acting on Dislocations
		Critical Shear Stress
		Dislocation Density and Shear Strain
		Types of Dislocations
			Edge Dislocations
			Screw Dislocations
			Mixed Dislocations
		Conservation of the Burgers Vector
		Dislocation Energy
		Growth of Slips: The Frank-Read Source
		Grain Boundary
	Suggested Reading
24
Amorphous Solids and Liquid Crystals
	Structure of Amorphous Solids
		Continuous Random Network Model
		Random Close Packing
		Long-Chain Molecular Compounds
		Copolymers
		Plasticizers
		Elastomers
	Characteristics of Amorphous Solids
	Applications of Amorphous Solids
	Liquid Crystals
		The Building Blocks
			Small Organic Molecules
			Long Helical Rods
			Associated Structures
		Nematics and Cholesterics
			Proper Nematics
			Cholesterics
		Smectics
			Smectic A
			Smectic C
			Smectic B
		Long-Range Order in a System of Long Rods
		Uses of Liquid Crystals
			Temperature Sensitivity
			Optical Properties
			Membrane Biophysics
			Physics of Detergents
	Suggested Reading
25
Physics of Nanomaterials
	Reduction in Dimensionality
		Quantum Well
		Quantum Wire
		Quantum Dot
		Quantum Ring
	Quantum Tunneling
	Nanoparticles
		Magnetic Nanoparticles
		Structure of Nanoparticles
		Methods of Synthesis of Nanoparticles
			Laser Beam Methods
			Thermal Decomposition
			Chemical Methods
			Self-Assembly Techniques
		Nanostructured Materials
			Crystalline Nanostructured Materials
			Amorphous Nanostructured Materials
		Computer Simulation Technique
	Nanomaterials of Carbon
		Nanoparticles of Carbon
			Structure of C60 Molecule
			Structure of C70 Molecule
			Crystalline C60 Solid
			Alkali-Doped Crystalline C60 Solid
		Carbon Nanotubes
	Microscopes Used for Nanomaterials
		Scanning Tunneling Microscope
		Atomic Force Microscope
			Contact Mode
			Dynamic Mode
				Amplitude Modulation
				Frequency Modulation
		Magnetic Force Microscope
	Applications
		Basic Sciences
		Nanoelectronics
		Smart Materials
		Nanocomposite Materials
		Nanopharmaceuticals
	Future Thrust
	References
	Suggested Reading
Appendix A
	Van der Waals-London Interaction
	Repulsive Interaction
Appendix B
Appendix C
Appendix D: Bose-Einstein Statistics
Appendix E: Density of Phonon States
	Three-Dimensional Solid
	Two-Dimensional Solid
Appendix F: Density of Electron States
	Three-Dimensional Solid
	Two-Dimensional Solid
Appendix G: Mean Displacement
Appendix H
	Bound States for One-Dimensional Free-Electron Gas
	Bound States for Two- and Three-Dimensional Free-Electron Gas
Appendix I: The Fermi Distribution Function Integral
Appendix J: Electron Motion in Magnetic Field
Appendix K
	One-Dimensional Solid
	Three-Dimensional Solid
Appendix L: Atomic Magnetic Dipole Moment
Appendix M: Larmor Precession
Further Reading
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
	X
	Z
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