Solid State Physics: An Introduction to Theory

✍ Scribed by Joginder Singh Galsin

• Publisher: Academic Press
• Year: 2019
• Tongue: English
• Leaves: 636
• Edition: 1
• Category: Library

✦ Synopsis

Solid State Physics: An Introduction to Theory presents an intermediate quantum approach to the properties of solids. Through this lens, the text explores different properties, such as lattice, electronic, elastic, thermal, dielectric, magnetic, semiconducting, superconducting and optical and transport properties, along with the structure of crystalline solids. The work presents the general theory for most of the properties of crystalline solids, along with the results for one-, two- and three-dimensional solids in particular cases. It also includes a brief description of emerging topics, such as the quantum hall effect and high superconductivity.

Building from fundamental principles and requiring only a minimal mathematical background, the book includes illustrative images and solved problems in all chapters to support student understanding.

✦ Table of Contents

Cover
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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