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More About This Textbook
Overview
In recent years, researchers have increasingly recognized the dominant role of the local atomic environment in controlling the electronic structure and properties of materials. This recognition has spawned the "real-space" approach that provides a coherent framework for the study of perfect and defective crystals and non-crystalline materials. In addition to presenting these ideas, this text details the reciprocal-space approach—exemplified in band theory—and draws powerful links between the two approaches. The book includes illustrations and examples of many up-to-date calculations based on density functional theory that are used today as predictive tools in materials science. Throughout the book, the mathematical complexity is kept to a minimum, while comprehensive problem sets allow readers to master the fundamental concepts. The text provides for students in materials science, physics, and chemistry a unique introduction to predictive modelling of the electronic structure and properties in today's materials.
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Table of Contents
1. Introduction
1.1. Aims of the Book
1.2. The "Universal" Equation of State for Metals
1.3. Structure Maps
1.4. The Hydrogen Atom
1.5. Metals, Semiconductors, and Insulators
2. The Diatomic Molecule
2.1. The Review of Bras, Kets and All That
2.2. A Homonuclear Diatomic Molecule: The Hydrogen Molecule
2.3. A Heteronuclear Diatomic Molecule
2.4. Electronegativity
2.5. Bond Energy and Bond Order
3. From the Finite to the Infinite
3.1. Chain Molecules and K-Space
3.2. Bond Order in an Infinite System
3.3. The Density of States: Total and Local
3.4. Band Energy and Bond Energy
3.5. The Moments Theorem
4. Into Two and Three Dimensions
4.1. Solids as Giant Molecules
4.2. The Square Lattice
4.3. The Simple Cubic Lattice
4.4. Brillouin Zones for the B.C.C. and F.C.C. Lattices
4.5. Equation of Motion of an Electron under an External Force
4.6. Holes
4.7. The Fermi Surface
4.8. The Density of States in Two-dimensional and Three-dimensional crystals
4.9. The Density Matrix, Bond Order, and Bond Energy
4.10. The Moments Theorem Applied to Two-dimensional and Three-dimensional Crystals
5. Band Gaps: Origins and Consequences
5.1. Band Gaps
5.2. Infinite Linear Chain with Two S-States per Atom
5.3. Energy Gap in a Binary AB Alloy Linear Chain Crystal
5.4. Peierls Distortions
5.5. Metals, Insulators, and the Metallic Bond
6. S-P Bonding—A Case Study in Silicon
6.1. S-P Bonding
6.2. S-P bonding between Two Silicon Atoms
6.3. Angular Dependence of S-P and P-P Hopping Integrals
6.4. SP Hybrids
6.5. Simple Models of the Electronic Structure of Tetrahedrally Bonded Silicon
6.6. The Band Structure of Silicon in a Minimal Atomic Basis Set
6.7. The Bond Order and Bond Energy in Silicon in a Minimal Atomic Basis Set
7. Free Electron Theory
7.1. Introduction to Free Electron Theory
7.2. The Free Electron Approximation
7.3. Electronics in a Box
7.4. Density of States
7.5. Free Electron Bands and LCAO Bands
7.6. The Nearly Free Electron Model
8. Properties of Free Electron Metals
8.1. Fermi-Dirac Statistics
8.2. Contact Potential
8.3. Electronic Specific Heat
8.4. Electrical Conductivity of Metals
8.5. Thermal Conductivity of Metals
8.6. The Wiedemann-Franz Ratio
8.7. The Hall Effect
8.8. The Cohesive Energy of Simple Metals and Its Volume Dependence
8.9. Structural Energy Differences
9. The Transition Metals
9.1. The Transition Metals
9.2. The Friedel Model
9.3. The Friedel Model in the Second Moment Approximation
9.4. Finnis-Sinclair Potentials for Computer Simulations of Transition Metals
9.5. D-D Bonding
9.6. Changes in Crystal Structure Across the Transition Metal Series
9.7. Bonding in Metallic Alloys
10. Structural Stability of Compounds
10.1. Hybridization and Crystal Structural Stability
10.2. Atomic Factors Influencing the Structures of Compounds
10.3. Structure Maps
10.4. Applications of Structure Maps
11. Introduction to Modern Quantitative Theory
11.1. Modern Quantitative Predictions of Crystal Structure and Stability
11.2. The Born-Oppenheimer Approximation
11.3. Outline of Density Functional Theory
11.4. Applications
12. Where Band Theory Breaks Down
12.1. Electrons in Non-crystalline Materials
12.2. The Energy Gap in Amorphous Silicon
12.3. Electron Localization
12.4. Polarons
12.5. Anderson Localization
12.6. Metal-Insulator Transitions, Or What is a Metal?
Set Problems