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Band Theory of Metals
The Elements
- 1st Edition - January 1, 1970
- Author: Simon L. Altmann
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 5 8 9 9 - 0
Band Theory of Metals: The Elements focuses on the band theory of solids. The book first discusses revision of quantum mechanics. Topics include Heisenberg’s uncertainty… Read more
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Request a sales quoteBand Theory of Metals: The Elements focuses on the band theory of solids. The book first discusses revision of quantum mechanics. Topics include Heisenberg’s uncertainty principle, normalization, stationary states, wave and group velocities, mean values, and variational method. The text takes a look at the free-electron theory of metals, including heat capacities, density of states, Fermi energy, core and metal electrons, and eigenfunctions in three dimensions. The book also reviews the effects of crystal fields in one dimension. The eigenfunctions of the translations; symmetry operations of the linear chain; use of translational symmetry; degeneracy of the Bloch functions; and effects of inversion are described. The text also focuses on Bloch functions and Brillouin zones in three dimensions. Concerns include symmetry in the reciprocal space; scalar product and reciprocal vectors; Brillouin zones of higher order; and conditions for the faces of the Brillouin zones. The book is a good source of data for readers interested in the band theory of solids.
Preface
How to Use this Book
Cross-References and Formulae
Heading Markings
Bullets
Exercises and Problems
Proofs
Notation
Warning. Asterisks
1. Revision of Quantum Mechanics
1. Basic Experimental Facts
2. Heisenberg's Uncertainty Principle
3. The State Function
4. Stationary States
5. Normalization
6. Operators and Eigenvalue Equations
7. The operator P
8. The operator x
9. The Hamiltonian and the Schrödinger Equation
10. Boundary conditions: Quantization
11. Degeneracy
12. Commuting Operators
13. Physical Meaning of Degeneracy
14. Exercise: Electron in a Box
15. Time Dependence
16. Wave and Group Velocities
17. Mean Values
18. The Variational Method
19. Exercises: The Hermitian Property. Orthogonality
2. Free-electron Theory of Metals
1. The One-Particle Approximation
2. Core and Metal Electrons. Pauli Principle
3. The Free-Electron Model
4. Periodic (Born-von Kármán) Boundary Conditions
5. The Wave Function: Normalization
6. The Eigenfunctions in Three Dimensions
7. Degeneracy of the Levels
8. The Fermi energy
9. The Density of States
10. Soft X-rays
11. Heat Capacities
3. The Effect of the Crystal Field in One Dimension: Bloch Functions
1. The Use of Translational Symmetry
1. Symmetry Operations
2. Symmetry Operators
3. The Eigenfunctions of the Symmetry Operators are Eigenfunctions of the Hamiltonian
4. S-Degeneracy
5. The Importance of Continuity
2. S-Degeneracy of the Eigenfunctions of the Translations
3. Symmetry Operations of the Linear Chain: Translations and Inversion
4. The Eigenfunctions of the Translations
1. Bloch Functions
2. Continuity: Bands
5. Quantization of k
6. Physical Considerations
1. The Weak-Field Limit
2. The Free-Atoms Limit
3. Energy Gaps
7. The Number of Eigenfunctions
1. The Number of Different Eigenvalues is N
2. Periodicity in k
3. The Number of Bloch Functions is N
8. The Effect of the Inversion
1. The Inversion Changes k Into —k: Proof
2. The Role of the Bloch Functions
9. Degeneracy of the Bloch Functions
10. Periodicity of the Energy
11. Change of Interval
12. Further Properties of the E(k) Curve
13. Extended and Reduced Band Schemes: Brillouin Zones
14. Band Crossings
15. Filling in of the Energy States
16. Propagation of an Electron in the Lattice: The Periodically Repeated Scheme
17. Bragg Reflections
18. Conductors and Insulators
19. Effective Mass. Holes
20. The Wave Functions
21. Lattice With Basis
22. Exercise: The Energy Gap
1. Method
2. Remarks
23. The Nearly Free-Electron Approximation
24. Fourier Coefficients of the Potential
4. Bloch Functions and Brillouin Zones in Three Dimensions
1. Crystal Periodicity
1. Primitive and Unit Cells
2. Bloch Functions in Three Dimensions
3. Scalar Product and Reciprocal Vectors
4. Reciprocal Lattice
5. The Bloch Functions in Vector Notation
6. The Wave Vector
7. Symmetry in the Reciprocal Space
8. E(k) = E{—k): Complex Conjugation
9. The First Brillouin Zone
10. Brillouin Zones of Higher Order
11. Number of States in the Brillouin Zone
12. Conditions for the Faces of the Brillouin Zones
13. Symmetry Elements and the Faces of the Brillouin Zone
14. Energy Contours, Filling-In of Zones, and Fermi Surfaces
15. Bands, Overlaps, Conductors, and Insulators
16. Velocity
17. The Brillouin Zone for Cubic Lattices
18. Hexagonal Close-Packed Lattice. Jones Zones
19. Sticking Together of Bands in the H.C.P. Lattice
20. Fourier Series in Three Dimensions
21. Lattice With Basis. Structure Factor
22. The Nearly Free-Electron Approximation
5. Some Applications of Brillouin Zone Theory
1. The Jones Theory of the Hume-Rothery Rules
2. Further Theories of Phase Stability
3. Peaks in the Density of States Curves
4. Effect of t Fermi Energy On Lattice Parameters
6. The Calculation of Band Structures and Fermi Surfaces
1. The Problem and the Basic Equations
2. The Tight-Binding Method
3. The Nearly Free-Electron and Orthogonalized Plane Waves Method
4. The Cellular Method
5. The Augmented Plane Wave Method (APW)
6. Density of States and Fermi Surfaces
7. Comparison With Experiment: Heat Capacities and de Haas-Van
8. The Band Structure and Fermi Surface of Copper
General References
Index
- No. of pages: 264
- Language: English
- Edition: 1
- Published: January 1, 1970
- Imprint: Pergamon
- eBook ISBN: 9781483158990
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