Altmann Band Theory of Metals

The Elements
1. Auflage 2013
ISBN: 978-1-4831-5899-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 264 Seiten, Web PDF

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 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.

Autoren/Hrsg.

Altmann, Simon L.

Inhaltsverzeichnis

1;Front Cover;1
2;Band Theory of Metals: The Elements;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;10
6;How to Use this Book;14
7;CROSS-REFERENCES AND FORMULAE;14
8;HEADING MARKINGS;14
9;BULLETS;14
10;EXERCISES AND PROBLEMS;14
11;PROOFS;15
12;NOTATION;15
13;WARNING. ASTERISKS;15
14;CHAPTER 1. Revision of Quantum Mechanics;16
14.1;1. Basic experimental facts;16
14.2;2. Heisenberg's uncertainty principle;17
14.3;3. The state function;19
14.4;4. Stationary states;23
14.5;5. Normalization;23
14.6;6. Operators and eigenvalue equations;24
14.7;7. The operator p;27
14.8;8. The operator x;29
14.9;9. The Hamiltonian and the Schrödinger equation;30
14.10;10. Boundary conditions: quantization;31
14.11;11. Degeneracy;32
14.12;12. Commuting operators;33
14.13;13. Physical meaning of degeneracy;35
14.14;14. Exercise: electron in a box;36
14.15;15. Time dependence;38
14.16;16. Wave and group velocities;39
14.17;17. Mean values;43
14.18;18. The variational method;44
14.19;19. Exercises: the hermitian property. Orthogonality;48
15;CHAPTER 2. Free-electron Theory of Metals;52
15.1;1. The one-particle approximation;52
15.2;2. Core and metal electrons. Pauli principle;56
15.3;3. The free-electron model;59
15.4;4. Periodic (Born-von Kármán) boundary conditions;59
15.5;5. The wave function: normalization;61
15.6;6. The eigenfunctions in three dimensions;63
15.7;7. Degeneracy of the levels;64
15.8;8. The Fermi energy;67
15.9;9. The density of states;69
15.10;10. Soft X-rays;72
15.11;11. Heat capacities;75
16;CHAPTER 3. The Effect of the Crystal Field in One Dimension: Bloch Functions;77
16.1;1. The use of translational symmetry;77
16.2;2. S-degeneracy of the eigenfunctions of the translations;83
16.3;3. Symmetry operations of the linear chain: translations and inversion;86
16.4;4. The eigenfunctions of the translations;89
16.5;5. Quantization of k;92
16.6;6. Physical considerations;92
16.7;7. The number of eigenfunctions;97
16.8;8. The effect of the inversion;100
16.9;9. Degeneracy of the Bloch functions;101
16.10;10. Periodicity of the energy;103
16.11;11. Change of interval;104
16.12;12. Further properties of the E(k) curve;105
16.13;13. Extended and reduced band schemes: Brillouin zones;107
16.14;14. Band crossings;112
16.15;15. Filling in of the energy states;113
16.16;16. Propagation of an electron in the lattice: the periodically repeated scheme;115
16.17;17. Bragg reflections;119
16.18;18. Conductors and insulators;120
16.19;19. Effective mass. Holes;122
16.20;20. The wave functions;123
16.21;21. Lattice with basis;128
16.22;22. Exercise: the energy gap;130
16.23;23· The nearly free-electron approximation;136
16.24;24. Fourier coefficients of the potential;138
17;CHAPTER 4. Bloch Functions and Brillouin Zones in Three Dimensions;143
17.1;1. Crystal periodicity;143
17.2;2. Bloch functions in three dimensions;145
17.3;3. Scalar product and reciprocal vectors;147
17.4;4. Reciprocal lattice;151
17.5;5. The Bloch functions in vector notation;156
17.6;6. The wave vector;158
17.7;7. Symmetry in the reciprocal space;159
17.8;8. E(K) = E(–K): complex conjugation;162
17.9;9. The first Brillouin zone;165
17.10;10. Brillouin zones of higher order;167
17.11;11. Number of states in the Brillouin zone;170
17.12;12. Conditions for the faces of the Brillouin zones;171
17.13;13. Symmetry elements and the faces of the Brillouin zone;175
17.14;14. Energy contours, filling-in of zones, and Fermi surfaces;177
17.15;15. Bands, overlaps, conductors, and insulators;185
17.16;16. Velocity;188
17.17;17. The Brillouin zone for cubic lattices;189
17.18;18. Hexagonal close-packed lattice. Jones zones;196
17.19;19. Sticking together of bands in the h.c.p. lattice;199
17.20;20. Fourier series in three dimensions;204
17.21;21. Lattice with basis. Structure factor;206
17.22;22. The nearly free-electron approximation;208
18;CHAPTER 5. Some Applications of Brillouin Zone Theory;215
18.1;1. The Jones theory of the Hume-Rothery rules;215
18.2;2. Further theories of phase stability;219
18.3;3. Peaks in the density of states curves;221
18.4;4. Effect of the Fermi energy on lattice parameters;224
19;CHAPTER 6. The Calculation of Band Structures and Fermi Surfaces;226
19.1;1. The problem and the basic equations;226
19.2;2. The tight-binding method;228
19.3;3. The nearly free-electron and orthogonalized plane waves method;238
19.4;4. The cellular method;240
19.5;5. The augmented plane wave method (APW);245
19.6;6. Density of states and Fermi surfaces;246
19.7;7. Comparison with experiment: heat capacities and de Haas–van Alphen effect;247
19.8;8. The band structure and Fermi surface of copper;250
20;General References;259
21;Index;260