In this book the behavior of electrons in a crystal is described in terms of the one-electron model. Clearly, such a system would be best approached by a many-body formalism but because of mathe matical complexities only a very few real problems can be solved in this way. In the one-electron model, each electron is considered separately as moving in the averaged field of the nuclei and all the other electrons. The resulting picture is simpler conceptually, much more tractable mathematically and, at the same time, is quite comprehensive, which makes the one-electron model the most popu lar approach currently in use in solid state physics.
Preface 7
Introduction 11
Chapter 1. Principles of the one-electron theory
Part 1 Theoretical principles of the pseudopotential method
Chapter 2. Scattering theory for “solid-state people”
2.1. Mathematical formalism 23
2.2. Scattering on an isolated potential 31
2.3. Pseudism and scattering 46
2.4. Bound states, pseudopotentials and the convergence of series 54
2.5. Scattering theory and potential form factors 61
Chapter 3. Theory of potential
3.1. Potential seen by an atomic electron 69
3.2. Dielectric screening 83
3.3. The self-consistency of pseudopotential and additive screening 99
3.4. Muffin-tin potential 107
3.5. Average value of the screened potential 124
Chapter 4. Theory of pseudopotential form factors
4.1. Nonlocality, the energy dependence of form factors and perturbation theory 132
4.2. The OPW formfactor 144
4.3. Phase-shift form factors 157
4.4. Effective medium and pseudopotential form factors 173
Chapter 5. Pseudism and the secular equations of band theory
5.1. The Green’s function (or KKR) method 181
5.2. Pseudopotential secular equations 196
Part 2 The use of pseudopotential theory for crystal-structure calculations
Chapter 6. Formalism of crystal-structure energy calculations
6.1. Basic assumptions 205
6.2. Band structure energy of pure metals and binary alloys 205
6.3. Electrostatic energy 223
6.4. The total internal energy of an alloy: second-order perturbation theory and the locality approximation 227
6.5. Higher-order perturbation analysis 232
6.6. OPW nonlocal alloy theory 236
Chapter 7. Pseudopotential theory of alloys. Structure stability application
7.1. Phase boundaries in terms of pseudopotential theory 241
7.2. Ordered phases, their structures, and existence conditions 245
7.3. Short-range order problems 256
7.4. Crystal structure stability in the OPW approach 261
Chapter 8. Pseudopotential theory and imperfections in crystals
8.1. Introductory remarks 267
8.2. Crystal lattice vibrations 267 8.3. Static imperfections 279
Chapter 9. Principles of pseudopotential calculations of the properties of metals
9.1. Genera 287
9.2. Calculation of the atomic properties of crystalline metals and alloys 287
9.3. Transport properties of noncrystalline metals and alloys 297
References 317
Index 331