The connection between a quantum behavior of the structure elements of a substance and the parameters that determine the macroscopic behavior of materials has a major influence on the properties exhibited by different solids. Although quantum theory and engineering should complement each other, this is not always the case. This book aims to demonstrate how the properties of materials can be derived and predicted proceeding from the features of their structural elements, generally electrons. In a sense, electronic structure forms the glue holding solids as whole, and it is central in determining structural, mechanical, chemical, electrical, magnetic and vibrational properties. The main part of the book is devoted an overview of the fundamentals of the density functional theory and its applications to computational solid state physics and chemistry. The author shows in detail the technique of construction of models and the methods of their computer simulation. He considers physical and chemical fundamentals of interatomic bonding in solids and analyzes the predicted theoretical outcome in comparison with experimental data. This is applying the first–principle simulation methods so as to predict the properties of transition metals, semiconductors, oxides, solid solutions, molecular and ionic crystals. Unique in presenting are novel theories of creep and fatigue that help to anticipate – and prevent – possible fatal material failures. As a result, users gain the knowledge and tools to simulate material properties and to design materials with desired characteristics. Due to the interdisciplinary nature of the book, it is suitable for a variety of markets from students and lectures to engineers and researchers. INDICE: Preface XI 1 Introduction 1 2 From Classical Bodies to Microscopic Particles 7 2.1 Concepts of Quantum Physics 7 2.2 Wave Motion 11 2.3 Wave Function 13 2.4 The SchrödingerWave Equation 14 2.5 An Electron in a SquareWell: One–Dimensional Case 16 2.6 Electron in a Potential Rectangular Box: k–Space 18 3 Electrons in Atoms 21 3.1 Atomic Units 21 3.2 One–Electron Atom: Quantum Numbers 22 3.3 Multi–Electron Atoms 30 3.4 The Hartree Theory 33 3.5 Results of the Hartree Theory 35 3.6 The Hartree–Fock Approximation 39 3.7 Multi–Electron Atoms in the Mendeleev Periodic Table 40 3.8 Diatomic Molecules 43 4 The Crystal Lattice 49 4.1 Close–Packed Structures 49 4.2 Some Examples of Crystal Structures 50 4.3 The Wigner–Seitz Cell 53 4.4 Reciprocal Lattice 54 4.5 The Brillouin Zone 59 5 Homogeneous Electron Gas and Simple Metals 63 5.1 Gas of Free Electrons 64 5.2 Parameters of the Free–Electron Gas 66 5.3 Notions Related to the Electron Gas 69 5.4 Bulk Modulus 69 5.5 Energy of Electrons 70 5.6 Exchange Energy and Correlation Energy 71 5.7 Low–Density Electron Gas: Wigner Lattice 74 5.8 Near–Free Electron Approximation: Pseudopotentials 74 5.9 Cohesive Energy of Simple Metals 77 6 Electrons in Crystals and the Bloch Waves in Crystals 79 6.1 The Bloch Waves 79 6.2 The One–Dimensional Kronig–Penney Model 82 6.3 Band Theory 85 6.4 General Band Structure: Energy Gaps 87 6.5 Conductors, Semiconductors, and Insulators 91 6.6 Classes of Solids 92 7 Criteria of Strength of Interatomic Bonding 95 7.1 Elastic Constants 95 7.2 Volume and Pressure as Fundamental Variables: Bulk Modulus 98 7.3 Amplitude of Lattice Vibration 98 7.4 The Debye Temperature 102 7.5 Melting Temperature 102 7.6 Cohesive Energy 103 7.7 Energy of Vacancy Formation and Surface Energy 105 7.8 The Stress–Strain Properties in Engineering 106 8 Simulation of Solids Starting from the First Principles (“ab initio” Models) 109 8.1 Many–Body Problem: Fundamentals 109 8.2 Milestones in Solution of the Many–Body Problem 112 8.3 More of the Hartree and Hartree–Fock Approximations 112 8.4 Density Functional Theory 115 8.5 The Kohn–Sham Auxiliary System of Equations 118 8.6 Exchange–Correlation Functional 119 8.7 Plane Wave Pseudopotential Method 121 8.8 Iterative Minimization Technique for Total Energy Calculations 124 8.9 Linearized Augmented PlaneWave Method 127 9 First–Principle Simulation in Materials Science 131 9.1 Strength Characteristics of Solids 131 9.2 Energy of Vacancy Formation 134 9.3 Density of States 135 9.4 Properties of Intermetallic Compounds 136 9.5 Structure, Electron Bands, and Superconductivity of MgB2 138 9.6 Embrittlement of Metals by Trace Impurities 142 10 Ab initio Simulation of the Ni3Al–based Solid Solutions 145 10.1 Phases in Superalloys 145 10.2 Mean–Square Amplitudes of Atomic Vibrations in γ0–based Phases 147 10.3 Simulation of the Intermetallic Phases 148 10.4 Electron Density 154 11 The Tight–Binding Model and Embedded–Atom Potentials 157 11.1 The Tight–Binding Approximation 157 11.2 The Procedure of Calculations 160 11.3 Applications of the Tight–Binding Method 160 11.4 Environment–Dependent Tight–Binding Potential Models 162 11.5 Embedded–Atom Potentials 166 11.6 The Embedding Function 168 11.7 Interatomic Pair Potentials 170 12 Lattice Vibration: The Force Coefficients 175 12.1 Dispersion Curves and the Born–von Karman Constants 176 12.2 Fourier Transformation of Dispersion Curves: Interplanar Force Constants 181 12.3 Group Velocity of the Lattice Waves 183 12.4 Vibration Frequencies and the Total Energy 187 13 Transition Metals 193 13.1 Cohesive Energy 194 13.2 The Rectangular d Band Model of Cohesion 200 13.3 Electronic Structure 201 13.4 Crystal Structures 205 13.5 Binary Intermetallic Phases 205 13.6 Vibrational Contribution to Structure 211 14 Semiconductors 215 14.1 Strength and Fracture 219 14.2 Fracture Processes in Silicon 223 14.3 Graphene 224 14.4 Nanomaterials 227 15 Molecular and Ionic Crystals 233 15.1 Interaction of Dipoles: The van der Waals Bond 233 15.2 The Hydrogen Bond 236 15.3 Structure and Strength of Ice 239 15.4 Solid Noble Gases 242 15.5 Cohesive Energy Calculation for Noble Gas Solids 244 15.6 Organic Molecular Crystals 246 15.7 Molecule–Based Networks 248 15.8 Ionic Compounds 250 16 High–Temperature Creep 253 16.1 Experimental Data: Evolution of Structural Parameters 254 16.2 Physical Model 258 16.3 Equations to the Model 260 16.4 Comparison with the Experimental Data 261 17 Fatigue of Metals 263 17.1 Crack Initiation 264 17.2 Periods of Fatigue–Crack Propagation 267 17.3 Fatigue Failure at Atomic Level 270 17.4 Rupture of Interatomic Bonding at the Crack Tip 276 18 Modeling of Kinetic Processes 279 18.1 System of Differential Equations 279 18.2 Crack Propagation 280 18.3 Parameters to Be Studied 281 18.4 Results 282 Appendix A Table of Symbols 285 Appendix B Wave Packet and the Group and Phase Velocity 289 Appendix C Solution of Equations of the Kronig–Penney Model 291 Appendix D Calculation of the Elastic Moduli 293 Appendix E Vibrations of One–Dimensional Atomic Chain 295 References 299 Index 303
- ISBN: 978-3-527-33507-7
- Editorial: Wiley VCH
- Encuadernacion: Cartoné
- Páginas: 320
- Fecha Publicación: 18/12/2013
- Nº Volúmenes: 1
- Idioma: Inglés