Interatomic Bonding in Solids: Fundamentals, Simulation, and Applications

The connection between the 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 engineering and theory 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 from the features of their structural elements, generally electrons. In a sense, electronic structure forms the glue holding solids together and it is central to determining structural, mechanical, chemical, electrical, magnetic, and vibrational properties. The main part of the book is devoted to an overview of the fundamentals of density functional theory and its applications to computational solid-state physics and chemistry. The author shows the technique for construction of models and the computer simulation methods in detail. He considers fundamentals of physical and chemical interatomic bonding in solids and analyzes the predicted theoretical outcome in comparison with experimental data. He applies first-principle simulation methods to predict the properties of transition metals, semiconductors, oxides, solid solutions, and molecular and ionic crystals. Uniquely, he presents novel theories of creep and fatigue that help to anticipate, and prevent, possibly fatal material failures. As a result, readers gain the knowledge and tools to simulate material properties and design materials with desired characteristics. Due to the interdisciplinary nature of the book, it is suitable for a variety of markets from students to engineers and researchers.

Table of Contents:
Preface INTRODUCTION FROM CLASSICAL BODIES TO MICROSCOPIC PARTICLES Concepts of Quantum Physics Wave Motion Wave Function The Schrödinger Wave Equation An Electron in a Square Well. One-Dimensional Case Electron in a Potential Rectangular Box. k-space ELECTRONS IN ATOMS Atomic Units One-Electron Atom. Quantum numbers Multi-Electron Atoms The Hartree Theory Results of the Hartree Theory The Hartree-Fock Approximation Multi-Electron Atoms in the Mendeleev Periodic Table Diatomic Molecules THE CRYSTAL LATTICE Close-Packed Structures Some Examples of Crystal Structures The Wigner-Seitz cell Reciprocal Lattice The Brillouin Zone HOMOGENEOUS ELECTRON GAS AND SIMPLE METALS Gas of Free Electrons Parameters of the Free-Electron Gas Notions Related to the Electron Gas Bulk Modulus Energy of Electrons Exchange Energy and Correlation Energy Low-Density Electron Gas: Wigner Lattice Near Free-Electron Approximation: Pseudopotentials Cohesive Energy of Simple Metals ELECTRONS IN CRYSTALS AND THE BLOCH WAVES IN CRYSTALS The Bloch Waves The One-Dimensional Kronig-Penney Model Band Theory General Band Structure: Energy Gaps Conductors, Semiconductors, and Insulators Classes of Solids CRITERIA OF STRENGTH OF INTERATOMIC BONDING Elastic Constants Volume and Pressure as Fundamental Variable: Bulk Modulus Amplitude of Lattice Vibration The Debye Temperature Melting Temperature Cohesive Energy Energy of Vacancy Formation and Surface Energy The Stress - Strain Properties in Engineering SIMULATION OF SOLIDS STARTING FROM THE FIRST PRINCIPLES (" AB INITIO" MODELS) Many Body Problem: Fundamentals Milestones in Solution of the Many Body Problem More of the Hartree and Hartree-Fock Approximations Density Functional Theory The Kohn-Sham Auxiliary System of Equations Exchange-Correlation Functional Plane Wave Pseudopotential Method Iterative Minimization Technique for Total Energy Calculations Linearized Augmented Plane Wave Method FIRST-PRINCIPLE SIMULATION IN MATERIALS SCIENCE Strength Characteristics of Solids Energy of Vacancy Formation Density of States Properties of Intermetallic Compounds Structure, Electron Bands, and Superconductivity of MgB2 Embrittlement of Metals by Trace Impurities AB INITIO SIMULATION OF Ni3Al-BASED SOLID SOLUTIONS Phases in Superalloys Mean-Square Amplitudes of Atomic Vibrations in Gamma-Based Phases Simulation of the Intermetallic Phases Electron Density THE TIGHT-BINDING MODEL. EMBEDDED ATOM POTENTIALS The Tight-Binding Approximation The Procedure of Calculations Applications of the Tight-Binding Method Environment-Dependent Tight-Binding Potential Models Embedded-Atom Potentials The Embedding Function Interatomic Pair Potentials LATTICE VIBRATIONS: THE FORCE COEFFICIENTS Dispersion Curves. The Born-von-Karman Constants Fourier Transformation of Dispersion Curves: Interplanar Force Constants Group Velocity of the Lattice Waves Vibration Frequencies and the Total Energy TRANSITION METALS Cohesive Energy The Rectangular d Band Model of Cohesion Electronic Structure Crystal Structures Binary Intermetallic Phases Vibrational Contribution to Structure SEMICONDUCTORS Strength and Fracture Fracture Processes in Silicon Graphene Nanomaterials MOLECULAR AND IONIC CRYSTALS Interaction of Dipoles: The van der Waals Bond The Hydrogen Bond Structure and Strength of Ice Solid Noble Gases Cohesive Energy Calculation for Noble Gas Solids Organic Molecular Crystals Molecule-Based Networks Ionic Compounds HIGH-TEMPERATURE CREEP Experimental Data: Evolution of Structural Parameters Physical Model Equations to the Model Comparison with the Experimental Data FATIGUE OF METALS Crack Initiation Periods of Fatigue-Crack Propagation Fatigue Failure at Atomic Level Rupture of Interatomic Bonding at the Crack Tip MODELING OF KINETIC PROCESSES System of Differential Equations Crack Propagation Parameters to be Studied Results APPENDIX A Table of Symbols APPENDIX B Wave Packet and the Group and Phase Velocity APPENDIX C Solution of Equations of the Kronig-Penney Model APPENDIX D Calculation of the Elastic Moduli APPENDIX E Vibrations of One-Dimensional Atomic Chain Index

About the Author :
Valim Levitin is a Professor and the Head of an internationally renowned research group at the National Technical University in Ukraine. His research focuses on studying nature of interatomic bonding, atom vibrations in solids, computer simulation of parameters that determine the behavior of solids, surface physics, and X-ray, TEM, and work-function studies into the fundamentals of material strength. He has published three books and numerous articles in the fields of materials science and solid-state physics.