Interatomic Bonding in Solids: Fundamentals, Simulation, and Applications

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.

Table of Contents:
INTRODUCTION FROM CLASSICAL BODIES TO MICROSCOPIC PARTICLES Concepts of Quantum Physics Wave Motion Wave Function The Schrodinger 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. SIMPLE METALS Gas of Free Electrons Parameters of the Free-Electron Gas Notions Related to the Electron Gas Energy of Electrons Near Free-Electron Approximation. Pseudopotentials Cohesive Energy of Simple Metals ELECTRONS IN CRYSTALS. 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 BOND 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 The Hartree and Hartree-Fock Approximation Revisited 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 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 HIGH TEMPERATURE CREEP Experimental Data. Evolution of Structural Parameters Physical Model Equations to the Model Comparison with the Experimental Data Ni3Al-BASED SOLID SOLUTIONS Phases in Superalloys Mean-Square Amplitudes of Atomic Vibrations in Gamma'-Based Phases Simulating of the Intermetallic Phases Electron Density PHYSICAL MECHANISM OF FATIGUE Crack Initiation Reversibility of Fatigue Starting Periods of Fatigue-Crack Propagation Crack Growth. Fatigue Failure at Atomic Level MODELING OF KINETIC PROCESSES Fatigue Crack Propagation Parameters to be Studied Results

About the Author :
Professor Valim Levitin is the Head of an internationally renowned Research Group at the National Technical University in Ukraine. His work focusses on problems of atom vibrations in solids, work function, physical bases of creep and fatigue and X-ray and TEM studies of the fundamentals of materials strength.