Interatomic Bonding in Solids

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.

Auteur
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.

Contenu

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