# Interatomic Bonding in Solids: Fundamentals, Simulation, and Applications

# Interatomic Bonding in Solids: Fundamentals, Simulation, and Applications

ISBN: 978-3-527-67157-1

Dec 2013

320 pages

$140.99

## Description

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.

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