Elements of Structures and Defects of Crystalline Materials

Tsang-Tse Fang

• Publisher: Elsevier
• Year: 2018
• Print ISBN:
  9780128142684
• eBook ISBN:
  9780128142691
• Topic: Technology & Engineering
• Subtopic: Materials Science
• Index: Technology & Engineering

Elements of Structures and Defects of Crystalline Materials has been written to cover not only the fundamental principles behind structures and defects, but also to provide deep insights into understanding the relationships of properties, defect chemistry and processing of the concerned materials. Part One deals with structures, while Part Two covers defects. Since the knowledge of the electron configuration of elements is necessary for understanding the nature of chemical bonding, it is discussed in the opening chapter. Chapter Two then describes the bonding formation within the crystal structures of varied materials, with Chapter Three delving into how a material's structure is formed. In view of the importance of the effects of the structure distortion on the material properties due to the fields, the related topics have been included in section 3.4. Moreover, several materials still under intensive investigation have been illustrated to provide deep insights into understanding the effects of the relationships of processing, structures and defects on the material properties. The defects of materials are explored in Part II. Chapter 4 deals with the point defects of metal and ceramics. Chapter 5 covers the fundamentals of the characteristics of dislocations, wherein physics and the atomic mechanics of several issues have been described in detail. In view of the significant influence of the morphologies including size, shape and distribution of grains, phases on the microstructure evolution, and, in turn, the properties of materials, the final chapter focuses on the fundamentals of interface energies, including single phase (grain) boundary and interphase boundary. - Discusses the relationship between properties, defect chemistry and the processing of materials - Presents coverage of the fundamental principles behind structures and defects - Includes information on two-dimensional and three-dimensional imperfections in solids

Part I

Structures of the Crystalline Materials

Outline

• Part I. Structures of the Crystalline Materials
• Chapter 1 The Electron Configuration of Atoms
• Chapter 2 Bonding Within Crystal Structures
• Chapter 3 The Structures of Crystalline Crystals

Part I. Structures of the Crystalline Materials

Concerning the structures of perfect crystalline solids, they possess a perfectly ordered, periodic arrangement of atoms or ions. The understanding of the structure of atoms would be a priori to describe the arrangement of atoms. This is necessary since the arrangement of atoms is dependent on the atom bonding whose origins are found to be in the electronic structure of atoms. The following chapter will deal with the electron configuration of atoms.

Chapter 1

The Electron Configuration of Atoms

Abstract

Since the knowledge of the electron configuration of elements is necessary for understanding the nature of chemical bonding, and in turn the structure of a perfectly ordered, periodic arrangement of atoms or ions, it is discussed in the first chapter. This chapter starts with the basic knowledge concerning the construction of the electron configuration of elements, and it proceeds to fairly advanced interpretations to understand the related issues. Moreover, although this chapter does not give detailed derivation of the Schrödinger’s wave equation, the spirit of this equation is presented, wherein the quantum numbers can be clearly defined and the electron density contours are well represented. Furthermore, on the basis of the comparison of the radial distribution functions, the significant influence of the penetration and shielding of electrons on constructing the electron configuration, especially, the energetic d-orbital collapse of 3d transition elements, can be perceived. The interpretation of the electron configuration of the half-filled and fully-filled 3d transition elements has been updated. This chapter is by no means intended to be comprehensive but to lend support to the fundamentals that are referred to in Section 3.4 of chapter 3 concerning d electron effects on crystal fields.

Keywords

Electron configuration; penetration; shielding; d-orbital collapse; half-filled orbital; fully-filled orbital; spin–orbital coupling; transition metals; radial distribution function

1.1 Atoms With a Single Electron

To appreciate the energetics and shapes of an atomic orbital is to solve the so-called Schrödinger’s wave equation. The simplest case is the hydrogen atom whose electron behavior is described by the following usual form of the Schrödinger’s wave equation:

${\nabla }^2\psi +\frac{8{\pi }^2{m}_e}{h^2}(E-V)\psi =0$ (1.1)

(1.1)

where ${\nabla }^2$

is the Laplacian operator, expressed in Cartesian coordinates as

${\nabla }^2=\frac{{\partial }^2}{\partial x^2}+\frac{{\partial }^2}{\partial y^2}+\frac{{\partial }^2}{\partial z^2}$

E and V are the total energy and the potential energy of electron in a hydrogen atom, respectively; m_e is the electron mass. The wave function, $\psi$

, is the solution of Eq. (1.1). Since the orbital of the hydrogen atom is spherically symmetrical, the description of the orbital would be easier to be tackled in spherical coordinates, as shown in Fig. 1.1. Eq. (1.1) can further be transformed in spherical coordinates as

$\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^2\frac{\partial \psi }{\partial r}\right)+...$

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Preface
• Acknowledgements
• Part I: Structures of the Crystalline Materials
• Part II: Defects of Crystalline Materials
• Appendix I. Spectroscopic Notation
• Appendix II. Band Structures of Mott–Hubbard Materials and the Transition Metal Ionic Compounds, and Polaron
• Bibliography
• Index