Electronic Structure of Materials By Rajendra Prasad

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Electronic Structure of Materials by Rajendra Prasad

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Contents of Electronic Structure of Materials eBook

  • Introduction
  • Quantum Description of Materials
  • Density Functional Theory
  • Energy Band Theory
  • Methods of Electronic Structure Calculations
  • Methods of Electronic Structure Calculations II
  • Methods of Electronic Structure Calculations III
  • Disordered Alloys
  • First-Principles Molecular Dynamics
  • Materials Design Using Electronic Structure Tools
  • Amorphous Materials
  • Atomic Clusters and Nanowires
  • Surfaces, Interfaces, and Superlattices
  • Graphene and Nanotubes
  • Quantum Hall Effects and Topological Insulators
  • Ferroelectric and Multiferroic Materials
  • High-Temperature Superconductors
  • Spintronic Materials
  • Battery Materials
  • Materials in Extreme Environments

Preface to Electronic Structure of Materials PDF

Recently there has been a move in various universities and Indian Institutes of Technology (IITs) to introduce research in the undergraduate curriculum (BS, BTech, and MSc) so that undergraduates can also experience the excitement of the current research.

The biggest problem one faces in implementing such a scheme is the shortage of textbooks that are written at the undergraduate level and at the same time that cover the topics of current research.

This book on the electronic structure of materials is a step in this direction.

It is aimed at the advanced undergraduate and graduate students who want to gain some understanding of electronic structure methods or want to use these tools in their research.

Electronic structure plays a fundamental role in determining the properties of materials such as the cohesive energy,

equilibrium crystal structure, phase transitions, transport properties, magnetism, ferroelectricity, optical properties, and so on.

The last two decades have seen an intense activity in the field of electronic structure of materials and the field has been gaining importance day by day. Several factors have contributed to this:

1. The theory of electronic structure has advanced to a level where it is possible to obtain good quantitative agreement with experiments without using any adjustable parameters. Thus, the theory has acquired some predictive power.

2. There has been an intense search for new materials for technological applications such as materials for computer memory, spintronic devices, quantum computations, rechargeable batteries, and so on.

There has been a realization that electronic structure studies can greatly help such a search.

The new emerging area of nanomaterials has given further impetus to this field.

3. With the advent of fast computers, there has been a tremendous increase in computing power.

Due to the development of fast algorithms and the easy availability of codes, complicated electronic structure calculations with large unit cells can be done quite efficiently.

With these developments, it is now possible to design a material with desired properties in a computer.

Realizing the importance of this field, a course on this subject was offered at IIT Kanpur for MSc and PhD students.

With increasing importance of materials, many other IITs and universities are likely to start such a course.

The existing textbooks in the field are either too advanced for MSc students or too elementary to bring them up to date with current research.

This book, which is a compilation of lecture notes given in this course, is an attempt to bridge this gap.

These notes were circulated among students and their feedback was taken. In addition to pointing out typographical mistakes, they gave some important suggestions that were incorporated in these notes.

Since the students attending this course were not only from physics but also from other disciplines such as materials science, chemical engineering, and chemistry,

I have only assumed some basic knowledge of quantum mechanics, statistical mechanics, and condensed matter physics.

Thus, in all the chapters, I start the subject at a very basic level, slowly come to an advanced level, and then refer the students to more recent work.

The idea is to get the students interested in the subject and prepare them adequately so that they can follow the more advanced material that has been referred to.

For this reason, I have given a longish list of references at the end. Some important references are given at the end of each chapter as Further Reading.

In this book, we take a microscopic view of materials as composed of interacting electrons and nuclei and aim at explaining all the properties of materials in terms of basic quantities of electrons and nuclei such as electronic charge, mass, and atomic number.

This is called the first-principles approach, which does not have any adjustable parameters and is based on quantum mechanics.

The book has been divided into two parts. The first part (Chapters 1 through 10) is concerned with the fundamentals and methods of electronic structure and the second part (Chapters 11 through 20) deals with the applications of these methods.

In the second part, some selected examples have been given to illustrate the applications of these methods to different materials.

The materials chosen include crystalline solids, disordered substitutional alloys, amorphous solids, nanoclusters, nanowires, graphene, topological insulators, battery materials, spintronic materials, materials under extreme conditions, and so on.

Chapter 1 gives a historical introduction and an overview of the electronic structure field.

Chapter 2 explains quantum description of matter in terms of electrons and nuclei and sets the stage for the rest of the book.

In Chapter 2, we try to solve the many-body problem of interacting electrons and nuclei by using the Born−Oppenheimer approximation.

After discussing the Born−Oppenheimer approximation, we focus on the electronic problem by keeping the nuclei fixed. Then Hartree and Hartree−Fock methods are discussed in detail with application to the jellium model.

Chapter 3 is devoted to the discussion of the density functional theory (DFT), which provides the foundation for the first-principles calculations discussed in the subsequent chapters.

We start with the Thomas−Fermi theory and then discuss basic theorems of the DFT and derivation of the Kohn–Sham (KS) equations.

We then discuss the approximations like LDA (local density approximation), GGA (generalized gradient approximation), LDA + U, GW, and so on.

We also discuss very briefly the time-dependent DFT. In Chapter 4, we discuss basic energy band theory and in Chapters 5 through 7,

various methods of electronic structure calculations such as
pseudopotential, the KKR (Korringa−Kohn−Rostoker) method, APW (augmented plane wave) methods, and so on are explained.

In Chapter 7, we introduce Green’s function, which we use extensively in Chapter 8.

In Chapter 8, we focus on disordered alloys and discuss approximations such as VCA (virtual crystal approximation), ATA (average t-matrix approximation),

CPA (coherent potential approximation), and KKR-CPA (Korringa−Kohn−Rostoker-coherent potential approximation).

We also discuss very briefly the attempts to go beyond CPA. In Chapter 9, we discuss first-principles molecular dynamics (MD).

We start with the discussion of classical MD, and then discuss Born–Oppenheimer MD (BOMD) and Car−Parrinello MD (CPMD), simulated annealing, the Hellman−Feynman theorem, and calculation of forces.

Chapter 10 discusses some general principles associated with materials design.

The second part of the book, from Chapters 11 through 20, discusses some applications of electronic structure.

In Chapter 11, we discuss amorphous semiconductors and Anderson localization.

It turns out that the firstprinciples approach is ideally suited for studying low-dimensional systems and nanomaterials, which are covered in most of the remaining chapters.

In Chapters 12 through 14, we discuss low-dimensional systems. Chapter 12 is devoted to atomic clusters and nanowires, Chapter 13 to surfaces, interfaces, and multilayers and Chapter 14 to graphene and nanotubes.

Chapter 15 discusses quantum Hall effects and recently discovered topological insulators.

In Chapters 16 through 20, we discuss ferroelectrics and multiferroics, high Tc materials, spintronic materials, battery materials, and materials under extreme conditions.

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