In a technology driven civilization the quest for new and smarter materials is everlasting. They are required as platforms for developing new technologies or for improving an already existing technology. The discovery of a new material is no longer chance driven or accidental, but is based on careful reasoning structured by deep understanding of the microconstituents of materials - the atoms and molecules in isolation or in an assembly. That requires fair amount of exposure to quantum and statistical mechanics. `Understanding Properties of Atoms, Molecules and Materials' is an effort (perhaps the first ever) to bring all the necessary theoretical ingredients and relevant physical information in a single volume. The book introduces the readers (first year graduates) or researchers in material chemistry/engineering to elementary quantum mechanics of atoms, molecules and solids and then goes on to make them acquainted with methods of statistical mechanics (classical as well as quantum) along with elementary principles of classical MD simulation. The basic concepts are introduced with clarity and illustrated with easy to grasp examples, thus preparing the readers for an exploration through the world of materials - the exotic and the mundane. The emphasis has been on the phenomena and what shapes them at the fundamental level. A comprehensive description of modern designing principles for materials with examples is a unique feature of the book.
The highlights of the book are comprehensive introduction and analysis of
- Quantum states of atoms and molecules
- The translational symmetry and quantum states in periodic and amorphous solids
- Band structure and tuning
- Classical and quantum statistics with applications to ideal gases (photons, phonons and electrons, molecules)
- Quantum states in type-I and type-II superconductors (elementary theory included)
- Magnetic materials, materials with GMR and CMR
- Shape memory effects in alloys and materials
- 2D materials (graphene and graphene analogus)
- NLO and photovoltaic materials
- Hydrogen storage material for mitigating the looming energy crisis
- Quantum states in low and high band gap semiconductors
- Semimetals
- Designer materials, etc.
The volume is designed and organized to create interest in the science of materials and the silent revolution that is redefining the goals and boundaries of materials science continuously.
Author(s): Pranab Sarkar, Sankar Prasad Bhattacharyya
Publisher: CRC Press
Year: 2021
Language: English
Pages: 376
City: Boca Raton
Cover Page
Half Title
Title Page
Contents
Preface
Authors
1 The Science of Materials
1.1 Introduction: The Age of Materials
1.2 Atoms, Molecules and Solids
1.2.1 More on Unit Cells
1.3 From Atoms and Molecules to Materials
1.4 The Need for Theoretical Understanding
1.5 Topics Covered
1.5.1 The Mechanics of the Microworld
1.5.2 Quantum Mechanics of Atoms
1.5.3 Quantum Mechanics of Molecules
1.5.4 Quantum States in Solids
1.5.5 Classical Statistical Mechanics
1.5.6 Quantum Statistical Mechanics
1.5.7 Traditional Materials
1.5.8 Smart Materials
1.5.9 Magnetic Materials
1.5.10 Low-Dimensional Materials
1.5.11 NLO and Energy Materials
1.5.12 Materials Design
1.6 Classification of Materials
1.7 Future Outlook
References
2 Quantum Mechanics
2.1 Introduction: Mechanics of the Microworld
2.2 Law of Quantum Evolution: The Schrödinger Equation
2.2.1 Axiomatic Foundation of Quantum Mechanics
2.2.2 Postulates of Quantum Mechanics
2.3 Observables, Operators and Their Eigenfunctions
2.3.1 More About Hermiticity and Hermitian Conjugates
2.4 Commuting and Non-Commuting Observables
2.5 Stationary States of Quantum Systems
2.5.1 The Free Particle
2.5.2 Stationary States of a Simple Harmonic Oscillator
2.6 The Tunnel Effect
2.6.1 Tunneling Across a Rectangular Potential Barrier
2.7 Heisenberg’s Formulation of Quantum Mechanics
2.7.1 Matrix Representations for x and px
2.7.2 Zero Point Oscillation
2.7.3 Harmonic Oscillator in Three Dimensions
2.7.4 Quantum States in Infinitely Deep Potential Wells
2.8 Representations in Quantum Mechanics
2.8.1 Coordinate Representation
2.8.2 Momentum Representation
2.8.3 Matrix Representation
2.8.4 Vector Space Formulation
References
3 Quantum Mechanics of Atoms
3.1 Introduction
3.2 The Periodic Table of Elements
3.3 The Quantum States of the Hydrogenic Atoms: Symmetry
3.4 Rotational Symmetry, Angular Momentum, Eigenstates and Parity
3.5 Orbital Angular Momentum of Electron
3.5.1 Spherical Harmonics and Eigenstates of Rigid Rotator
3.5.2 Radial Motion of the Electron in H-Atom
3.5.3 Asymptotic Forms of R(r) and Continuous Energy Spectrum
3.5.4 Discrete Spectrum of Energy
3.5.5 Energy Degeneracy: Discrete Spectrum
3.5.6 Complete Wavefunction of a Hydrogen Atom
3.6 Spin Angular Momentum
3.7 Total Angular Momentum (J): General Addition of Angular Momentum
3.8 Many Electron Atoms: Aufbau Principle
3.8.1 Periods and Shells
3.8.2 Groups and Outer Shells
3.8.3 A Case Study of Two-Electrons Atoms: He
3.8.4 Designating Electronic States of a He Atom
3.8.5 Constructing Wavefunctions for the Two-Electron States of the He Atom
3.8.6 Calculating Energy of He Atom in the Ground State: Variational Approximation
3.9 More on Variational Methods
References
4 Molecular Quantum Mechanics
4.1 Introduction: Molecules as Building Blocks
4.2 The Quantum States of Hydrogen Molecule Ion (H+2 )
4.3 The Quantum States of Hydrogen Molecule
4.4 Quantum Mechanics of Covalent Bond
4.4.1 Energetics of Covalent Bond in H2
4.4.2 Electron Probability Density Distribution in Heitler-London States
4.4.3 Valency and Quantum Mechanics
4.5 Dynamics of Electron Exchange in Covalent Bond Formation
4.6 Forces in Molecules, Bonding and Equilibrium Structures
4.7 Bonding and Anti-bonding Region in a Molecule, Berlin Diagrams
4.8 Ionic Bonds and Ionic Solids
4.8.1 Cohesive Energy of Ionic Solids
4.9 Weak-Binding
4.10 Weak-Binding: Hydrogen Bonds
4.11 Directed Valence and Chemical Binding
4.12 Many Electron Systems
4.13 Hartree Method
4.13.1 Slater Condon Rules
4.14 Hartree-Fock Method
4.15 LCAO-MO-SCF-CI Calculations
4.16 Perturbative Correction to HF Wavefunction and Energy
4.17 The Rise of Density Functional Theory
4.17.1 The Kohn-Sham Method
4.18 The Basis Sets for Molecular Calculation
References
5 Quantum States of Solids
5.1 Introduction
5.2 One-Electron Approximation, Translational Symmetry, Bloch States and Brillouin Zone
5.3 Formation of Energy Bands
5.3.1 Nearly Free Electron Model of Band Structure
5.3.2 Kronig-Penny Problem and Structure of Energy Bands
5.3.3 The Tight Binding Model of Periodic Solids
5.4 The Idea of Band Gap and Electrical Transport in Solids
5.4.1 Electrical Conductors: Partially Filled Valence Band
5.4.2 Insulators: Completely Filled Valence Band
5.4.3 Semiconductors
5.4.4 Effective Mass (m*)
5.4.5 Lattice Vibrations, Phonons and Electrical Conductivity
5.5 Symmetry and Splitting of Bands
5.6 Amorphous Solids and Localized Electronic States
5.6.1 Localization in Disordered Solids
References
6 Classical Statistical Mechanics
6.1 Introduction
6.2 Types of Probability Distributions
6.2.1 Probability and Unexpectedness: The Entropy
6.3 The Equilibrium State and Distribution Functions
6.3.1 Maxwell’s Distribution
6.3.2 The Equilibrium State and Boltzmann Distribution
6.3.3 Maxwell-Boltzmann Distribution
6.4 Gibbs Distribution
6.4.1 Maxwell-Boltzmann Probability Density
6.4.2 The Gibbs Distribution: Probability of an Equilibrium State
6.5 Classical Statistical Mechanics
6.6 Classical Statistical Mechanics and Macroscopic Properties
6.6.1 Gibbs-Helmholtz Equation from Classical Statistical Mechanics: Internal Energy (U)
6.6.2 Entropy: Statistical Mechanical and Thermodynamic Interpretation
6.7 Statistical Mechanics and Numerical Simulation
6.7.1 MD Simulations (Basic Idea)
6.7.2 Calculation of Thermodynamic Properties
6.7.3 Microcanonical Ensemble Molecular Dynamics
6.7.4 Monte-Carlo Simulations
6.7.5 Transition Probabilities and Metropolis Method
References
7 Quantum Statistical Mechanics
7.1 Introduction
7.2 The Canonical Gibbs Distribution in Quantum Statistics
7.2.1 Canonical Gibbs’ Distribution For Discrete States
7.2.2 Quantum Gibbs’ Distribution and Entropy
7.3 Entropy and the Entropy Maximal State
7.4 The Grand Canonical Potential
7.4.1 Thermodynamic Meaning of *, µ and T
7.5 Quantum Statistics of Bosons and Fermions
7.5.1 Bose-Einstein Distribution
7.5.2 Fermi-Dirac Distribution
7.5.3 Boson Statistics and Indistinguishability Principle
7.6 Applications of Bose Statistics to Ideal Photon and Phonon Gas
7.6.1 Photon Gas (Ideal)
7.6.2 Phonon Gas (Ideal)
7.7 Quantum Statistics for Electron Gas in a Potential Well
7.7.1 Non-Degenerate Electron Gas
7.7.2 Degenerate Electron Gas
7.8 Quantum Effects in Heat Capacity of Gases
7.8.1 AModel Application of Quantum Statistics
7.9 Bose-Einstein Condensation
References
8 Traditional Materials
8.1 Introduction: Atom-Based Materials
8.2 Conducting, Superconducting and Insulating Materials
8.3 Metallic Conductivity: A Rudimentary Theory
8.4 Quantum Theory of Metallic Conductivity, Electron Phonon Interactions
8.5 Superconductivity and Superconducting State
8.5.1 The Nature of the Superconducting State
8.5.2 Binding Energy of a Cooper-Pair
8.5.3 Superconducting State Function
8.5.4 Special Features of the Superconducting State
8.6 Semiconducting Materials and Insulators
8.6.1 Equilibrium Statistics of Electrons in Semiconductors and Metal
8.6.2 Equilibrium Statistics of Electron Gas in Semiconductors
8.6.3 Semimetals
8.6.4 Compound Semiconductors
8.7 Insulators
8.7.1 Ferroelectric Materials
8.8 High Temperature or Type II Superconductors
8.8.1 Ceramics and Their Structures
8.8.2 High Tc Superconducting Materials
8.8.3 Understanding High Tc Superconductivity
8.9 Metal Alloys
8.9.1 Ferrous Alloys
8.9.2 Steels
8.9.3 Non-Ferrous Alloys
8.9.4 Special Materials
References
9 The Advent of Smart Materials
9.1 Introduction
9.2 Electrochromic (EC) Materials
9.3 Piezoelectric Materials
9.4 Shape Memory Materials (SMM)
9.5 Photochromic Materials (PM)
9.6 Quantum Tunneling Composites (QTC)
9.7 Quantum Materials (QMs)
9.8 Organic Superconductors
References
10 Magnetic Materials
10.1 Introduction: Magnetic Materials
10.2 Important Magnetic Vectors
10.3 Types of Magnetism and Magnetic Materials
10.4 Types of Magnetism: Theoretical
10.5 Exchange Interaction, Heisenberg’s Exchange Hamiltonian and Magnetic Hamiltonian
10.5.1 Diamagnetic Materials
10.5.2 Paramagnetic Material
10.5.3 Ferromagnetic, Antiferromagnetic and Ferrimagnetic Materials
10.5.3.1 Ferromagnetic Ordering
10.5.3.2 Antiferromagnetic Ordering
10.5.3.3 Ferrimagnetic Ordering
10.5.4 Superparamagnetism
10.6 Paramagnetic Susceptibility of Gases and Conduction Electrons of Metals
10.6.1 Quantum Model for Paramagnetic Susceptibility
10.6.2 Paramagnetism of a Free-Electron Gas
10.6.3 Paramagnetism of Conduction Electrons
10.6.4 Paramagnetic Resonance
10.7 Diamagnetism of Atoms and Conduction Electrons
10.8 Ferromagnetic Susceptibility
10.9 Giant Magneto Resistance (GMR)
10.10 Materials with Ferromagnetic plus Ferroelectric Order
10.11 Molecular Magnets
10.12 Soft Magnetic Materials
References
11 Low-Dimensional Materials
11.1 Introduction: The New Age Materials
11.2 Graphene
11.2.1 Geometry and Crystal Structure
11.2.2 Electronic Structure of Graphene
11.3 Graphene Nanoribbons
11.3.1 Electronic Structure of aGNRs
11.3.2 Electronic Structure of zGNRs
11.3.3 Transport Properties of GNRs
11.4 Carbon Nanotubes (CNTs)
11.4.1 Geometric Features of CNTs
11.4.2 Electronic Structure of CNTs
11.4.3 Effect of Curvature on Electronic Structure of CNTs
11.5 Graphene Quantum Dots (GQDs)
11.5.1 Electronic Structure of GQDs
11.6 New 2D Carbon Allotropes: Defected Graphenes and Pentagraphene
11.7 White Graphene
11.7.1 Geometry and Crystal Structure
11.7.2 Electronic Structure of h-BN
11.7.3 General Properties and Applications of h-BN
11.8 Boron Nitride Nanoribbons (BNNRs)
11.9 Boron Nitride Nanotubes (BNNTs)
11.9.1 Morphology and Crystal Structure of BNNTs
11.9.2 Electronic Structure of BNNTs
11.9.3 General Properties and Applications of BNNTs
11.10 Phosphorene
11.10.1 Geometry and Crystal Structure
11.10.2 Mechanical Properties
11.10.3 Electronic Structure and General Properties of Phosphorene
11.11 Transition Metal Dichalcogenides (TMDs)
11.11.1 Geometry and Crystal Structure of TMDs
11.11.2 Mechanical Properties
11.11.3 Electronic Structure of TMDs
11.11.4 Optical Properties of TMDs
11.12 Pristine and TM-doped PtSe2 Monolayers
11.13 Other Nanomaterials: Special Emphasis on Nanoclusters or Quantum Dots (QDs)
11.13.1 Classification of Nanoclusters
11.13.2 Reactivity of Nanoclusters
11.14 Nanocomposites or Nanohybrid Materials
11.15 Nanomaterials for Energy Conversion Processes
References
12 Energy Materials
12.1 Introduction
12.2 The Looming Energy Crisis
12.3 Materials for Hydrogen Storage
12.3.1 Microporous Materials for H2-Storage
12.3.2 Carbon-Based Solid State Materials for Hydrogen Storage
12.3.3 Zeolites
12.3.4 Metal Organic Frameworks (MOFs)
12.3.5 Organic Polymers for Hydrogen Storage
12.3.6 Interstitial Hydrides
12.3.7 Intermetallic Compounds
12.3.7.1 AB5 Intermetallics
12.3.7.2 AB2 Intermetallics
12.3.7.3 AB – Intermetallics
12.3.8 Modified Binary Hydrides
12.3.9 Quasi-crystalline Materials
12.3.10 Complex Hydrides
12.4 Optical Properties of Materials and Lasers
12.4.1 Optical Properties ofMetals and Nonmetals
12.4.1.1 Metals
12.4.1.2 Non-metals
12.5 Photonic Materials
12.6 Photovoltaic Materials
12.6.1 Generation I Materials
12.6.2 Generation II Materials
12.6.3 Generation III Materials
12.7 Materials that Change Light
12.8 Non-Linear Optical Response of Materials
12.9 Thermoelectric Materials
References
13 Designer Materials
13.1 Introduction: Design by Thumb Rules
13.2 Materials by Design: Beyond Thumb Rules
13.3 Designing Materials: Beyond Thumb Rules
13.4 The Advent Computational Material Science
13.4.1 Designing Hard and Superhard Materials
13.4.2 Adaptive Design in Materials Discovery
13.4.3 Accelerated Discovery of New Magnetic Materials
13.4.4 Materials Informatics in the Search for Novel Materials
13.4.4.1 Stannates
13.4.4.2 Ruthenates
13.4.5 Computational Design of New MOF-Based Material for Hydrogen Storage
13.4.6 Miscellaneous Materials Designing Approach
References
14 Current Status and Outlook for Future
14.1 Introduction
14.2 Where Do We Stand?
14.3 Future Outlook
References
Index
