For the past three decades, many scientists have been jumping onto the bandwagon of applied science, thereby hampering lhe development of basic science. If this emerging trend is permitted to persist over a long period of time, research in applied science will find itself at a crossroad. Recent years have been characterized by debates at the international level over attracting intelligent people to the basic sciences. During my entire professional career, which spans more than 40years in the field of theoretical solid state physics, I have found that textbooks on solid state physics greatly outnumber books on theoretical solid state physics. This unfortunate trend motivated me to write an elementary textbook on lheoreiical solid stale physics. A major portion of this book has been derived from lectures I delivered on solid state physics at various Indian universities over a period of three decades. I began writing this book in 2000 and it took me almost 17 years of concentrated effort to accomplish a task of such magnitude. Needless to say, the collection of material commenced much earlier.
Solid stale physics is such a diverse field that it cannot be covered in a single book. Further, the theory of solids is progressing al a very fast pace and is reaching an increased level of sophistication, greatly complicating the task of providing up-to-date knowledge of the whole subject. Therefore, I have tried to concentrate on the fundamentals of the theoretical aspects of those topics that are required in a first course for undergraduate students of physics, chemistry, materials science, and engineering at various universities across the globe. There are two approaches involved in the development of a book on solid state physics. First is the phenomenological approach, which includes hypotheses and models that are important in the development of the subject. Second is the fundamental approach, based on quantum mechanics and statistical mechanics, which provides greater insight into the actual processes responsible for the various properties of solids. I have tried to present a unified quantum mechanical treatment for the different properties of solids, touching upon phenomenological models wherever necessary. Some of the salient features of the book are discussed later.
For the study of the various properties of solids, a general formalism for the fundamentals has been derived wherever possible. Detailed mathematical steps are presented to make it comprehensible even to students with a minimal mathematical background. The results for simple structures in one-, two-, and three-dimensional solids are derived for particular cases. All of the chapters of the book are coherently interrelated. Elementary courses in quantum mechanics and statistical mechanics may be considered prerequisites for understanding the subject matter.
Dirac's notation has been used, which highlights the physics contained in the mathematics in a befitting and compact manner.
More than 400 diagrams and geometrical constructions of the elementary processes present in solids have been used to enable studenis to easily comprehend the subject matter.
A considerable number of problems have been inserted at appropriate places in all the chapters with the aim of providing deeper insight into the subject. Throughout the text, bold letters represent vector quantities. Greek letters with arrows also represent vector quantities.
The book contains an elementary account of some recent topics, such as the quantum Hall effect, high-Tc superconductivity, and nanomaterials. The topics of elasticity in solids, dislocations, polymers, point defects, and nanomaterials are of special interest for engineering students. The inclusion of abstract methods of quantum field theory, though important in many-body problems, have been deliberately avoided as they may not be very relevant to the diverse student communities for whom this book was written.
At the end of the book, some elementary textbooks on solid state physics are listed for supplementary reading. Advanced books on the topics covered in the present text are also included in the list, which may be helpful to advanced learners in carrying out further work.
I am indebted to Professor K.N. Pathak, former Vice Chancellor of Panjab University, Chandigarh, for fostering and nurtLiring my interest in the subject of solid stale physics while I was a student. I am thankful to my daughters Amardeep Gaisin, Manveen Gaisin, my son-in-law Dr. Nirjhar Hore, and my son Damanjit Singh Gaisin, who have been a constant source of encouragement and support for me during the completion of this work. I am very grateful to my wife. Professor Surinder Kaur, for encouraging me to liberally devote time to the writing of this book and also for editing the technical aspects of the English language. I am grateful to Mr. Rakesh Kumar (Somalya Printers, Ludhiana) for undertaking the artwork for this book so diligently and efficiently. I am also thankful to all my loved ones, colleagues, and well-wishers especially Dr. Jagtar Singh Dhiman. Dr. Nathi Singh and Dr. Paramjit Singh, who silently urged me to move on toward the successful completion of this momentous project. Last but not least, my journey with the Elsevier team, from the submission of the manuscript to the finished product, has been very pleasant. The book has not been read by any subject expert, therefore, any omission or error is my sole responsibility. I would welcome and appreciate comments/suggestions/ feedback for the improvement of the book in the near future. A big thanks to Lord Almighty-our creator.

About the Author xiii

Preface xv

1. Crystal Structure of Solids

1.1. Close Packing of Atoms in Solids 1

1.2. Crystal Lattice and Basis 3

1.3. Periodicities in Crystalline Solids 5

      1.3.1. Structural Periodicity 6

      1.3.2 Rotational Symmetry 10

1.4. One-Dimensional Crystals 13

1.5. Two-Dimensional Crystals 14

1.6. Three-Dimensional Crystals 14

1.7. Simple Crystal Structures 17

      1.7.1. Simple Cubic Structure 17

      1.7.2. Body-Centered Cubic Structure 18

      1.7.3. Face-Centered Cubic Structure 20

      1.7.4. Hexagonal Structure 22

      1.7.5. Hexagonal Close-packed Structure 24

1.8. Miller Indices 25

1.9. Other Structures 30

      1.9.1. Zinc Sulfide Structure 30

      1.9.2. Diamond Structure 31

      1.9.3. Wurtzite Structure 31

      1.9.4. Perovskite Structure 31

      1.9.5. High-T_c Superconductors 33

1.10. Quasicrystals 33

Suggested Reading 36

2. Crystal Structure in Reciprocal Space

2.1. X-Ray Diffraction 37

      2.1.1. Bragg's Law of X-Ray Diffraction 38

2.2. Electron Diffraction 38

2.3. Neutron Diffraction 39

2.4. Laue Scattering Theory 40

2.5. Reciprocal Lattice 42

      2.5.1. Periodicity of Electron Density 43

      2.5.2. Periodicity of Atomic Density 44

2.6. Primitive Cell in Reciprocal Space 46

      2.6.1. Linear Monatomic Lattice 46

      2.6.2. Square Lattice 47

      2.6.3. sc Lattice 47

      2.6.4. fcc Crystal Structure 50

      2.6.5. Hexagonal Crystal Structure 51

2.7. Importance of Reciprocal Space and BZs 54

      2.7.1. Bragg Reflection 54

      2.7.2. Significant Wave Vectors 56

      2.7.3. Construction of Reciprocal Lattice 57

2.8. Atomic Scattering Factor 57

2.9. Geometrical Structure Factor 58

      2.9.1. sc Crystal Structure 58

      2.9.2. fcc Crystal Structure 59

      2.9.3. bcc Crystal Structure 59

      References 60

      Suggested Reading 60

3. Approximations in the Study of Solids

3.1. Separation of Ion-Core and Valence Electrons 61

3.2. Rigid Ion-Core Approximation 61

3.3. Self-Consistent Potential Approximation 62

3.4. The Born-Oppenheimer Approximation 62

3.5. One-Electron Approximation 63

3.6. Electron Exchange and Correlation Interactions 64

      3.6.1. Electron Exchange Interactions 64

      3.6.2. Electron Correlation Interactions 66

      References 67

      Suggested Reading 67

4. Bonding in Solids

4.1. Interactions Between Atoms 69

4.2. Cohesive Energy 73

4.3. Equilibrium Distance 73

4.4. Bulk Modulus and Compressibility 74

4.5. Inert Gas Crystals 75

      4.5.1. Equilibrium Lattice Constant 76

      4.5.2. Cohesive Energy of Inert Gas Crystals 77

      4.5.3. Bulk Modulus 77

4.6. Ionic Bonding 78

      4.6.1. Ionic-Bond Energy 78

      4.6.2. Lattice Energy 79

      4.6.3. Difference Between Bond Energy, Cohesive Energy, and Lattice Energy 80

      4.6.4. Bulk Modulus of Ionic Crystals 80

      4.6.5. Exponential Repulsive Potential 82

      4.6.6. Calculation of the Madelung Constant 83

4.7. Covalent Bond 84

4.8. Mixed Bond 86

4.9. Metallic Bond 88

4.10. Hydrogen Bond 90

Suggested Reading 91

5. Elastic Properties of Solids

5.1. Strain Tensor 93

5.2. Dilation 95

5.3. Stress Tensor 96

5.4. Elastic Constants of Solids 96

5.5. Elastic Energy Density 97

5.6. Elastic Constants in Cubic Solids 98

5.7. Elastic Energy Density in Cubic Solids 102

5.8. Bulk Modulus in Cubic Solids 102

5.9. Elastic Waves in Cubic Solids 103

      5.9.1. Elastic Waves in the [100] Direction 105

      5.9.2. Elastic Waves in the [110] Direction 106

      5.9.3. Elastic Waves in the [111] Direction 108

5.10. Isotropic Elasticity 110

5.11. Experimental Measurement of Elastic Constants 111

Suggested Reading 113

6. Lattice Vibrations-1

6.1. Vibrations in a Homogeneous Elastic Medium 115

6.2. Interatomic Potential in Solids 117

      6.2.1. Square-Well Potential 119

      6.2.2. Harmonic Interaction Potential 120

6.3. Lattice Vibrations in a Discrete One-Dimensional Lattice 121

      6.3.1. Monatomic Linear Lattice 121

      6.3.2. Diatomic Linear Lattice 124

6.4. Excitation of Ionic Lattice in Infrared Region 130

7. Lattice Vibrations-2

7.1. Equation of Motion of the Lattice 133

      7.1.1. Restrictions on Atomic Force Constants 135

7.2. Normal Coordinate Transformation 136

7.3. Properties of Dynamical Matrix and Eigenvectors 137

7.4. Quantization of Lattice Hamiltonian 140

7.5. Simple Applications 141

      7.5.1. Linear Monatomic Lattice 141

      7.5.2. Linear Diatomic Lattice 142

      7.5.3. Simple Cubic Lattice 144

7.6. Experimental Determination of Phonon Frequencies 146

      7.6.1. Neutron Diffraction Technique 146

      References 148

      Suggested Reading 148

      Further Reading 148

8. Specific Heat of Solids

8.1. Experimental Facts 150

8.2. Thermodynamical Definition 150

8.3. Phase Space 151

8.4. Classical Theories of Lattice Specific Heat 152

      8.4.1. Free Atom Model 153

      8.4.2. Fixed Classical Harmonic Oscillator Model 156

8.5. Quantum Mechanical Theories 158

      8.5.1. Einstein Theory of Specific Heat 158

      8.5.2. Debye Theory of Specific Heat 160

8.6. Effect of Electrons on Specific Heat 167

8.7. Ideal Phonon Gas 167

8.8. Interacting Phonon Gas 168

8.9. Thermal Expansion of Solids 169

8.10. Thermal Conductivity of Solids 171

      8.10.1. Thermal Conductivity for an Ideal Gas of Atoms 172

      8.10.2. Thermal Conductivity in Insulators and Dielectrics 173

      8.10.3. Thermal Conductivity of Metals 174

      Further Reading 176

9. Free-Electron Theory of Metals

9.1. Free-Electron Approximation 177

9.2. Three-Dimensional Free-Electron Gas 177

9.3. Two-Dimensional Free-Electron Gas 182

9.4. Cohesive Energy and Interatomic Spacing of Ideal Metal 184

9.5. The Fermi-Dirac Distribution Function 186

9.6. Specific Heat of Electron Gas 187

      9.6.1. One-Dimensional Free-Electron Gas 188

      9.6.2. Two-Dimensional Free-Electron Gas 189

      9.6.3. Three-Dimensional Free-Electron Gas 190

9.7. Paramagnetic Susceptibility of Free-Electron Gas 192

      9.7.1. One-Dimensional Free-Electron Gas 195

      9.7.2. Two-Dimensional Free-Electron Gas 195

      9.7.3. Three-Dimensional Free-Electron Gas 196

9.8. Classical Spin Susceptibility 197

Reference 197

Suggested Reading 198

10. Electrons in Electric and Magnetic Fields

10.1. Equation of Motion 199

10.2. Free Electrons in a Static Electric Field 200

10.3. Free Electrons in a Static Magnetic Field 201

10.4. Electrons in Static Electric and Magnetic Fields 202

10.5. The Hall Effect in Metals 204

10.6. Free Electrons in an Alternating Electric Field 206

10.7. Quantum Mechanical Theory of Electrons in Static Electric and Magnetic Fields 208

10.8. Quantum Hall Effect 212

      10.8.1. Two-Dimensional Electron System 213

      10.8.2. Classical Theory of Conductivity in a Magnetic Field 214

      10.8.3. Quantum Theory of a 2D Free-Electron Gas in a Magnetic Field 215

      10.8.4. Experimental Setup for QHE 217

      10.8.5. Integral Quantum Hall Effect 219

      10.8.6. Fractional Quantum Hall Effect 220

10.9. Wiedemann-Franz-Lorentz Law 220

References 221

Suggested Reading 221

11. Transport Phenomena

11.1. Velocity Distribution Function 223

11.2. Electric Current and Electrical Conductivity 223

      11.2.1. Electrostatic Interactions 224

      11.2.2. Collision Interactions 224

11.3. Heat Current and Thermal Conductivity 225

11.4. The Boltzmann Transport Equation 225

      11.4.1. Classical Formulation 225

      11.4.2. Quantum Formulation 227

11.5. Linearization of Boltzmann Equation 227

11.6. Electrical Conductivity 228

      11.6.1. Classical Theory 230

      11.6.2. Quantum Theory 231

11.7. Thermal Conductivity 232

      11.7.1. Classical Theory 232

      11.7.2. Quantum Theory 234

11.8. Hall Effect 237

11.9. Mobility of Charge Carriers in Solids 239

Suggested Reading 242

12. Energy Bands in Crystalline Solids

12.1. Bloch Theorem 243

      12.1.1. One-Dimensional Solid 243

      12.1.2. Three-dimensional Solid 245

12.2. The Kronig-Penney Model 247

12.3. Nearly Free-Electron Theory 251

      12.3.1. Application to One-Dimensional Solid 255

12.4. Different Energy Zone Schemes 257

      12.4.1. Extended Zone Scheme 257

      12.4.2. Periodic Zone Scheme 257

      12.4.3. Reduced Zone Scheme 258

12.5. Tight-Binding Theory 259

      12.5.1. Linear Monatomic Lattice 263

      12.5.2. Two-Dimensional Square Lattice 264

      12.5.3. Three-Dimensional sc Lattice 266

12.6. Orthogonalized Plane Wave (OPW) Method 268

12.7. Augmented Plane Wave (APW) Method 270

12.8. Dynamics of Electrons in Energy Bands 272

      12.8.1. Behavior of Electrons in Free-Electron Theory 274

      12.8.2. Behavior of Electrons in Tight-Binding Approximation 274

12.9. Distinction Between Metals, Insulators, and Semiconductors 275

References 278

Suggested Reading 278

13. The Fermi Surfaces

13.1. Constant Energy Surfaces 279

13.2. The Fermi Surfaces 279

13.3. The Fermi Surface in the Free-Electron Approximation 279

      13.3.1. Type I Fermi Surface 280

      13.3.2. Type II Fermi Surface 281

      13.3.3. Type III Fermi Surface 282

13.4. Harrisons Construction of the Fermi Surface 283

13.5. Nearly Free-Electron Approximation 285

13.6. The Actual Fermi Surfaces 287

      13.6.1. Monovalent Metals 287

      13.6.2. Polyvalent Metals 291

13.7. Experimental Methods in Fermi Surface Studies 293

      13.7.1. de Haas-van Alphen Effect 293

      13.7.2. Cyclotron Resonance 296

      References 298

      Suggested Reading 298

      Further Reading 298

14. Semiconductors

14.1. Intrinsic Semiconductors 299

14.2. Extrinsic Semiconductors 301

      14.2.1. n-Type Semiconductors 302

      14.2.2. p-Type Semiconductors 302

14.3. Ionization Energy of Impurity 303

14.4. Carrier Mobility 304

14.5. Theory of Intrinsic Semiconductors 306

      14.5.1. Concentration of Charge Carriers 306

14.6. Model for Extrinsic Semiconductors 309

      14.6.1. n-Type Semiconductors 309

      14.6.2. p-Type Semiconductors 310

14.7. Effect of Temperature on Carrier Density 311

14.8. Temperature Dependence of Mobility 312

14.9. The Hall Effect 313

14.10. Electrical Conductivity in Semiconductors 317

      14.10.1. Intrinsic Semiconductors 317

      14.10.2. Extrinsic Semiconductors 317

14.11. Nondegenerate Semiconductors 318

14.12. Degenerate Semiconductors 318

14.13. Compensated Semiconductors 319

Suggested Reading 319

15. Dielectric Properties of Nonconducting Solids

15.1. Nonpolar Solids 321

15.2. Polar Solids 321

15.3. Electric Dipole Moment 322

15.4. Macroscopic Electric Field 323

15.5. Potential due to an Electric Dipole 324

15.6. Depolarization Field due to Cuboid 324

15.7. Polarization 325

15.8. Dielectric Matrix 326

15.9. Experimental Measurement of Dielectric Constant 327

15.10. Local Electric Field at an Atom 328

15.11. Polarizability 330

15.12. Polarization 330

15.13. Types of Polarizabilities 331

15.14. Variation of Polarizability With Frequency 332

15.15. Orientational Polarizability 333

15.16. Classical Theory of Electronic Polarizability 335

Suggested Reading 337

16. Ferroelectric Solids

16.1. Classification of Ferroelectric Solids 340

      16.1.1. Tartrate Group 340

      16.1.2. Dihydrophosphates and Arsenates 342

      16.1.3. Perovskite Structure 342

16.2. Theories of Ferroelectricity 343

      16.2.1. Atomic Models 343

16.3. Thermodynamics of Ferroelectric Solids 348

      16.3.1. Second-Order Transition in Ferroelectric Solids 349

      16.3.2. First-Order Transition in Ferroelectric Solids 351

16.4. Ferroelectric Domains 353

Suggested Reading 354

17. Optical Properties of Solids

17.1. Plane Waves in a Nonconducting Medium 355

17.2. Reflection and Refraction at a Plane Interface 357

      17.2.1. Kinematic Properties 357

      17.2.2. Dynamic Properties 359

17.3. Electromagnetic Waves in a Conducting Medium 362

17.4. Reflectivity From Metallic Solids 365

17.5. Reflectivity and Conductivity 366

17.6. Kramers-Kronig Relations 367

17.7. Optical Models 368

      17.7.1. Drude Model 369

      17.7.2. Lorentz Model for Insulators 375

17.8. Lyddane-Sachs-Teller Relation 378

Suggested Reading 381

18. Magnetism

18.1. Atomic Magnetic Dipole Moment 383

      18.1.1. Orbital Magnetic Moment 384

      18.1.2. Spin Magnetic Moment 385

      18.1.3. Nuclear Magnetic Moment 387

18.2. Magnetization 387

18.3. Magnetic Induction 387

18.4. Potential Energy of Magnetic Dipole Moment 387

18.5. Larmor Precession 388

18.6. Quantum Theory of Diamagnetism 389

18.7. Paramagnetism 392

      18.7.1. Classical Theory of Paramagnetism 395

      18.7.2. Quantum Theory of Paramagnetism 395

18.8. Hund's Rule 397

      18.8.1. Applications of Hunds Rule 401

18.9. Crystal Field Splitting 401

      18.9.1. Quenching of Orbital Angular Momentum 404

      Suggested Reading 405

19. Ferromagnetism

19.1. Weiss Molecular Field Theory 407

19.2. Classical Theory of Ferromagnetism 408

19.3. Quantum Theory of Ferromagnetism 410

19.4. Comparison of Weiss Theory With Experiment 412

19.5. Heisenberg Theory of Ferromagnetism 414

19.6. Spin Waves 419

      19.6.1. Bloch Theory of Spin Waves 420

      19.6.2. Magnons in Monatomic Linear Lattice 423

      19.6.3. Magnons in Square Lattice 423

      19.6.4. Magnons in sc Lattice 424

19.7. Quantization of Spin Waves 425

19.8. Thermal Excitation of Magnons 428

19.9. Hysteresis Curve 429

Suggested Reading 430

20. Antiferromagnetism and Ferrimagnetism

20.1. Antiferromagnetism 431

      20.1.1. Two-Sublattice Model 431

      20.1.2. Spin Waves in Antiferromagnetism 437

20.2. Ferrimagnetism 441

      20.2.1. Structure of Ferrites 441

      20.2.2. Two-Sublattice Model 442

      Reference 443

      Suggested Reading 443

21. Magnetic Resonance

21.1. Nuclear Magnetic Moment 445

21.2. Zeeman Effect 446

21.3. Relaxation Phenomena 448

      21.3.1. Spin-Lattice Relaxation 448

      21.3.2. Spin-Spin Relaxation 450

21.4. Equation of Motion 450

21.5. Magnetic Resonance in the Absence of Relaxation Phenomena 452

21.6. Bloch Equations 454

      21.6.1. Free Precession in Static Magnetic Field 455

21.7. Magnetic Broadening of Resonance Lines 457

21.8. Effect of Molecular Motion on Resonance 457

21.9. Electron Spin Resonance 458

21.10. Hyperfine Interactions 459

21.11. Knight Shift 460

21.12. Quadrupole Interactions in Magnetic Resonance 461

      21.12.1. Nuclear Quadrupole Resonance 462

21.13. Ferromagnetic Resonance 464

21.14. Spin Wave Resonance 464

21.15. Antiferromagnetic Resonance 464

Reference 464

Suggested Reading 464

22. Superconductivity

22.1. Experimental Survey 465

      22.1.1. Electrical Properties 465

      22.1.2. Magnetic Properties 466

      22.1.3. Thermal Properties 466

      22.1.4. Isotopic Effect 469

22.2. Occurrence of Superconductivity 470

22.3. Theoretical Aspects of Superconductivity 471

      22.3.1. Failure of Ohm's Law in Superconductors 471

      22.3.2. London Theory 472

      22.3.3. Penetration Depth 475

      22.3.4. Coherence Length 476

      22.3.5. Destruction of Superconductivity by Magnetic Field 477

      22.3.6. Stabilization Energy 478

      22.3.7. Classification of Superconductors 480

      22.3.8. Persistent Currents 481

      22.3.9. Thermodynamics of Superconductors 483

      22.3.10. Bardeen-Cooper-Schrieffer (BCS) Theory 488

      22.3.11. Criterion for the Existence of Superconductivity 494

      22.3.12. Why Do Magnetic Impurities Lower T_c? 494

22.4. Superconducting Quantum Tunneling 494

      22.4.1. Single-Electron Superconducting Tunneling 494

      22.4.2. Josephson Tunneling 502

22.5. High-Tc Superconductivity 506

      22.5.1. Chevrel Phases and Superconductivity 506

      22.5.2. Perovskite Superconductivity 507

      22.5.3. Cu-Oxide Superconductors 508

      22.5.4. A2BX4 Superconductors 508

      22.5.5. Quaternary Copper Oxides 509

      22.5.6. Bismates and Thallates 508

      References 511

      Suggested Reading 511

23. Defects in Crystalline Solids

23.1. Point Defects in Solids 513

      23.1.1. Solid Solutions 514

      23.1.2. Types of Point Defects 514

      23.1.3. Excitons 520

      23.1.4. Statistical Distribution of Point Defects 522

23.2. Dislocations 525

      23.2.1. Plastic Deformation of Crystals 525

      23.2.2. Definition of Dislocation 525

      23.2.3. Force Acting on Dislocations 527

      23.2.4. Critical Shear Stress 528

      23.2.5. Dislocation Density and Shear Strain 530

      23.2.6. Types of Dislocations 530

      23.2.7. Conservation of the Burgers Vector 533

      23.2.8. Dislocation Energy 534

      23.2.9. Growth of Slips: The Frank-Read Source 536

      23.2.10. Grain Boundary 537

      Suggested Reading 537

24. Amorphous Solids and Liquid Crystals 540

24.1. Structure of Amorphous Solids 541

      24.1.1. Continuous Random Network Model 542

      24.1.2. Random Close Packing 543

      24.1.3. Long-Chain Molecular Compounds 544

      24.1.4. Copolymers 544

      24.1.5. Plasticizers 544

      24.1.6. Elastomers 544

24.2. Characteristics of Amorphous Solids 545

24.3. Applications of Amorphous Solids 546

24.4. Liquid Crystals 547

      24.4.1. The Building Blocks 548

      24.4.2. Nematics and Cholesterics 549

      24.4.3. Smectics 551

      24.4.4. Long-Range Order in a System of Long Rods 552

      24.4.5. Uses of Liquid Crystals 552

      Suggested Reading 554

25. Physics of Nanomaterials

25.1. Reduction in Dimensionality 555

      25.1.1. Quantum Well 556

      25.1.2. Quantum Wire 562

      25.1.3. Quantum Dot 566

      25.1.4. Quantum Ring 567

25.2. Quantum Tunneling 568

25.3. Nanoparticles 570

      25.3.1. Magnetic Nanoparticles 571

      25.3.2. Structure of Nanoparticles 572

      25.3.3. Methods of Synthesis of Nanoparticles 574

      25.3.4. Nanostructured Materials 577

      25.3.5. Computer Simulation Technique 578

25.4. Nanomaterials of Carbon 579

      25.4.1. Nanoparticles of Carbon 579

      25.4.2. Carbon Nanotubes 581

25.5. Microscopes Used for Nanomaterials 584

      25.5.1. Scanning Tunneling Microscope 585

      25.5.2. Atomic Force Microscope 586

      25.5.3. Magnetic Force Microscope 588

25.6. Applications 589

      25.6.1. Basic Sciences 589

      25.6.2. Nanoelectronics 589

      25.6.3. Smart Materials 589

      25.6.4. Nanocomposite Materials 589

      25.6.5. Nanopharmaceuticals 590

25.7. Future Thrust 590

References 590

Suggested Reading 591

Appendix A 593

Appendix B 595

Appendix C 597

Appendix D: Bose-Einstein Statistics 599

Appendix E: Density of Phonon States 601

Appendix F: Density of Electron States 605

Appendix G: Mean Displacement 609

Appendix H 611

Appendix I: The Fermi Distribution Function Integral 615

Appendix J: Electron Motion in Magnetic Field 617

Appendix K 619

Appendix L: Atomic Magnetic Dipole Moment 623

Appendix M: Larmor Precession 625

Further Reading 627

Index 631

Dr· Joginder Singh Gaisin is a physicist who was born in the north Indian city of Ludhiana, Punjab. After graduating in science, he went on to acquire an MSc (Honors School) degree and a PhD in theoretical solid state physics from Punjab University, Chandigarh. He later worked as a postdoctoral fellow for 1 year in the same departmeni.PF\He started his professional career in 1977 as an assistant professor of physics in Punjab Agricultural University, Ludhiana and, over the next 30 years, became a powerhouse in the Sciences Department there. In 2007, he retired from the University at the age of 60 as professor and head. Department of Mathematics, Statistics and Physics, with a brief stint as reader in physics at Guru Nanak Dev University, Amritsar, from 1984 to 1986. After his retirement, he served for another 7 years in three institutions in various capacities: as head, Department of Physics, Lovely Professional University, Jalandhar; as director, Gulzar Institute of Engineering & Technology, Khanna; and as professor, Ludhiana Institute of Engineering & Technology, Katani Kalan, Ludhiana. He eventually retired from service in 2014 at the age of 67 after 37 long years of committed and dedicated educative service in various educational institutions.PF\Over the course of his academic years, he was an external expert on various academic/professional committees, including lhe Board of Studies in Physics, Punjabi University, Patiala; the Faculty of Physical Sciences of Punjabi University, Patiala, and M.D. University, Rohtak; and the Research Degree Committee of Guru Nanak Dev University, Amritsar. He was a member of lhe Academic Councils of Punjab Technical University, Jalandhar, and Lovely Professional University, Jalandhar.PF\He was awarded the Best Teacher Award in 1982 by The Punjab Agricultural University Teachers Association. He has more than 80 research papers in journals of national/intemational repute to his credit (41 in international and 39 in national joumals/conferences). The areas of his professional and personal experience and interest include the lattice dynamics of transition metals, band magnetism in metals, and the electronic structure of metallic alloys. He has supervised a number of MSc and MPhil students and jointly supervised PhD students in the above-mentioned fields. He attended a number of national and international conferences in the above-mentioned fields and delivered invited talks on various teachi ng and research topics, including nanotechnology.PF\He authored a book called Impurity Scattering in Metallic Alloys, which was published by Kluwer Academic/Plenum Publishers, New York, in 2002 (now with Springer). Il is a fulfilling moment to mention that the present book entitled Solid State Physics: An Introduction to Theory^ the outcome of 16 committed years, is sure lo be of immense value to the physics community.

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