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Contents Preface to Fourth Edition .............................................................................. (vii) ...

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Contents Preface to Fourth Edition .............................................................................. (vii)

CHAPTER - 1

| Bonding in Solids

1.1 1.2

Introduction ........................................................................................................... 1 Types of Bonding .................................................................................................. 3 1.2.1 Ionic Bond ............................................................................................. 3 1.2.2 Lattice Energy in Ionic Solids ............................................................... 5 1.2.3 Ionic Radii and Coordination Number .................................................. 7 1.2.4 Properties of Ionic Crystals ................................................................... 9 1.3 Covalent Bond and Covalent Crystals 1.3.1 Covalent Bonds in Crystals ................................................................. 10 1.3.2 Properties of Covalent Crystals ........................................................... 11 1.4 Metallic Bonding ................................................................................................. 12 1.4.1 Nature of Metallic Bonding ................................................................. 12 1.4.2 Properties of Metallic Bonding ........................................................... 13 1.5 Hydrogen Bonding .............................................................................................. 13 1.6 Secondary (Van der Waals) Bonding .................................................................. 15 1.7 Cohesive Energy ................................................................................................. 17 1.8 Born Repulsive Exponent ................................................................................... 20 Questions ................................................................................................................ 21 Objective Questions ..................................................................................................... 22

CHAPTER - 2 2.1 2.2 2.3 2.4

| Crystallography and Crystal Structures

Introduction ......................................................................................................... 27 Space Lattice ....................................................................................................... 29 Two-dimensional Lattice ..................................................................................... 30 Crystal Systems and Bravais Lattices ................................................................. 33 (ix)

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2.5 2.6 2.7

Crystal Planes and Miller Indices ....................................................................... 35 Representation of Directions in a Crystal ........................................................... 40 Interplanar Spacing ............................................................................................. 43 2.7.1 Separation Between Successive Planes ............................................... 43 2.8 Cubic Crystal Systems ........................................................................................ 45 2.9 Atomic Packing Fraction in Crystal .................................................................... 47 2.9.1 Simple Cubic Structure ........................................................................ 47 2.9.2 BCC Structure ...................................................................................... 47 2.9.3 FCC Structure ...................................................................................... 49 2.9.4 Diamond Structure ............................................................................... 51 2.9.5 Hexagonal Close Packed Crystal Structure ......................................... 53 2.10 Sodium Chloride (Rock Salt) Structure .............................................................. 54 2.11 Zinc Sulphide Structure ...................................................................................... 55 2.12 CsCl Structure ..................................................................................................... 55 Questions ................................................................................................................ 56 Objective Questions ..................................................................................................... 57

CHAPTER - 3

| X-Ray Diffraction

3.1 Basic Principles ................................................................................................... 61 3.2 Bragg Law ........................................................................................................... 61 3.3 Laue Method ....................................................................................................... 63 3.4 Powder Method ................................................................................................... 65 3.5 Difference in the Diffraction Pattern of fcc and bcc Crystals ............................. 70 3.6 X-ray Diffractometer ........................................................................................... 71 3.7 Applications of X-ray Diffraction (XRD) ........................................................... 72 Questions ................................................................................................................ 74 Objective Questions ..................................................................................................... 75

CHAPTER - 4 4.1 4.2

| Defects in Crystals

Introduction ......................................................................................................... 78 Point Defects ....................................................................................................... 79 4.2.1 Vacancies ............................................................................................. 79 4.2.2 Impurities: Substitutional and Interstitial ............................................ 80 4.2.3 Frenkel Defects .................................................................................... 81 4.2.4 Equilibrium Concentration of Schottky Defects in Metals ................. 82

Contents 4.3 4.4

Study of Existence of Points Defects in crystals ................................................ 84 Line Defects ........................................................................................................ 84 4.4.1 Theoretical Shear Stress ...................................................................... 84 4.4.2 Edge Dislocation .................................................................................. 86 4.4.3 Screw Dislocation ................................................................................ 87 4.4.4 Burger’s Vector and Burger’s Circuit .................................................. 88 4.5 Two dimensional Defects or Surface Defects ..................................................... 91 4.5.1 Surfaces ................................................................................................ 91 4.5.2 Grain Boundaries ................................................................................. 91 4.5.3 Twin Boundaries .................................................................................. 93 4.5.4 Microcracks ......................................................................................... 93 4.5.5 Phase Boundaries ................................................................................. 93 4.6 Volume Defects ................................................................................................... 94 4.6.1 Voids .................................................................................................... 94 Questions ................................................................................................................ 96 Objective Questions ..................................................................................................... 98

CHAPTER - 5 5.1 5.2

5.3

5.4

5.5 5.6

| Elements of Statistical Mechanics

Introduction ....................................................................................................... 102 Statistical Mechanics ......................................................................................... 103 5.2.1 What is statistical mechanics? ........................................................... 103 5.2.2 The characteristics or features of a ‘system’ ..................................... 104 Maxwell-Boltzmann distribution ...................................................................... 106 5.3.1 Particles of Maxwell-Boltzmann (MB) distribution ......................... 106 5.3.2 MB Statistics ...................................................................................... 107 5.3.3 M.B Distribution Function ................................................................ 108 5.3.4 Maxwell – Boltzmann distribution of energy .................................... 110 Bose-Einstein (BE) Statistics ............................................................................ 110 5.4.1 Introduction ....................................................................................... 110 5.4.2 A Case Study of MB and BE Statistics .............................................. 111 5.4.3 Bose-Einstein Statistics ..................................................................... 113 5.4.4 Bose-Einstein Distribution Function ................................................. 114 Fermi-Dirac (FD) Statistics ............................................................................... 116 5.5.1 The characteristic features or postulates Fermi-Dirac statistics: .......... 116 Black Body Radiation Law ............................................................................... 120 5.6.1 Early Models ...................................................................................... 120 5.6.2 Wien’s Displacement law .................................................................. 121 5.6.3 Rayleigh-Jeans Radiation Law .......................................................... 121 5.6.4 Failure of Rayleigh-Jean’s Law ......................................................... 123

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5.7

Planck’s Black Body Radiation Law ................................................................ 123 5.7.1 Max Planck’s Modification ............................................................... 123 5.7.2 Derivation of Planck’s Black Body Radiation Law .......................... 124 5.7.3 Wien’s Displacement Law ................................................................. 125

5.8

Planck’s Black Body Radiation Law on the Basis of BE Statistics .................. 127 5.8.1A Characteristics of Photon gas ............................................................ 127 5.8.1B Number of Energy States ................................................................... 128 5.8.1C Planck’s Radiation Law ..................................................................... 128

5.9

Electron Theory ................................................................................................. 129 5.9.1 A Metals ................................................................................................ 129 5.9.2 B The Free Electron .............................................................................. 129 5.9.2 Electrons are Quantum Particles ........................................................ 130 5.9.3 Electrons as Fermions ........................................................................ 131 5.9.4 Fermi-Dirac Distribution in the Case of Electron Gas ...................... 132 5.9.5 Density of States ................................................................................ 133

5.10 Fermi Energy ..................................................................................................... 134 5.10.1 Expression for Fermi energy of a metal ............................................ 134 5.10.2 Electron – Energy distribution ........................................................... 135 5.10.3 Occupation of Energy Levels ............................................................ 135 5.11 Summary of the Three Statistical Functions – A Comparison .......................... 136 Questions

.............................................................................................................. 136

Objective Questions ................................................................................................... 138

CHAPTER - 6

| Principles of Quantum Mechanics

6.1

Introduction ....................................................................................................... 145

6.2

Dual Nature of Wave-Particle ........................................................................... 146 6.2.1 de Broglie’s Hypothesis ..................................................................... 146 6.2.2 Characteristics of Matter Waves ........................................................ 148

6.3

Relativistic Mass, and Matter Waves ................................................................ 148

6.4

Davisson and Germer Experiment (1927) ........................................................ 150

6.5

G. P. Thomson Experiment (1928) .................................................................... 153

6.6

Heiserberg’s Uncertainty Principle ................................................................... 155

6.7

Schrodinger Wave Equation .............................................................................. 159

6.8

Time-Dependent Schrodinger Equation ............................................................ 159

6.9

The Time-independent Schrodinger Equation .................................................. 162

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6.10 Physical Significance of Wave Function .......................................................... 163 6.11 Postulates of Wave Mechanics or Quantum Mechanics ................................... 164 6.12 Particle in One Dimensional Potential Box ...................................................... 166 Questions and Problems............................................................................................ 171 Objective Questions ................................................................................................... 173

CHAPTER - 7

| Band Theory of Solids

7.1

Introduction ....................................................................................................... 178

7.2

Electron in a Periodic Potential ......................................................................... 178 7.2.1 Formation of Energy Bands ............................................................... 179 7.2.2 Periodic potential and Bloch Theorem .............................................. 180

7.3

The Kronig - Penney Model ............................................................................. 182

7.4

Origin of Energy Band Formation in Solids ..................................................... 185

7.5

Concept of Effective Mass of an Electron and Hole ......................................... 186 7.5.1 Energy and Velocity of an Electron ................................................... 186 7.5.2 Effective Mass of the Electron .......................................................... 187

7.7

Classification of Metals, Conductors Semiconductors and Insulators ............. 189

Questions

.............................................................................................................. 191

Objective Questions ................................................................................................... 193

CHAPTER - 8

| Semiconductor Physics

8.1

Introduction ....................................................................................................... 196

8.2

Electron and Hole Densities .............................................................................. 200 8.2.1 Fermilevel and Carrier Concentration in Intrinsic Semiconductors .. 200 8.2.2 Carrier Concentration ........................................................................ 201 8.2.3 Fermi Level Intrinsic Semiconductors .............................................. 202 8.2.4 Intrinsic Concentration ...................................................................... 203

8.3

Carrier Concentration in Extrinsic Semiconductors ......................................... 204

8.4

Currents in Semiconductors .............................................................................. 209 8.4.1 Drift Current ...................................................................................... 209 8.4.2 The conductivity of and intrinsic semiconductor .............................. 210 8.4.3 Diffusion Currents ............................................................................. 211

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8.5

Equation of Continuity ...................................................................................... 212

8.6

Einstein’s Relation ............................................................................................ 214

8.7 Direct and Indirect Band-Gap Semiconductors ................................................ 214 8.8 Hall Effect ......................................................................................................... 215 Questions .............................................................................................................. 222 Objective Questions ................................................................................................... 224

CHAPTER - 9

| Physics of Semiconductor Devices

9.1 9.2

Introduction ....................................................................................................... 229 Fabrication of pn Junction Diodes .................................................................... 231 Formation of P-N Junction........................................................................... 231 Formation of depletion layer ........................................................................ 231 Equilibrium in a pn Junction Diode ............................................................. 233 Balance of drift and diffusion ...................................................................... 233 Calculation of Diode Current-Voltage Relationship .................................... 234 Majority and Minority Carrier Currents ...................................................... 235 9.3 Volt-ampere Characteristics of pn junction Diode ............................................ 235 Forward biased diode ................................................................................... 236 Under forward bias ...................................................................................... 237 Reverse biased diode .................................................................................... 238 Under reverse bias ........................................................................................ 239 Voltage-Current characteristic of a diode: ................................................... 240 Break down voltage in the reverse bias: ...................................................... 241 Approximate diode models: ......................................................................... 241 Photo diodes ................................................................................................. 242 Light emitting diode ..................................................................................... 244 Liquid crystal display: Principles and Applications .................................... 247 Questions .............................................................................................................. 251 Objective Questions ................................................................................................... 252

CHAPTER - 10 | Dielectric Properties 10.1 Introduction ....................................................................................................... 254 10.1.1 Dielectric Medium Between the Plates of a Capacitor ...................... 255 10.1.2 Atomic View of a Dielectric Polarization .......................................... 257 10.2 Electric Flux Density, Electrical Field and ....................................................... 258 10.3 Polar and Non-Polar Dielectrics ....................................................................... 260

Contents 10.4 10.5 10.6 10.7 10.8

Electronic, Ionic and Orientation Polarization ................................................. 261 Internal Field in a Dielectric Medium and Clausius - Mosotti Equation .......... 262 Electronic Polarisability .................................................................................... 265 Orientation Polarization .................................................................................... 268 Behaviour of Dielectric in Alternating Fields ................................................... 272 10.8.1 Dielectric Loss and Dielectric Relaxation ............................................ 273 10.8.2 Frequency Dependence of Electronic Polarizability ............................ 275 10.9 Frequency Dependence of Dielectric Constant Over a Wide Frequency Range ..................................................................................... 277 10.10 Ferroelectricity and Piezoelectricity ................................................................. 278 10.10.1 Ferroelectricity ................................................................................... 278 10.10.2 Important Characterstics of ferroeletric Materials ............................ 280 10.10.3 Piezoelectricity .................................................................................. 284 10.10.4 Piezoelectric Materials ...................................................................... 287 10.10.5 Applications of Piezoelectrics ........................................................... 288 10.11 Pyroelectricity ................................................................................................... 291 Questions .............................................................................................................. 294 Objective Questions ................................................................................................... 296

CHAPTER - 11 | Magnetic properties 11.1 Introduction ......................................................................................................... 303 11.2 A Magnetic Material in an External Magnetic Field: The Three Vectors B, H and M Field ................................................................ 306 11.3 Origin of Magnetic Moment of Atoms ............................................................. 308 11.4 Diamagnetism.................................................................................................... 311 11.5 Paramegnetism .................................................................................................. 316 11.5.1 Magnetic moment ................................................................................. 316 11.5.2 Langevin’s Classical Theory of Paramagnetism................................... 317 11.5.3 Quantum approach ................................................................................ 320 11.6 Ferromagnetism ................................................................................................. 322 11.6.1 The Characterstics Associated with Ferromagnetism ........................... 322 11.6.2 Molecular Field-Weiss Domain Model ................................................ 324 11.6.3 Temperature Dependence of Spontaneous Magnetization ................... 325 11.6.4 Curie-Weiss Law ................................................................................... 327 11.6.5 Exchange Energy .................................................................................. 328 11.6.6 Domains and Magnetization ................................................................. 330 11.6.7 Hysteresis Loop .................................................................................... 330

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Contents 11.6.8 Magneto Crystalline Anisotropy ........................................................... 334 11.6.9 Magnetostriction .................................................................................... 335 11.6.10 Applications of Ferromagnetic Materials ............................................. 335

11.7 Antiferromagnetism .......................................................................................... 337 11.8 Ferrimagnetism ................................................................................................. 338 11.8.1 Ferrites .................................................................................................. 338 11.8.2 Structure of Ferrites .............................................................................. 339 11.8.3 Susceptibility of ferrites ........................................................................ 341 11.8.4 Characteristics of Ferrites ..................................................................... 341 11.8.5 Applications of Ferrites ........................................................................ 343 11.9 Maxwell’s Equations ......................................................................................... 345 11.10 Faraday’s Law ................................................................................................... 354 11.11 Ampere’s Law ................................................................................................... 354 11.12 Displacement Current........................................................................................ 355 Questions .................................................................................................................... 357 Objective Questions ................................................................................................... 359

CHAPTER - 12 | Lasers 12.1 Introduction ....................................................................................................... 365 12.2 Characterstics of Lasers .................................................................................... 366 12.2.1 Coherence and Monochromaticity .................................................... 367 12.2.2 Directionality ..................................................................................... 367 12.2.3 Speckle nature .................................................................................... 367 12.3 Principle of Laser Emission .............................................................................. 368 12.3.1 Spontanous and Stimulated Emissions .............................................. 368 12.3.2 Einstein Coefficients .......................................................................... 369 12.3.3 Light Amplification and Laser oscillations ....................................... 371 12.3.4 Laser Oscillations .............................................................................. 372 12.4 Population Inversion ......................................................................................... 373 12.5 Methods for Producing Population Invertion ................................................... 374 12.6 Solid State Laser - Ruby Laser ......................................................................... 375 12.7 Gas Lasers ......................................................................................................... 377 12.7.1 He-Ne laser ........................................................................................ 377 12.7.2 The CO2 laser: ................................................................................... 379 12.7.3 Other gas lasers : ................................................................................ 382