Table Of ContentEngineering Physics-II
As per the revised syllabus of Uttar Pradesh
Technical University
R. K. Shukla
Associate Professor
Department of Physics
HBTI, Kanpur
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ISBN: 9789332526433
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First Impression
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Syllabus
Engineering Physics-II
Unit-I 07 Hrs
Crystal Structures and X-ray Diffraction
Space lattice, basis, Unit cell, Lattice parameter, Seven crystal systems and fourteen Bravais lat-
tices, Crystal-system structure, Packing factor (cubic, body, and face), Crystal structure of NaCL
and diamond, Lattice planes and Miller, Reciprocal lattice, Diffraction of X-rays by crystal,
Laue’s experiment, Bragg’s law, Bragg’s spectrometer.
Unit-II 08 Hrs
Dielectric and Magnetic Properties of materials
Dielectric Properties: Dielectric constant and Polarization of dielectric materials, Types of
Polarization (polarizability). Equation of internal fields in liquid and solid (One Dimensional),
Claussius Mussoti-equation, Frequency dependence of dielectric constant, Dielectric losses,
Important applications of dielectric material,
Magnetic Properties: Magnetization, Origin of magnetic moment, Dia-, para- and ferromagne-
tism, Langevin’s theory for diamagnetic material, Phenomena of hysteresis and its applications.
Unit-III 06 Hrs
Electromagnetic Theory
Current, Equation of continuity, Maxwell’s Equations (Integral and Differential Forms), Poynting
theorem and Poynting vectors, EM-wave equation and its propagation characteristics in free
space, non-conducting and in conducting media, Skin depth.
Unit-IV 09 Hrs
Physics of some Technologically important Materials
Semiconductors: Band theory of solids, density of states, Fermi-Dirac distribution, Free carrier
density (electrons and holes), Conductivity of semiconductors, Position of Fermi level in intrin-
sic and in extrinsic semiconductors.
Superconductors: Temperature dependence of resistivity in superconducting materials, Effect
of magnetic field, (Meissner effect), Temperature dependence of critical field, Type I and II super-
conductors, BCS theory (Qualitative), High temperature superconductors and applications of
superconductors.
Nano-materials: Basic principles of nanoscience and technology, structure, Properties and uses
of Fullerene and carbon nanotubes, Applications of nanotechnology.
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Contents
Preface, xi
About the Author, xiii
Acknowledgement, xv
Chapter 1: Crystal Structure X-ray Diffraction
1.1 Introduction, 1
1.2 Space Lattice, 2
1.3 Unit Cell and Primitive Cell, 3
1.4 Basic Crystal Structures and their Characteristics, 4
1.5 Bravais Space Lattice, 4
1.6 Calculation of the Number of Atoms Per Unit Cell, 6
1.7 Coordination Number, 6
1.8 Atomic Radii, 7
1.9 Ionic Radii, 8
1.10 Calculation of Lattice Constant, 9
1.11 Lattice Planes and Miller Indices, 11
1.12 Atomic Packing Factor: Packing Efficiency, 14
1.12.1 Atomic packing factor of simple cubic lattice, 15
1.12.2 Atomic packing factor of Fcc lattice, 15
1.12.3 Atomic packing factor of Bcc lattice, 16
1.13 Interplanar Spacing (d ), 17
HKL
1.13.1 Spacing between lattice planes in Bcc crystal, 20
1.13.2 Spacing between lattice planes in Fcc crystal, 21
1.14 Some Common Crystal Structures, 21
1.15 X-Ray Diffraction, 24
1.16 Laue Experiment, 24
1.17 Bragg’s Study of the Pattern, 25
1.18 Bragg’s Law, 25
1.19 Bragg’s X-Ray Spectrometer, 26
1.19.1 Main components, 27
1.19.2 X-Ray source, 27
1.19.3 Graduated circular table, 27
1.19.4 Detector, 27
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vi Contents
1.20 Determination of Crystal Structure Using Bragg’s Law, 27
1.21 Reciprocal Lattice, 28
Summary, 33
Exercises, 34
Chapter 2: Dielectric Properties of Materials
2.1 Introduction, 41
2.2 Classification of Dielectric Materials, 42
2.3 Polar Dielectric Materials, 43
2.4 Non-Polar Dielectric Materials, 43
2.5 Different Kinds of Polarization, 44
2.6 Behaviour of Dielectric Materials, 45
2.6.1 Behaviour of non-polar dielectric materials in D.C. field:
electronic polarization, 45
2.6.2 Theory of orientational polarization of polar dielectrics:
Langevin–Debye theory, 46
2.6.3 Clausius–Mossotti equation: (non-polar dielectric in D.C. field), 53
2.7 Three Electric Vectors E, D, and P, 55
2.8 Gauss’s Law in Dielectric, 57
2.9 Electric Susceptibility and Static Dielectric Constant (c and ∈), 60
e r
2.10 Effect of Dielectric Medium Upon Capacitance, 62
2.11 Macroscopic Electric Field, 65
2.12 Microscopic Electric Field, 65
2.13 Internal (Local) Fields in Liquid and Solid Dielectrics:
One-dimensional Case, 65
2.14 Temperature Dependence of Dielectric Constant, 67
2.15 Response of Dielectric to A.C. (Time-Varying) Field:
Frequency Dependence of Dielectric Loss, 68
2.16 Complex Dielectric Constant, 68
2.17 Dielectric Loss, 69
2.18 Loss Tangent or Power Factor: tan d, 70
2.19 Physical Significance of Loss Tangent, 70
2.20 Dielectric Strength and Dielectric Breakdown, 73
2.21 Various Kinds of Dielectric Materials, 73
2.22 Ferroelectric Dielectrics, 74
2.23 Applications of Ferroelectric Materials in Devices, 74
2.24 Electrostriction Effect and Electrostrictive Materials, 75
2.25 Direct and Inverse Piezoelectric Effect, 75
2.25.1 Applications of piezoelectric materials, 75
2.26 Pyroelectric Materials, 76
2.27 Difference Between Ferroelectricity and Piezoelectricity, 76
Summary, 76
Exercises, 78
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Contents vii
Chapter 3: Magnetic Properties of Materials
3.1 Introduction, 83
3.2 Origin of Magnetic Moment: (Smallest Magnetic Moment), 84
3.3 Some Important Magnetic Parameters, 86
3.3.1 Magnetic flux (F ), 86
m
3.3.2 Magnetization vector (M), 87
3.3.3 Flux density: Magnetic induction (B), 87
3.3.4 Magnetic permeability (m), 88
3.3.5 Magnetic susceptibility (c ), 88
m
3.4 Relation Between Magnetic Permeability and Susceptibility, 88
3.5 Classification of Magnetic Materials, 93
3.6 Characteristics of Diamagnetic Materials, 94
3.7 Characteristics of Paramagnetic Materials, 95
3.8 Characteristics of Ferromagnetic Materials, 96
3.9 Characteristics of Antiferro Magnetic Materials, 97
3.10 Characteristic of Ferrimagnetic Materials, 97
3.11 Langevin’s Theory of Diamagnetism, 97
3.12 Explanation of Dia-, Para-, and Ferromagnetism, 101
3.13 Demagnetization, 102
r r r
3.14 Relation Between H, B, and M Vectors, 102
3.14.1 Restatement of ampere’s law, 104
3.15 Hysteresis, 106
3.16 Antiferro Magnetism and Neel Temperature, 108
3.17 Ferrimagnetic Materials, 109
3.18 Properties of Some Magnetic Materials, 110
3.19 Hard and Soft Ferromagnetic Materials, 112
3.19.1 Soft ferromagnetic materials, 113
3.19.2 Hard magnetic materials, 113
3.20 Hysteresis Curve of a Ferrite, 113
3.21 Applications of Ferrites, 114
3.22 Applications of Hysteresis Curve, 114
Summary, 116
Exercises, 116
Chapter 4: Electromagnetic Theory
4.1 Introduction, 123
4.2 Equation of Continuity (Principle of Conservation of Charge), 125
4.3 Conduction Current and Displacement Current, 125
4.4 Fundamental Laws of Electricity and Magnetism, 127
4.5 Differential Form of Maxwell’s Equations, 127
4.6 Derivation of Maxwell’s Equations, 128
4.7 Properties of Displacement Current, 131
4.8 Maxwell’s Equations in Integral Form, 131
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viii Contents
4.9 Significance of Maxwell’s Equations, 133
4.10 Poisson’s Equation, 133
4.11 Laplace Equation, 133
4.12 Characteristics of Electromagnetic Waves, 136
4.12.1 Transverse nature of plane electromagnetic waves, 138
4.12.2 Ratio of E and B vectors is equal to C, 140
4.13 Poynting Theorem, 141
4.14 Interpretation of Terms, 142
4.15 Poynting Vector, 143
4.16 Electromagnetic Waves in Conducting Medium, 145
4.17 Equation of Plane Polarized Electromagnetic Waves, 146
4.18 Skin Depth: Depth of Penetration, 147
4.19 Significance of Skin Depth, 148
4.19.1 Some useful facts on ‘skin depth’, 149
4.20 Plane Electromagnetic Waves in a Non-conducting
Isotropic (Dielectric Medium), 151
4.20.1 Nature of electromagnet in non-conducting isotropic medium, 151
Summary, 153
Exercises, 154
Chapter 5: Superconductors
5.1 Introduction, 163
5.2 Temperature Dependence of Resistivity: Critical Temperature, 163
5.3 Elemental Superconductors, 164
5.4 Explanation of Superconductivity on the Basis
of Free Electron Theory, 165
5.5 Isotope Effect, 166
5.6 Temperature Dependence of Critical Magnetic Field, 167
5.7 Critical Current: Silsbee’s Rule, 171
5.8 Effect of Magnetic Field: Meissner Effect, 172
5.9 Experimental Demonstration of Meissner Effect, 173
5.9.1 Working mechanism, 174
5.10 Classification of Superconductors, 174
5.11 Electrodynamics of Superconductors
(Explanation of Meissner Effect), 176
5.12 London’s Penetration Depth, 178
5.13 BCS Theory of Superconductors, 182
5.14 Formation and Characteristics of Cooper Pairs, 182
5.14.1 Important characteristics of cooper pairs, 182
5.15 Experimental Evidence for the Energy Gap, 183
5.16 Flux Quantization, 183
5.17 Josephson Effect, 183
5.18 Characteristics of Superconductors, 184
5.19 Effect in Thermodynamic Parameters in Superconducting State, 185
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Contents ix
5.20 Frequency Dependence of Superconductivity, 186
5.21 Present Status of High-temperature Superconductors, 187
5.21.1 Desirable characteristics, 188
5.22 Practical Applications of Superconductors, 188
5.22.1 Electrical applications, 189
Summary, 190
Exercises, 191
Chapter 6: Semiconductors
6.1 Introduction, 197
6.2 Position of Semiconductors in Periodic Table, 198
6.3 Basic Structure of Ge and Si, 198
6.3.1 Comparison between certain parameters of Ge and Si, 200
6.4 Classification of Semiconductors, 200
6.5 Elemental Semiconductors, 202
6.6 Formation of Energy Bands in Solid Material: Kronig–Penny Model, 202
6.6.1 Interpretation of solution, 204
6.7 Formation of Energy Bands in Semiconductors and Insulators, 205
6.8 Classification of Materials on the Basis of Band Structure, 206
6.9 Explanation for the Difference in the Electrical Properties of Different
Materials, 208
6.10 Important Characteristics of a Band Electron, 210
6.11 Concept of Hole: A Remarkable Contribution of Band Theory, 210
6.12 Classification of Elemental Semiconductors, 211
6.12.1 Intrinsic semiconductors, 211
6.13 Impurity Addition in Semiconductors: Doping, 211
6.14 Extrinsic Semiconductors, 212
6.15 Selection of Semiconductor Materials for Various Devices, 214
6.16 Fermi–Dirac Statistics, 214
6.17 Fermi–Dirac Distribution, 215
6.18 Fermi Function: Occupation Index, 216
6.19 Fermi–Dirac Energy Distribution Law, 217
6.20 Determination of the Number of Microstates or Phase Cells, 217
6.21 Significance of Fermi Energy, 219
6.22 Motion of Electron in Solid: Effective Mass of Charge Carriers, 220
6.23 Concentration of Free Charge Carrier in Intrinsic Semiconductor, 221
6.24 Position of Fermi Level in Intrinsic Semiconductor, 223
6.25 Temperature Dependence of Carrier Concentration, 224
6.26 Position of Fermi Level in Extrinsic Semiconductor, 225
6.27 Intrinsic Conductivity of Semiconductor, 229
6.28 Position of Donor Energy Level in n-Type Semiconductor, 229
6.29 Position of Acceptor Levels in p-Type Semiconductor, 231
6.30 Transport Mechanism in Semiconductors, 232
6.30.1 Carrier drift and drift mobility, 232
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