Pillai SO Solid State Physics PDF

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About the Book: The ninth multicolour edition of this book has been prepared with a few additional features. It includes three new topics–Matter Waves, Uncertainty Principle with Experimental Illustrations and Physical Interpretation of the Wave Function Ѱ, which may be of immense use for the studen...

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Dedication Dedicated to my father the late Mr. Sivathanu Pillai who learnt English language from his British Professors at Scott Christan College, Nagercoil around 1910 which in turn helped his last son S.O. Pillai to pick up this language with anxiety and fondling even though the native language was in practice everywhere. S.O. PILLAI

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Preface to the Ninth Edition

We are aware of the present day standard of the students and of the difficulties of the teachers lecturing the innumerable topics on Solid State Physics or Study of the condensed Materials. The feedback and comments from the students and the professors were of immense use for the author in bringing out the new edition with two newer topics with problems and solutions. Again number of figures in the previous editon have been replaced by new sketches. With half mind the author tells that highly accelerated electrons are needed to go for further study of nuclear physics and the one on space science. Hence some essential topics in nutshells have been treated in a humble way in this edition. Computation of de Broglie wavelength of electron applying relativistic correction followed by a few interesting problems with solutions has been treated in this edition with all mathematical steps hoping the readers will welcome it. As uncertainty principle helped to pull out events that led to the development of present day physics, religion and meta physics. Its applications in the study and behaviour of micro particles such as electrons under an applied field or otherwise helped our physicists to expand their activities further. Niels Bohr was the first scientist who pointed out in his principle of complementary how the ideas of waves and particles complement rather than contradict. Hence the author brought out this topic in his style, to wear you in your style. Feed back, Please. The good fortune of the author was to bring in more than a lakh of readers nearer to him. They now join with the author for congratulating the Publishers, New Age International P (Ltd), New Delhi for the excellent work carried out in the last two decades. I also annotate that the colour code used at the required junctions cool our eyes and make the brain to work hard. Kozhikode

S.O. PILLAI

ix

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Contents Foreword Preface to the Ninth Edition Preface to the First Edition Acknowledgements Elements and their Symbols Conversion Table List of Physical Constants with their Units List of Tables

(vii) (ix) (x) (xi) (xxii) (xxiii) (xxiv) (xxvi)

1. INTRODUCTION 2. REVIEW OF ATOMIC STRUCTURE I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII XIX XX XXI

: : : : : : : : : : : : : : : : : : : : :

1 3

The Rutherford Model of the Atom ................................................................................ 3 Conclusion of Rutherfords Theory ............................................................................... 4 Drawbacks of the Rutherford Model of the Atom ......................................................... 4 Bohr Model of Atom ....................................................................................................... 4 Bohrs Theory of Hydrogen Atom.................................................................................. 5 Total Energy of the Electron in the Stationary Orbits .................................................... 7 Calculation of rn and En for Hydrogen Atom ................................................................. 8 Bohrs Interpretation of Hydrogen Spectrum ................................................................. 9 Spectral Series of Hydrogen ......................................................................................... 10 Shortcomings of Bohrs Theory .................................................................................. 12 Sommerfelds Relativistic Atom Model ........................................................................ 13 Elliptical Orbits for Hydrogen ....................................................................................... 13 Total Energy of an Electron in an Elliptical Orbit ......................................................... 18 Sommerfelds Relativistic Correction ........................................................................... 22 Fine Structure of Hα Line ............................................................................................. 23 Drawbacks of Bohr-Sommerfeld Atom Model ............................................................. 23 Vector Atom Model ....................................................................................................... 24 The Characteristic Quantum Numbers ......................................................................... 24 The Paulis Exclusion Principle .................................................................................... 27 Application of Paulis Exclusion Principle .................................................................... 27 Electron Configuration .................................................................................................. 30

xii

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xiii

CONTENTS

XXII : The Periodic Table ........................................................................................................ 30 XXIII : Wave Mechanical Concept of the Atom ....................................................................... 38 l l l l

Objective Questions ................................................................................................................. 39 Short Questions ........................................................................................................................ 42 Review Questions ..................................................................................................................... 43 Problems ................................................................................................................................... 45

3. INTERATOMIC FORCES AND BONDINGS IN SOLIDS

47

I : Introduction .................................................................................................................. 47 II : Forces between Atoms ................................................................................................. 47 III

: Cohesion of Atoms and Cohesive Energy..................................................................... 48

IV : Calculation of Cohesive Energy .................................................................................... 50 V : Bonding in Solids .......................................................................................................... 51 VI

: Ionic Bonding ................................................................................................................ 52

VII VIII

: Bond Energy of NaCl Molecule .................................................................................... 53 : Calculation of Lattice Energy of Ionic Crystals ........................................................... 55

IX

: Calculation of Madelung Constant of Ionic Crystals .................................................... 57

X XI

: Calculation of Repulsive Exponent from Compressibility Data .................................... 59 : The Born-Haber Cycle .................................................................................................. 62

XII

: Properties of Ionic Solids ............................................................................................. 64

XIII

: Examples of Ionic Solids .............................................................................................. 65

XIV XV

: Covalent Bond ............................................................................................................... 65 : Saturation in Covalent Bonds ........................................................................................ 68

XVI

: Directional Nature of a Covalent Bond ......................................................................... 68

XVII : Hybridization ................................................................................................................. 70 XVIII : Properties of Covalent Compounds .............................................................................. 71 XIX

: Metallic Bond ................................................................................................................ 72

XX XXI

: Properties of Metallic Crystals...................................................................................... 74 : Intermolecular Bonds .................................................................................................... 74

XXII

: Dispersion Bonds .......................................................................................................... 74

XXIII

: Dipole Bonds ................................................................................................................. 75

XXIV

: Hydrogen Bonds ............................................................................................................ 76

l l l l

Objective Questions ................................................................................................................. 79 Short Questions ........................................................................................................................ 81 Review Questions ..................................................................................................................... 81 Problems ................................................................................................................................... 83

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xiv

CONTENTS

4. STRUCTURAL STUDY OF CRYSTALLINE SOLIDS

87

I

: Introduction .................................................................................................................. 87

II

: Lattice Points and Space Lattice ................................................................................... 87

III : The Basis and Crystal Structure ................................................................................... 88 IV : Unit Cells and Lattice Parameters ................................................................................. 89 V : Unit Cell versus Primitive Cell ...................................................................................... 90 VI : Crystal Systems ............................................................................................................ 90 VII : Crystal Symmetry (Symmetry Elements in Crystals) .................................................. 92 VIII

: The Twenty-three Symmetry Elements in a Cubic Crystal .......................................... 94

IX

: To show that Five-fold Rotation Axis is not Compatible with a Lattice ...................... 97

X XI

: Combination of Symmetry Elements ............................................................................ 98 : Rotation-Inversion Axis ................................................................................................. 98

XII

: Translation Symmetry Elements ................................................................................... 98

XIII : Space Groups ................................................................................................................ 99 XIV : The Bravais Space Lattices ......................................................................................... 100 XV

: Metallic Crystal Structures ......................................................................................... 100

XVI

: Relation between the Density of Crystal Material and Lattice Constant in a Cubic Lattice ......................................................................................... 110

XVII

: Other Cubic Structures ............................................................................................... 110

XVIII

: Directions, Planes and Miller Indices ......................................................................... 112

XIX XX

: Important Features of Miller Indices of Crystal Planes ............................................. 119 : Important Planes and Directions in a Cubic Crystal .................................................. 119

XXI

: Distribution of Atoms in the Atomic Planes of a Simple Cubic Crystal ..................... 120

XXII : Separation between Lattice Planes in a Cubic Crystal ................................................ 120 XXIII : Allotropy and Polymorphism ...................................................................................... 123 XXIV

: Imperfections in Crystals ............................................................................................ 124

XXV : Reciprocal Lattice ....................................................................................................... 137 XXVI : X-ray Diffraction ........................................................................................................ 147 l l

Objective Questions ............................................................................................................... 148 Short Questions ...................................................................................................................... 151

5. WAVE NATURE OF MATTER AND X-RAY DIFFRACTION

158

I : Introduction ................................................................................................................ 158 II : The de Broglie Hypothesis .......................................................................................... 158 III : Relativistic Correction ................................................................................................. 160 IV : Experimental Study of Matter Waves ......................................................................... 161 V : The Davisson-Germer Experiment ............................................................................. 161

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xv

CONTENTS

VI VII VIII IX X XI XII l l l l

: : : : : : :

Heisenbergs Uncertainty Principle ............................................................................. 163 X-ray Diffraction ........................................................................................................ 165 Braggs Law ................................................................................................................ 166 Braggs X-ray Spectrometer ....................................................................................... 167 Powder Crystal Method .............................................................................................. 169 Rotating Crystal Method ............................................................................................. 170 Correction for Braggs Equation ................................................................................. 170

Objective Questions ............................................................................................................... 172 Short Questions ...................................................................................................................... 175 Review Questions ................................................................................................................... 175 Problems ................................................................................................................................. 176

6. ELECTRICAL PROPERTIES OF METALS

180

I

: Introduction ................................................................................................................ 180

II III

: Classical Free Electron Theory of Metals ................................................................... 181 : Drawbacks of Classical Theory ................................................................................. 190

IV

: Relaxation Time, Collision Time and Mean Free Path................................................ 194

V : Quantum Theory of Free Electrons ............................................................................ 197 VI : Classical Wave Equation ............................................................................................. 198 VII

: Schrödingers Wave Equation ..................................................................................... 200

VIII

: Schrödingers Equation for Stationary States ............................................................ 202

IX X

: Importance of Schrödinger Equation ......................................................................... 204 : Physical Significance of the Wave Function Ψ .......................................................... 205

XI

: Limitations on ψ and Normalisation of Wave Function ............................................. 206

XII XIII

: The Quantum Mechanics of Simple Problems ........................................................... 207 : Particles in a Box with Impenetrable Walls ................................................................. 219

XIV

: Fermi-Dirac Statistics and Electronic Distribution in Solids ...................................... 232

XV XVI

: Density of Energy States and Fermi Energy .............................................................. 233 : The Fermi Distribution Function ................................................................................ 237

XVII

: Heat Capacity of the Electron Gas .............................................................................. 239

XVIII

: Mean Energy of Electron Gas at Absolute Zero ......................................................... 240

XIX XX

: Effect of Temperature on Fermi Distribution Function ............................................. 241 : Electrical Conductivity from Quantum Mechanical Considerations ........................... 249

XXI

: Electron Scattering and Sources of Resistance in Metals .......................................... 252

XXII : Electron Scattering Mechanisms and Variation of Resistivity with Temperature....... 255 XXIII : Resistivity of Alloys .................................................................................................... 261 XXIV

: Variation of Resistivity with Pressure ......................................................................... 262

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xvi

CONTENTS

XXV

: Thermal Conductivity in Metals.................................................................................. 262

XXVI XXVII

: Thermal Expansion ..................................................................................................... 265 : Mechanical Effects on Electrical Resistance .............................................................. 2...