INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500043 U NIT-I 1. Crystallography: Ionic Bond, Covalent Bond, Metallic Bond, Hydrogen Bond, Vander-Waal’s Bond, Calculation of Cohesive Energy of diatomic molecule- Space Lattice, Unit Cell, Lattice Parameters, Crystal Systems, Bravais Lattices, Atomic Radius, Co-ordination Number and Packing Factor of SC, BCC, FCC, Miller Indices, Crystal Planes and Directions, Inter Planar Spacing of Orthogonal Crystal Systems, Structure of D iamond and NaCl. 2.X-ray Diffraction & Defects in Crystals: Bragg’s Law, X-Ray diffraction methods: Laue Method, Powder Method: Point Defects: Vacancies, Substitutional, Interstitial, Frenkel and Schottky Defects, line defects (Qualitative) & Burger’s Vector. UNIT-II 3. Principles of Quantum Mechanics: Waves and Particles, de Broglie Hypothesis , Matter Waves, Davisson and Germer’s Experiment, Heisenberg’s Uncertainty Principle, Schrödinger’s Time Independent Wave Equation - Physical Significance of the Wave Function – Infinite square well potential extension to three dimensions 4. Elements of Statistical Mechanics& Electron theory of Solids: Phase space, Ensembles, Micro Canonical , Canonical and Grand Canonical Ensembles - Maxwell- Boltzmann, Bose-Einstein and Fermi-Dirac Statistics (Qualitative Treatment), Concept of Electron Gas, , Density of States, Fermi Energy- Electron in a periodic Potential, Bloch Theorem, Kronig-Penny Model (Qualitative Treatment), E-K curve, Origin of Energy Band Formation in Solids, Concept of Effective Mass of an Electron, Classification of Materials into Conductors, Semi Conductors & Insulators. UNIT-III 5. Dielectric Properties: Electric Dipole, Dipole Moment, Dielectric Constant, Polarizability, Electric Susceptibility, Displacement Vector, Electronic, Ionic and Orientation Polarizations and Calculation of Polarizabilities: Ionic and Electronic - Internal Fields in Solids, Clausius - Mossotti Equation, Piezo -electricity and Ferro- electricity. 6. Magnetic Properties & Superconducting Properties: Permeability, Field Intensity, Magnetic Field Induction, Magnetization, Magnetic Susceptibility, Origin of Magnetic Moment, Bohr Magneton, Classification of Dia, Para and Ferro Magnetic Materials on the basis of Magnetic Moment, Domain Theory of Ferro Magnetism on the basis of Hysteresis Curve, Soft and Hard Magnetic Materials, Properties of Anti-Ferro and Ferri Magnetic Materials and their Applications, Superconductivity, Meissner Effect, Effect of Magnetic field, Type-I & Type-II Superconductors, Applications of Superconductors UNIT-IV 7.Optics: Interference-Interference in thin films(Reflected light), Newton rings experiment- Fraunhofer diffraction due to single slit, N-slits, Diffraction grating e xperiment , Double refraction-construction and working, Nicol’s Prism 8. Lasers & Fiber Optics: Characteristics of Lasers, Spontaneous and Stimulated Emission of Radiation, Einstein’s Coefficients and Relation between them, Population Inversion, Lasing Action, Ruby Laser, Helium-Neon Laser, Semiconductor Diode Laser, Applications of Lasers- Principle of Optical Fiber, Construction of fiber, Acceptance Angle and Acceptance Cone, Numerical Aperture, Types of Optical Fibers: Step Index 1 INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500043 and Graded Index Fibers, Attenuation in Optical Fibers, Application of Optical Fiber in communication systems. UNIT-V: 9. Semiconductor Physics: Fermi Level in Intrinsic and Extrinsic Semiconductors, Calculation of carrier concentration in Intrinsic &, Extrinsic Semiconductors, Direct and Indirect Band gap semiconductors, Hall Effect-Formation of PN Junction, Open Circuit PN Junction, Energy Diagram of PN Diode, Diode Equation, I-V Characteristics of PN Junction diode, Solar cell, LED & Photo Diodes. Acoustics of Buildings & Acoustic Quieting:, Reverberation and Time of Reverberation, Sabine’s Formula for Reverberation Time, Measurement of Absorption Coefficient of a Material, Factors Affecting The A rchitectural Acoustics and their Remedies 10. Nanotechnology: Origin of Nanotechnology, Nano Scale, Surface to Volume Ratio, Quantum Confinement, Bottom-up Fabrication: Sol-gel, Top-down Fabrication: Chemical Vapour Deposition, Characterization by TEM. TEXT BOOKS: 1. Engineering Physics,K. Malik, A. K. Singh, Tata Mc Graw Hill Book Publishers 2. Engineering Physics, V. Rajendran, Tata Mc Graw Hill Book Publishers REFERENCES: 1. Fundamentals of Physics, David Halliday, Robert Resnick, Jearl Walker by John Wiley & Sons 2. Sears and Zemansky's University Physics (10th Edition) by Hugh D. Young Roger A. Freedman, T. R. Sandin, A. Lewis FordAddison-Wesley Publishers; 3. Applied Physics for Engineers – P. Madhusudana Rao (Academic Publishing company, 2013) 4. Solid State Physics – M. Armugam (Anuradha Publications). 5. Modern Physics – R. Murugeshan & K. Siva Prasath – S. Chand & Co. (for Statistical Mechanics). 6. A Text Book of Engg Physics – M. N. Avadhanulu & P. G. Khsirsagar– S. Chand & Co. (for acoustics). 7. Modern Physics by K. Vijaya Kumar, S. Chandralingam: S. Chand & Co.Ltd 8. Nanotechnology – M.Ratner & D. Ratner (Pearson Ed.). 9. Introduction to Solid State Physics – C. Kittel (Wiley Eastern). 10. Solid State Physics – A.J. Dekker (Macmillan). 11. Applied Physics – Mani Naidu Pearson Education 2 INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500043 INDEX Contents Page Unit 1.Crystallography 4 I 2.X-ray Diffraction & Defects in Crystals 31 3.Principles of Quantum Mechanics 43 II 4.Elements of Statistical Mechanics& Electron 59 theory of Solids 5.Dielectric Properties 94 III 6.Magnetic Properties & Superconducting 116 Properties 7.Optics 151 IV 8.Lasers & Fiber Optics 185 9.Semiconductor Physics 229 V 10.Nanotechnology 297 3 INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500043 UNIT-I CRYSTALLOGRAPHY Chapter-1 1.1.1. Introduction to Bonding in Solids Atom consists of a positively charge nucleus surrounded by a negatively charged electron cloud. When the two atoms are brought closer, there will be both attractive and repulsive forces acting on them. Therefore, the two atoms take relative positions when there is a balance between these two forces. This is known as equilibrium position. The bonding forces which bind the atoms in a molecule and in the molecules in a solid are mainly four types of forces i.e. gravitational, electrical, and nuclear and weak forces. Chemical bond is defined as inter-atomic or inter-molecular or inter-ionic force of attraction which holds the atoms together. When the two atoms attain the equilibrium position, then the value of energy needed to move an atom completely away from its equilibrium position is termed as binding energy or cohesive energy. On the basis of the nature of forces which bind solid lattice together, the solids can be divided two mainly groups namely.  Primary bonds  Secondary bonds Primary bonds: Primary bonds are the strongest bonds which hold atoms together. The three types of primary bonds are,  Ionic bond  Covalent bond  Metallic bond Secondary bonds: Secondary bonds are much weaker than primary bonds. Two types of Secondary bonds are,  Hydrogen bond  Vander Waals bond 1.2. Primary bonds 1. Ionic bond: This bond is the simplest type of chemical bond called ‘Hetero polar Bond’. Ionic bonds are mostly insulating in character. These are not pure elements, but they are compounds. Eg:- NaCl, KCl, KBr etc. 4 INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500043 The electronic structure of atoms is relatively stable when the outer shells contain eight electrons (two in the case of 1st shell). Sometimes it is possible by transferring the electrons from one atom to another, electron shells are filled the donor atom will take a positive charge and the acceptance will have a negative charge. When Na and Cl atoms are placed together, these are transfer of electrons from Na to Cl atoms resulting in a strong electrostatic attraction between the positive Na ion and negative Cl ions. Let us examine Na and Cl electronic configuration how they tends to form an ionic bond. Atomic number of Na is 11 Electronic configuration of Na is: 1s22s2 2p 63s1 It has one electron in the outer most orbits, this electron is called as valence electron Na atom try to lose this valence electron in order to attain insert gas configuration. The minimum energy required to detach the electron from Na atom is called as ionization energy. Na + ionization energy → Na+ + e- Ionization energy required = 5.1 eV Atomic number of Cl is 17 Electronic configuration is 1s22s2 2p 63s2 3s5 It has 7 electrons in its outermost orbit. It needs one electron to insert gas configuration. It readily accepts an electron and release some energy called electron affinity. Cl + e- → Cl- + Electron Affinity Electron Affinity = 3.6ev In order to produce two ions, NaCl needs energy equal to5.1ev-3.6eV = 1.5ev Na + Cl + 1.5 eV → Na+ + Cl- Na+ and Cl- attract each other and form a bond. This bond is called “Ionic Bond”. 5 INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500043 Characteristics of ionic bonded Materials  Ionic bonds are strong.  They have high melting points and boiling points.  They are transparent to visible light.  They have closed packed structure.  They are highly soluble in polar solvents like H 0, liquid NH and insoluble in 2 3 non-polar solvent.  Non directional, because the charge distribution is special in nature. 2. Covalent Bond: covalent bonds are called homo polar bounds. In this neighboring atoms share their valence electrons in the formation of a strong covalent bound. Eg: Cl , O etc. 2 2, Consider the Cl atom, which has seven electrons in the valence shell. Spins of 6 electrons are paired, where as the spin of 7 the electron is unpaired. The unpaired electron is always looking for another unpaired electron. Which comes closer to it. In such case another Cl atom comes near the first Cl atom. The two unpaired electrons of the two atoms get paired. . Characteristics of covalent bonded materials  These bounds are usually hard and brittle.  Binding energy is high.  M.P and B.P are high but low compared to ionic crystal.  Covalent bonds are insoluble in H o. 2 6 INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500043  These materials are soluble in non-polar solvents like C H 6 6.  They are transparent to longer wavelengths, but opaque to shorter wavelength. 3. Metallic Bond: Metallic bonds are similar to covalent bonds. In this outer electrons have high mobility. In metallic bonding each atom of metal give one or two value electrons to the crystal. These hold the atoms together and are not bound to individual atoms, but move freely throughout the whole metal. In metal, the ionization energies are low, so metallic atoms gives their valence electrons to crystal. The valence electrons will form electron cloud or electron gas, which is occupied throughout the metal space. The positive ions are held together by the electrostatic forces due to the free electrons. The electrostatic interaction between the positive ion and the surrounding electron could hold the metal together. So it is called the metallic bond. Eg; - Al, Ag, Na, Cu etc. Fig: Atomic arrangement in metallic crystals Characteristics of Metallic bonded materials  They have high thermal conductivity due to the presence of free electrons.  They have high electrical conductivity.  Metallic bonds are non directional.  The metallic bound is comparatively weaker than the ionic and covalent bounds. 1.3. Secondary bonds 4. Hydrogen bond: covalently bonded atoms often produce an electronic dipole configuration. The hydrogen atom has the positive end of dipole. If the bonds arise as the result of electrostatic attraction between the atoms. It is known as hydrogen bound. The hydrogen form bounding with electro negative. Ni, O , Fl usually of another 2 2 molecule. Let us consider the example of H O molecule. The greater electro-negative of O . The 2 2 electrons tend to stay closer to O atom than the hydrogen atoms. The O atom acts as 2 2 negative end of the dipole. While H+ atom acts as the positive end. The positive end 7 INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500043 attracts the negative end of another. H O molecule and thus bonding the molecules 2 together. Characteristics of Hydrogen bonded materials  The bonding is relating strong as compared to other dipole-dipole interactions.  The hydrogen bounds are directional.  They have low melting points.  They are transparent to light.  They are soluble in both polar and non-polar solvents.  They are good insulators of electricity.  They have low densities. 5. Van der Waal’s Bond Weak and temporary (fluctuating) dipole bounds between hydrogen are known as vandarwaals bounding. They are non-directional. If the symmetrical distribution of electrons around the nucleus is distributed, the center of positive and negative charges may not coincide at that movement giving rise to weak fluctuating dipole. Fig: Van der Waal’s bond Characteristics of van der waal’s bonded materials  The molecular crystals have small binding energy.  Molecule structure can be both crystalline and non-crystalline.  They are usually transparent to light.  They have low melting point. 8 INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500043  They are soluble in both polar and non-polar solvents.  They are good insulators. 1.4. Variation of Interatomic Forces with Interatomic Spacing Electrical forces are responsible to binding the atoms gives different solid structures. Magnetic and gravitational forces are negligible in the formation of solids. NaCl crystal is more stable than the Na and Cl atoms. Similarly silicon is more stable than silicon atoms. This shows that silicon atoms attract each other, when they come closer. This is the force which is responsible in the forming are crystal. It means that the energy of crystal is lower than the energy of these energies is called as cohesive energy of the crystal. Sometimes it also called as building energy. Consider two atoms at a separate ion of ‘r’ where both the attractive and repulsive forces are present. The net force between the atoms is given as, F(r) = - → (1) Where A, B, M, N are constants which are the characteristics of the atom. Fig: Variaration of interatomic force with interatomic spacing The first term in the above equation represents attractive force. Where M approximately equal to 2. i.e. M 2 (according to inverse quire law). The second term represents repulsive force which is very strong at small distances and the value is 9. N 9 N>M The variation of the attractive and repulsive forces with distance of separation r 0 Where the separation between atoms = The resultant force = 0 9 INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500043 This separation is called equilibrium distance, at equilibrium position, F(r= =0 - =0 = = = = 1.5. Cohesive Energy The potential energy is due to the interaction between the two atoms and it depends on the interaction spacing. The potential energy is, W(r) = = → (1) F(r) = - → (2) Substitute eq (2) in eq(1) W(r) = dr W(r) = A dr – B dr W(r) = A - + C W(r) = + + W(r) = - + + C = a; = b; M-1 = m; N-1 = n W(r) = + + C Applying boundary conditions r , W 0, we get C=0 W(r) = + → (3) In eq(3), the quality represents attractive potential energy and represents repulsive potential energy. At equilibrium distance ( ) the potential energy should be minimum mathematically it is represented as, =0 r=0 = 0 -a + b = 0 -a (-m) + b(-n) ) =0 - 10