SEMESTER I 18LN01 COMPUTATIONAL MATHEMATICS 2 2 0 3 NUMERICAL SOLUTION OF SYSTEM OF EQUATIONS: Solving system of linear equations – Gauss Jacobi and Gauss Siedel methods, successive over relaxation method, system of non-linear equations – Newton’s method. Interpolation: cubic spline interpolation, Bezier curves and B-spline curves, least squares approximations. (8+7) NUMERICAL SOLUTION TO ODE: Initial value problem: Runge Kutta method, Milne’s method. Boundary value problem: Finite Element Method - Rayleigh-Ritz method, Collocation and Galerkin methods. (8+7) NUMERICAL SOLUTION TO PDE: Finite difference method: Liebmann’s method for Laplace equation and Poisson equation, explicit method and Crank-Nicolson method for parabolic equations, explicit method for hyperbolic equations. (8+7) MODELLING AND SIMULATION: Simulating deterministic behaviour, area under a curve, generating random numbers, simulating probabilistic behaviour, inventory model: gasoline and consumer demand. (8+7) Total L:32 + T:28 = 60 REFERENCES: 1. John H Mathews and Kurtis D Fink, Numerical Methods using MATLAB, Pearson Education, New Delhi, 2018. 2. Steven C Chapra and Raymond P Canale, Numerical Methods for Engineers, Tata McGraw-Hill, New Delhi, 2017. 3. Frank R Giordano, William P Fox and Steven B Horton, A first course in Mathematical Modeling, Cengage Learning, New Delhi, 2014. 4. Curtis F Gerald and Patrick O Wheatly, Applied Numerical Analysis, Pearson Education, New Delhi, 2013. 5. Douglas J Faires and Richard Burden, Numerical Methods, Cengage Learning, New Delhi, 2013. 18LN02 FUNDAMENTALS OF NANOSCIENCE AND TECHNOLOGY 3 2 0 4 NANO EVOLUTION: Scientific evolution - Feynman’s quantum electrodynamics – Taniguchi’s nanotechnology – Drexler’s engines of creation – Definition of a nanosystem – Dimensionality and size dependent phenomena - Nanostructures – Naturally occurring nanomaterials - Nanoscale properties - Magnetic Moment in clusters/Nanoparticles – Coercivity – Thermal activation and superparamagnetic effects, Excitonic binding and recombination Energies, Capacitance in a nanoparticle, Optical properties - Surface Plasmon Resonance, Nanotechnology Initiatives – challenges and future prospects of nanoscience. (12+6) QUANTUM CONCEPTS: Inadequacies of Classical Mechanics – Duality nature of electromagnetic radiation – De Broglie hypothesis for matter waves – Heisenberg’s uncertainty principle – Schrödinger's wave equation - Energy levels of a particle, Density of states (DOS) - DOS of 3D, 2D, 1D and 0D materials - Quantum confinement - Penetration of a barrier, Tunnel effect - Ballistic transport - Coulomb blockade. (11+8) INTERMOLECULAR AND INTRAMOLECULAR FORCES: Atomic structure - bonds, chemical bonds, ionic interactions, covalent bonds, metal bonds, hydrogen bonds – covalent and coulomb interactions – electrostatic stabilization - surface charge density - electric potential at the proximity of solid surface - van der Waals forces - dipole-dipole interactions – repulsive forces - hydrophobic and hydrophilic interactions, super-hydrophobicity. (11+8) TRANSPORT IN THE NANOSCALE: Size effect on electronic properties – phonons in nanostructures - size effect on electron – phonon coupling, evolution of band structures and Fermi surface - fraction of surface atoms – surface energy and surface stress, size-induced metal-insulator-transition (SIMIT)- electron transport and kinetics in zero, one and two dimensional nanostructures - nanocrystalline materials, effect of grain size and grain boundaries. (11+8) Total L: 45 + T: 30 = 75 TUTORIAL COMPONENTS: x Size dependendent optical properties of nanoparticles x Tunneling measurements x Surface morphology and grain size measurement x Compression and hardness tests REFERENCES: 1. Pradeep T, “Nano: The Essentials Understanding Nanoscience and Nanotechnology”, Tata Mc-Graw Hill, New Delhi, 2012. 2. Masaru Kuno, “Introductory Nanoscience: Physical and Chemical Concepts”, Taylor and Francis, New York, 2012. 3. Aruldhas G, “Quantum Mechanics”, PHI Learning Pvt. Ltd., New Delhi. 2013. 4. Hornyak G L, Tibbals H F and Dutta J, “Introduction to Nanoscience and Nanotechnology”, CRC Press, London, 2009. 5. Mathews P M and Venkatesan K, “A Text book of Quantum Mechanics”, Tata McGraw Hill, New Delhi, 2017. 376 18LN03 SYNTHESIS OF NANOMATERIALS 3 0 0 3 GENERAL CHEMISTRY: Acidity – basicity and pKa – measurement of acid and base strength surface energy, chemical potential as a function of surface curvature- electrostatic stabilization – steric stabilization – coagulation – aggregation, functional groups- classification of nanomaterials. (11) SELF ASSEMBLY AND ELECTROCHEMICAL APPROACH: Self assembly – classification of self assembly process, Self Assembled Monolayer, Monolayers of organosilicon, alkanethiols and sulfides, Langmuir Blodgett (LB) films – micelle formation– Biomemmitic approach-lotus effect surfaces. Electrochemical approach: Electrochemical Deposition, Electrophoretic deposition, Electrospinning. (11) CHEMICAL APPROACH: Homogeneous Nucleation-wet chemical reduction-Influence of stabilizer- vapor phase reaction-solid phase reactions, Nanoparticles through Heterogeneous Nucleation, Spray pyrolysis- Fundamental aspects of VLS and SLS growth, Atomic Layer Deposition , Chemical vapor deposition- plasma enhanced chemical vapor deposition, Sol-Gel. (12) PHYSICAL APPROACH: Thin Film Growth modes- importance of Vacuum - Physical Vapor Deposition - Evaporation- Molecular beam epitaxy (MBE)-Sputtering-Comparison of evaporation and sputtering, Pulsed Laser Deposition , Ball milling process, Template-based synthesis- liposomes- Epitaxial Core-Shell Nanoparticles- Track etched alumina- polycarbonate membranes. (11) Total L: 45 REFERENCES: 1. Vikas Mittal, “Characterization Techniques for Polymer Nanocomposites”, Wiley-VCH, Germany, 2012. 2. Cao G, “Nanostructures and Nanomaterials: Synthesis, Properties and Applications”, World Scientific Publishing, Singapore, 2011. 3. Pradeep T, “Nano: The essentials, Understanding Nanoscience and Nanotechnology”, Tata McGraw Hill, New Delhi, 2007. 4. Rao C N R, Muller A and Cheetham A K, “The Chemistry of Nanomaterials Synthesis, Properties and Applications”, Wiley- VCH, Germany, 2006. 5. Nalwa H S, “Encyclopedia of Nanoscience and Nanotechnology”, American scientific, New York, 2004. 18LN04 MATERIALS SCIENCE 3 2 0 4 STRUCTURE OF CRYSTALLINE SOLIDS: Atomic bonding – crystalline state of solids-Crystal structure – Unit cell – Bravais Lattice-Crystal systems-Lattice parameters-Crystallographic planes and directions- Miller Indices- Diffraction of X-rays by simple space lattice- Bragg’s law- Experimental methods of X-ray diffraction- Diffraction of electrons from crystals- Diffraction of neutrons from crystals. Crystal imperfections. (11+6) ELECTRICAL PROPERTIES: Free electron theory – Fermi Dirac distribution- Density of States- Sommerfeld’s theory of electrical conductivity- Kronig-Penny model – Brillouin zones- Band model for metals, semiconductors and insulators. Dielectric properties: static dielectric constant – Complex dielectric constant- Dielectric losses and relaxation time- ferroelectrics and piezoelectrics: Classification and properties of ferroelectrics, piezoelectric materials and applications. (11+8) SEMICONDUCTORS AND MAGNETIC MATERIALS: Electronic degeneracy in semiconductors- Carrier concentration in intrinsic and extrinsic semiconductors- Law of Mass action-Fermi level- Hall effect and its applications-I-V Characteristics of nanomaterials, size effects on electrical properties of materials-Origin of magnetism-Types of magnetic materials- ferromagnetism- Domain theory- Magnetic hysteresis- Weiss molecular field theory- Hard and soft magnetic materials-applications –Anti-ferromagnetism – Ferrites- Superconductors - Meissner effect-Type I and II superconductors-Josephson effect -SQUID. Size effects on magnetic and superconducting properties of materials. (12+8) OPTICAL AND THERMAL PROPERTIES: Optical Reflectance: Kramer-Kronig relations- Excitons and their types, luminescence – types of decay mechanisms- Types of luminescence–Einstein’s theory of specific heat- Debye theory- Elastic waves in an infinite 1D array of identical atoms- vibrational modes of a finite 1D lattice of identical atoms, Size effects on optical and thermal properties of materials. (11+8) Total L: 45 + T: 30 = 75 TUTORIAL COMPONENTS x Indexing of diffraction patterns and identification of crystal structure x I-V characteristics and dielectric measurements through impedance analysis x Characterisation of semiconductors through hall effect x Optical studies using photoluminescence measurement REFERENCES: 1. Charles Kittel, “Introduction to Solid State Physics”, Wiley India P. Ltd.,2013. 2. Dekker A J, “Solid State Physics”, Macmillan Publications,2012. 3. Callister W D, “Materials Science and Engineering”, Wiley Publications,2010. 4. V. Raghavan, “Materials Science and Engineering: A First Course", Prentice Hall, 2006 5. Pillai S O, “Solid State Physics, New Age International”, 2005. 6. Michael Shur, “Physics of Semiconductor Devices”, Prentice Hall,1995. 377 18LN05 INDUSTRIAL NANOTECHNOLOGY 3 0 0 3 NANOTECHNOLOGY IN ELECTRICAL AND ELECTRONICS INDUSTRIES: Advantages of nano devices, electronic circuit chips, lasers, micro and nano electromechanical systems (MEMS) -optical switches - bio-MEMS - diodes and nano-wire transistors - data memory - lighting and displays - energy storage - fuel cells and photo-voltaic cells. (11) NANOTECHNOLOGY IN BIOMEDICAL AND PHARMACEUTICAL INDUSTRIES: Nanoparticles in