Coming soon
Computational Physics
This course will enable the students to –
- understands the basic Numerical methods and programming.
- learn techniques to apply numerical methods to research areas.
- ·acquire working knowledge and practice for electronic structure studies of materials by using WIEN2K and Quantum Espresso software based on DFT.
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Course Code |
Course Title |
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24PHY323
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Computational Physics (Theory)
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CO85: Obtain numerical solutions of the system of linear equations with accuracy and obtain numerical solutions of algebraic transcendental equations. CO86: Develop deepknowledge about various interpolating and extrapolating methods. CO87: Solve initial and boundary value problems in differential equations using numerical methods and explain various numerical methods in real-life problems. CO88: Elaborate calculations of DOS using WIEN2k and interpret the results. CO89: Comprehensive understanding of Quantum Espresso and be able to apply it to a wide range of materials science and condensed matter physics problems. CO90: Contribute effectively in Course specific interaction. |
Approach in teaching: Interactive Lectures, Discussion, Tutorials, , Demonstration, Problem Solving in tutorials.
Learning activities for the students: Self- learning assignments, Effective questions, Seminar presentation, Solving numerical, Additional learning through online videos and MOOC courses |
Class test, Semester end examinations, Quiz, Solving problems, Assignments, Presentations |
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Introduction to PSpice software, file types, netlist commands. Basic analyses: DC, AC, Transient. Analog behavioural models (ABM): equations setup, IF statement, voltage/current/ frequency dependent sources. Models of resistor, capacitor, inductor, energy sources (VCVS, CCVS, Sinusoidal source, pulse, etc), transformer, DIODE, BJT, FET, MOSFET, etc.
(a)Basic concepts of DFT: Periodic boundary conditions, Brillouin zone, Symmetry points in Brillouin zone of common types of lattices, Fermi Energy, Energy Band Diagram, effective mass of electron, Density of States, Fermi surface, Nature of Wave-function of the system, its plane wave expansion, pseudo potentials, Form factor, Structure factor, Dielectric screening, Exchange and Correlation, Various contributions to total energy of a system, Density Functional Theory, The LAPW Method, The APW+lo method.
(b) WIEN2k Software: its structure, W2web server, Brief description of using W2web for: Creating a new session and directory, Creating the input and its setting of RMT values, sample structure file (Case. struct) file, Viewing the structure, Initialization of the calculation. Setting up of RMT*Kmax and k-points. The SCF calculation and convergence limits, flow of WIEN2k program, Saving the calculation, spin polarized calculation, spin- orbit interaction. Calculation and Plotting of Electron Density distribution, Density of States, X-ray spectra, Band Structure, Fermi Surface. Volume Optimization, Super cell creation and addition of impurity atoms to the system. Serial and Parallel execution of WIEN2k, Working on a cluster, Working on a remote computing system.
Essential Linux Commands. Pseudopotentials in Quantum Espresso. Structure of a program in Quantum Espresso: Symbolizing lattice types, Cell parameters, Atomic Species, Atomic positions, Irreducible Brillouin zone sampling, k-point sampling and other parameters. A sample PW scf code. Self consistent solution of Schrödinger equation. Total energy, Various contributions to total energy, convergence tests for ecut-wfc, ecut-rho and k-points. Structure-stability considerations. Energy lattice constant Diagram and Equation of state.
Structure of files for calculation of electron density, density of states and band structure. Plotting of diagrams with gnuplot. Calculation and Plotting of Fermi surface. Super cell construction, introduction of impurity in the cell. Sample code for a system with impurity. Running of Quantum Espresso programs in serial and parallel mode and on a cluster of computers.
Least square line, Methods of curve fitting, chi-square test, Interpolation by Spline functions, Fourier series and trigonometric polynomials, Bezier curve
Introduction to Quadrature, Composite trapezoidal and Simpson’s Rule, Recursive rules, Adaptive Quadrature, Gauss-Legendre Integration
·P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, and J. Luitz, “WIEN2k- An augmented Plan Wave Plus Local Orbitals Program for Calculating Crystal Properties”, User’s Guide, Vienna University of Technology, Vienna (Austria)
·D. Singh, Plane Waves, Pseudopotentials and the LAPW method, Kluwer Academic (1994).
·Users’ Guide for Quantum Espresso (V.6.2).
·Cottenier, “Density Functional Theory and the family of (L) APW-methods: a step by step introduction”, WIEN2k website (2013).
· “Numerical Methods using MATLAB.”, John H. Mathews and Kurtis D. Fink, PHI
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