Computational Methods for Materials Science

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

The final goal of the course is to acquire advanced knowledge of Classical and Quantum Mechanics to design in-silico experiments within the Materials Science field.

At the end of the course, the students will know:

- the fundaments of thermodynamics, newtonian and statistical mechanics, and how the relative formalism is implemented in order to calculate thermodynamical properties;

- how the Schrödinger equation is setup and solved in order to calculate physical quantities;

- how to combine the classical and quantum mechanics to model experimental results; and

- a general protocol through which to design new materials at the atomic scale.

By means of simulation laboratory experience, the students will eventually learn how to setup and run simulations, and how to analyse and present the results by using post-processing softwares.

Requirements:

Derivative of a function, definite and indefinite integral, Newton‘s equations, laws of thermodynamics, basic usage of a computer.

Syllabus of lectures:

1. Introduction to the course: lessons outline, introduction to the computational environment (shell: bash/Cygwin, compiling a code, ...)

2.Fundaments of thermodynamics and statistical mechanics (state variables, laws of thermodynamics, phase space, partition functions, ensembles, ...)

3.Units & dimensions, periodic boundaries conditions, integrators (Verlet, Leapfrog, ASPC, ...)

4.Classical force fields, potential energy surfaces, types of interaction, calculation techniques (Ewald sum, neighbor list, ...)

5.Basics of Monte Carlo (MC) sampling and Markov processes

6.Non-Hamiltonian dynamics, thermostats & barostats (Berendsen, Nose-Hoover/Rahman-Parrinello, Langevin, ...)

7.Non-equilibrium MD simulations, external forces, constraints

8.Introduction to quantum mechanics: the postulates of quantum mechanics, the uncertainty principle, time dependent and time independent Schrödinger equation, Hamiltonians, observable quantities and expectation values

9.The hydrogen atom and the hydrogen-like orbitals, Molecular Orbitals

10.Crystal structures and reciprocal lattice, the Born-Oppenheimer approximation, the Hellmann-Feynman theorem

11.Free electron model, the Bloch's theorem, energy bands

12.Phonon description of atomic motions

13.Phonon description of thermal properties, anharmonic interactions

14.Atomic-scale design of new materials

Syllabus of tutorials:

1.Introduction to LAMMPS, preparing an input script for energy minimization, introduction to VMD

2.NVE molecular dynamics (MD) simulations, case study: calculation of the self-diffusion coefficient for the LJ fluid

3.MC simulations, case study: calculation of methane hydration free energy

4.NpT MD simulations, case study: calculation of structural and dynamical properties of water

5.Steered MD simulations, case study: sliding of a MoS2 flake on a substrate

6.Introduction to parallel environment in MD simulations

7.Individual student projects on MD simulations and remarks

8.Introduction to ABINIT, preparing an input script for electronic energy minimization, introduction to visualization software for solid state physics (e.g. VESTA)

9.Visualization of hydrogen orbitals and relative energies, analysis of electronic charge density of molecular systems (e.g. electronic charge differences, Electron Localization Function, Bader analysis, Orbital Population)

10.Construction of crystal unit cells, application of the Hellmann-Feynmann theorem: optimization of atomic geometries

11.Electron Density of States, bond covalency analysis

12.Calculation and visualization of phonon modes, phonon Density of States

13.Calculation and analysis of thermal properties from phonon modes

14.Materials design, case study: layer shift in MX2 transition metal dichalcogenides

Study Objective:

Study materials:

P. W. Atkins and R. S. Friedman, Molecular Quantum Mechanics, 3rd edition, Oxford University Press, ISBN 0-19-855947-X

Charles Kittel, Introduction to Solid State Physics, 8th edition, Wiley IPL, ISBN-13: 9788126535187

Peter Atkins,‎ Julio de Paula, Physical Chemistry, 9th Edition, Oxford University Press, ISBN-13: 9780199543373

Daan Frenkel, Berend Smit, Understanding Molecular Simulation, 2nd Edition, Academic Press, ISBN-13: 9780122673511

H. Goldstein, C. P. Poole and John Safko, Classical Mechanics, 3rd edition, Pearson Education, ISBN-13: 9788131758915

C. Cohen-Tannoudji, B. Diu and Frank Laloe, Quantum Mechanics Vol.1, 1st edition, Wiley, ISBN-13: 9780471164333

Note:

Further information:

https://intranet.fel.cvut.cz/en/education/bk/predmety/56/75/p5675206.html

No time-table has been prepared for this course

The course is a part of the following study plans:

• Doctoral studies, daily studies (compulsory elective course)
• Doctoral studies, combined studies (compulsory elective course)
• Doctoral studies, structured daily studies (compulsory elective course)
• Doctoral studies, structured combined studies (compulsory elective course)