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Všechny skupiny předmětů |
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Vysvětlivky
Návod
Webová stránka:
https://intranet.fel.cvut.cz/en/education/bk/predmety/56/75/p5675206.html
Anotace:
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 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 atomistic simulations, and how to analyse and present the results by using post-processing software packages.
Cíle studia:
The aim of this course is to give an advanced knowledge of the principles and techniques of computational materials science. At the end of the course, the student will be able to setup simulations to study atomic-scale material properties and to lay the foundations of a material design project; eventually, the student will gain the proper background to extend her/his own academic formation towards postdoctoral or industrial positions. The course covers the physical understanding of matter from an atomic point of view. Topics covered include static and dynamical description of matter at the atomic level. The course is tailored for PhD students with basic knowledge of laws of thermodynamics and Newton's laws. Fundamental theories in solid state physics are introduced together with their software implementation, showing how to use them in current-day technology, industry, and research. The course has a theoretical lecture component and laboratory experiences, making extensive use of examples and exercises to illustrate the material.
Obsah:
| 1. | | Introduction to the course: lessons outline; computational environment; atomic geometry representation; precision, accuracy and error in atomistic simulations |
| 2. | | Fundaments of thermodynamics and statistical mechanics (state variables, laws of thermodynamics, phase space, partition functions, ensembles, ...) |
| 3. | | Integration of Newton's equation of motions: molecular dynamics simulations |
| 4. | | Non-Hamiltonian dynamics, thermostats and barostats |
| 5. | | Geometric optimisation, search for global and local minima |
| 6. | | Phase transformations and reaction paths |
| 7. | | 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 |
| 8. | | The hydrogen atom and the hydrogen-like orbitals, molecular orbitals |
| 9. | | Numerical solutions of the Schrödinger equation; Hartree-Fock, post-Hartree-Fock and DFT methods; the Born-Oppenheimer approximation; the Hellmann-Feynman theorem |
| 10. | | Crystal structures, reciprocal lattice, crystal space groups |
| 11. | | Free electron model; Bloch's theorem; total and atom/orbital resolved density of states and energy bands |
| 12. | | Phonon theory; total and atom-resolved phonon density of states and band structure |
| 13. | | Phonon-based description of physical quantities, anharmonic interactions, electron-phonon coupling |
| 14. | | Atomic-scale design of new materials |
Osnovy přednášek:
| 1. | | Introduction to LAMMPS: how to prepare an input (atom positions, box size, boundary conditions, force field) |
| 2. | | Equilibrium lattice constant of Fcc silicon: geometry optimisation, NVE timestep benchmark; equilibration, measurement and analysis (NPT) |
| 3. | | Equilibrium properties of Argon: a) geometry optimisation, heating, cooling |
| 4. | | Equilibrium properties of Argon: b) equilibration, measurement and analysis (NVT) |
| 5. | | Introduction to the Nudged Elastic Band (NEB) method in LAMMPS |
| 6. | | Introduction to Abinit: how to prepare an input (crystal structure, boundary conditions, energy functional, convergence parameters) |
| 7. | | H2 molecule: electronic properties |
| 8. | | H atom: visualisation of hydrogen orbitals |
| 9. | | H2O molecule: importance of geometry and the exchange correlation functional |
| 10. | | Silicon diamond: geometry optimisation, band structure, convergence studies |
| 11. | | Carbon diamond: geometry optimisation, band structure |
| 12. | | Phonon DOS/band structure of the isolated H2O molecule |
| 13. | | Phonon DOS/band structure of crystalline bilayer MoS2 |
| 14. | | Case studies proposed by the student |
Osnovy cvičení:
| 1. | | Introduction to LAMMPS: how to prepare an input (atom positions, box size, boundary conditions, force field) |
| 2. | | Equilibrium lattice constant of Fcc silicon: geometry optimisation, NVE timestep benchmark; equilibration, measurement and analysis (NPT) |
| 3. | | Equilibrium properties of Argon: a) geometry optimisation, heating, cooling |
| 4. | | Equilibrium properties of Argon: b) equilibration, measurement and analysis (NVT) |
| 5. | | Introduction to the Nudged Elastic Band (NEB) method in LAMMPS |
| 6. | | Introduction to Abinit: how to prepare an input (crystal structure, boundary conditions, energy functional, convergence parameters) |
| 7. | | H2 molecule: electronic properties |
| 8. | | H atom: visualisation of hydrogen orbitals |
| 9. | | H2O molecule: importance of geometry and the exchange correlation functional |
| 10. | | Silicon diamond: geometry optimisation, band structure, convergence studies |
| 11. | | Carbon diamond: geometry optimisation, band structure |
| 12. | | Phonon DOS/band structure of the isolated H2O molecule |
| 13. | | Phonon DOS/band structure of crystalline bilayer MoS2 |
| 14. | | Case studies proposed by the student |
Literatura:
- 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
Požadavky:
Derivative of a function, definite and indefinite integral, Newton‘s equations, laws of thermodynamics, basic usage of a computer.
Klíčová slova:
materiály, simulace, nanoinženýrství, klasická mechanika, kvantová mechanika
Předmět je zahrnut do těchto studijních plánů:
| Stránka vytvořena 12.3.2026 05:51:33, semestry: L/2027-8, L/2025-6, Z,L/2026-7, Z/2027-8, Z/2025-6, připomínky k informační náplni zasílejte správci studijních plánů |
Návrh a realizace: I. Halaška (K336), J. Novák (K336) |