Modeling of nanostructures and materials 1100-4INZ21
Following topics will be discussed during the series of lectures:
1. Physics on Different Length- and Timescales
- Electronic/Atomic Scale
- Atomistic/Microscopic
- Microscopic/Mesoscopic
- Mesoscopic/Macroscopic
2. Computer Simulations and Computational Materials Science
- What is Computational Material Science on Multiscales ?
- What is a Model? – Scientific Method
- Hierarchical Modeling Concepts above the Atomic Scale
3. Computational Methods on Electronic/Atomistic Scale
(a) Ab-initio methods
- Hamiltonian for condensed matter systems
- The adiabatic and Born-Oppenheimer Approximation
(b) Density Functional Theory – Basic concepts
- Kohn-Sham realization of the Density Functional Theory
- Derivation of the Kohn-Sham equations
- Approximations to the exchange-correlation functionals
- Methods of solving the Kohn-Sham equations
- Concept of pseudopotentials and plane wave method
- Linear combination of atomic orbitals
- Linearized Augmented Plane Waves method (LAPW)
- Linearized Muffin-Tin Orbitals method (LMTO)
- Concept of multiple-scattering, Green's function, random systems
- Force calculations; The Hellmann-Feynman Theorem
(c) – Car-Parrinello Molecular Dynamics
(d) – Survey of numerical codes for solving K-S equations
(e) Theory of excitations
- GW method for energies of one-particle excitations
- Time dependent DFT
(f) Semi-empirical Methods
- Tight-Binding Method
- Semi-empirical pseudopotential method
4. Computational Methods on Atomistic/Microscopic Scale
(a) Fundamentals of Statistical Physics and Thermodynamics
- Statistical ensambles
- Virtual ensembles
- Entropy and temperature
(b) Classical Interatomic and Intermolecular Potentials
- Charged systems, Ewald summation
- Van der Waals Potential
- Covalent Bonds
- Embedded Atom Potentials
- Pair Potentials
- Valence Force Field Models
(c) Classical Molecular Dynamics Simulations
- Numerical Ingredients of MD Simulations
- Integrating the Equations of Motion
- Periodic Boundary Conditions
- Making Measurements
(d) Monte Carlo Method
- Basic concepts
- Markov chains
- Metropolis Algorithm
5. Computational Methods on Mesoscopic/Macroscopic Scale
(a) Physical Theories for Macroscopic Phenomena
- The Continuum Hypothesis
- Theory of elasticity as an example of continuum theory
- Bridging Scale Applications: Crack Propagation in a Brittle Specimen
(b) Gizburg-Landau/Cahn-Hiliard Field Theoretic Mesoscale Simulation Method
6. Perspectives in Multiscale Materials Modeling
Main fields of studies for MISMaP
chemistry
Mode
Prerequisites (description)
Course coordinators
Learning outcomes
After the lecture, the students will get familiar with knowledge of the basic methods for modeling of nanostructures and materials on atomistic, mesoscopic, and macroscopic length.
Practical exercises will learn the students how to perform modeling of nanostructures and materials employing state-of-the-art numerical codes on high performance computing (HPC) environment.
Assessment criteria
There are three components of the final note:
(i) multiple-choice test from the lecture's material
(ii) points for the work during the computer exercises
(iii) small modeling project at the end of the course
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: