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- Lehrende: Yurii Genenko
- Lehrende: Robert Stark
Lehrinhalte
This course is an introduction to the quantum mechanics of functional materials. We will cover fundamental concepts such as phonons, crystal electrons and other quasi particles which are used to model functional properties of materials such as metals, semi-conductors, magnets, superconductors etc. A profound knowledge of these concepts is essential to pass most compulsory modules of our master's programme.
The lecture starts with the very basics such as atomic orbitals, the periodic table and crystal lattices in the first two weeks to get everybody on board. Then we will move on the the quantum mechanical description of lattice vibration, the quantum mechanics of electrons in metals, semiconductors and other quantum related phenomena.
A word of caution: To our experience, the difficulty to understand quantum mechanics and to apply it to solid state phenomena is often underestimated. If you are not yet fluent with Hamilton operators, second quantization or other qm concepts you will need your time to digest the topic. We thus strongly recommend that you attend the lecture, tutorials and excercises in person.
[b]Content[/b]
• Properties of crystalline solids: orientation dependence, lattice and reciprocal lattice, semiconductors, metals and isolators.
• Lattice dynamics: lattice with monatomic and diatomic basis, dispersion relation, Brillouin zones, acoustic and optical modes, phonons, density of states, specific heat, thermal transport, thermal expansion.
• Metals: electronic structure, band model, free electron gas, density of states, Fermi-Dirac statistics, Bloch functions
• Electronic transport: Drude model, Drude-Sommerfeld model, thermal properties of the electron gas.
• Semiconductors: synthesis (examples), doping, electronic transport, effective mass, chemical potential, optical properties, density of states, diodes.
• Solid state ionics: ionic and mixed transport.
• Dielectric properties: polarisation and polarizability, electronic and ionic polarization, optical properties, electro-elastic properties
• Magnetism: para, dia- and ferromagnetism, magnetism of solids.
Literatur
Online @ ULB:
[list]
[*]Hofmann, Philip; Solid state physics : an Introduction
[*]John J. Quinn, Kyung-Soo Yi Solid State Physics : Principles and Modern Applications
[*]Harald Ibach, Hans LüthSolid-State, Physics : An Introduction to Principles of Materials Science
[/list]
The books of C. Kittel und Ashcroft/Mermin are available in print.
At https://libretexts.org you find a collection of open textbooks. Hava a look at the chemistry section.
Voraussetzungen
The module exam is an individual obligation (admission letter) or requires individual permission by the examination board.
The module exam is an individual obligation (admission letter). If it is not an obligation an individual permission by the examination board is needed to participate in the exam.
Offizielle Kursbeschreibung
[b]Learning Outcomes[/b]
On successful completion of the module, students are able to:
[list=1]
[*]describe crystals as the combination of a lattice with a pattern and can explain interference phenomena using the concept of the reciprocal lattice;
[*]explain diffraction of electromagnetic waves, electron waves or collective excitations in a lattice;
[*]critically discuss electrical and thermal transport properties based on crystal structure, phononic and/or electronic structure;
[*]explain fundamental material properties in appropriate pictures of quasi-particles and collective excitations based on a quantum mechanical approach;
[*]explain ionic transport in solid;
[*]explain the interaction of electromagnetic fields and waves with materials;
[/list]
Online-Angebote
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Content
This course is an introduction to the quantum mechanics of solid state physics. We will cover fundamental concepts such as phonons, crystal electrons and other quasi particles which are used to model functional properties of materials such as metals, semi-conductors, magnets, superconductors etc. A profound knowledge of these concepts is essential to pass most compulsury modules of our master's programme.
The lecture starts with the basics such as the PSE and lattices in the first two weeks. Then we will move on the the quantum mechanical description of lattice vibration, the quantum mechanics of electrons in metals, semiconductors and other quantum related phenomena.
A word of caution: To our experience, the difficulty to understand quantum mechanics and to apply it to solid state phenomena is often underestimated. If you are not yet fluent with Hamilton operators, second quantization or other concepts you will need your time to digest the topic. We thus strongly recommend that you attend the lecture, tutorials and excercises.
Lehrinhalte
Density functional theory (DFT) is one of the most frequently used computational tools for studying and predicting the properties of isolated molecules, bulk solids, and material interfaces, including surfaces.
In this lecture the basic theoretical underpinnings and concepts underlying DFT calculations are introduced.
Practical applications of DFT, focusing on plane-wave DFT, are discussed and hands-on training is provided
using the open-source code GPAW.
The course is well-suited for students of materials science, physics and chemistry who want to use DFT in their work, but who do not require extensive knowledge of theory and mathematical details.
Literatur
[b][/b][list][*]D. Sholl, J. A. Steckel, "Density Functional Theory: A Practical Introduction", Wiley 2009[*]http://www.abinit.org
[/list]
Voraussetzungen
Background in materials science, physics or chemistry on the bachelor.
Erwartete Teilnehmerzahl
10
Offizielle Kursbeschreibung
Density functional theory (DFT) is one of the most frequently used
computational tools for studying and predicting the properties of
isolated molecules, bulk solids, and material interfaces, including
surfaces.
In this lecture the basic theoretical underpinnings and concepts underlying DFT calculations are introduced.
Practical applications of DFT, focusing on plane-wave DFT, are discussed and hands-on training is provided
using the open-source code GPAW.
The
course is well-suited for students of materials science, physics and
chemistry who want to use DFT in their work, but who do not require
extensive knowledge of theory and mathematical details.
Online-Angebote
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Density functional theory (DFT) is the most frequently used computational electronic-structure method for studying and predicting properties of isolated molecules, bulk solids and interfaces, including surfaces. From being used by only a few specialists, DFT hast become a standard tool in Materials Science that can (in principle) be used by any educated researcher, and is now even transitioning from academia into industry.
This course aims at equipping students from Materials Science, Physics and Chemistry with
basic concepts of DFT (Hohennberg-Kohn theorems, Thomas-Fermi-Dirac vs. Kohn-Sham theory, exchange and correlation),
most relevant numerical aspects (planewave, LCAO and finite-difference methods),
practical experience in applying DFT to selected problems (elastic properties, phonons and thermodynamics, diffusion and catalysis, electronic structure)
The course is divided into two parts. In the first part, the focus is on concepts and numerical aspects. These concepts and numerical aspects will be introduced in a set of 7 regular lectures and reinforced by students implementing (parts of) their own DFT code (using python, under guidance, no need to worry) in dedicated exercise sessions. In the second part, hands-on tutorials will introduce the students to the state-of-the-art DFT package GPAW (https://wiki.fysik.dtu.dk/gpaw/) and how to use it for solving practical problems. Further training will be obtained in guided exercise sessions.
Online-Angebote
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Digitale Lehre
Digitale Kursmaterialien; Interaktive Tutorials und Programmierbeispiele (mit MATLAB, Python, TensorFlow, Jupyter, GitHub, ...)
Lehrinhalte
[list]
[*]Physikbewusstes maschinelles Lernen (ML) vereint klassische, physikbasierte Modellierungsansätze mit ML-Methoden, um die Generalisierungsfähigkeiten, Interpretierbarkeit, Robustheit, Verlässlichkeit und Effizienz von ML-Methoden in Ingenieursanwendungen zu verbessern
[*]Einführung in ML-Methoden und deren wesentliche theoretische Eigenschaften, darunter insbes. künstliche neuronale Netze (Approximationsfähigkeiten, Training, Gradienten, etc.)
[*]Grundlagen der physikbasierten Modellierung und Simulation mittels Differentialgleichungen und geeigneter Zeit- und Orts-Diskretisierungsverfahren (z.B. Zeitintegration und Finite Elemente)
[*]Physikbasierte und datengetriebene Modellreduktion und Surrogat-Modellierung (z.B. Modalanalyse, orthogonale Zerlegungen, Kriging, Kernel-Methoden, u.Ä.)
[*]Mathematische Wissensrepräsentationen von Erhaltungsgleichungen & -größen, Symmetrien, Invarianzen, usw. für physikbewusstes ML
[*]Konstruktionsprinzipien zur Information oder Augmentierung von ML-Methoden durch entsprechende Gestaltung von Trainingsdaten, Hypothesen für Eingangs- und Ausgangsgrößen der ML-Modelle, ML-Modellarchitekturen, oder Lern- bzw. Trainingsalgorithmen
[*]Methoden umfassen z.B. Sobolev-Training, konvexe & monotone NN, physikinformierte NN (PINNs), Langrangesche NN, neurale Operatoren, stochastische NN, rekurrente NN, faltende NN, Graphen-NN, Autoencoder, generative NN, Gaußsche Prozesse & Kernel-Methoden, u.Ä.
[*]Anwendungen und Beispiele für Festkörpermechanik, Strukturdynamik, Materialmodellierung, dynamische Systeme, Multiskalen- und Multiphysik-Probleme, (additive) Fertigungsprozesse, digitale Zwillinge, u.Ä.
[/list]
Voraussetzungen
Grundkenntnisse in Maschinellem Lernen, physikalischer Modellierung und numerischer Simulation (insbes. Differentialgleichungen, Zeitintegration, Finite Elemente) sind empfohlen.
Erfahrung mit maschinellem Lernen und Programmierkenntnisse sind vorteilhaft, aber nicht zwingend erforderlich.
Offizielle Kursbeschreibung
Nach erfolgreichem Abschluss des Moduls sollten die Studierenden in der Lage sein:
1. Anwendungsmöglichkeiten für physikbewusstes maschinelles Lernen in der ingenieurwissenschaftlichen Modellierung und Simulation zu kennen und identifizieren zu können
2. Physikalische und mathematische Eigenschaften wie Energieerhaltung, Symmetrien, Invarianzen und Lösbarkeitsanforderungen mathematisch zu formalisieren
3. Grundlegende Ansätze und Algorithmen des physikbewussten ML beschreiben, erläutern und diskutieren zu können
4. Passende physikinformierte und physikaugmentierte Modellarchitekturen mit neuronalen Netzen für verschiedene Anwendungsfelder erläutern und evaluieren zu können
5. Die verbesserten Generalisierungsfähigkeiten, Interpretierbarkeit, Robustheit, Verlässlichkeit und Effizienz von physikbewussten ML-Konzepten erläutern und erklären zu können
Online-Angebote
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