Computational Materials Physics

quick start
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practical info
about you
setting the stage
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the creation of materials from thought
the ab initio way  
solids as quantum systems
so what’s the problem?
advantages
theory versus computation
hardware
software
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density functional theory 
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a DFT teaser
functions and functionals
the Schrödinger equation
the Born-Oppenheimer approximation
(post-)Hartree-Fock method(s)
the external potential
the electron density
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first Hohenberg-Kohn theorem
second Hohenberg-Kohn theorem
Kohn-Sham equations
XC-functional
correlation
Hartree-Fock versus DFT
numerical solution methods
for later use
(optional) basis sets in more depth
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crystallography
8 Topics
CIF files and how to find them
what’s in a cif ?
more useful tools
(optional) more on crystallography
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geometry optimization
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hands-on task
step 1: volume optimization
bulk modulus and pressure
step 2: cell shape
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introduction to forces
classical forces
quantum forces
symmetry and forces
step 3: position optimization
full optimization
phase diagrams
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electronic structure
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reciprocal space
plane waves and the reciprocal lattice
quantum numbers
plotting wave functions and densities
quantum numbers for a crystal
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chemical bonding
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chemical bonding in textbooks
cohesive energy problem
chemical bonding from DFT
an old puzzle
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elasticity
9 Topics
elastic constants: definition
computing elastic constants
applications of elastic constants
a hard example ;-)
a database of elastic constants
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supercells and surfaces
3 Topics
concept and uses
surface properties
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precision and accuracy
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P&A lecture
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magnetism
4 Topics
spin magnetism
orbital magnetism
long-range magnetic order
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phonons and temperature
4 Topics
the basics of phonons
the Phonopy code : a guided example
phonons by QE + visualizer
soft modes and phase transitions
band gaps
2 Topics
which gap?
gap predictions
let’s play!
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setting the stage – prepare your environment
setting the stage – HPC info (Flanders only)
setting the stage – help section
density functional theory 1 – a basic calculation
density functional theory 2 – basis set size and k-mesh
density functional theory 2 – convergence testing
crystallography – crystal viewers
crystallography – from cif to DFT input
geometry optimization – geometry: towards the ground state
geometry optimization – geometry: E(V) and EOS
electronic structure – band structure and DOS
chemical bonding – charge density difference plots
elasticity – elasticity
supercells and surfaces – creating supercells
supercells and surfaces – work function
magnetism
a frozen phonon calculation
project
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w2 – project 2024-2025
w2 – assessment choice / sign up for project
w4 – project milestone 1
w8 – project milestone 2
w9 – online writing in latex
w12 – submit your project
w12 – gallery of project results (2024)
w12 – self-assessment and team introspection
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applications of elastic constants

Computational Materials Physics elasticity applications of elastic constants

Once you know the stress-strain relationship, several other engineering properties of a crystal are readily available too. In this video, you meet some of them:

Download printable slides

Mandatory task

The video mentions the experimental values for the elastic constants of fcc-Cu. Verify that the Born stability conditions are valid for this material. In case you meet problems, please report them in the forum underneath. If you can answer the questions raised by your fellow students, please do so.

Optional task

Use DFT to calculate the elastic constants of nonmagnetic bcc-Fe (δ-Fe). Examine whether the Born stability conditions are fulfilled (the result might not be what you expect – feel free to speculate about how to reconcile this with the experimental existence of this crystal). If you meet issues or have questions, post them in the forum underneath.

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