Computational Materials Physics

quick start
2 Topics
practical info
about you
setting the stage
11 Topics
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
let’s play (w1)
exit (w1)
webinar (w1)
density functional theory 
24 Topics
a DFT teaser
functions and functionals
the Schrödinger equation
the Born-Oppenheimer approximation
(post-)Hartree-Fock method(s)
the external potential
the electron density
let’s play (w2)
for project only (w2)
exit (w2)
webinar (w2)
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
(optional) back to the teaser
let’s play (w3)
exit (w3)
webinar (w3)
crystallography
8 Topics
CIF files and how to find them
what’s in a cif ?
more useful tools
(optional) more on crystallography
let’s play (w4)
for project only (w4)
exit (w4)
webinar (w4)
geometry optimization
18 Topics
hands-on task
step 1: volume optimization
bulk modulus and pressure
step 2: cell shape
upload your answer (geom 1)
exit (w5)
webinar (w5)
introduction to forces
classical forces
quantum forces
symmetry and forces
step 3: position optimization
full optimization
phase diagrams
upload your answer (geom 2)
let’s play (w5-6)
exit (w6)
webinar (w6)
electronic structure
8 Topics
reciprocal space
plane waves and the reciprocal lattice
quantum numbers
plotting wave functions and densities
quantum numbers for a crystal
let’s play (w7)
exit (w7)
webinar (w7)
chemical bonding
8 Topics
chemical bonding in textbooks
cohesive energy problem
chemical bonding from DFT
an old puzzle
let’s play (w8)
exit (w8)
only for project (w8)
webinar (w8)
elasticity
9 Topics
elastic constants: definition
computing elastic constants
applications of elastic constants
a hard example ;-)
a database of elastic constants
let’s play (w9)
only for project (w9)
exit (w9)
webinar (w9)
supercells and surfaces
3 Topics
concept and uses
surface properties
exit (w10-part 1)
precision and accuracy
6 Topics
P&A lecture
P&A tasks
let’s play (w10)
for project only (w10)
exit (w10-part 2)
webinar (w10)
magnetism
4 Topics
spin magnetism
orbital magnetism
long-range magnetic order
exit (magnetism)
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!
17 Topics
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
8 Topics
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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supercells and surfaces

Computational Materials Physics supercells and surfaces

2

TOPICS

2:30h

Duration

If you follow this course in sync with the live classes (September-December), then this chapter is the first part of your main content for week 10 of the fall term (see list of due dates).

So far, we have been looking at perfect single crystals. At most, we squeezed or deformed them, but even then the regular pattern of atoms kept repeating in the same way up to infinity. However, real crystals as we find them in nature or in the lab, are not always perfect. They contain defects (point defects, line defects, planar defects). Sometimes these defects are innocent, sometimes they contribute in an essential way to the observable properties of the crystal.

How do we model defects by DFT, using codes that have periodic boundary conditions? That’s what this chapter is about. The same strategy — using supercells — can also be used to model surfaces. And also to mimick free atoms. Going thoroughly through this chapter will take you about 2h30m.

Don’t forget the next chapter, which is part of this week’s material too.

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