In this course, we will focus on the fundamental aspects of designing materials using quantum mechanics and how to perform density functional theory calculations including the following aspects:
1. Introduction
2. Crystal structures
(a) Unit cell and translational symmetry
(b) 2D and 3D Bravais lattice
(c) Miller indices
(d) Reciprocal space and Brillouin zone (e) Space group
(f) Symmetry operations and their mathematical description
(g) Wyckoff position Reading: How to read the international Tables for Crystallography
(i) Misc: Bilbao crystallographic server, crystal structure databases, and visulization 3. Thermodynamic stability
(a) Gibbs free energy
(b) Formation energy and convex hull
(c) Reading: Prediction of metastable nitrides
4. Mechanical stability
(a) Strain and stress
(b) Elastic constants and their tensor form (c) Mechanical properties
(d) How to evaluate the elastic constants? (e) Equation of states
(f) Reading: Theory of elasticity
5. Phonons
(a) Concepts of molecular eigenmodes
(b) Eigenmodes and irreducible representation
(c) Periodic modulation in crystalline materials
(d) Longitudinal vs. transverse, acoustic vs. optic
- Lehrende: Stephan Diefenbach
- Lehrende: Hongbin Zhang