From WolfWikis

Short course

This short course is mostly intended to facilitate self-study by the graduate students in the Martin group in the Dept of Chemistry.

Some of the material is covered in the Solid State course (only given every other year), but the overlap is only partial and the approach is different. A second purpose is to serve as background information for future cumes.

Correspondence on my user page or -if you are a visitor from outside- at folmer dot jaap at gmail please. Jcfolmer 16:13, 9 May 2008 (EDT)

Assumed previous knowledge

The symmetry of crystalline solids can in general be described by one of the 230 space groups and their representations, unless the material is magnetic in which case we need to use double groups of which there are ca. 1500.

Space groups are an extension of point groups and are groups in the mathematical sense of that word. This short course assumes that you are familiar with point group theory although we will start with a bit of a refresher.

It also assumes that you are familiar with:

1. Basic math
   1. Complex numbers
   2. Matrices
2. Basic symmetry
   1. Point group symmetry
   2. Basic group theory of point groups
3. Basic Physical Chemistry
   1. Basic phase diagrams

Topics

1. Basic group theory; elements, representations
2. Abelian groups, closure and translation groups
3. The irreps of translation groups
4. Basis functions; frequency or reciprocal space
5. Decomposing in normal modes of the translation group
6. FFT's and conjugate symmetry
7. Brillouin zones, aliasing, time reversal
8. Metals as 'free' electron gases
9. Diffraction
10. Tight binding and Peierls' distortions
11. Phonons
12. 3D Space groups
13. Irreps of space groups
14. Landau theory
15. Phase diagrams with continuous transitions