Crystal Symmetry and X-ray Crystallography

Peter Franz Rogl

1. Crystals, Lattices, Unit Cells, Atom Coordinates, Miller indices,

2. Symmetry in Solids (symmetry operations, Bravais lattices, crystal classes, HM symbols, space group types)

3. Choices of space group settings - structure tidy programme

4. Affine transformations, invariant points of transformation, properties of rotation axes, axes transformations , base transformations, invariance of symmetry operator transformations

5. Lage-vectors

6. groups of symmetry operations, coset decomposition, normal group, factor group, space group types.

7. Examples of space groups mm2, 4mm and others

8. calculation of point group coordinates for several space group types (group work)

9. X ray Crystallography (Bragg law, waves, Argand diagram, atom scattering factor, structure factor, the phase problem

10. Crystal Structure Analysis (Rietveld method, Rietveld refinement with some practical exercises),

11. Direct Methods (Harker Kasper inequalities, Sayres equation, Karle-Hauptmann determinant, sign probabilities

12. Example of a structure solution from a given data set

13. Description/Notation of crystal structures

14. How to construct a structure formula

15. Standardization of crystal structures – Typix