School
on Symmetry of Crystals
Introduction to International Tables
for Crystallography, Vol. A
conducted by
Prof. Theo Hahn and
Prof. Hans Wondratschek
The school aims at a precise but
also illustrative introduction to the theory of point and space
groups. To achieve this, the theory as well as clear examples and
exercises for its application to everyday problems of
crystallography are provided. An introductory text will be
distributed to the participants in advance.
Provisional
PROGRAMME
Wednesday,
August 12
- 08.00-09.00
- Registration
- 09.00-09.15
- Introduction
- 09.15-09.45
- General introduction: Scope of the course, International
Tables
- 09.45-10.30
- Basic concepts: Space groups and X-ray diffraction
- 10.30-11.00
- Break
- 11.00-11.30
- Introduction to group theory I : Definition of a group,
order, subgroups
- 11.30-12.15
- Problem 1 : Group tables of the symmetry groups of the
rectangle and of the crystallographic 41
symbol
- 12.15-12.30
- Isomorphism of groups
- 12.30-14.00
- Lunch
- 14.00-15.00
- Matrices I: matrix representations of symmetry operations
- 15.00-15.30
- Problem 2: Symmetry operations of space group C1m1 (No.1)
- 15.30-16.00
- Break
- 16.00-16.30
- Matrices II: Geometric interpretation of symmetry
matrices
- 16.30-17.30
- Introduction to group theory II: Coset decomposition of a
group; index of a subgroup; Theorem of Langrange
-
Thursday,
August 13
- 9.00-10.00
- Problem 3 : Coset decomposition of point group 4mm
relative to various subgroups
- 10.00-10.30
- Introduction to group theory III: Normal subgroups,
factor groups, conjugate subgroups
- 10.30-11.00
- Break
- 11.00-12.00
- Basic facts on space groups I : Translation subgroups;
general positions; point groups; site symmetry groups;
special positions
- 12.00-12.30
- Problem 4: Geometric interpretation of some
crystallographic symmetry operations
Afternoon -
Excursion
Friday,
August 14
- 09.00-10.00
- Basic facts on space groups II: Sections and projections
of space groups
- 10.00-10.45
- Problem 5: Symmetry of the projection along [001] of
space group Pbca
- 10.45-11.15
- Break
- 11.15-12.15
- Matrices III: Change of coordinate system
- 12.15-12.30
- Discussion
- 12.30-14.00
- Lunch
- 14.00-14.30
- Treatment of monoclinic space groups in IT
- 14.30-15.30
- Problem 6: Transformation of the general position of the
space group P121/a1
- 15.30-16.00
- Break
- 16.00-16.45
- Reflection conditions I: Systematic absences; diffraction
symbols
- 16.45-17.30
- Problem 7 : Space-group determination from systematic
absences
-
Saturday,
August 15
- 09.00-09.30
- Problem 8: Reflection conditions of a given space group
- 09.30-10.00
- Reflection conditions II: Alternative derivation
- 10.00-10.30
- Subgroups of space groups I: General survey
- 10.30-11.00
- Break
- 11.00-11.45
- Subgroups of space groups II: Translationengleiche and
klassengleiche subgroups
- 11.45-12.30
- Problem 9 : Translationengleiche subgroups of space
groups
- 13.00
- Finish of the course
Prof Hans Wondratschek
Institut fuer Kristallographie, Universitaet
D-76128 Karlsruhe
GERMANY
Theo Hahn,
Institut fuer Kristallographie,
RWTH Aachen
Germany
-