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