International Union of Crystallography Commission on Mathematical and Theoretical Crystallography

School on Fundamental Crystallography

Bloemfontein, South Africa, 12 - 16 April 2010

Organized by the Commission on Mathematical and Theoretical Crystallography (MaThCryst) in cooperation with the IUCr Commission on Crystallographic Teaching (CT).

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Program

FUNDAMENTALS

• Introduction to matrix algebra
• Symmetry in nature and in human life

BASIC CONCEPTS

• Affine spaces vs. vector spaces
• Mappings: affine and Euclidean; isometries and symmetry operations
• Sets; homomorphisms, isomorphisms, automorphisms
• Introduction to group theory: abstract groups, subgroups, cosets

CRYSTALLOGRAPHY IN DIRECT SPACE

• Periodic structure of the crystalline matter
• Crystal lattice vs. crystal pattern and crystal structure
• Symmetry directions in a lattice
• Unit cells: primitive cells, multiple cells, conventional cells in 2D and 3D
• Crystal families
• Symmetry groups and types of symmetry in direct space
  • morphological symmetry
  • symmetry of physical properties
  • symmetry of lattices
  • symmetry of the unit cell content
  • symmetry of crystallographic patterns
  • Hermann-Mauguin symbols for point groups
• lattice systems
• Crystal systems
• Stereographic projection and the morphology of crystals
• Types of crystallographic point groups through the stereographic projection
• Generation of space groups. Symmetry operations with and without a glide component. Hermann-Mauguin symbols for space groups
• Orthogonal projections of space groups. General and special positions, site-symmetry groups, crystallographic orbits
• Introduction to crystallographic calculations through matrix algebra. Abstract groups, subgroups, cosets
• Short introduction to the subgroups and supergroups of space groups
• Exercises on the space group diagrams from Volume A of the International Tables for Crystallography

PHYSICS OF DIFFRACTION AND CRYSTALLOGRAPHIC IN RECIPROCAL SPACE

• Interaction of X-rays with crystalline matter
• Fourier transforms and convolutions
• Crystallographic calculations in reciprocal space
• Diffraction symmetry: Laue classes, Friedel's law, resonant scattering
• Integral, zonal and serial reflection conditions and their use to determine the space-group type
• Structure solution and refinement: introductory strategies

CRYSTALLOGRAPHY ONLINE: SHORT PRACTICAL COURSE ON THE USE AND APPLICATIONS OF THE BILBAO CRYSTALLOGRAPHIC SERVER

The aim of the course is to give a tutorial and practical guide to the crystallographic databases and some of the computer tools available on the Bilbao Crystallographic Server (www.cryst.ehu.es). Online exercises will help the participants to get some practical experience in the use and applications of the computer programs in treating problems of theoretical crystallography, solid-state physics and crystal chemistry.

1. Databases and computer tools for group-subgroup relations between space groups
   1. Crystallographic databases and access tools
      1. Space-group symmetry databases (International Tables for Crystallography, Volume A: Space-group symmetry)
      2. Maximal subgroups and minimal supergroups (International Tables for Crystallography, Volume A1: Symmetry relations between space groups)
      3. Brillouin-zone database
   2. Group-subgroup relations between space groups
      1. Study of general group-subgroup pair of space groups; Hermann theorem: twins and antiphase domains; coset decompositions. Supergroups of space groups
      2. Symmetry relations between Wyckoff positions for group-subgroup pairs; Baernighausen trees constructions
   3. Structure utilities and tools
      1. Equivalent structure descriptions; structure descriptions with respect to different space-group settings
      2. Comparison between different descriptions of the same structure
      3. Computer tools for the study of structural relationships
2. Tools for structural phase transitions on the Bilbao Crystallographic Server
   1. Structural pseudosymmetry
      1. Methods of pseudosymmetry search using supergroups of space groups
      2. Search for new ferroelectric and ferroelastic materials
   2. Phase transitions with group-subgroup relations between the space groups of the two phases
      1. Inverse Landau problem
      2. Symmetry-mode analysis of displacive phase transitions

Language

The official language of the Schools is English. No simultaneous interpretation has been provided.

Venue

The School was held at Faculty of Natural and Agricultural Sciences of the University of the Free State. Details at the local website.

International Program Committee

Prof. Massimo Nespolo, Nancy (MaThCryst, Chair)
Prof. Mois Ilia Aroyo, Bilbao
Prof. Paola Spadon, Padua (CT)
Prof. Andreas Roodt, Bloemfontein
Dr. Melanie Rademeyer, Pretoria

Local Organizing Committee

Prof. Andreas Roodt, Bloemfontein
Prof. Hendrik Visser, Bloemfontein
Miss Marietjie Schutte, Secretary: Email:

Lecturers

Prof. Massimo Nespolo, Nancy
Prof. Mois Ilia Aroyo, Bilbao
Prof Len Barbour, Stellenbosch
Prof. Andreas Roodt, Bloemfontein
Dr. Melanie Rademeyer, Pretoria
Prof Dave Billing, Wits, Johannesburg

Contact

Inquiries about the scientific program of the school should be sent to . For inquiries about organisation please contact the local organizing committee.

List of participants

1. Dr Melanie Rademeyer University of Pretoria
2. Prof Massimo Nespolo Nancy University, France
3. Prof Mois Ilia Aroyo Bilbao University, Spain
4. Prof Len Barbour University of Stellenbosch
5. Prof Dave Billing Wits University
6. Prof Andreas Roodt University of the Free State
7. Prof Deon Visser University of the Free State
8. Mr Banele Vatsha University of Kwazulu-Natal
9. Miss Alice Brink University of the Free State
10. Miss Tania Hill University of the Free State
11. Miss Kina van der Merwe University of the Free State
12. Mr Theuns Muller University of the Free State [Namibia]
13. Mr Tinus Viljoen University of the Free State
14. Ms Maryke Steyn University of the Free State
15. Ms Truidie Venter University of the Free State
16. Ms Ilana Engelbrecht University of the Free State
17. Prof Gideon Steyl University of the Free State
18. Mr Leo Kirsten University of the Free State
19. Ms Carla Pretorius University of the Free State
20. Ms Leandra Herbst University of the Free State
21. Mr Renier Koen University of the Free State
22. Mnr Ricky Kotze University of the Free State
23. Dr Johan Venter University of the Free State
24. Mr Cyril Young University of the Free State
25. Mr Armand Bester University of the Free State
26. Dr Esna Du Plessis SASOL
27. Ms Marietjie Schutte University of the Free State
28. Ms Roxanne Freitag University of the Free State
29. Mr Dingizulu Machobane University of the Free State
30. Mr Kholile Matroos University of the Free State
31. Mr Pule Molokoane University of the Free State
32. Mr Lebohang Mphure University of the Free State
33. Mr Vutomi Nukeri University of the Free State
34. Mr Esemem Bungu Paul University of the Free State [Cameroon]
35. Ms Tanya Pieterse University of the Free State
36. Ms Maretha Serdyn University of the Free State
37. Mr Thabang Sethole University of the Free State
38. Mr Flip Van der Berg University of the Free State
39. Ms Amanda-Lee Volmink University of the Free State
40. Mr Siyanda Lubhelwana SASOL
41. Ms Dorota Komornicka ILTSR PAS Wroclaw, Poland
42. Ms Kate Davies University of Cape Town
43. Ms Lee Trollope University of Cape Town

Ten Institutions; Six countries of origin

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The Organizers of the Bloemfontein school have observed the basic policy of non-discrimination and affirms the right and freedom of scientists to associate in international scientific activity without regard to such factors as citizenship, religion, creed, political stance, ethnic origin, race, colour, language, age or sex, in accordance with the Statutes of the International Council for Science. At this school no barriers existed which would have prevented the participation of bona fide scientists.

Last updated: 8 June 2010
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