International Union of 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).
Program
FUNDAMENTALS Introduction to matrix algebra
 Symmetry in nature and in human life
 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
 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
 HermannMauguin 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. HermannMauguin symbols for space groups
 Orthogonal projections of space groups. General and special positions, sitesymmetry 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
 Interaction of Xrays 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 spacegroup type
 Structure solution and refinement: introductory strategies
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, solidstate physics and crystal chemistry.
 Databases and computer tools for groupsubgroup relations between space groups
 Crystallographic databases and access tools
 Spacegroup symmetry databases (International Tables for Crystallography, Volume A: Spacegroup symmetry)
 Maximal subgroups and minimal supergroups (International Tables for Crystallography, Volume A1: Symmetry relations between space groups)
 Brillouinzone database
 Groupsubgroup relations between space groups
 Study of general groupsubgroup pair of space groups; Hermann theorem: twins and antiphase domains; coset decompositions. Supergroups of space groups
 Symmetry relations between Wyckoff positions for groupsubgroup pairs; Baernighausen trees constructions
 Structure utilities and tools
 Equivalent structure descriptions; structure descriptions with respect to different spacegroup settings
 Comparison between different descriptions of the same structure
 Computer tools for the study of structural relationships
 Crystallographic databases and access tools
 Tools for structural phase transitions on the Bilbao Crystallographic Server
 Structural pseudosymmetry
 Methods of pseudosymmetry search using supergroups of space groups
 Search for new ferroelectric and ferroelastic materials
 Phase transitions with groupsubgroup relations between the space groups of the two
phases
 Inverse Landau problem
 Symmetrymode analysis of displacive phase transitions
 Structural pseudosymmetry
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, BloemfonteinProf. Hendrik Visser, Bloemfontein
Miss Marietjie Schutte, Secretary: Email:
Lecturers
Prof. Massimo Nespolo, NancyProf. 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
 Dr Melanie Rademeyer University of Pretoria
 Prof Massimo Nespolo Nancy University, France
 Prof Mois Ilia Aroyo Bilbao University, Spain
 Prof Len Barbour University of Stellenbosch
 Prof Dave Billing Wits University
 Prof Andreas Roodt University of the Free State
 Prof Deon Visser University of the Free State
 Mr Banele Vatsha University of KwazuluNatal
 Miss Alice Brink University of the Free State
 Miss Tania Hill University of the Free State
 Miss Kina van der Merwe University of the Free State
 Mr Theuns Muller University of the Free State [Namibia]
 Mr Tinus Viljoen University of the Free State
 Ms Maryke Steyn University of the Free State
 Ms Truidie Venter University of the Free State
 Ms Ilana Engelbrecht University of the Free State
 Prof Gideon Steyl University of the Free State
 Mr Leo Kirsten University of the Free State
 Ms Carla Pretorius University of the Free State
 Ms Leandra Herbst University of the Free State
 Mr Renier Koen University of the Free State
 Mnr Ricky Kotze University of the Free State
 Dr Johan Venter University of the Free State
 Mr Cyril Young University of the Free State
 Mr Armand Bester University of the Free State
 Dr Esna Du Plessis SASOL
 Ms Marietjie Schutte University of the Free State
 Ms Roxanne Freitag University of the Free State
 Mr Dingizulu Machobane University of the Free State
 Mr Kholile Matroos University of the Free State
 Mr Pule Molokoane University of the Free State
 Mr Lebohang Mphure University of the Free State
 Mr Vutomi Nukeri University of the Free State
 Mr Esemem Bungu Paul University of the Free State [Cameroon]
 Ms Tanya Pieterse University of the Free State
 Ms Maretha Serdyn University of the Free State
 Mr Thabang Sethole University of the Free State
 Mr Flip Van der Berg University of the Free State
 Ms AmandaLee Volmink University of the Free State
 Mr Siyanda Lubhelwana SASOL
 Ms Dorota Komornicka ILTSR PAS Wroclaw, Poland
 Ms Kate Davies University of Cape Town
 Ms Lee Trollope University of Cape Town
Ten Institutions; Six countries of origin
The Organizers of the Bloemfontein school have observed the basic policy of nondiscrimination 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.