Event Name

School on Fundamental Crystallography

Start Date 9th Apr 2012
End Date 13th Apr 2012
Description

International Union of Crystallography

Commission on Mathematical and Theoretical Crystallography

School on Fundamental Crystallography

Mahdia, Tunisia, 9-13 April 2012

Organized by the Commission on Mathematical and Theoretical Crystallography (MaThCryst) and the Tunisian Crystallographic Association (Association Tunisienne de Cristallographie), in cooperation with the IUCr Commission on Crystallographic Teaching (CT).

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 CRYSTALLOGRAPHY 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 languages of the Schools were English and French. Bilingual tutors helped the participants during the guided exercises.
Venue
The School was held at the Hotel Thalassa. It had been postponed from the initial dates of 25-29 April 2011.
Location Mahdia
Tunisia
Contact
URL http://www.crystallography.fr/mathcryst/mahdia2012.php
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Category IUCr sponsored meetings | Schools
Topics Mathematical and Theoretical Crystallography