International Union of Crystallography Commission on Mathematical and Theoretical Crystallography

International School on Fundamental Crystallography

Uberlândia, Brazil, 25 November - 3 December 2012

The Commission on Mathematical and Theoretical Crystallography is strongly committed to promote education in all the fundamental aspects of crystallography that nowadays are overlooked in common University courses. This mission is accomplished through a series of meetings in a wide range of regions. In fall 2012 we organize a school in Brazil, that continues our activity in the region after the previous shools in Havana and in Montevideo.

Program

FUNDAMENTALS

• Introduction to matrix algebra.
• Basics of group theory. Space groups and space group types.

BASIC CONCEPTS

• Affine spaces vs. vector spaces
• Mappings: affine and Euclidean; isometries
• Sets; homomorphisms, isomorphisms, automorphisms
• Symmetry operations as special case of isometries
• 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
• Crystallographic calculations in direct space
• 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
• Symmetry operations with a glide component
• Space groups and types of space groups
• Exercises on the space group diagrams from Volume A of the International Tables for Crystallography
• Online tools 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. Introduction to JANA software. Examples.

CRYSTALLOGRAPHY ONLINE

• Introduction to the Bilbao Crystallographic Server
• Space Groups Retrieval Tools
• Group - Subgroup Relations of Space Groups
• Structure utilities and computer tools: different structure descriptions and structural relationships
• Tools for the study of structural phase transitions on the Bilbao Crystallographic Server

TWINNED CRYSTALS

• Reticular classification of twins and its extensions
• Methods of calculations of twin elements and derivation of twin laws.
• The Coincidence-Site Lattice theory: application to the derivation of twin lattices and their classification in terms of twin index and obliquity.
• Translational and point symmetry of twins: twin point groups and their chromatic features.
• Diffraction patterns of twinned crystals.

Language

The official language of the Schools is English. No simultaneous interpretation will provided. However, local tutors woll help the participants during the exercises.

Venue

The School will be held at the Institute of Physics of the Federal University of Uberlândia, in the southeast of Brazil.

International Program Committee

• Prof. Massimo Nespolo, Université de Lorraine, France, Chair.
• Prof. Mois Ilia Aroyo, Universidad del País Vasco, Bilbao, Spain.
• Prof. Ernesto Estevez Rams, Universidad de la Habana, Cuba.
• Prof. Raimundo Lora Serrano, Universidade Federal de Uberlândia, Brazil.
• Prof. Eduardo Granado, Universidade Estadual de Campinas, Brazil.
• Prof. Michal Dusek, Academy of Sciences. Czech Republic.
• Prof. Leopoldo Suescun, Universidad de la Repéblica, Uruguay.
• Prof. Rômulo Simões Angélica, Universidade Federal do Pará, Brazil.

Lecturers

• Prof. Massimo Nespolo, Université de Lorraine, France.
• Prof. Mois Ilia Aroyo, Universidad del País Vasco, Bilbao, Spain.
• Prof. Ernesto Estevez Rams, Universidad de la Habana, Cuba.
• Prof. Michal Dusek, Academy of Sciences. Czech Republic.
• Prof. Eduardo Granado, Universidade Estadual de Campinas, Brazil.
• Prof. Leopoldo Suescun, Universidad de la Repéblica, Uruguay.

Local Organizing Committee

• Prof. Raimundo Lora Serrano, Chair
• Prof. Omar de Oliveira Diniz Neto
• Prof. Augusto Miguel Alcalde Milla
• Prof. Silvana Guilardi
• Prof. Eduardo de Faria Franca
• Prof. José de los Santos Guerra.
• Vinicius Soares O. de Sousa (Secretary)

Registration and accommodation

Details about the registration fees and procedure, as well as accommodation, will be announced at a later time.

Poster presentations

Participants are welcome to submit abstracts for poster presentations. Poster will remain on display during the whole school/

Financial support

Limited financial support for students and young scientits will be available. Details will be announced later.

Contact

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

Last updated: 12 Augurst 2011
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