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International Union of Crystallography
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International School on Fundamental Crystallography
Third MaThCryst school in Latin America
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 organized a school in Brazil, in continuation of our activity in the region after the previous shools in Havana and in Montevideo.
Scientific 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.
| Preparatory Session | International School on Fundamental Crystallography (ISFC) | Workshop on twinned crystals | ISFC (cont.) | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Day/Time | Sunday (Nov. 25) | Monday (Nov. 26) | Tuesday (Nov 27) | Wednesday (Nov 28) | Thursday (Nov 29) |
Friday (Nov 30) | Saturday (Dec 01) | Sunday (Dec 02) | Monday (Dec 3) |
| 8:30 - 9:00 | Registration | Registration/ Opening |
Tutorial on point groups Nespolo/Aroyo | Group-subgroup relations Aroyo | Physics of Diffraction (I) Fourier transforms. Space group in reciprocal space. Estevez | Search for pseudosymmetries Aroyo | Twinned crystals - Introduction and definitions Nespolo | Free | Tutorial on Jana2006 (III) Twinned crystals - basic examples Dusek |
| 9:00 - 10:00 | Introduction to abstract groups Nespolo | ||||||||
| 10:00 - 10:30 | Coffee break | Coffee break | Coffee break | Coffee break | Coffee break | Coffee break | Coffee break | Coffee break | |
| 10:30 - 12:30 | Matrix Algebra Estevez | Crystallographic symmetry in E2 Nespolo | Crystallographic symmetry in E3 - part II: space groups Nespolo | Bilbao Crystallographic Server for subgroups Aroyo | Data processing and reduction Suescun | Symmetry-mode analysis with Amplimodes Aroyo | Twinned crystals - Calculations of twin parameters Nespolo | Tutorial on Jana2006 (VI) Twinned crystals - advanced examples Dusek | |
| 12:00 - 14:00 | Lunch | Lunch | Lunch | Lunch | Lunch | Lunch | Lunch | Lunch | |
| 14:00 - 16:00 | Fourier Transform Estevez/Serrano | Crystallographic symmetry in E3 - part 1: point groups Nespolo | Exercises on space groups construction and use of Volume A of the International Tables Nespolo | Structure Utilities Aroyo | Physics of Diffraction (II). Systematic absences, reflection conditions and space group determination Granado | Tutorial on Jana2006 (I) Introduction to Jana2006. Basic single crystal example Dusek | Twinned crystals - polychromatic symmetry Nespolo | Tutorial on Jana2006 (V) Simple modulated structure application of rigid body for powders Dusek | |
| 16:00 - 16:30 | Coffee break | Coffee break | Coffee break | Coffee break | Coffee break | Coffee break | Coffee break | Coffee break | |
| 16:30 - 18:30 | Diffraction Physics Estevez/Serrano | Tutorial on point groups Nespolo/Aroyo | Bilbao Crystallographc Server: retrieval of space group information Aroyo | Structure Utilities Aroyo | Strategies for structure solution and refinement Suescun/Granado | Tutorial on Jana2006 (II). Basic powder example. Disorder Dusek | Twinned crystals - Tutorial on the software GEMINOGRAPHY Nespolo | Closing | |
| Welcome reception | |||||||||
Language
The official language of the Schools was English. No simultaneous interpretation was provided. However, local tutors helped the participants during the exercises.
Venue
The School was held at the Institute of Physics of the Federal University of Uberlândia, in the southeast of Brazil. PDF of the Campus Map available for download.
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 República, 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 República, Uruguay.
- Prof. Raimundo Lora Serrano, Universidade Federal de Uberlândia, Brazil.
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)
Poster presentations
Abstracts from poster presentations are available for download in PDF format.
Didactic material
See also the list of didactic material for the MaThCryst schools.
- Mois I. Aroyo: Crystallographic Point Groups
- Mois I. Aroyo: Space Group Symmetry
- Mois I. Aroyo: Group-subgroup relations
- Mois I. Aroyo: Structure Tools
- Mois I. Aroyo: Pseudo
- Massimo Nespolo: Twins: definitions
- Massimo Nespolo: How to compute the twin index
- Massimo Nespolo: Hybrid twins
- Massimo Nespolo: Twin point groups
- Ernesto Estévez Rams: Dirac's Delta
- Ernesto Estévez Rams: Fourier Transform
- Ernesto Estévez Rams: Reciprocal Lattice
- Ernesto Estévez Rams: Diffraction
- Ernesto Estévez Rams: Limiting sphere (movie)
- Leopoldo Suescun: Data Processing and Reduction
- Michal Dusek: Jana 2006 overview
- Michal Dusek: Jana 2006 powder examples
- Michal Dusek: Jana 2006 twinning
- Michal Dusek: Jana 2006 rigib body and modulated structures
List of participants
| Ariane Carla Campos de Melo | Universidade Federal de Goiás | Brazil | |
| Amanda Laura Ibiapino | Universidade Federal do ABC | Brazil | |
| Cinthia Antunes Corrêa | Universidade Federal de Goiás | Brazil | |
| Ciro Alves Justino Nunes | Universidade Federal de Uberlândia | Brazil | |
| Cláudia Adriana da Silva | Universidade Federal de Sergipe | Brazil | |
| Drielly Aparecida Paixão | Universidade Federal de Uberlândia | Brazil | |
| Edson Costa Santos | Kyushu University | Japan | |
| Eduardo de Faria Franca | Universidade Federal de Uberlândia | Brazil | |
| Evandro Ares de Araújo | Universidade Federal de São Carlos | Brazil | |
| Fernandes Tenório Gomes Rodrigues | Universidade Federal de Minas Gerais | Brazil | |
| Fernando Assis Garcia | UNICAMP | Brazil | |
| Hector Enrique Rojas | Universidade Federal de Uberlandia | Brazil | |
| Horácio Coelho Júnior | Universidade de Brasília | Brazil | |
| Irisnei Luzia Ferreira | UFU | Brazil | |
| José Alberto de Sousa | Universidade Federal de Uberlândia | Brazil | |
| José de los Santos Guerra | Universidade Federal de Ubelândia | Brazil | |
| Juan Carlos Tenorio | Instituto de Física de São Carlos- USP | Brazil | |
| Juliana Alves Pereira Sato | Universidade Federal do ABC - UFABC | Brazil | |
| Justiniano Quispe Marcatoma | Centro Brazileiro De Pesquisas Fisicas | Brazil | |
| Kelly Cristina de Lira Lixandrão | UFABC | Brazil | |
| Laysa Pires de Figueiredo | UFABC | Brazil | |
| Leonardo de Sousa Silva | Universidade Federal de Sergipe | Brazil | |
| Lizbet León Félix | Universidade de Brasília | Brazil | |
| Lóide Oliveira Sallum | Universidade Estadual de Goiás | Brazil | |
| Marco Antonio Seiki Kadowaki | IFSC-USP | Brazil | |
| Marco Aurelio de Oliveira | Universidade Federal de Uberlândia | Brazil | |
| Marina Quádrio Rodrigues | UFMG | Brazil | |
| Mirtha Pillaca Quispe | Universidad Nacional Mayor de San Marcos | Perú | |
| Nilmar Silva Camilo | Universidade Federal de Uberlândia | Brazil | |
| Omar Carlos Herrera Asmat | Universidad Peruana Cayetano Heredia | Perú | |
| Paulo de Sousa Carvalho Júnior | Universidade de São Paulo | Brazil | |
| Pedro A. Marinho Castellanos | Universidad de Oriente/CBPF | Cuba/Brazil | |
| Rafael Victor Helerbrock de Melo | Universidade Federal de Goiás | Brazil | |
| Roberto Gomes de Aguiar Veiga | Universidade de São Paulo | Brazil | |
| Roney Junio de Portugal | Universidade Federal de Uberlândia | Brazil | |
| Santiago Vázquez | Fac. de Química- Universidad de la República - Uruguay | Uruguay | |
| Sebastián Davyt | Fac. Quimica-Universidad de la República - Uruguay | Uruguay | |
| Silvana Guilardi | Universidade Federal de Uberlândia | Brazil | |
| Tiago Gonçalves Santos | Universidade do Vale do Paraíba | Brazil | |
| Valdeir Antonio da Silva | Universidade de Brasília | Brazil | |
| Vânia Mendes do Prado | UFABC | Brazil | |
| Victor (Yehuda) Zenou | Ben-Gurion University | Israel | |
| Wellington Luis de Almeida | Universidade Estadual de Ponta Gossa (UEPG) | Brazil | |
| Erika Nascimento Lima | Universidade Federal de Uberlândia | Brazil | |
| Dominike Pacine de Andrade | Universidade Federal de Uberlândia | Brazil | |
| Robert Prudêncio Amaral | Universidade Federal de Uberlândia | Brazil | |
| Augusto Miguel Alcalde Milla | Universidade Federal de Uberlândia | Brazil | |
| Andrea Antunes Pereira | Universidade Federal de Uberlândia | Brazil | |
| Breno Fernandes Paula | Universidade Federal de Uberlândia | Brazil | |
| Athos Machado Silva | Universidade Federal de Uberlândia | Brazil |
Photos
A selection of ptohos is available at the IUCr gallery website (three pages, clic on the "Next" link in the bottom-right corner).
Contact
Inquiries about the scientific program of the school should be sent to . For inquiries about organisation please contact .
The Organizers of the Uberlândia 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.
