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International Union of Crystallography
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Summer School on Mathematical Crystallography
Nancy, France, 3 - 7 June 2019
Lecturers
- Massimo Nespolo, Université de Lorraine, France
- Benoît Guillot, Université de Lorraine, France
- Gemma de la Flor Martin, Karlsruhe Institute for Technology, Germany
Tutors
- Isabella Pignatelli, Université de Lorraine, France
- Berthold Stöger, Technische Universität Wien, Austria
Local Organizing Committee
- Prof. Massimo Nespolo, CRM2 laboratory, chair
- Dr. Isabella Pignatelli, Géoressources laboratory
- Mrs Valérie Richalet, CRM2 laboratory, secretary
Didactic Material
See also the list of didactic material for the MaThCryst schools.
Timetable
Morning session (3:00 hours):
Lectures 9:00 - 10:30
Coffee break: 10:30 11:00
Lectures 11:30 - 13:00
Lunch: 13:00 14:30
Afternoon session (4:00 hours):
Lectures 14:30 16:30
Coffee break: 16:30 17:00
Lectures 17:00 - 19:00
Scientific Program
1st Day Monday, 3 June, morning session:
9:00 - 9:10 Opening of the SchoolGeneral introduction to crystallographic symmetry and application to two-dimensional space
Lecturer: Massimo Nespolo
- Basic properties of groups (group axioms, order, multiplication tables, etc.). Homomorphism and isomorphism.
- Symmetry groups and types of symmetry in the two-dimensional space.
- Bravais lattices, conventional and non-conventional unit cells.
- Point symmetry of lattices and symmetry directions. Hermann-Mauguin symbols for point groups. Symmetry of crystallographic patterns: holohedries and merohedries.
- Subgroups, index, coset decompositions. Lagrange theorem. Normal and conjugate subgroups of two-dimensional point groups.
- Crystal families, lattice systems and crystal systems.
1st Day Monday, afternoon session:
Lecturer: Massimo Nespolo
- Extension of the results in two dimensions to the three-dimensional space.
- Miller indices. Morphological symmetry, forms and zone. Stereographic projection and its use for the derivation of crystallographic point groups. Wyckoff positions for point groups. Subgroups and supergroups of point groups. Bravais-Miller indices, Laue indices, Weber indices. Curie law for the study of physical properties of crystals (generalities).
2nd Day, Tuesday, 4 June, morning session
Lecturer: Massimo Nespolo
- Space groups, general introduction: screw axes and glide planes.
- Orthogonal projections of space groups. Exercises on space-group diagrams from Volume A of the International Tables for Crystallography. General and special positions, site-symmetry groups.
2nd Day, afternoon session
Lecturer: Massimo Nespolo
- Exercises on space-group diagrams from Volume A of the International Tables for Crystallography (II).
- Metric tensor. Matrix-column presentation of symmetry operations. Symmetry elements: geometric elements and element sets. Geometric interpretation of the matrix-column presentation of the symmetry operations.Transformations of the coordinate systems: change of origin and orientation.
3rd Day, Wednesday, 5 June, morning session
Lecturers: Massimo Nespolo, Gemma de la Flor
- Conventional and non-conventional descriptions of space groups; ITA settings.
- Computer databases and access tools to crystallographic symmetry data forspace groups (International Tables for Crystallography, Volume A: Space-group symmetry): symmetry operations and their matrix-column presentation; geometric interpretation; general and special Wyckoff positions, site symmetry.
3rd Day, afternoon session
Lecturer: Massimo Nespolo
- Normalizers of space groups
- Group-subgroup relations between space groups: Subgroups of space groups: types of subgroups of space groups; Hermann theorem; maximal subgroups; series of isomorphic subgroups. Coset decomposition. Factor group. Symmorphic and non-symmorphic types of space groups
4th Day, Thursday, 6 June, morning session:
Lecturer Massimo Nespolo
- Reciprocal space
- Integral, zonal and serial reflection conditions and their use to determine the space-group type
- Diffraction symmetry, and Laue classes
4th Day: afternoon session
Lecturer Massimo Nespolo, Gemma de la Flor
- Crystallographic orbits
- Special reflection conditions
- Maximal subgroups data and related computer applications: (i) Introduction and use of the databases of the IT-Online server and the Bilbao Crystallographic server of maximal subgroups, series of isomorphic subgroups and minimal supergroups; (ii) General group-subgroup relations between space groups: computer programs on the IT-Online server and the Bilbao Crystallographic Server.
5th Day, Friday, 7 June, morning session:
Lecturer: Gemma de la Flor
- Relations of Wyckoff positions for a group-subgroup pair. Supergroups of space groups.
- Crystal-structure descriptions I. Basis transformations and crystal-structure descriptions; structure descriptions compatible with symmetry reduction (the program TRANSTRU). Descriptions of crystal structures with respect to different ITA settings of the space groups (the program SETSTRU). Equivalent crystal structure descriptions (the programs EQUIVSTRU and COMPSTRU).
- Crystal-structure relations. Group-subgroup relations between space groups and the construction of structure family trees (Baernighausen trees (the program STRUCTURE RELATIONS)
5th Day: afternoon session
Lecturer Benoît Guillot
- Symmetry considerations and restraints and constraints in structure refinement from single-crystal X-ray diffraction data
Venue
The school was held at the Amphitheatre No. 8, Faculty of Sciences and Technologies, Université de Lorraine.
Language
The official language of the school is English. No simultaneous translations has been provided
Special issue announcement
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A special issue of Crystal Research and Technology has published a special issue containing a collection of papers submitted on the occasion of MaThCryst 2019 Summer events. |
Poster presentations
Participants had the occasion to present their work with posters that remained on display during the whole school. Abstracts of poster presentations are available for download this link.
Photos and report
A photo gallery is available at the IUCr website. A short report of hte school has been published in the IUCr newsletter.
List of participants
| Name | Surname | Nationality | Institution | Country of institution | email address |
|---|---|---|---|---|---|
| Amani Hind | Benahsene | Algeria | Univeristé frères Mentouri Constantine 1 | Algeria | |
| Rodrigo | Uchida Ichikawa | Brazil | Nuclear and Energy Research Institute | Brazil | |
| Jean Marcos Ferreira | Custodio | Brazil | Universidade Federal de Goias | Brazil | |
| Neetesh | Soni | India | Southwest Petroleum University | China | |
| Prabal | Dasgupta | India | Jimma University | Ethiopia | |
| Zhong | Wuyang | China | CentraleSupelec | France | |
| Alam Tonaltzin | Osorio Delgadillo | Mexico | Grenoble INP | France | |
| Cyril | Langlois | France | INSA Lyon | France | |
| Maxime | Dottor | France | Institut de Chimie et des Matériaux Paris Est | France | |
| Alexandre | Courac | France | Sorbonne Université | France | |
| Penda Seydi | Deme | Senegal | Université de Lorraine | France | |
| Mamoudou | Diallo | Senegal | Université de Lorraine | France | |
| Daniel Pepin | Fowan | Cameroon | Université de Lorraine | France | |
| Ridvan | Ince | France | Université de Lorraine | France | |
| Hassan | Khoder | Lebanon | Université de Lorraine | France | |
| Soumeya Deghdegh | Maza | Algeria | Université de Lorraine | France | |
| Phuong Anh | Nguyen | Vietnam | Université de Lorraine | France | |
| Akihiro | Umayahara | Japan | Université de Lorraine | France | |
| Vishnu | Vijayakumar Syamala | India | Université de Lorraine | France | |
| Anna Sophia | Hartl | France | Universite de Rennes 1 | France | |
| Ali | Bedidi | France | Université Paris-Est | France | |
| Christelle | Combescure | France | Université Paris-Est | France | |
| Chloé | Fourdrin | France | Université Paris-Est | France | |
| Victoria | Kononikhina | Russia | Helmoltz-Zentrum | Germany | |
| Daria | Lazurenko | Russia | Helmoltz-Zentrum | Germany | |
| Zhida | Liang | China | Helmoltz-Zentrum | Germany | |
| Sergei | Ivlev | Russia | Philipps-Universität Marburg | Germany | |
| Niloofar | Hadaeghi | Iran | Technische Universität Darmstadt | Germany | |
| Ilias | Samathrakis | Greece | Technische Universität Darmstadt | Germany | |
| Lorenzo | Villa | Italy | Technische Universität Darmstadt | Germany | |
| Peng | Chen | China | Istituto Italiano di Tecnologia | Italy | |
| Emanuele | Priola | Italy | University of Torino | Italy | |
| Junichiro | Kishine | Japan | The Open University of Japan | Japan | |
| Jeanine Concepcion | Arias | Phillippines | University of the Philippines | Philippines | |
| Rosa Micaela | Danisi | Italy | Karlsruhe Institute of Technology | Russia | |
| Vladimir | Lazarenko | Russia | Kurchatov institute | Russia | |
| Ren | Qiu | China | Chalmers University of Technology | Sweden | |
| Xiao | Hua | China | Oxford University | UK | |
| Peter | Moeck | Germany | Portland State University | USA | |
| Stephanie | Mackley | USA | University of Notre Dame | USA |
Contact
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The Organizers of the Nancy 2019 MaThCryst 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.
