International Union of Crystallography

MaThCryst forthcoming activities
Ninth training course on symmetry and group theory, last summer 2020, Tsukuba (Japan)
Seventh MaThCryst School in Latin America, November 2020, Lima (Peru)
SIAM conference on mathematical aspects of Material Science, May 2021, Bilbao (Spain)
MaThCryst recent activities
AMS Sectional Meeting, November 2019, Gainesville, FL (USA)
ECM32 Satellite, August 2019, Wien (Austria)
Eighth training course on symmetry and group theory, July 2019, Tsukuba (Japan)
Second Shanghai International Crystallographic School, July 2019, Shanghai (China)
Summer School, June 2019, Nancy (France)
Sixth MaThCryst School in Latin America, November 2018, Bogotà (Colombia)
Seventh training course on symmetry and group theory, August 2018, Tsukuba (Japan)
Topological Methods in Materials Science 2017, October 2017, Beijing (China)
International Autumn School on Fundamental and Electron Crystallography (IASFEC), October 2017, Sofia, (Bulgaria)
IUCr 2017 Satellite, September 2017, Rourkela, (India)
Sixth training course on symmetry and group theory, August 2017, Tsukuba (Japan)
Shanghai International Crystallographic School, June 2017, Shanghai (China)
Second Workshop on Mathematical Crystallography, May 2017, Manila (Philippines)
Fifth training course on symmetry and group theory, March 2017, Tsukuba (Japan)
More...
International School on Fundamental Crystallography with applications to Electron Crystallography
University of Antwerp, Belgium, 27 June  2 July 2016,
In cooperation with the IUCr Commission on Electron Crystallography
Venue
University of Antwerp, Antwerp, BELGIUM
Necessary background (assumed achieved by all participants)
 Interaction of radiation with matter.
 Elementary physics of scattering and diffraction. Structure factor.
 Bragg's law and Ewald's sphere.
Topics not developed during the school
Fundamentals of TEM: the microscope, sample preparation, resolution.
Program
Day 0 (optional)
 Basics of matrix algebra (vectors and matrices; dot and cross product; types of matrices and matrix operations).
 Fourier series and Fourier transforms.
Day 1
 Introduction to group theory: algebraic categories, homomorphisms, isomorphisms, automorphisms.
 The notion of symmetry and symmetry groups.
 Crystallographic symmetry in two and three dimensions: Bravais lattices, point groups, holohedries and merohedries, point groups; HermannMauguin symbols for point groups.
 Hierarchy of classification: Crystal families, lattice systems, crystal systems, arithmetic and geometric crystal classes, Bravais classes, Bravais flocks.
 Lattice planes, Miller indices and BravaisMiller indices. Forms, zones and zone axes.
 Choice of the zones to look at in ED for the different crystal systems.
 Introduction to the stereographic projection.
Day 2
 Exercises on the stereographic projection to build crystallographic point groups.
 Metric tensor and crystallographic calculations: norm of a vector, angle between vectors, change of basis.
 Polar and reciprocal lattice.
 Indexing of a stereographic projection through the polar or the reciprocal lattice.
 Symmetry operations with a screw or glide component.
 From point to space groups.
 Examples and exercises on space group diagrams.
 Projections of space groups and their twodimensional symmetry
 Groupsubgroup relations. Klassengleiche, translationengleiche, isomorphic subgroups. Change of basis from group to subgroup. Definition and basic features of parent and daughter phases.
 Integral, zonal and serial diffraction conditions.
 Diffraction symbol and possible space groups corresponding to it.
Day 3
 Indexing of an ED pattern.
 Calculation / simulation of a SAED pattern for a given compound (from cell parameters and zone axis).
 Reconstruction of the unit cell from SAED along different zone axes.
 Connection of the symmetry in real space to that of the ED pattern.
 Analysis of the information one can obtain from CBED.
 Differences between the symmetry information from SAED (addition of inversion centre, can't distinguish m or 2) and CBED (can distinguish all point symmetry elements).
 Exercises on experimental SAED and CBED patterns.
 From superlattices (subcells) in ED to sublattices (supercells) in real space.
 Determination of point groups and space groups from ED patterns.
Day 4
 Domains (twins, antiphase domains); effect of twinning on the diffraction pattern.
 Calculation of twin index, obliquity, unit cell of the twin lattice.
 Splitting of reflections following a phase transition to a lower lattice system.
 Effect of the presence of symmetry operations with a glide component on ED patterns, effect of screw axes, GjonnesMoodie lines
 Determination of space groups from ED patterns
 Dynamical effects of the (multiple diffractions) and their effect on the reflection conditions and expected equivalence of reflections.
 Partial reconstruction of the space group symmetry from atomic resolution images (projection of space groups, effects of misorientation).
 Exercises on the determination of space group from electron diffraction patterns.
Day 5
 Morphology of nanoparticles and their ED patterns. Tomography.
 Modulates structures (commensurate and incommensurate): indexing, displacement vs. compositional modulation on an atomic resolution image of the structure.
 Quasicrystals and their ED patterns.
 Characteristics of subcells and supercells on ED patterns, how to describe the supercell observed on an ED pattern of a new compound relative to a known subcell, effect of supercells on the intensity distribution of the reflections. Effects of substitutions, distortions, vacancies,... on the ED patterns when starting from the same subcell, connected to a calculation of the structure factors of those cases.
 Short introduction on the possibilities of extracting and using the reflections on ED patterns in a quantitative manner to solve structures ab initio and to refine structures.
Speakers
 Prof. Joke Hadermann, Universiteit Antwerp, Belgium
 Prof. Massimo Nespolo, Université de Lorraine, France
 Prof. Mois I. Aroyo, Universidad del País Vasco, Spain
Local website
Detailed information is available at the local website.
Didactic material
 Slides from Mois Aroyo lectures
 Slides from Massimo Nespolo lectures
 Slides from Joke Hadermann lectures
Photos
A gallery of photos is available at the IUCr website.
List of participants
Family name  First names  Country of birth  Email address  Home Institution 

Al Haqbani  Norah  Saudi Arabia  King Saud University  
Antunes  Correa Cinthia  Brazil  Charles University Prague  
Ben Hafsia  Ahmed Lamine  Tunisia  Universiteit Antwerpen  
Callaert  Carolien  Belgium  Universiteit Antwerpen  
Cautaerts  Niels  Belgium  Universiteit Antwerpen  
Charalampopoulou  Evangelia  Greece  Universiteit Antwerpen  
De Mello Timm  Mariana  Brazil  Universidade Federal do Rio Grande do Sul  
Engun  Semih  Turkey  Bulent Ecevit University  
Geerts  Lisa  Belgium  KU Leuven  
Ghadimi  Mohammed Reza  Iran  Tietz Video and Image Processing Systems GmbH.  
Gomez  Perez Alejandro  Spain  Nanomegas  
Gondek  Jan  Slovakia  Slovak University of Technology  
Gupta  Deepali  India  All India Institute of Medical Sciences  
Hrebik  Dominik  Slovakia  Masaryk University  
Karakulina  Olesia  Russia  Universiteit Antwerpen  
Khadiev  Azat  Russia  Kazan National Research Technical University  
Knotek  Miroslav  Czech Republic  Tescan Orsay Holding  
Kumar  Arun  India  a  Università degli Studi di Verona 
Lampronti  Giulio Isacco  Italy  University of Cambridge  
Luginina  Marina  Ukraine  ISMAN Russian Academy of Sciences  
MaciasSanchez  Elena  Spain  Universidad de Granada  
Malakhova  Daria  Ukraine  University of South Bohemia  
Matus  Krzysztof Michał  Poland  Silesian University of Technology  
Morozov  Anatolii  Russia  Moscow State University  
Nagapuri  Raju  India  Osmania University  
O'Connell  Eoghan  Ireland  University of Limerick  
Paria  Sena Robert  Peru  Universiteit Antwerpen  
Petrenec  Martin  Czech Republic  Tescan Orsay Holding  
Satalkina  Ekaterina  Russia  Gokhran of Russia  
Savaci  Umut  Turkey  Anadolu University  
Schneider  Rauber Gabriela  Brazil  University of Cambridge  
Sedykh  Oxana  Russia  Gokhran of Russia  
Siskins  Makars  Latvia  University of Manchester  
Solla  Agra Eugenio Luis  Spain  Universidad de Vigo  
Tunca  Altintas Bensu  Turkey  KU Leuven  
Wallisch  Wolfgang  Austria  Technische Universität Wien  
Wolf  Witor  Brazil  Universidade Federal de Sao Carlos  
Zackova  Paulina  Slovakia  Slovak University of Technology  
Zavašnik  Janez  Slovenia  Institut Jožef Stefan Ljubljana 
The Organizers of the International School on Fundamental Crystallography with applications to Electron Crystallography 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 barrier existed which would have prevented the participation of bona fide scientists.