MaThCryst forthcoming activities


Sixth training course on symmetry and group theory, August 2017, Tsukuba (Japan)


IUCr 2017 Satellite, September 2017, Rourkela, (India)


International Autumn School on Fundamental and Electron Crystallography (IASFEC), October 2017, Sofia, (Bulgaria)





MaThCryst recent activities

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)


Fifth MaThCryst School in Latin America, October 2016, Havana (Cuba)


AIC School 2016, 7-11 September 2016, Rimini, (Italy)


First advanced training course on symmetry and group theory, August 2016, Tsukuba (Japan)


International Scientific School 'Combined topological and DFT methods for prediction of new materials II', July 2016, Samara (Russia)


International School on Fundamental Crystallography with applications to Electron Crystallography, June - July 2016, Antwerp (Belgium)


SIAM conference on mathematical aspects of Material Science, May 2016, Philadelphia (USA)


More...


International Autumn School on Fundamental and Electron Crystallography (IASFEC)

8-13 October 2017, Sofia, Bulgaria

Invited lecturers

Organizing Committee

Necessary background (assumed achieved by all participants)

Scientific Program

Day 1: 08 October 2017, Sunday
Arrival, registration and accommodation
Day 2: 09 October 2017, Monday
9:15 - 9:30 Opening of the School (Dr. Daniela Karashanova)
Lecturers: Prof. Mois Aroyo, Prof. Massimo Nespolo
9:30 - 11:00
  • Introduction to group theory: the notion of symmetry and symmetry groups.
  • Lattices and unit cells. Crystallographic symmetry in two dimensions
11:00 - 11:30 Coffee break
11:30 - 13:30 Crystallographic symmetry in three dimensions: Bravais lattices, point groups, holohedries and merohedries, point groups; Hermann-Mauguin symbols for point groups.
13:30 - 15:00 Lunch
15:00 - 16:30
  • Lattice planes, Miller indices and Bravais-Miller 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 and exercises on the stereographic projection to build crystallographic point groups.
16:30 - 17:00 Coffee break
17:00 - 18:30 Subgroups of point groups
19:00 - 20:00 Dinner
Day 3: 10 October 2017, Tuesday
Lecturers: Prof. Massimo Nespolo, Prof. Mois Aroyo
9:30 - 11:00 Metric tensor and crystallographic calculations: norm of a vector, angle between vectors, change of basis.
11:00 - 11:30 Coffee break
11:30 - 13:30
  • Symmetry operations with a screw or glide component.
  • From point to space groups.
13:30 - 15:00 Lunch
15:00 - 16:30
  • Examples and exercises on space group diagrams.
  • Projections of space groups and their two-dimensional symmetry.
16:30 - 17:00 Coffee break
17:00 - 18:30
  • Group-subgroup 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.
19:00 - 20:00 Dinner
Day 4: 11 October 2017, Wednesday
Lecturers and guidance: Dr. Daniela Karashanova, Dr. Diana Nihtianova, Dr. Bogdan Ranguelov, Dr. Mihail Tarassov
Work in 4 groups at rotational principle
All dayTransmission Electron Microscopy (TEM) laboratory visit
  • basics of TEM
  • sample preparation for TEM
  • experimental SAED and CBED patterns caption
All day
  • Scanning electron microscopy (SEM) - laboratory visit
  • basics of SEM
  • sample preparation for SEM
  • Electron Back Scattered Diffraction (EBSD)
11:00 - 11:30 & 16:30 - 17:00 Coffee breaks and exchange of groups
13:30 - 15:00 Lunch
19:00 - 20:00 Dinner
Day 5: 12 October 2017, Thursday
Lecturer: Prof. Joke Hadermann
9:30 - 11:00
  • 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.
11:00 - 11:30 Coffee break
11:30 - 13:30
  • Connection of the symmetry in real space to that of the ED pattern.
  • Analysis of the information one can obtain from CBED.
13:30 - 15:00 Lunch
15:00 - 16:30
  • 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
16:30 - 17:00 Coffee break
17:00 - 18:30
  • From superlattices (subcells) in ED to sublattices (supercells) in real space.
  • Determination of point groups and space groups from ED patterns.
19:00 - 20:00 Dinner
Day 6: 13 October 2017, Friday
Lecturer: Prof. Massimo Nespolo
9:30 - 11:00
  • 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.
11:00 - 11:30 Coffee break
Lecturer: Prof. Joke Hadermann
11:30 - 13:30
  • Effect of the presence of symmetry operations with a glide component on ED patterns, effect of screw axes, Gjonnes-Moodie lines
  • Determination of space groups from ED patterns
13:30 - 15:00 Lunch
15:00 - 16:30
  • 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).
16:30 - 17:00 Coffee break
17:00 - 18:30
  • 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.
  • Exercises on the determination of space group from electron diffraction patterns.
18:30 - 18:45 Concluding remarks (Dr. Daniela Karashanova)
19:00 - 21:00 Farewell dinner

Registration and accommodation

Details are available at the local website.


The Organizers of the International School on Fundamental and Electron Crystallography will observ 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 barrier will exist which would prevent the participation of bona fide scientists.