International Union of Crystallography Commission on Mathematical and Theoretical Crystallography

Summer School on Mathematical Crystallography

Nancy, France, 12 - 16 June 2023

Lecturers

• Massimo Nespolo, Université de Lorraine, France
• Mois Ilia Aroyo, Universidad del País Vasco, Spain
• Michal Dušek, Czech Academy of Sciences, Czech Republic
• Andrey Zameshin, Malvern Panalytical, The Netherlands
• Tutor: Isabella Pignatelli, Géoressources laboratory, Université de Lorraine, France

Local Organizing Committee

• Prof. Massimo Nespolo, CRM2 laboratory, chair
• Mrs Valérie Richalet, CRM2 laboratory, secretary

Timetable

Morning session (3:00 hours):
Lectures 9:00 - 10:30
Coffee break: 10:30 11:00
Lectures 11:00 - 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

Lunches were served at the Restaurant Universitaire Vélodrome..

Scientific Program

1st Day Monday, 12 June, morning session:

9:00 - 9:10 Opening of the School

General introduction to crystallographic symmetry and application to two-dimensional space

Lecturers: Massimo Nespolo, Mois Ilia Aroyo

• Symmetry groups and their classification with in terms of periodicity (MN).
• Symmetry groups and types of symmetry in the two-dimensional space (MN).
• Bravais lattices, conventional and non-conventional unit cells (MN).
• Point symmetry of lattices and symmetry directions. Hermann-Mauguin symbols for point groups. Symmetry of crystallographic patterns: holohedries and merohedries (MN).
• Subgroups, index, coset decompositions. Lagrange theorem (MIA).
• Normal and conjugate subgroups of two-dimensional point groups. Factor group (MIA).
• General and special Wyckoff positions, site symmetry (MIA).
• Supergroups and normalizers

1st Day Monday, afternoon session

Crystallographic symmetry in the three-dimensional space

Lecturer: Massimo Nespolo

• Crystal families, lattice systems and crystal systems.
• 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. Diffraction and Laue indices.

2nd Day, Tuesday, 13 June, morning session

Presentation of symmetry operations

Lecturer: Mois Ilia Aroyo

• Symmetry elements: geometric elements and element sets.
• Symmetry operations and their matrix-column presentation; geometric interpretation.
• Transformations of the coordinate systems: change of origin and orientation.
• Metric tensor.

2nd Day, afternoon session

Space groups: theory and exercises

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.

3rd Day, Wednesday, 14 June, morning session

Lecturer: Mois Ilia Aroyo

(i) Description of space-group symmetry in ITA

• Conventional and non-conventional descriptions of space groups; ITA settings.
• Coset decomposition. Factor group. Symmorphic and non-symmorphic types of space groups.
• General and special Wyckoff positions, site symmetry.

(ii) Computer tools for space-group symmetry

• Computer databases and access tools to crystallographic symmetry data for space groups of the Bilbao Crystallographic Server (BCS) and Symmetry Database (IT-Online server).M

3rd Day, afternoon session

Symmetry relations between space groups

Lecturer: Mois Ilia Aroyo

• 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.
• Introduction and use of the databases of the IT-Online server and BCS of maximal subgroups, series of isomorphic subgroups.
• General group-subgroup relations between space groups: computer programs on the IT-Online server and BCS.

4th Day, Thursday, 15 June, morning session:

Reciprocal space and diffraction

Lecturers: Massimo Nespolo, Andrey Zameshin

• Reciprocal space
• Simplified theory of diffraction. Information retrievable from X-ray diffraction data collection.
• Integral, zonal and serial reflection conditions and their use to determine the space-group type.
• Reciprocal-space sampling.

4th Day: afternoon session

Applications of symmetry relations between space groups

Lecturers: Massimo Nespolo, Mois Ilia Aroyo

• Crystallographic orbits (MN).
• Special reflection conditions (MN).

(i) Subgroups data and related computer applications

• Domain-structure analysis in phase transition problems (initial steps) (MIA).
• Supergroups and Normalizers of space groups (MIA).

(ii) Basic structure utilities of BCS and comparison of crystal structures.

• Search for pseudo-symmetry.

5th Day, Friday, 16 June, morning session:

Solution and refinement of crystal structure models

Lecturer: Michal Dušek

• General introduction to structure solution and refinement methods and approaches.
• Jana2020: installation, deployment, interface, commands and practical use.

5th Day: afternoon session

Exercises and tutorial on Jana2020

Lecturers: Michal Dušek, Andrey Zameshin

• Overview of Charge flipping
• Exercises on structure solution and refinement with Jana2020.

Venue

The school was at the Amphitheatre No. 1, Faculty of Sciences and Technologies, Université de Lorraine.

Language

The official language of the school was English. No simultaneous translations was provided

Poster presentations

Abstracts of poster presentations by the participants are available for download.

List of participants

Gender	Name	Surname	Citizenship	Affiliation	Country
M	Yacine Malik	Chaib Draa	Algeria	Université Haute-Alsace	France
F	Raounek	Rouag	Algeria	Université freres Mentouri Constantine 1	Algeria
F	Khatira	Mehtiyeva	Azerbaijan	Baku State University	Azerbaijan
M	Igor Dalamelino	Borges	Brazil	University of Goias	Brazil
F	Gergana Georgieva	Velyanova	Bulgaria	Sofia University	Bulgaria
F	Gordana	Garapic	Croatia	New Paltz State University of New York	USA
F	Corinne	Arrouvel	France	Universidade Federal de São Carlos	Brazil
F	Florentine	Guiot	France	Université de Rennes	France
M	Antoine	Roll	France	CEA Saclay	France
F	Claudia	Schoeberl	Germany	Esslingen University of Applied Sciences	Germany
F	Vincentia Emerson	Agbemeh	Ghana	Italian Institute of Technology	Italy
M	Marco	Brasini	Italy	Université de Picardie Jules Verne	France
M	Giulio Isacco	Lampronti	Italy	University of Cambridge	UK
M	Luca	Monetta	Italy	Università degli Studi di Salerno	Italy
F	Beatriz	Mendoza Sanchez	Mexico	Institute for Applied Materials Energy Storage Systems, Karlsruhe	Germany
M	Ricardo Guillermo	Torres Ramìrez	Mexico	Institut de physique de Rennes	France
M	Ghenadie	Novitchi	Moldova	Laboratoire National des Champs Magnétiques Intenses, Grenoble	France
F	Sara	El Houbbadi	Morocco	Université de Lorraine	France
M	Yassine	Oubaid	Morocco	Université Paris-Saclay	France
F	Temitope Olabisi	Abodunrin	Nigeria	Landmark University	Nigeria
M	Chinedu Uduma	Ibe	Nigeria	Università degli Studi di Bari	Italy
F	April Lynne Dampo	Say-awen	Philippines	Ateneo de Manila University	Philippines
M	Andrey	Zameshin	Russia	Malvern Panalytical	Netherlands
M	Jungyoun	Cho	South Korea	Stockholm University	Sweden
M	Faye Diouf	Moussa Diame	Spain	Italian Institute of Technology	Italy
M	Wayne	Skelton-Hough	UK	University of Cambridge	UK
M	Daniel Robert	Hummer	USA	Southern Illinois University	USA
M	Dongzhou	Zhang	USA	Argonne IL	USA
16M, 12F			19, 4 continents	26 institutions	13, 4 continents

Contact

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The Organizers of the Nancy 2023 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 heve prevented the participation of bona fide scientists.

Last updated: 18^th June 2023
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