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; Hermann-Mauguin 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 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.

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 two-dimensional symmetry
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.

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, Gjonnes-Moodie 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

Photos

A gallery of photos is available at the IUCr website.

List of participants

Family name	First names	Country of birth	E-mail 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
Macias-Sanchez	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 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 existed which would have prevented the participation of bona fide scientists.