Organised by the Bulgarian Crystallographic Association, the Institute of Mineralogy and Crystallography “Acad. Ivan Kostov" and the IUCr Commission on Mathematical and Theoretical Crystallography

International school on fundamental crystallography:

Introduction to International Tables for Crystallography,Â
Vol. A: Space-group symmetry andÂ
Vol. A1: Symmetry relations between space groups

Gulechitza, Bulgaria, 30 September - 5 October 2013

 Chair of the Organizing Committee and contact person: Dr. Rosica Nikolova (Institute of Mineralogy and Crystallography, Bulgarian Academy of Sciences) rosica.pn@clmc.bas.bg

Language

The official language of the Schools is English. No simultaneous interpretation will provided. However, local tutors will help the participants during the exercises.

Venue

The School will be held at the mountain base Guletchitza (1600 m) of  Sofia University,  in the northern slopes of Rila Mountain - Maliovitza area (~1h30min from Sofia).

International School on Fundamental Crystallography

Third MaThCryst school in Latin America

Uberlândia, Brazil, 25 November - 3 December 2012
The Commission on Mathematical and Theoretical Crystallography is strongly committed to promote education in all the fundamental aspects of crystallography that nowadays are overlooked in common University courses. This mission is accomplished through a series of meetings in a wide range of regions. In fall 2012 we organized a school in Brazil, in continuation of our activity in the region after the previous shools in Havana and in Montevideo.

MaThCryst Workshop on Mathematical Crystallography

Manila, 2-6 November 2011
Mathematical crystallography in the previous century dealt primarily with the theory of space groups. However, advances in materials science during the past decades have broadened the horizons of mathematical crystallography. Recent works delve into higher-dimensional crystallography, non-Euclidean spaces, and aperiodic structures, and involve a wide array of mathematical tools such as topology, discrete geometry, graph theory, and harmonic analysis. The goal of this workshop was to give a firm introduction on current topics in mathematical crystallography and its applications. In particular, the geometry of periodic and crystalline networks, color symmetry, coincident site lattices, twinning in crystals, mathematical diffraction theory, and crystal GAP shall be discussed. The workshop was intended for young scientists (graduate students and post-doctoral associates) and researchers in mathematics, materials science, structural chemistry, solid state and condensed matter physics. Exposure to research opportunities in mathematical crystallography, a heightened awareness of scientists in the Philippines and the Asia-Pacific region on the relevance of mathematical crystallography in their respective researches, and collaborations between researchers in mathematical crystallography and experimentalists were among the expected outcomes from this workshop.

Venue

National Institute of Physics Building, University of the Philippines, Diliman, Quezon City.

Crystal structure prediction using the USPEX code

October 22, 2012 to October 26, 2012 Location : CECAM-HQ-EPFL, Lausanne, Switzerland

Organisers

• Andriy Lyakhov (SUNY Stony Brook, USA)
• Gilles Frapper (University of Poitiers, France)
• Artem Oganov (SUNY Stony Brook, USA)
• Mario Valle (Swiss National Supercomputing Centre, Switzerland)

Description

Crystal structure prediction has long remained a major unsolved problem in physical sciences [1]. A number of approaches have been formulated over years - most of these are summarized in the recent book [2]. Crystal structure prediction is a powerful tool for designing new materials "in silico", thus replacing the traditional Edisonian trial-and-error approach with design by artificial intelligence. It is also a major instrument for discovering new phenomena at extreme conditions. Crystal structure prediction should thus be an everyday tool at the hands of nearly every computational materials scientist.Â

A major advance in this field happened with the development of the evolutionary algorithm USPEX for crystal structure prediction [3], which has led to a number of important findings [4-6]. This proved to be a very efficient and reliable method, and the USPEX code, based on it and freely distributed to academic scientists, is currently used by over 500 researchers worldwide and this number grows rapidly. We should note that in addition to the evolutionary structure prediction, USPEX code features many other techniques, such as random sampling, metadynamics, minima hopping, particle swarm optimization - all of which can be used in real applications or tested against one another. Thus, familiarity with this code will imply a solid background in other structure prediction techniques. USPEX is the widest used crystal structure prediction code and there is a need to train new users through hands-on tutorials and workshops. One such workshop was organized in Poitiers, France (June 2011) and proved to be a great success. Another workshop will take place in Xi'an, China (August 2011). Through a regular series of such pedagogical events we want to train a new generation of users and developers of crystal structure prediction techniques.
Our program will consist of theory lectures, hands-on tutorial sessions, and round table discussions. Morning theory lectures will focus on the nature of the crystal structure prediction problem, various ways to address it (in particular evolutionary algorithms), theory of energy landscapes, applications of crystal structure prediction, problems related to low-dimensional systems. Afternoon tutorials will give each participant to tackle a real research project, and special attention will be paid to the tools for data analysis and visualization.

References

 [1] Maddox J. (1988). Crystals from first principles. Nature 335, 201.Â

[2] Oganov A.R. (Ed.) (2010). Â Modern methods of crystal structure prediction. Berlin: Wiley-VCH, ISBN 978-3-527-40939-6.Â

[3] Oganov A.R., Glass C.W. (2006). Crystal structure prediction using ab initio evolutionary techniques: principles and applications. J. Chem. Phys. 124, 244704.Â

[4] Ma Y., Eremets M.I., Oganov A.R., Xie Y., Trojan I., Medvedev S., Lyakhov A.O., Valle M., Prakapenka V. (2009). Transparent dense sodium. Nature 458, 182-185.

[5] Oganov A.R., Chen J., Gatti C., Ma Y.-M., Yu T., Liu Z., Glass C.W., Ma Y.-Z., Kurakevych O.O., Solozhenko V.L. (2009). Ionic high-pressure form of elemental boron. Nature 457, 863-867.

[6] Oganov A.R., Lyakhov A.O., Valle M. (2011). How evolutionary crystal structure prediction works - and why. Acc. Chem. Res. 44, 227-237.

Purpose of the Course

The determination of three dimensional structures of new materials is frequently the starting point for mechanistic studies, revealing structure-property relationships, modelling of molecular variants and intelligent design for specific properties. However, these are traditionally static results and although we can follow structure evolution with temperature and pressure, it is far less easy to study time evolution when the time scales of the processes involved are short. The latest high intensity X-ray sources, fast detectors, new techniques and modern software are now taking us into the regime of conducting timeâ€"resolved studies and it is this aspect of structural science that we shall be exploring during this course.

X-ray and neutron diffraction are the most powerful methods for elucidating full 3-D structures from single crystals and microcrystalline powder samples for many forms of matter. The techniques are continuously evolving enabling ever more challenging questions to be addressed and the most difficult of problems to be solved. We shall be describing time resolved studies in crystallography, spectroscopy and computation and looking also at applications of this work as well as looking forward to the future and exciting opportunities and challenges that facilities such as XFEL will bring to the field.

We shall concentrate during the course on:

1) Photocrystallography â€" obtaining structural information from short lived crystalline species.

2) Time resolved spectroscopy - identifying and characterising intermediates and correlating these results with structural data.

3) The future â€" current and upcoming developments in dynamic structural techniques.

4) Theoretical calculation â€" correlating with and supporting experimental studies through computational calculations.

And in addition to the lectures we shall be presenting demonstration and workshop sessions providing training in using modern computer programs in these aforementioned areas.

International Union of Crystallography Commission on Mathematical and Theoretical Crystallography

International School on Fundamental Crystallography

followed by a one-day Workshop day on the Representation Theory of Space Groups

Second MaThCryst School in Latin America

Montevideo, Uruguay, 29 November - 4 December 2010
The Commission on Mathematical and Theoretical Crystallography is strongly committed to promote education in all the fundamental aspects of crystallography that nowadays are overlooked in common University courses. This mission is accomplished through a series of meetings in a wide range of regions. In fall 2010 we organized a school in Montevideo, Uruguay, that continues our activity in the region after the previous school in Havana.

International Union of Crystallography

Commission on Mathematical and Theoretical Crystallography

School on Fundamental Crystallography

Mahdia, Tunisia, 9-13 April 2012
Organized by the Commission on Mathematical and Theoretical Crystallography (MaThCryst) and the Tunisian Crystallographic Association (Association Tunisienne de Cristallographie), in cooperation with the IUCr Commission on Crystallographic Teaching (CT).

Program

FUNDAMENTALS

• Introduction to matrix algebra
• Symmetry in nature and in human life

BASIC CONCEPTS

• Affine spaces vs. vector spaces
• Mappings: affine and Euclidean; isometries and symmetry operations
• Sets; homomorphisms, isomorphisms, automorphisms
• Introduction to group theory: abstract groups, subgroups, cosets

CRYSTALLOGRAPHY IN DIRECT SPACE

• Periodic structure of the crystalline matter
• Crystal lattice vs. crystal pattern and crystal structure
• Symmetry directions in a lattice
• Unit cells: primitive cells, multiple cells, conventional cells in 2D and 3D
• Crystal families
• Symmetry groups and types of symmetry in direct space
• • morphological symmetry
  • symmetry of physical properties
  • symmetry of lattices
  • symmetry of the unit cell content
  • symmetry of crystallographic patterns
• Hermann-Mauguin symbols for point groups
• lattice systems
• Crystal systems
• Stereographic projection and the morphology of crystals
• Types of crystallographic point groups through the stereographic projection
• Generation of space groups. Symmetry operations with and without a glide component. Hermann-Mauguin symbols for space groups
• Orthogonal projections of space groups. General and special positions, site-symmetry groups, crystallographic orbits
• Introduction to crystallographic calculations through matrix algebra. Abstract groups, subgroups, cosets
• Short introduction to the subgroups and supergroups of space groups
• Exercises on the space group diagrams from Volume A of the International Tables for Crystallography

PHYSICS OF DIFFRACTION AND CRYSTALLOGRAPHY IN RECIPROCAL SPACE

• Interaction of X-rays with crystalline matter
• Fourier transforms and convolutions
• Crystallographic calculations in reciprocal space
• Diffraction symmetry: Laue classes, Friedel's law, resonant scattering
• Integral, zonal and serial reflection conditions and their use to determine the space-group type
• Structure solution and refinement: introductory strategies

CRYSTALLOGRAPHY ONLINE: SHORT PRACTICAL COURSE ON THE USE AND APPLICATIONS OF THE BILBAO CRYSTALLOGRAPHIC SERVER

The aim of the course is to give a tutorial and practical guide to the crystallographic databases and some of the computer tools available on the Bilbao Crystallographic Server (www.cryst.ehu.es). Online exercises will help the participants to get some practical experience in the use and applications of the computer programs in treating problems of theoretical crystallography, solid-state physics and crystal chemistry.

1. Databases and computer tools for group-subgroup relations between space groups
   1. Crystallographic databases and access tools
      1. Space-group symmetry databases (International Tables for Crystallography, Volume A: Space-group symmetry)
      2. Maximal subgroups and minimal supergroups (International Tables for Crystallography, Volume A1: Symmetry relations between space groups)
      3. Brillouin-zone database
   2. Group-subgroup relations between space groups
      1. Study of general group-subgroup pair of space groups; Hermann theorem: twins and antiphase domains; coset decompositions. Supergroups of space groups
      2. Symmetry relations between Wyckoff positions for group-subgroup pairs; Baernighausen trees constructions
   3. Structure utilities and tools
      1. Equivalent structure descriptions; structure descriptions with respect to different space-group settings
      2. Comparison between different descriptions of the same structure
      3. Computer tools for the study of structural relationships
2. Tools for structural phase transitions on the Bilbao Crystallographic Server
   1. Structural pseudosymmetry
      1. Methods of pseudosymmetry search using supergroups of space groups
      2. Search for new ferroelectric and ferroelastic materials
   2. Phase transitions with group-subgroup relations between the space groups of the two phases
      1. Inverse Landau problem
      2. Symmetry-mode analysis of displacive phase transitions

Language

The official languages of the Schools were English and French. Bilingual tutors helped the participants during the guided exercises.

Venue

The School was held at the Hotel Thalassa. It had been postponed from the initial dates of 25-29 April 2011.

Summer Schools on Mathematical Crystallography

Nancy, France, 21 June - 2 July 2010
On the occasion of the fifth anniversary of its foundation, the Commission on Mathematical and Theoretical Crystallography organised two summer schools devoted to the topology of crystal structures and to the irreducible representations of space groups

Topological Crystal Chemistry: Theory and Practice

The explosive growth in inorganic and organic materials chemistry has seen a great upsurge in the synthesis of crystalline materials with extended framework structures (zeolites, coordination polymers/coordination networks, Metal Organic Frameworks MOFs, supramolecular architectures formed by Hydrogen bonds and/or Halogen bonds etc.). There is a concomitant interest in simulating such materials and in designing new ones. However, it is a truism that before one can embark on systematic design of materials, one must know what the possibilities are. Indeed, in the last two decades there have been many parallel outcomes in the theoretical aspects of description and analysis of periodic structures (nets, tilings, surfaces, etc.), in the elaboration of databases, and in the development of software for analyzing and describing (illustrating) topological aspects of both real crystal structures and theoretical extended architectures. With these achievements, materials science and crystal chemistry comes up to a new level of their development that is characterized by deeper integration of mathematical methods, computer algorithms and programs into modeling and interpretation of periodic systems of chemical bonds in crystals.
The goal of this school is to give an introduction to this whole new area that we call Topological Crystal Chemistry. There will be large time dedicated to hands-on session on the use of the novel and still not widespread computer methods/software/databases so the student at the end of the course should be able to analyze any kind of extended structure through the eye of the topology and describe it in term of nets, entanglements, catenation etc.
The target audience is young scientists (graduate students and postdoctoral associates) actively engaged in materials research, (experimental and/or theoretical) but also crystallographers who want to look at familiar structure types with a different eye. Some basic knowledge in chemistry and crystallography will be assumed which will provided during the pre-school day, for those needing a basic introduction .

Irreducible representations of space groups

Group Theory is an indispensable mathematical tool in many branches of chemistry and physics. The school aims at giving the necessary background and practical skills for an efficient use of the group-theoretical methods in specific problems of solid-state physics, structural chemistry and material sciences. After a revision of the basic concepts of spatial symmetry and its description by crystallographic point and space groups according to International Tables of Crystallography, the principal results of the theory of group representations will be introduced with an emphasis on the practical aspects of the subject. Irreducible representations of crystallographic point and space groups and their derivation will be discussed in details. The abstract theory is limited to a reduced set of fundamental facts and statements. More attention is paid to different tools and techniques necessary for practical applications of the symmetry methods in solid-state problems as molecular dynamics, spectroscopy, electronic bands, phonon spectra, Landau theory of phase transitions.
The applications of group-theoretical methods to molecular vibrations including the concept of normal modes of vibrations will be discussed in details. The students will learn how, starting from symmetry requirements, to determine the spectral-transition selection rules with special attention to infrared and Raman spectra. The important role of representations of crystallographic groups in the classification, labeling and the analysis of the degeneracies of the lattice vibrations and electronic energy bands of crystalline solids will be reviewed. The applications related to phase transition studies will include the introduction of efficient techniques allowing the determination of the principle characteristics of a system undergoing a phase transition. For example, the determination of the order parameter from the knowledge of the initial and final phases, or the enumeration of all symmetry allowed phases that can result from a continuous phase transition. The symmetry-mode analysis of structural phase transitions results in the decomposition of the symmetry-breaking distortion, present in the distorted structure into contributions from different symmetry modes. The exposition of the general theory and methods will be illustrated with number of examples of typical phase transitions of different nature so that the participant can learn to apply the group-theoretical procedures in practice for the analysis of phase-transition mechanisms and in the search for new functional materials.
A tutorial and practical guide to the Bilbao Crystallographic server (www.cryst.ehu.es) forms an essential part of the course. The server provides an excellent on-line tool for the study of crystallographic symmetry and its applications. It gives access to databases with symmetry information on crystallographic groups, their group-subgroup relations and irreducible representations. The school aims at giving the necessary background and practical skills for an efficient use of the computer databases and programs on the Bilbao Crystallographic Server focused on solid-state physics and chemistry applications.
The participants of the school will benefit from the practical training in the application of advanced symmetry methods in solid state physics and crystal chemistry problems. The minimal mathematical prerequisites for the school widen the participation audience to students and researchers from chemistry, physics, geological sciences and engineering.

Crystallography online: International School on the use and application of the Bilbao Crystallographic Server

Lekeitio, Spain, 21-27 June 2009
Supported by the:

• Spanish National Committee for Crystallography
• IUCr Commission on Teaching Crystallography
• ECA Special Interest Group No. 5 "Mineral and Inorganic Crystallography"

The IUCr MaThCryst commission has organized a school on the use and application of the Bilbao Crystallographic Server, a full-featured series of tools and routines for the analysis of crystallographic, crystal-chemical and solid-state physical problems.

List of main topics

• Symmetry databases for point and space groups
• Applications of group-subgroup relations between space groups
• Crystal structure transformations and alternative descriptions
• Solid-state physics and chemistry applications of group theory
• Selection rules in spectroscopy; phonon selection rules
• Structural pseudosymmetry
• Symmetry-mode analysis of ferroic structures
• Domain-structure analysis
• Structural phase transitions
• Symmetry in ab-initio calculations

Lectures

• Mois I. Aroyo (Bilbao, Spain)
• J. Manuel Perez-Mato (Bilbao, Spain)
• Karen Friese (Bilbao, Spain)
• Massimo Nespolo (Nancy, France)
• Gervais Chapuis (Lausanne, Switzerland)
• Michele Catti (Milan, Italy)
• Yuri Kitaev (Saint-Petersburg, Russia)
• Juan Rodriguez-Carvajal (Grenoble, France)
• Harold Stokes (Utah, USA)

Program

Monday April 28, morning. Introduction to crystallographic symmetry I. Massimo Nespolo, Université Henri Poincaré Nancy I, France

• Basics of group theory. Space groups and space group types. Hermann-Mauguin symbols. Wyckoff positions, site symmetry. Unconventional settings of space groups. Extracting information from Volume A of the International Tables for Crystallography

Monday April 28, afternoon. Introduction to crystallographic symmetry II. Mois I. Aroyo, Universidad del Pais Vasco, Bilbao, Spain

• Mappings, symmetry operations, 4x4 matrices. Basis and coordinate transformations, origin shifts. Subgroups and splitting of Wyckoff positions.

Tuesday April 29. Group theory applied to crystallography. Bernd Souvignier, Radboud University Nijmegen, The Netherlands

• Dimension-independent fundamental notions of crystallographic groups (lattices, point groups, vector systems); classification of crystallographic groups (arithmetic/geometric classes, crystal systems, lattice systems, crystal families). Equivalent descriptions for a crystal structure (use of normalizers).

Wednesday April 30, morning. Subgroups of space groups. Mois I. Aroyo, Universidad del Pais Vasco, Bilbao, Spain

• Exercises on the Volume A1 of the International Tables for Crystallography

Wednesday April 30, afternoon. The symmetry principle in crystal chemistry - I. Ulrich Müller, University of Marburg, Germany

• Instructions how to build trees of group-subgroup relations between space groups. Examples for translationengleiche, klassengleiche and isomorphic subgroups; space groups related by a common supergroup; large structural families. Pitfalls and possible sources of errors.

Thursday May 1, morning. The symmetry principle in crystal chemistry - II. Ulrich Müller, University of Marburg, Germany

• Applications: Structures with close-packed atoms and occupied interstices; symmetry aspects at phase transitions and topotactic reactions, twinning, domains; wrong structure determinations due to twinning; symmetry relations among molecular structures

Thursday May 1, afternoon. Role of symmetry and energy in structural phase transitions. Michele Catti, University of Milano-Bicocca, Italy

• Elements of Landau theory of structural phase transitions. Symmetry group-subgroup relationships. Reconstructive, displacive and order-disorder solid-solid transformations. Evaluation of the crystal energy by periodic quantum-mechanical techniques. Applications to thermodynamic and kinetic aspects of displacive and reconstructive phase transitions of inorganic crystals.

Friday May 2, morning. Computer tools in mathematical crystallography. Mois I. Aroyo, Universidad del Pais Vasco, Bilbao, Spain

• Introduction to the Bilbao Crystallographic Server

Friday May 2, afternoon. Understanding organic crystal packing: how intermolecular energies determine crystal symmetry and intermolecular geometry. Angelo Gavezzotti, University of Milano, Italy

• Fundamentals of intermolecular potentials. Correlation-dispersion and exchange-repulsion. Close packing symmetry elements. Restrictions on space groups for organic crystals. Use of crystallographic Databases. Models for the calculation of intermolecular energies: recognition in gas-phase dimers versus pairwise molecular interactions in crystals. Quantitative ranking of approach modes: the hydrogen bond versus other bonding interactions. Quantitative ranking of lattice energies among polymorphs; crystals structure 'prediction'.

Conference venue

The school took place at Palazzo Feltrinelli, on the Garda Lake. This beautiful historical Villa is now owned by the University of Milan and is dedicated to Workshop and Meeting activities. Gargnano is a small resort village on Garda Lake, about 150 km east of Milan.

International School on Mathematical and Theoretical Crystallography

First MaThCryst School in Latin America

The University of Havana, Cuba

15-20 July 2007
The IUCr-MaThCryst commission, in cooperation with the IUCr Commission on Crystallographic Teaching (CTC) and with the IUCr Commission on Inorganic and Mineral Structures (CIMS), has organised an International School on Mathematical and Theoretical Crystallography at the The school was held at the Universidad de la Habana Cuba.

Program

• 15 July, Sunday: arrival and registration
• 16 July, Monday: Group theory applied to crystallography: part I. Dimension-independent fundamental notions of crystallographic groups (lattices, point groups, vector systems); classification of crystallographic groups (arithmetic/geometric classes, crystal systems, lattice systems, crystal families). Bernd Souvignier, Radboud University Nijmegen, The Netherlands
• 17 July, Tuesday: Group theory applied to crystallography: part II. Application of crystallographic group theory to concrete problems in lower dimensional space. Marjorie Senechal, Smith College Northampton U.S.A.
• 18 July, Wednesday: Twinned crystals as polychromatic objects
• Morning session:Polychromatic point groups and their mathematics Marjorie Senechal, Smith College Northampton, U.S.A.
• Afternoon session:Reticular and symmetry theory of twins Massimo Nespolo, Université Henri Poincaré Nancy I, France
• 19 July, Thursday: OD structures Stefano Merlino, Università di Pisa, Italy
• 20 July, Friday, morning session: The mathematics of Polytypes Ernesto Estévez Rams, Institute for Materials and Reagents, Cuba
• 20 July, Friday, afternoon session: Modeling modular inorganic structures Giovanni Ferraris, Università di Torino, Italy

International Program Committe

Prof. Massimo Nespolo, Chair (MaThCryst) Prof. Paola Spadon (CTC) Prof. Giovanni Ferraris (CIMS) Prof. Ernesto Estevez Rams (IMRE)

Local Organizing Committee

Prof. Ernesto Estevez Rams , Chair Dr. Arbelio Penton Madrigal , Vice-chair MSc. Cristy Azanza Ricardo Ms. Mariela Hurtado Carnero , Secretary