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International Union of Crystallography
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MaThCryst forthcoming activities
Thirteenth basic training course on symmetry and group theory, July 2025, Tsukuba (Japan)
MaThCryst recent activities
MACSMIN 2024 hybrid conference, September 2024, Liverpool (UK)
Seventh MaThCryst School in Latin America, August 2024, Lima (Peru)
Twelth basic training course on symmetry and group theory, July 2024, Tsukuba (Japan)
Third Shanghai International Crystallographic School, June 2024, Shanghai (China)
Eleventh basic and second advanced training course on symmetry and group theory, July 2023, Tsukuba (Japan)
Summer School, June 2023, Nancy (France)
Tenth training course on symmetry and group theory, August 2022, Tsukuba (Japan)
2022 Spring Festival Crystallographic School and Workshop on Crystal-field Applications February 2022, Berijing (China)
Crystallography Online: Workshop on the use and applications of the structural and magnetic tools of the Bilbao Crystallographic Server January 2022, Leioa (Spain)
Mathematics and Computer Science for Materials Innovation, September 2021, online
Ninth training course on symmetry and group theory, September 2021, Tsukuba (Japan)
2021 SIAM Conference on Mathematical Aspects of Materials Science, May 2021, Bilbao (Spain)
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MaThCryst Workshop on Mathematical Crystallography
Symmetry relationships between crystal structures with application to structural phase transitions
Banaras, India, 27-31 October 2014
In cooperation with the IUCr Commission on Inorganic and Mineral Structures
Venue
Indian Institute of Technology, Banaras Hindu University, Varanasi-221005, INDIA
The main focus of the workshop was on the application of representation theory to structural and magnetic phase transitions in functional materials like ferroics and multiferroics. The workshop had foundation lectures on topics like basics of crystallographic groups, symmetry relationships between crystal structures and representations of crystallographic groups. This was followed by interpretation of x-ray and neutron diffraction patterns from crystals undergoing structural and magnetic phase transitions. There were hands on practicals on description of space groups in International Tables for Crystallography, Vol. A and online training for determination of subgroups of space groups, crystal structure relations and pseudosymmetry, representations of space groups and symmetry mode analysis using Bilbao Crystallographic Server. Practicals on refinement of magnetic and nuclear structures using FullProf Suite were also given.
Speakers
- Prof. Massimo Nespolo, Université de Lorraine, France
- Prof. Mois Ilia Aroyo, Universidad del País Vasco, Bilbao, Spain
- Prof. Juan Rodriguez-Carvajal,Institut Laue-Langevin, Grenoble, France
- Prof. Dhananjai Pandey, Indian Institute of Technology (BHU), India.
Organizers
- IUCr Commission on Mathematical and Theoretical Crystallography (MaThCryst)
- IUCr Commission on Inorganic and Mineral Structures (CIMS)
- School of Materials Science and Technology, Indian Institute of Technology(BHU)
Sponsors
- International Union of Crystallography (IUCr)
- Indian Institute of Technology (Banaras Hindu University), Varanasi, India.
- Indian National Science Academy (INSA)
- Rigaku Corporation, Japan and IR Technology Services Pvt. Ltd., India
International Program Committee
- Prof. Dananjai Pandey, Banaras Hindu University, India (Chairman)
- Prof. Massimo Nespolo, Université de Lorraine, France (on behalf of MaThCryst)
- Prof. Joao Rocha, University of Aveiro, Portugal (on behalf of CIMS)
- Prof. Mois Ilia Aroyo, Universidad del País Vasco, Bilbao, Spain
- Prof. Juan Menuel Perez-Mato, Universidad del País Vasco, Bilbao, Spain
Local Organizing Committee
- Prof. R. Prakash, Indian Institute of Technology (BHU), Varanasi, Chairman
- Dr. C. Rath, Indian Institute of Technology (BHU), Varanasi, Treasurer
- Dr. A. K. Singh, Indian Institute of Technology (BHU), Varanasi, Secretary
- Dr. C. Upadhyay, Indian Institute of Technology (BHU), Varanasi, Jt. Secretary
Workshop Coordinator
Prof. Dhananjai Pandey, Indian Institute of Technology (BHU), Varanasi
Bursary Award
Thanks to IUCr, young scientists (e.g. PhD students, post-docs, and recent graduates who have not yet secured permanent employment) from outside India, preferably below the age of 30 years but in no case above 35 years, were eligible to apply for bursary awards to support their attendance at the workshop. In order to be eligible for the IUCr bursary awards, the applicant had to register, if not already registered, in the World Database of Crystallographers (WDC - registration is free of charge)
Contact
Secretary, IUCr Workshop, School of Materials Science and Technology, IIT(BHU), Varanasi, India. 221005 Email: , homepage: iitbhu.ac.in/conferences/mst/IUCr/.
Accommodation
On-Campus (Institute Guest House) Accommodation
Limited on-campus accommodation on twin sharing basis (US$ 30 or Rs. 1800 per bed per night) in the Institute guest house were available on first-come, first-serve basis. The accommodation charge included morning breakfast.
About the city
Varanasi, also known as Kashi or Benares or Banaras, is one of world's oldest living cities. It is regarded as the religious capital of India. The city is located on the left bank of the holy river Ganga (Ganges), and is one of the seven sacred pilgrimage cities for Hindus. In the words of Mark Twain, the famous English author and litt?rateur: "Benaras is older than history, older than tradition, older even than legend and looks twice as old as all of them put together". Lord Budha gave his first set of sermons at Sarnath, located in the outskirts of Varanasi, nearly 2500 years ago. Buddhists from all over the world visit the holy city on pilgrimage. To be in Varanasi is an experience in itself. The majestic ghats on the banks of Ganga, morning sunrise at the ghats, visit to famous temples and evening Ganga Aarati are some of the special attractions. Varanasi is also renowned for its rich tradition of music, arts, crafts and education. For more details, visit varanasi.nic.in.
Daily timetable:
Morning session (4 hours):
Lectures 9:00 - 11:00 11:30 - 13:30
Coffee break: 11:00 - 11:30
Lunch: 13:30 - 14:30
Afternoon session (4 hours):
Lectures: 14:30 - 16:30 17:00 - 19:00
Coffee break: 16:30 - 17:00
Program
1st day (morning session): Basic facts on crystallographic groups (part 1)
Coordinators and main lecturers: M. Nespolo and M.I. Aroyo
- 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.
- Basic properties of groups (group axioms, order, multiplication tables, etc.). Subgroups, index, coset decompositions, Lagrange theorem. Concepts of isomorphism and homomorphism. Group actions: conjugation and normalizers.
1st day (afternoon session): Basic facts on crystallographic groups (part 2)
Coordinators and main lecturers: M. Nespolo and M.I. Aroyo
- Group-subgroup relations (general considerations): index, coset decomposition and normal subgroups; conjugate elements and conjugate subgroups; factor groups and homomorphism.
- Wyckoff positions for point groups. Relations of Wyckoff positions for a group-subgroup pair. Supergroups of point groups.
2nd day (morning session): Space groups and their symmetry relations (part 1)
Coordinators and main lecturers: M. Nespolo and M.I. Aroyo
Space groups and their descriptions in International Tables for Crystallography, Vol. A. Classification of space groups: Lattice systems and crystal systems. Hermann-Mauguin symbols for space groups. Symmetry-elements and general-position space-group diagrams. General and special positions, site-symmetry groups, crystallographic orbits.
Practical: Description of space groups in International Tables for Crystallography, Vol. A.
2nd day (afternoon session): Space groups and their symmetry relations (part 2)
Coordinators and main lecturers: M. Nespolo and M.I. Aroyo
Group-subgroup relations (general considerations): index, coset decomposition and normal and conjugate subgroups. Subgroups of space groups: types of subgroups of space groups; Hermann theorem and maximal subgroups. Relations of Wyckoff positions for a group-subgroup pair. Supergroups of space groups.
Practical: Online tools for subgroups of space groups on the Bilbao Crystallographic Server.
3rd day (morning session): Representations of crystallographic groups (part 1)
Coordinator and main lecturer: M.I. Aroyo
Representations of point groups: General remarks on representations. Equivalent, reducible and irreducible representations. Characters of representations and character tables. Simple applications of representations in solid-state physics and chemistry problems.
Practical: Online tools for representations of point groups on the Bilbao Crystallographic Server.
3rd day (afternoon session): Representations of crystallographic groups (part 2)
Coordinator and main lecturer: M.I. Aroyo
Representations of space groups: Representation of the translation group. Star of a representation. Little groups and small representations. Representations of symmorphic and non-symmorphic groups.
Practical: Online tools for representations of space groups on the Bilbao Crystallographic Server.
4th day (morning session): Structural phase transitions
Coordinators and main lecturers: D. Pandey and M.I. Aroyo
- General introduction to phase transitions.
- Phase-transition studies of advanced materials. Structural aspects of Ferroelectric, Antiferroelectric, Quantum Ferroelectric, Antiferrodistortive and Multiferroic Phase Transitions
- Representation theory in the analysis of phase transitions. Primary and secondary order parameters; couplings and faintness index. Order parameter direction and isotropy subgroups. Group-theoretical formulation of the necessary conditions for second-order phase transitions.
- Symmetry-mode analysis of structural phase transitions. Hierarchy of modes. Symmetry-modes applications in structure refinement.
Practical: Online tools for symmetry-mode analysis: Amplimodes.
4th day (afternoon session): Structure refinement with FULLPROF (part 1)
Coordinator and main lecturer: Juan Rodriguez-Carvajal
- Structure refinement with FULLPROF: general introduction to the FullProf Suite. Working with the Toolbar and WinPLOTR. Setting up the input control file for FullProf for structure refinement.
- Using AMPLIMODES for setting up a template for symmetry modes structure refinement with FullProf.
- Using Simulated Annealing combined with symmetry modes as a tool for solving superstructures and low symmetry structures derived from a known higher symmetry structure.
- Structure refinement using symmetry modes. Visualization of results and interpretation of the output files.
5th day (morning session): Structure refinement with FULLPROF (part 2)
Coordinator and main lecturer: Juan Rodriguez-Carvajal
- Application of representation theory to magnetic structures and magnetic phase transitions.
- Derivation of some simple magnetic configurations with an introduction to Bertaut's representation analysis. The use of the program BasIreps. Setting up of input control file containing magnetic information for FullProf
Practical: Refinement and comparison of the crystal structures of CaTiO3 and LaMnO3 using symmetry modes. Magnetic structure determination and refinement of LaMnO3 and Ho2BaNiO5.
5th day (afternoon session): Symmetry relationships between crystal structures
Coordinator and main lecturer: M. I. Aroyo
- Crystal-structure descriptions. Basis transformations and crystal-structure descriptions; structure descriptions compatible with symmetry. Equivalent crystal structure descriptions. Comparison of crystal structures.
Practical: Online tools for representations of point groups on the Bilbao Crystallographic Server. - Crystal-structure relations. Group-subgroup relations between space groups and the construction of structure family trees (Baernighausen trees). Structural pseudosymmetry. Pseudosymmetry search for new ferroics.
Practical: Online tools for the analysis of crystal-structure relations and pseudosymmetry search on the Bilbao Crystallographic Server.
Didactic material
See also the list of didactic material for the MaThCryst schools.
- M. Aroyo: Crystallographic point groups I: basic facts
- M. Aroyo: Crystallographic point groups II: further developments
- M. Aroyo: Space group symmetry
- M. Aroyo: Group-subgroup relations
- M. Aroyo: Crystal-structure tools
- M. Aroyo: Representation of crystallographic groups. I. General introduction
- M. Aroyo: Representation of crystallographic groups. II. Space groups
- M. Aroyo: Representation of crystallographic groups. III. Bilbao Crystallographic Server
- M. Aroyo: Symmetry considerations in structural phase transitions
- M. Aroyo: Crystal-structure tools: Pseudo
- M. Aroyo: Exercises
- J. Rodriguez-Carvajal: Introduction to Magnetic Structures and Symmetry
- J. Rodriguez-Carvajal: The Rietveld Method
- J. Rodriguez-Carvajal: FullProf introduction, tutorials and examples (compressed archive, 7-zip format)
The Organizers of the MaThCryst Workshop on mathematical 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 workshop no barriers existed which would have prevented the participation of bona fide scientists.