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International Union of Crystallography |
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International School on Fundamental Crystallography
Sixth MaThCryst school in Latin America
Workshop on the Applications of Group Theory in the Study of Phase Transitions
Bogotá, Colombia, 26 November - 1st December 2018
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 2018 we have organized a school in Bogotá following the previous schools in Havana, followed by schools in Montevideo, in Uberlândia, in La Plata. and again in Havana.
Lecturers
- Mois I. Aroyo, University of the Basque Country, Spain
- Massimo Nespolo, Université de Lorraine, France
- Leopoldo Suescun, Universidad de la Republica, Uruguay
- Arbelio Penton-Madrigal, Universidad de la Habana, Cuba
- Mike Glazer, University of Oxford, United Kingdom
Venue
Faculty of Sciences, Universidad de Los Andes, Bogotá
Timetable
Morning session (3:30 hours):
Lectures 8:30 - 10:00
Coffee break: 10:00 10:30
Lectures 10:30 - 12:30
Lunch: 12:30 14:00
Afternoon session (4:00 hours):
Lectures 14:00 16:00
Coffee break: 16:00 16:30
Lectures 16:30 - 18:30
Scientific Program
1st Day Monday, 26 november, morning session:
8:30 - 8:40 Opening of the School
Lecturer Massimo Nespolo
Symmetry groups and types of symmetry in direct space. Bravais lattices, conventional and non-conventional unit cells. Symmetry of lattices and symmetry directions. Hermann-Mauguin symbols for point groups. Symmetry of crystallographic patterns: holohedries and merohedries. Crystal families, lattice systems and crystal systems.
1st Day: afternoon session
Lecturers Massimo Nespolo, Mois Aroyo
- Miller indices. Morphological symmetry, forms and zone. Stereographic projection and its use for the derivation of crystallographic point groups.
- Basic properties of groups (group axioms, order, multiplication tables, etc.).
- Subgroups, index, coset decompositions, Lagrange theorem. Concept of isomorphism and homomorphism. Matrix-column presentation of symmetry operations. Symmetry elements: geometric elements and element sets. Geometric interpretation of the matrix-column presentation of the symmetry operations. Transformations of the coordinate systems: change of origin and orientation.
2nd Day, Tuesday, 27, morning session:
Lecturer Mois Arroyo
- Group-subgroup relations (general considerations): index, coset decomposition and normal subgroups. Conjugation and normalizers; conjugate elements and conjugate subgroups; factor groups and homomorphism.
- Wyckoff positions for point group. Relations of Wyckoff positions for a group-subgroup pair. Supergroups of point groups.
2nd Day: afternoon session
Lecturer: Massimo Nespolo
- Space groups - general introduction: periodic structure of the crystalline matter. 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, 28 November, morning session:
Lecturer Mois I. Aroyo
- Space groups and their description in International Tables for Crystallography, Vol. A. Algebraic determination of Wyckoff positions and site-symmetry groups.
- Computer databases and access tools to crystallographic symmetry data forspace groups (International Tables for Crystallography, Volume A: Space-group symmetry): symmetry operations and their matrix-column presentation; geometric interpretation; general and special Wyckoff positions, site symmetry.
3rd Day: afternoon session:
Lecturer Mois I. Aroyo
- Conventional and non-conventional descriptions of space groups; ITA settings.
- Group-subgroup relations between space groups: Subgroups of space groups: types of subgroups of space groups; Hermann theorem; maximal subgroups; series of isomorphic subgroups. Coset decomposition.
4th Day, Thursday, 29 November, morning session:
Lecturers Leopoldo Suescun, Arbelio Penton-Madrigal
- Reciprocal space
- Crystallographic calculations in reciprocal space
- Introduction to diffraction
4th Day: afternoon session
Lecturers Leopoldo Suescun, Arbelio Penton-Madrigal
- Diffraction symmetry: Laue classes, Friedel's law, resonant scattering.
- Integral, zonal and serial reflection conditions and their use to determine the space-group type. Special reflection conditions.
5th Day, Friday, 30 November, morning session:
Lecturer Mois I. Aroyo
- Maximal subgroups data and related computer applications: (i) Introduction and use of the databases of the IT-Online server and the Bilbao Crystallographic server of maximal subgroups, series of isomorphic subgroups and minimal supergroups; (ii) General group-subgroup relations between space groups: computer programs on the IT-Online server and the Bilbao Crystallographic Server.
- Relations of Wyckoff positions for a group-subgroup pair. Supergroups of space groups.
5th Day: afternoon session
Lecturers Mois I. Aroyo, Leopoldo Suescun
- Crystal-structure descriptions I. Basis transformations and crystal-structure descriptions; structure descriptions compatible with symmetry reduction (the program TRANSTRU). Descriptions of crystal structures with respect to different ITA settings of the space groups (the program SETSTRU). Equivalent crystal structure descriptions (the programs EQUIVSTRU and COMPSTRU).
- Crystal-structure relations. Group-subgroup relations between space groups and the construction of structure family trees (Baernighausen trees (the program STRUCTURE RELATIONS).
Workshop: Applications of Group Theory in the Study of Phase Transitions
Saturday, 1st December 2018
Lecturer A. M. Glazer
Language
The official language of the school is English but the presence of Spanish speaking tutors familiarized in advance with the lectures provided assistance to those needing it by translation or answering questions on the topic.
International Program Committee
- Prof. Dhananjai Pandey, Banaras Hindu University, india (MaThCryst Chair)
- Prof. Massimo Nespolo, Université de Lorraine, France
- Prof. Mois Ilia Aroyo, Universidad del País Vasco, Bilbao, Spain
- Prof. Ernesto Estévez Rams, Universidad de la Habana, Cuba
- Prof. Leopoldo Suescun, Universidad de la República, Uruguay
- Prof. Mario Alberto Macias Lopez, Bogotá Colombia
Local Organizing Committee
- Prof. Mario Alberto Macias Lopez (Depart. Quimica, Universidad de los Andes, Bogotá)
- Prof. Andreas Reiber (Depart. Quimica, Universidad de los Andes, Bogotá)
- Prof. Edgar Vargas (Depart. Quimica, Universidad de los Andes, Bogotá)
- Prof. Wolfram Baumann (Depart. Quimica, Universidad de los Andes, Bogotá)
- Prof. Elizabeth Jimenez (Depart. Quimica, Universidad de los Andes, Bogotá)
Didactic Material
Examples data and solution available on request. See also the list of didactic material for the MaThCryst schools.
- A.P. Madrigal: Reciprocal space
- A.P. Madrigal: Diffraction symmetry
- M.I. Aroyo: Crystallographic Point Groups
- M.I. Aroyo: Crystallographic Symmetry Operations
- M.I. Aroyo: Space Groups
- M.I. Aroyo: Symmetry relations of space groups
- M.I. Aroyo: Crystal Structure Tools
- M.I. Aroyo: Pseudosymmetry
- A.M. Glazer: Phase transitions, part I
- A.M. Glazer: Phase transitions, part II
- L. Suescun: Systematic Absences and Space Group Determination
- L. Suescun: Diffraction Experiments, Data processing and reduction
Abstracts of poster presentations
Abstracts of a few poster presentations are available at this address.
List of participants: (see also the photo gallery at IUCr website).
| Name | Country | Institution | |
|---|---|---|---|
| Mauro Melone | Argentina | IB/UNCuyo - CNEA - CCT Patagonia /CONICET | |
| Federico Movilla | Argentina | DQIAQF/INQUIMAE-UBA | |
| Jhoan Francisco Téllez Bernal | Argentina | Universidad Nacional de Córdoba INFIQC-CONICET | |
| Tábata Peres Cardoso | Brasil | UNESP - Universidade Estadual Paulista | |
| Andrea Pastrana Davila | Colombia | Universidad Santiago de Cali | |
| Stephanny Villamizar Delgado | Colombia | Universidad Santiago de Cali | |
| Richard Fernando DVries | Colombia | Universidad Santiago de Cali | |
| Wilder Acuña Gonzalez | Colombia | Universidad Industrial de Santander | |
| Kevin Arango Daraviña | Colombia | Universidad del Valle | |
| Daniela Cardona González | Colombia | Universidad Nacional de Colombia-Sede Medellin | |
| Astrid Elena Sánchez Pino | Colombia | Universidad Nacional de Colombia-Sede Medellin | |
| Robinson Moreno Mendoza | Colombia | Universidad Nacional de Colombia | |
| Jorge Andres Cardona Vasquez | Colombia | Universidad Nacional de Colombia | |
| Manuel Jonathan Pinzón Cárdenas | Colombia | Universidad ECCI | |
| David Arsenio Landinez Tellez | Colombia | Universidad Nacional de Colombia | |
| Julian Esteban León Ibañez | Colombia | Universidad de los Andes | |
| Andres Felipe Perez | Colombia | Universidad de los Andes | |
| Carol P. Melo Torres | Colombia | Universidad de los Andes | |
| Catherine Eliana Cabrera Diaz | Colombia | Universidad de los Andes | |
| Jonathan Andrés Niño Cortés | Colombia | Universidad de los Andes | |
| Daniela Fonseca López | Colombia | Universidad de los Andes | |
| Paula Daniela Mestizo Melo | Colombia | Universidad de los Andes | |
| Andrés Camilo Ballesteros | Colombia | Universidad de los Andes | |
| Néstor Fabian Bravo Piñeros | Colombia | Universidad de los Andes | |
| Jhon Danis Puerres | Colombia | Universidad de los Andes | |
| Eider Erazo Moreno | Colombia | Universidad de los Andes | |
| Camilo Prada Latorre | Colombia | Universidad de los Andes | |
| Diego Alejandro Garzón Castellanos | Colombia | Universidad de los Andes | |
| Cristian Camilo Granados Cerón | Colombia | Universidad de los Andes | |
| Katherine Chaves Carballo | Costa Rica | Universidad de Costa Rica | |
| Manuel Alejandro Peñafiel Guamán | Ecuador | Universidad Técnica Particular de Loja | |
| Jairo Israel Escobar Peralta | Ecuador | Universidad Técnica Particular de Loja | |
| Lucero Torres López | Mexico | Instituto Politécnico Nacional | |
| Jovana Pérez Pérez | Mexico | UNAM | j |
| Gerardo Aguirre Hernández | Mexico | Instituto Tecnológico de Tijuana | |
| Esteban Elvis Asto Ramos | Peru | Universidad Nacional Mayor de San Marcos | |
| Bastien Francesco Grosso | Switzerland | ETH Zurich | |
| Joaquin Grassi | Uruguay | Facultad de Quimica - Universidad de la República | |
| Natasha Di Benedetto Sviridenko | Uruguay | Facultad de Quimica - Universidad de la República |
Contact:
For inquiries about the scientific program, please contact
. For all inquiries about the organisation, please contact:
Dr. Mario Alberto Macias Lopez
Universidad de los Andes
.
The Organizers of the ISFC6 school have observed the basic policy of non-discrimination and affirmed 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 could have prevented the participation of bona fide scientists.
