 |
International Union of Crystallography
|
International School on Fundamental Crystallography
Fifth MaThCryst school in Latin America
Workshop on nanocrystallography
Havana, Cuba, 30 October - 5 November 2016
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 2016 we have organized a school in Havana, where the series started in 2007, followed by schools in Montevideo, in Uberlândia and in La Plata.
Lecturers
- Mois I. Aroyo, University of the Basque Country, Spain
- Massimo Nespolo, Université de Lorraine, France
- Ernesto Estevez Rams, Universidad de la Habana, Cuba
- Leopoldo Suescun, Universidad de la Republica, Uruguay
- Raimundo Lora Serrano, Universidade Federal de Uberlandia, Brazil
- Arbelio Penton Madrigal, Universidad de la Habana, Cuba
- Cristy Leonor Azanza Ricardo, Universidad Nacional Autònoma de México
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 13:30
Afternoon session (3:30 hours):
Lectures 13:30 17:00
Scientific Program
ISFC5: October 30 - November 4
Preliminary day Sunday, 30 October:
- Matrix algebra. Ernesto Estevez Rams
- Fourier transforms and convolutions. Ernesto Estevez and Leopoldo Suescun
1st Day Monday, 31 October, 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, 1 November, 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, 2 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, 3 November, morning session:
Lecturer Ernesto Estevez Rams
- Reciprocal space
- Crystallographic calculations in reciprocal space
- Introduction to diffraction
4th Day: afternoon session
Lecturer Leopoldo Suescun
- 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, 4 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 on nanocrystallography: November 5
Lecturers: Ernesto Estevez, Raimundo Lora, Arbelio Penton and Cristy Leonor Azanza Ricardo
Definition of nanocrystals. The truncated crystal model. Diffraction effect in nanocrystals. Surface relaxion in nanocrystals. Total scattering methods in nanocrystallography. Diffraction characterization of nanocrystals.
Posters exhibition
Monday, October 31 to Saturday, November 5
Venue
ISFC5 and workshop will be held at the Universidad des la Habana. Detailed information will follow.
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. Mois Ilia Aroyo, Universidad del País Vasco, Bilbao, Spain, Chair
- Prof. Massimo Nespolo, Université de Lorraine, France
- Prof. Ernesto Estévez Rams, Universidad de la Habana, Cuba (1st and 5th ISFC, 2007, 2016)
- Prof. Leopoldo Suescun, Universidad de la República, Uruguay (2nd ISCF, 2010)
- Prof. Raimundo Lora Serrano, Universidade Federal de Uberlandia, Brazil (3rd ISCF, 2012)
- Prof. Gustavo A. Echeverría, Universidad Nacional de La Plata, Argentina (4th ISFC, 2014)
Local Organizing Committee
- Prof. Ernesto Estévez (Chair)
- Dr. Arbelio Penton Madrigal
- Dr. Beatriz Concepcion Rosabal
Local website
Logistic information are available at the local website.
Contact:
For inquiries about the scientific program, please contact
. For all inquiries about the organisation, please contact:
Prof. Ernesto Estévez Rams
Universidad de la Habana, Cuba
.
Group photo (click to enlarge)
Photo gallery
A photo gallery is available from the IUCr website.
The Organizers of the ISFC5 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.
