# Scientific Program

#### FUNDAMENTALS

• Introduction to matrix algebra.
• Basics of group theory. Space groups and space group types.

#### BASIC CONCEPTS

• Affine spaces vs. vector spaces
• Mappings: affine and Euclidean; isometries
• Sets; homomorphisms, isomorphisms, automorphisms
• Symmetry operations as special case of isometries
• 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
• Crystallographic calculations in direct space
• 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
• Symmetry operations with a glide component
• Space groups and types of space groups
• Exercises on the space group diagrams from Volume A of the International Tables for Crystallography
• Online tools 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. Introduction to JANA software. Examples.

#### CRYSTALLOGRAPHY ONLINE

• Introduction to the Bilbao Crystallographic Server
• Space Groups Retrieval Tools
• Group - Subgroup Relations of Space Groups
• Structure utilities and computer tools: different structure descriptions and structural relationships
• Tools for the study of structural phase transitions on the Bilbao Crystallographic Server

#### TWINNED CRYSTALS

• Reticular classification of twins and its extensions
• Methods of calculations of twin elements and derivation of twin laws.
• The Coincidence-Site Lattice theory: application to the derivation of twin lattices and their classification in terms of twin index and obliquity.
• Translational and point symmetry of twins: twin point groups and their chromatic features.
• Diffraction patterns of twinned crystals.
Details of the program
Preparatory SessionInternational School on Fundamental Crystallography (ISFC)Workshop on twinned crystalsISFC (cont.)
Day/TimeSunday
(Nov. 25)
Monday
(Nov. 26)
Tuesday
(Nov 27)
Wednesday
(Nov 28)
Thursday
(Nov 29)
Friday
(Nov 30)
Saturday
(Dec 01)
Sunday
(Dec 02)
Monday
(Dec 3)
8:30 - 9:00Registration Registration/
Opening
Tutorial on point groups Nespolo/Aroyo Group-subgroup relations Aroyo Physics of Diffraction (I) Fourier transforms. Space group in reciprocal space. Estevez Search for pseudosymmetries Aroyo Twinned crystals - Introduction and definitions Nespolo Free Tutorial on Jana2006 (III) Twinned crystals - basic examples Dusek
9:00 - 10:00 Introduction to abstract groups Nespolo
10:00 - 10:30Coffee break Coffee break Coffee break Coffee break Coffee break Coffee break Coffee break Coffee break
10:30 - 12:30Matrix Algebra Estevez Crystallographic symmetry in E2 Nespolo Crystallographic symmetry in E3 - part II: space groups Nespolo Bilbao Crystallographic Server for subgroups Aroyo Data processing and reduction Suescun Symmetry-mode analysis with Amplimodes Aroyo Twinned crystals - Calculations of twin parameters Nespolo Tutorial on Jana2006 (VI) Twinned crystals - advanced examples Dusek
12:00 - 14:00Lunch Lunch Lunch Lunch Lunch Lunch Lunch Lunch
14:00 - 16:00Fourier Transform Estevez/Serrano Crystallographic symmetry in E3 - part 1: point groups Nespolo Exercises on space groups construction and use of Volume A of the International Tables Nespolo Structure Utilities Aroyo Physics of Diffraction (II). Systematic absences, reflection conditions and space group determination Granado Tutorial on Jana2006 (I) Introduction to Jana2006. Basic single crystal example Dusek Twinned crystals - polychromatic symmetry Nespolo Tutorial on Jana2006 (V) Simple modulated structure application of rigid body for powders Dusek
16:00 - 16:30Coffee break Coffee break Coffee break Coffee break Coffee break Coffee break Coffee break Coffee break
16:30 - 18:30Diffraction Physics Estevez/Serrano Tutorial on point groups Nespolo/Aroyo Bilbao Crystallographc Server: retrieval of space group information Aroyo Structure Utilities Aroyo Strategies for structure solution and refinement Suescun/Granado Tutorial on Jana2006 (II). Basic powder example. Disorder Dusek Twinned crystals - Tutorial on the software GEMINOGRAPHY Nespolo Closing
Welcome reception

## Language

The official language of the Schools was English. No simultaneous interpretation was provided. However, local tutors helped the participants during the exercises.

### Venue

The School was held at the Institute of Physics of the Federal University of Uberlândia, in the southeast of Brazil. PDF of the Campus Map available for download.

### International Program Committee

• Prof. Massimo Nespolo, Université de Lorraine, France, Chair.
• Prof. Mois Ilia Aroyo, Universidad del País Vasco, Bilbao, Spain.
• Prof. Ernesto Estevez Rams, Universidad de la Habana, Cuba.
• Prof. Raimundo Lora Serrano, Universidade Federal de Uberlândia, Brazil.
• Prof. Michal Dusek, Academy of Sciences. Czech Republic.
• Prof. Leopoldo Suescun, Universidad de la República, Uruguay.
• Prof. Rômulo Simões Angélica, Universidade Federal do Pará, Brazil.

### Lecturers

• Prof. Massimo Nespolo, Université de Lorraine, France.
• Prof. Mois Ilia Aroyo, Universidad del País Vasco, Bilbao, Spain.
• Prof. Ernesto Estevez Rams, Universidad de la Habana, Cuba.
• Prof. Michal Dusek, Academy of Sciences. Czech Republic.
• Prof. Leopoldo Suescun, Universidad de la República, Uruguay.
• Prof. Raimundo Lora Serrano, Universidade Federal de Uberlândia, Brazil.

### Local Organizing Committee

• Prof. Raimundo Lora Serrano, Chair
• Prof. Omar de Oliveira Diniz Neto
• Prof. Augusto Miguel Alcalde Milla
• Prof. Silvana Guilardi
• Prof. Eduardo de Faria Franca
• Prof. José de los Santos Guerra.
• Vinicius Soares O. de Sousa (Secretary)

### Photos

A selection of ptohos is available at the IUCr gallery website (three pages, clic on the "Next" link in the bottom-right corner).