Event Name

International School on Fundamental Crystallography (Fifth MaThCryst school in Latin America)/Workshop on nanocrystallography

Start Date 30th Oct 2016
End Date 5th Nov 2016

International School on Fundamental Crystallography
Fifth MaThCryst school in Latin America
Workshop on nanocrystallography

Havana, Cuba, 30 October - 5 November 2016

Change of date

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 2016we organize a school in Havana, where the series started in 2007, followed by schools in Montevideo, in Uberlândia and in La Plata.

Scientific Program

ISFC5: October 30 - November 4

Optional pre-school day: Sunday, October 30

Lecturers: Arbelio Penton Madrigal, Ernesto Estevez Rams, Leopoldo Suescun

  • Introduction to matrix algebra with exercises
  • Fourier transforms and convolutions

Monday, October 31, to Friday, November 4


Lecturers: Massimo Nespolo, Mois I. Aroyo

  • 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


Lecturers: Massimo Nespolo, Mois I. Aroyo

  • 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

Lecturers: Ernesto Estevez Rams, Leopoldo Suescun

  • 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


Lecturers: Mois I. Aroyo, Massimo Nespolo

  • 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

Workshop on nanocrystallography: November 5

Lecturers: Ernesto Estevez Rams, Ramundo Lora Serrano, Arbelio Penton Madrigal

  • 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


ISFC5 and workshop will be held at the Universidad des la Habana. Detailed information will follow.


The official language of the school is English but the presence of Spanish speaking tutors familiarized in advance with the lectures will provid 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


For inquiries about the scientific program, please contact mathcryst@iucr.org. For all inquiries about the organisation, please contact:
Prof. Ernesto Estévez Rams
Universidad de la Habana, Cuba

Location Havana
Contact Prof. Ernesto Estévez Rams
URL http://www.crystallography.fr/mathcryst/havana2016.php

Category Schools | Workshops
Topics Materials | Mathematical and Theoretical Crystallography | Nanomaterials