Event Name

Symmetry Relationships between Crystal Structures with Applications to Structural Phase Transitions

Start Date 27th Oct 2014
End Date 31st Oct 2014
Description

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

Program 

1st day: Basic facts on crystallographic groups

Coordinator and main lecturer: M. Nespolo
  • 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.
  • Space groups and their description 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: Symmetry relationships between crystal structures

Coordinator and main lecturer: 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.
  • 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 comparison of crystal structures 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.

3rd day: Representations of crystallographic groups

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.
  • 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: Structural phase transitions

Coordinator and main lecturer: J.M. Perez-Mato
  • Representation theory tools 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.
  • Practical: Online tools for analysis of structural 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.

5th day: Phase-transition studies of advanced materials

Coordinator: D. Pandey
  • 1. Lecturer: Juan Rodriguez Carvazal / J.M. Perez-Mato
    • 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.
    • Practical : Simultaneous Rietveld refinement of magnetic and nuclear structures
  • 2. Lecturer: B Mihailova
    • Interpretation of Raman and IR spectra of displacive ferroelectrics using representation theory
  • 3. Lecturer: D Pandey
    • Structural aspects of Ferroelectric, Antiferroelectric, Quantum Ferroelectric, Antiferrodistortive and Multiferroic Phase Transitions
Location Varanasi
India
Contact
URL http://www.crystallography.fr/mathcryst/banaras2014.php
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Category IUCr sponsored meetings | Workshops
Topics Mathematical and Theoretical Crystallography