Symmetry Relationships between Crystal Structures with Applications to Structural Phase Transitions

In Varanasi

MaThCryst Workshop on Mathematical Crystallography

Banaras, India, 27-31 October 2014

Indian Institute of Technology, Banaras Hindu University, Varanasi-221005, INDIA

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.

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.

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.

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.

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