Symmetry and group theory

Pre-requisites

The participants are expected to know basic matrix algebra (how to multiply matrices and vectors, how calculate determinant and trace of a matrix: however, an optional half-day is devoted to revise these notions), fundamental electromagnetism (waves, diffraction) and basic chemistry.

Program

The training course will span five full days, from 9 to 13 March, 2015. Monday morning (March 9) is optional for those needing to revise general concepts about matrix algebra and abstract algebra (general introduction to group theory). Exercices proposed during the whole course are integral part of the course: participants are expected to actively participate and solve the proposed exercises.

Monday, 9 March

• Morning: optional session on matrix and abstract algebra
  
• Afternoon: introduction to crystallographic symmetry and lattices
  

Tuesday, 10 March 15

• Morphological symmetry
• Stereographic projection, with exercises
• Crystallographic point groups and geometric crystal classes
• Matrix representation of point group operations
• Symmetry elements with a translational component (screw axes and glide planes)

Wednesday, 11 March

• Introduction to space groups
• Graphical construction of space groups
• Metric tensor and applications
• Change of axial settings and alternative settings of space groups

Thursday, 12 March

• Reciprocal lattice and systematic absences
• Matrix representation of space group operations
• Crystallographic orbits

Friday, 13 March

• Group-subgroup relations
• Structure-substructure relations and applications to displacive phase transitions