Space groups and crystallographic symmetry: writing a multi-featured tutorial in a new style

Abstract

Knowledge of space groups and the implications of space group symmetry on the physical and chemical properties of solids are pivotal factors in all areas of crystalline solids. As Jerry Jasinski and I met to bring our ideas in teaching this subject to life, we both felt that `early and often' – teaching the concepts with textual and visual reinforcement, is the key to providing a sound basis for students in this subject. The tutorial contains > 200 PowerPoint `slides', in five modules, arranged by crystal class; a sixth module covers special topics. A `credits' module gives the direct addresses of all embedded links. Space-group diagrams appear in International Tables format. The triclinic and monoclinic groups (2 + 13) are built from `scratch', and are derived from the Hermann–Mauguin symbol. An additional section provides practice on many (but not all) of the orthorhombic groups in crystal class 222. Finally, a `Special Topics' section on enantiomorphous space groups features space groups P41 and P43. In the tutorial, lattice points build iteratively and interactively via keyclick, and the coordinates of points `pop up' as the unit cell is filled. We trust that the elements of guidance, inquiry and occasional humor will make the learning process enjoyable.

Keywords

• space groups
• symmetry
• crystallographic teaching