Syllabus
* I. Crystals and their symmetry.
Historic introduction. Local symmetry of atoms in solids, directional and isotropic bonds of atoms. Construction of crystals with the aid of the atomic layers with different symmetry - close packed structures, primitive and centered structures. Interstitial structures. Crystal representation with the aid of projections - crystallographic planes.
* II. Representation of symmetry of ordered structures
Translation periodicity of crystals. Plane and space (Bravais) lattices. Crystallogrpahic classes. Notation of planes, directions and points. Reciprocal lattice. Miller indeces. Crystallographic symmetry elements. Matrix representation of symmetry elements. Macroscopic symmetry of crystals and point group. Plane and space groups. Stereographic projection.
* III. Representation of crystallographic groups
Introduction to group theory. Basic definitions. Crystallogrpahic groups. Sub-groups and super-groups. Examples of groups. Classification of plane and space groups in International Tables of Crystallography.
International (Hermann-Mauguin) and Schoenflies symbols. Diagrams of space groups. Generators. Wyckoff positions.
* IV. Symmetry and physiacl properties of crystals
Anisotropy of physical properties and their tensor description. Anisotropic temperature factor. Electric and elastic properties of crystals - pyroelectricity, dielectric and optical properties, piezoelectricity
Annotation
Crystal structures and symmetry. History, crystal lattice, plane and space lattices.
Symmetry operations. Point, plane and space groups.
Symmetry and physical properties. Chemical crystallography, structure databases, crystal structure visualization.
Some properties of groups, groups in different dimensions. Comparison of structures.