Short Course Description
Instructors: Dr Semyon Gorfman (lectures), Lior Wertheim (exercises)
Language: English (lectures) / Hebrew (exercises).
The goal of the course: to become familiar with the description of crystal structures and experimental methods for their investigations.
Prerequisites: all the basic courses in mathematics and physics.
Format: 3 hours per week lectures (English) + 1 hour per week tutorials (Hebrew).
Grading: The final grade will be calculated from the written exam (75 %) and the solved assignment (25%). The exam questions / problems will be similar to those appearing in the assignment. Home work must be solved and submitted individually. Extra-tasks for additional points will be distributed during the semester (most of these tasks require programming skills).
Tentative topics of the lectures:
1. Introduction. The history of crystallography. The development of ideas about crystalline and amorphous solids. Long-range and short-range order. Crystal lattice.
2. Reciprocal lattice. Lattice planes and Miller indices. Inter-planar distances and inter-planar angles. Natural facets and growth of crystals. Wulff's plots.
3. Crystallographic computing: Operations with vectors and matrices. Coordinate systems in crystallography and transformation between them. Orientation matrices and matrices of dot products. Calculation of inter-planar distances and interfacial angles. Transformation between coordinate systems.
4. X-ray diffraction by crystals: Generation and properties of X-rays. Interferences of waves. Bragg's approach to the description of X-ray diffraction by crystals. Bragg's equation. Laue equation. Ewald sphere.
5. Single crystal X-ray diffraction, powder X-ray diffraction. Calculation of diffraction peak positions and multiplicities.
6. Symmetry in crystallography. Definitions of symmetry operations. Point and space symmetry operations. Symmetry of crystal structures. Symmetry of crystals lattices.
7. Crystal systems and Bravais types of lattices. Primitive and non-primitive unit cells. Cell centering and cell settings.
8. Point symmetry groups: 32 point symmetry groups and crystal classes. Holohedries and mehohedries.
9. Introduction to space symmetry groups. Mathematical expressions for crystallographic space symmetry operations. Wyckoff positions and local symmetries.
10. International Tables for Crystallography and Bilbao Crystallographic Server. 17 planar space groups and 230 three-dimensional space groups. Using space groups for the description of crystal structures.
11. Simple crystal structures: BCC-metals, FCC-metals, Rock-salt, Diamond, Sphalerite, Fluorite, Perovskite, Graphite, Spinel, Quartz, Wurzite.
12. Stacking faults and models of structural disorder.
Recommended literature:
[1]. Marc De Graef and Michael E. McHenry. Structure of Materials. An Introduction to Crystallography, Diffraction and Symmetry. Cambridge University Press. 2012.
[2]. Carnelio Giacovazzo. Fundamentals of Crystallography. Oxford University Press, 1992
[3]. International Tables for Crystallography, Volume A. International Union of Crystallography, 2016.
Full syllabus is to be published
