engleski

Basic concepts of group theory in crystallography

Symmetry is one of the central concepts in crystallography. When you think about it, it is hard to expect that it could be any other way, because the very objects of crystallographic research, the crystals themselves, exhibit such remarkable perfection. Humans have been fascinated by the beauty of symmetry since the beginning of time, to the point that the symmetry has been considered beauty itself. This all shows that the appearance of symmetry in the world around us is connected deeply to the human experience of the universe. But what has all this to do with purely mathematical subject of the theory of groups? What are groups anyway and what is their relationship with symmetry in general? In the lecture the emphasis will be on the notion that the group theory, in the crystallographic context, is merely a mathematical formalism that describes symmetry. Sometimes though, the rigour of the mathematical concepts tends to obscure the simplicity of the underlying principles. It is therefore beneficial to use more visual approach and let the natural human ability to apprehend symmetry do its work. Although group theory will be introduced in general terms, the two dimensional plane groups will be described in more detail. Plane groups are easily visualized and contain all the necessary formalism that can than readily be mentally extended to space groups that dictate the packing of molecules in crystals.

Group theory in crystallography ; Space groups ; visualization

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