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Georg Thimm, Björn Winkler

Net topologies, space groups, and crystal phases

Keywords: Quotient graph, Symmetry, Isomorphism, Space group, Voltage graph

Quotient graphs and nets — the graph theore tical correspondences of cells and crystal structures — are reintroduced independent from crystal structures. Based on this, the issue of iso- and automorphism of nets, the graph theoretical equivalent of symmetry operations, is closely examined. A result, it is shown that the topology of a net (that is the bonds in a crystal) constrains severely the symmetry of the embedding (that is the crystal), and in the case of connected nets the space group except for the setting. Several examples are studied and conclusions on phases are drawn (pseudo-cubic FeS₂ versus pyrite; α-versus β-quartz; marcasite-versus rutile-like phases).

Zeitschrift für Kristallographie, Oldenbourg Wissenschaftsverlag

Print ISSN: 0044-2968
Volume: 221, 12/2006
Pages: 749 - 758

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