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Net topologies, space groups, and crystal phases
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Georg Thimm
Published/Copyright:
September 25, 2009
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 FeS2versus pyrite; α-versusβ-quartz; marcasite-versus rutile-like phases).
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Received: 2006-March-2
Accepted: 2006-June-27
Published Online: 2009-9-25
Published in Print: 2006-11-1
© Oldenbourg Wissenschaftsverlag
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Articles in the same Issue
- In memory of Professor Dr. Erwin Parthé
- Net topologies, space groups, and crystal phases
- Quasiperiodic-periodic structures by projection in two stages: an illustrative example
- The common role of water molecule and lone electron pair as a bond-valence mediator in oxalate complexes: the crystal structures of Rb2(C2O4) · H2O and Tl2(C2O4)
- Synthesis and crystal structure of Sr(AsO3OH) and Ba(AsO3OH): crystal chemistry of related MHXO4 (X = As, P, S) compounds
- Single crystal X-ray structure analysis of the spin ladder compounds SrCu2O3 and Sr2Cu3O5 between 300 K and 100 K
- New hybrid diphosphates Ln2(NH2(CH2)2NH2)(HP2O7)2 · 4 H2O(Ln = Eu, Tb, Er): synthesis, single crystal and powder X-ray crystal structure
