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M. Nespolo, B. Souvignier, B. Stöger:
"Groupoid description of modular structures";
Acta Crystallographica Section A, 76 (2020), 334 - 344.

Modular structures are crystal structures built by subperiodic (zero-, mono- or diperiodic) substructures, called modules. The whole set of partial operations relating substructures in a modular structure build up a groupoid; modular structures composed of identical substructures are described by connected groupoids, or groupoids in the sense of Brandt. A general approach is presented to describe modular structures by Brandt´s groupoids and how to obtain the corresponding space groups, in which only the partial operations that have an extension to the whole crystal space appear.

modular crystal structures; groupoids; subperiodic groups; superposition structures; polytypism

http://dx.doi.org/10.1107/S2053273320000650