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Groupoid description of modular structures
Author(s) -
Nespolo Massimo,
Souvignier Bernd,
Stöger Berthold
Publication year - 2020
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273320000650
Subject(s) - modular design , extension (predicate logic) , set (abstract data type) , space (punctuation) , algebra over a field , computer science , pure mathematics , mathematics , programming language , operating system
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.