A general algorithm for generating isotropy subgroups in superspace. Issue 1 (29th November 2016)

• Record Type: Journal Article
• Authors: Stokes, Harold T.; Campbell, Branton J.
• Is Part Of: Acta crystallographica. Volume 73:Issue 1(2017:Jan.)
• Page Start: 4
• Page End: 13
• Publication Date: 2016-11-29
• Subjects: irreducible representations -- isotropy subgroups -- incommensurate structures -- modulated structures -- superspace groups -- order parameter; Crystallography -- Periodicals; Condensed matter -- Periodicals; 548
• DOI: 10.1107/S2053273316017629
• Languages: English
• ISSNs: 2053-2733

Abstract

Abstract : Irreducible representations can now be used to derive the isotropy subgroups at irrational wavevectors, making it relatively easy to explore the (3 + d )‐dimensional superspace‐group symmetries that arise from incommensurate modulations of a parent crystal structure. A general algorithm capable of arbitrary superpositions of multiple incommensurate and commensurate order parameters is presented. Abstract : This paper presents a general algorithm for generating the isotropy subgroups of superspace extensions of crystallographic space groups involving arbitrary superpositions of multi‐k order parameters from incommensurate and commensuratek vectors. Several examples are presented in detail in order to illuminate each step of the algorithm. The practical outcome is that one can now start with any commensurate parent crystal structure and generate a structure model for any conceivable incommensurate modulation of that parent, fully parameterized in terms of order parameters of irreducible representations at the relevant wavevectors. The resulting modulated structures have (3 + d )‐dimensional superspace‐group symmetry. Because incommensurate structures are now commonly encountered in the context of many scientifically and technologically important functional materials, the opportunity to apply the powerful methods of group representation theory to this broader class of structural distortions is very timely.