A general algorithm for generating isotropy subgroups in superspace

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• 作者：Harold T. Stokes and Branton J. Campbell
• 关键词：irreducible representations ; isotropy subgroups ; incommensurate structures ; modulated structures ; superspace groups ; order parameter
• 刊名：Acta Crystallographica Section A
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：73
• 期：1
• 页码：4-13
• 全文大小：412K
• ISSN：1600-5724

文摘

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 commensurate k 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.