晶体学空间群及其超空间扩展的不可约表示的制表。

IF 1.8 4区 材料科学
Acta Crystallographica Section A Pub Date : 2013-07-01 Epub Date: 2013-05-08 DOI:10.1107/S0108767313007538
Harold T Stokes, Branton J Campbell, Ryan Cordes
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引用次数: 27

摘要

介绍了三维空间中230个晶体空间群(SGs)在特殊和非特殊k向量上的不可约表示(IRs)的新表,以及它们向(3 + d)维超空间的扩展(“超空间扩展SGs”或ssesg)。非特殊k向量的SG IR矩阵表和d > 1的SSESG IR矩阵表以前都没有发表过。这些表格通过一种新的形式成为可能,在这种形式中,SGs的IR矩阵作为平移部分T和点操作部分P的乘积分离,其中ssesg的IR矩阵作为相移部分Q和点操作部分P(s)的乘积分离。T和Q都有一个简单的规定形式,不需要制作表格。此外,新的IR矩阵是方便的块形式,允许人们通过检查矩阵的哪些部分和相关的阶参数属于k的星的哪条臂。除了复杂的IR矩阵,真正的物理不可约表示(PIR)矩阵被制成表格。新的IR和PIR表格可在ISO-IR网站(http://stokes.byu.edu/iso/irtables.php)上以方便的人类可读和计算机可读的形式获得。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Tabulation of irreducible representations of the crystallographic space groups and their superspace extensions.

New tables of irreducible representations (IRs) are introduced for the 230 crystallographic space groups (SGs) in three-dimensional space, at both special and non-special k vectors, and for their extensions to (3 + d)-dimensional superspace (`superspace-extended SGs' or SSESGs). Neither a tabulation of SG IR matrices for non-special k vectors nor a tabulation of SSESG IR matrices for d > 1 have been previously published. These tabulations are made possible by a new form in which the IR matrices of SGs are separated as a product of a translation part T and a point-operation part P, and where the IR matrices of SSESGs are separated as a product of a phase-shift part Q and a point-operation part P(s). Both T and Q have a simple prescribed form that does not need to be tabulated. Also, the new IR matrices are in a convenient block form which allows one to see by inspection which parts of the matrices and the associated order parameters belong to which arm of the star of k. In addition to complex IR matrices, real physically irreducible representation (PIR) matrices are tabulated. The new IR and PIR tables are available on the ISO-IR website (http://stokes.byu.edu/iso/irtables.php) in both convenient human-readable and computer-readable forms.

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来源期刊
自引率
11.10%
发文量
0
审稿时长
3 months
期刊介绍: Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials. The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial. The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.
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