C70, C80, C90 and carbon nanotubes by breaking of the icosahedral symmetry of C60.

IF 1.8 4区 材料科学
Acta Crystallographica Section A Pub Date : 2013-11-01 Epub Date: 2013-09-12 DOI:10.1107/S0108767313021375
Mark Bodner, Jiří Patera, Marzena Szajewska
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引用次数: 14

Abstract

The icosahedral symmetry group H3 of order 120 and its dihedral subgroup H2 of order 10 are used for exact geometric construction of polytopes that are known to exist in nature. The branching rule for the H3 orbit of the fullerene C60 to the subgroup H2 yields a union of eight orbits of H2: four of them are regular pentagons and four are regular decagons. By inserting into the branching rule one, two, three or n additional decagonal orbits of H2, one builds the polytopes C70, C80, C90 and nanotubes in general. A minute difference should be taken into account depending on whether an even or odd number of H2 decagons are inserted. Vertices of all the structures are given in exact coordinates relative to a non-orthogonal basis naturally appropriate for the icosahedral group, as well as relative to an orthonormal basis. Twisted fullerenes are defined. Their surface consists of 12 regular pentagons and 20 hexagons that have three and three edges of equal length. There is an uncountable number of different twisted fullerenes, all with precise icosahedral symmetry. Two examples of the twisted C60 are described.

C70, C80, C90和碳纳米管通过打破C60的二十面体对称。
120阶的二十面体对称群H3及其10阶的二面体子群H2被用来精确地构造自然界中已知存在的多面体。富勒烯C60的H3轨道到H2亚群的分支规则产生了H2的8个轨道:其中4个是正五边形,4个是正十边形。通过在分支规则中插入1个、2个、3个或n个额外的H2的十角形轨道,可以构建出C70、C80、C90多面体和一般的纳米管。根据插入的H2十位数是偶数还是奇数,应该考虑到一分钟的差异。所有结构的顶点都以精确坐标给出,相对于自然适合于二十面体基团的非正交基,以及相对于标准正交基。扭曲的富勒烯被定义。它们的表面由12个正五边形和20个六边形组成,这些六边形有三条等长的边和三条边。有无数种不同的扭曲富勒烯,它们都具有精确的二十面体对称。介绍了双绞线C60的两个实例。
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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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