大学化学 >> 2016, Vol. 31 >> Issue (11): 76-80.doi: 10.3866/PKU.DXHX201603005

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Dnd点群的几点释疑

朱艳艳,魏东辉,张文静,唐明生*()   

  • 发布日期:2016-11-30
  • 通讯作者: 唐明生 E-mail:mstang@zzu.edu.cn
  • 基金资助:
    国家自然科学基金(21001095)

Interpretation on Point Group of Dnd

Yan-Yan ZHU,Dong-Hui WEI,Wen-Jing ZHANG,Ming-Sheng TANG*()   

  • Published:2016-11-30
  • Contact: Ming-Sheng TANG E-mail:mstang@zzu.edu.cn
  • Supported by:
    国家自然科学基金(21001095)

摘要:

晶体学点群是结构化学中的重要内容之一,内容繁多而复杂。有些内容不易理解,如为什么晶体学点群中D2d点群属于四方晶系?为什么32种晶体学点群中没有D4dD6d?如果我们清楚Dnd点群中,当n为奇数时包含一个In轴,当n为偶数时包含一个I2n轴,那么前面的两个问题将迎刃而解。本文采用图解法和矩阵法详细阐述论证了Dnd点群中包含S2n轴,并讨论了如何从S2n得到In或I2n,圆满解释了D2d点群属于四方晶系和32种晶体学点群中没有D4dD6d的疑惑。

关键词: 点群, Dnd, 对称操作, 矩阵

Abstract:

Point group in crystallography is one of the important subjects in structural chemistry.Some topics are very difficult to understand.To name a few, why does point group of D2d belong to tetragonal? Why are D4d and D6d not included in 32 kinds of crystallographic point groups? The two questions are easy to answer if we understand the following topic:for the Dnd point group, when n is odd, it contains an In symmetry axis; when n is even, it contains an I2n symmetry axis.In this work, graphic method and matrix method are adopted to clarify why the Dnd point group includes an S2n axis, and thus give explanations that D2d belongs to tetragonal as well as D4d and D6d are not included in 32 kinds of crystallographic point groups.

Key words: Point group, Dnd, Symmetry operation, Matrix

MSC2000: 

  • G64