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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fractional coordinates ： ウィキペディア英語版 Fractional coordinates In crystallography, a fractional coordinate system is a coordinate system in which the edges of the unit cell are used as the basic vectors to describe the positions of atomic nuclei. The unit cell is a parallelepiped defined by the lengths of its edges a, b, c and angles between them α, β, γ as shown in the figure below. ==Conversion to cartesian coordinates== If the fractional coordinate system has the same origin as the cartesian coordinate system, the a-axis is collinear with the x-axis, and the b-axis lies in the xy-plane, fractional coordinates can be converted to cartesian coordinates through the following transformation matrix:〔(http://graphics.med.yale.edu:5080/TriposBookshelf/sybyl/crystal/crystal_appendix2.html ) Probably a slightly unstable reference for the transformation matrix〕〔OpenBabel source code〕〔(http://www.angelfire.com/linux/myp/FracCor/fraccor.html ) Another transformation matrix that is defined differently〕 :$\backslash begin\; x\; \backslash \backslash \; y\; \backslash \backslash \; z\; \backslash \backslash \; \backslash end\; =$ \begin a & b\cos(\gamma) & c\cos(\beta) \\ 0 & b\sin(\gamma) & c\frac \\ 0 & 0 & c\frac \\ \end \begin \hat \\ \hat \\ \hat \\ \end where $v$ is the volume of a unit parallelepiped defined as :$$ v =\sqrt For the special case of a monoclinic cell (a common case) where α=γ=90° and β>90°, this gives: :$$ x=a\,x_ + c\,z_\,\cos(\beta) :$$ y=b\,y_ :$$ z=c\,v\,z_ = c\, z_\,\sin(\beta) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fractional coordinates」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.