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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〕 : where is the volume of a unit parallelepiped defined as : For the special case of a monoclinic cell (a common case) where α=γ=90° and β>90°, this gives: : : : 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
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