Twofold Screw Axis (21)

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The symbol above shows a twofold screw axis perpendicular to the plane of the screen, i.e parallel to Z. A twofold screw axis is equivalent to a rotation of 180° about a line followed by a translation parallel to that line. A two-one screw axis with a twofold rotation about the c-axis, i.e. about the line 0,0,z, followed by a translation of 1/2 c along it, will have the corresponding symmetry operator -x,-y,1/2+z. This axis has the written symbol "21".
2(1)
The symbol shown above corresponds to a twofold screw axis, but now parallel to the Cartesian X direction. A twofold rotation about the x-axis, followed by a 1/2 a translation along it, will have the corresponding symmetry operator 1/2+x,-y,-z. A fractional value next to the symbol indicates the height of the axis of rotation above the XY plane.
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In space group diagrams for cubic symmetry, twofold screw axes may appear inclined at an angle of 45° to the XY plane. The symbol for these is shown above, the dot indicating the exact position of intersection with the plane.


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© Copyright 1995-2006.  Birkbeck College, University of London. Author(s): Jeremy Karl Cockcroft