Fourfold Screw Axes (4n)
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The symbols above show fourfold screw axes perpendicular to the
plane of the screen, i.e parallel to Z.
A fourfold screw axis is equivalent to an anticlockwise rotation of 90°
about a line followed by a translation parallel to that line.
The translation is either 1/4, 1/2, or 3/4 of the repeat distance
in the lattice along the axis for four-one, four-two, and
four-three screw axes, respectively.
A four-one screw axis with
a fourfold rotation about the c-axis, i.e. about
the line 0,0,z, followed by a translation of 1/4 c
along it, will have
the corresponding symmetry operator -y,x,1/4+z.
Note that four-one and four-three are equivalent
except for handedness (right- and left-handed, respectively),
in contrast to the four-two axis which has no handedness.
These axes have the written symbols "41",
In space group diagrams for cubic symmetry, fourfold screw axes
are shown along both X and Y directions as well as along the Z direction
A fractional value next to the symbol indicates the height
of the axis of rotation above the XY plane.
© Copyright 1997-1999.
Birkbeck College, University of London.