page_title: Fiber diffraction
section_title: Pattern correction
hierarchical_section_title: Fiber diffraction / Pattern correction
caption_attribution_description: English: Fiber Diffraction data of WaxsPPrawlfig.png after mapping into the reciprocal space. Polypropylene
context_page_description: Fiber diffraction is a subarea of scattering, an area in which molecular structure is determined from scattering data. In fiber diffraction the scattering pattern does not change, as the sample is rotated about a unique axis. Such uniaxial symmetry is frequent with filaments or fibers consisting of biological or man-made macromolecules. In crystallography fiber symmetry is an aggravation regarding the determination of crystal structure, because reflexions are smeared and may overlap in the fiber diffraction pattern. Materials science considers fiber symmetry a simplification, because almost the complete obtainable structure information is in a single two-dimensional diffraction pattern exposed on photographic film or on a 2D detector. 2 instead of 3 co-ordinate directions suffice to describe fiber diffraction.
  The ideal fiber pattern exhibits 4-quadrant symmetry. In the ideal pattern the fiber axis is called the meridian, the perpendicular direction is called equator. In case of fiber symmetry, many more reflexions than in single-crystal diffraction show up in the 2D pattern.
context_section_description: The figure on the left shows a typical fiber pattern of polypropylene before mapping it into reciprocal space. The mirror axis in the pattern is rotated by the angle  with respect to the vertical direction. This shortcoming is compensated by simple rotation of the picture. 4 straight arrows point at 4 reflexion images of a chosen reference reflexion. Their positions are used to determine the fiber tilt angle . The image has been recorded on a CCD detector. It shows the logarithmic intensitity in pseudo-color representation. Here bright colors represent high intensity.
  After determination of  the distance between sample and detector is computed using known crystallographic data of the reference reflexion, a uniformly gridded map for the representative fiber plane in reciprocal space is constructed and the diffraction data are fed into this map. The figure on the right shows the result. Change of scattering intensity has been considered in the unwarping process. Because of the curvature of the surface of the Ewald sphere there remain white spots at the meridian, in which structure information is missing. Only in the center of the image and at an s-value related to the scattering angle  there is structure information on the meridian. Of course, there is now 4-quadrant symmetry. This means that in the example pattern part of the missing information may be copied "from the lower half to the upper half" into the white areas. Thus, it frequently makes sense to tilt the fiber intentionally.
  The three-dimensional sketch demonstrates that in the example experiment the collected information on the molecular structure of the polypropylene fiber is almost complete. By rotation of the plane pattern about the meridian the scattering data collected in 4 s fill an almost spherical volume of s-space. In the example the 4-quadrant symmetry has not yet been considered to fill part of the white spots. For clarity a quarter of the sphere has been cut out, but keeping the equatorial plane itself.
caption: Fiber pattern of polypropylene mapped into (the representative plane of) reciprocal space
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