Fiber diffraction

Fiber diffraction is a subarea of scattering, an area in which molecular structure is determined from scattering data (usually of X-rays, electrons or neutrons). In fiber diffraction the scattering pattern does not change, as the sample is rotated about a unique axis (the fiber 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 (2D) 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. In fiber patterns these reflexions clearly appear arranged along lines (layer lines) running almost parallel to the equator. Thus, in fiber diffraction the layer line concept of crystallography becomes palpable. Bent layer lines indicate that the pattern must be straightened. Reflexions are labelled by the Miller index hkl, i.e. 3 digits. Reflexions on the i-th layer line share l=i. Reflexions on the meridian are 00l-reflexions. In crystallography artificial fiber diffraction patterns are generated by rotating a single crystal about an axis (rotating crystal method). Non-ideal fiber patterns are obtained in experiments. They only show mirror symmetry about the meridian. The reason is that the fiber axis and the incident beam (X-rays, electrons, neutrons) cannot be perfectly oriented perpendicular to each other.