Noncrystallographic diffraction symmetries

To date, aU known 2-D quasiperiodic materials exhibit noncrystallographic diffraction symmetries of 8/mmm, 10/mmm, or 12/mram. The structures of these materials are called octagonal, decagonal, and do-decagonal structures, respectively. Quasiperiodicity is present only in planes stacked along a perpendicular periodic direction. To index the lattice points in a plane, four basis vectors a, 2. 4 are needed a fifth one,... 

The X-ray diffraction pattern of a quasicrystal exhibits noncrystallographic symmetry. In addition, the number of observable reflections increases more and more the more intense the X-ray radiation is or the longer the exposure time is (in a similar way to the number of stars visible in the sky with a more potent telescope). 

Once diffraction data have been gathered the next stage in the structure analysis is usually focused on seeking a definition of the orientation of the particle and, often, its position in the crystal cell. This information is essential for both phase refinement and the analysis of isomorphous replacement experiments. Because of the inevitable noncrystallographic redundancy (a minimum of 5-fold) and the fixed relationship between the various icosahedral symmetry axes it is often possible to solve the orientation problem by analysis of the diffraction data in the absence of a model, usually by use of a self-rotation function. 

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