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Abstract:
This chapter explores circular crystals. Translational symmetry is considered a prerequisite for a perfect long-range organization of matter. This is realized for crystals in all three dimensions. However, there is material architecture with perfect long-range three-dimensional order and no translational symmetry, such as mesostructured silica fibers consisting of channels wound around the fiber axis, thereby forming an array with hexagonal short-range order. The whole structure is controlled by a singularity, which is the fiber axis. In reciprocal space, the fibers are represented by a system of rings known for crystals. A physical consequence of this is unusual X-ray diffraction properties. Becuase of the new reciprocal space representation, the circular architecture has to be regarded as a qualitatively new form of solid-state organization.
