X-ray diffraction from single crystals of polyacrylonitrile shows that the diffuse nature of the nonequatorial scattering maxima cannot be accounted for by crystal size. The theory of paracrystals may be used to set both an upper and a lower limit to the amount of lattice distortion and yields a plausible explanation for the absence or extreme weakness of higher-order reflections. Finally, it is shown why the diffuse maxima cannot be used directly in measuring lattice parameters and the method which must be used to obtain a more definite crystal structure for polyacrylonitrile is indicated.
It has now been established that paracrystals are the 'building blocks' of many materials including polymers, biological materials, colloids, molten metals and alloys, and catalysts. The concept of paracrystallinity and the main equations which are needed for the practical application of the theory to X-ray, neutron and electron diffraction are presented in a simplified style which can be easily grasped by scientists from all disciplines. Examples of the application and usefulness of the theory which support the fact that paracrystals are the building blocks of condensed matter are presented. X-ray diffraction, neutron diffraction, electron diffraction, scanning electron microscopy and transmission electron microscopy are among the techniques which have been used for the assessment of the paracrystalline nature of the materials given in the examples.
A revision of the mathematical concept of paracrystals is proposed. Hermann's IZ. Electrochem. (1940), 46, 425-4361 early theory of mesophases represents a special case of a paracrystal where the statistical parameters introduced were merely crystalline or gas-like. The theory of paracrystals removes the black-white picture of crystalline and amorphous phases by introducing 18 new statistical parameters into conventional crystallography. It is shown that a real paracrystal can be defined by a three-dimensional convolution polynomial in combination with an empirically derived +t* law. Hence, a missing corner-stone of colloid science is established.
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