MICROPARACRYSTALS - THE BUILDING MATERIAL IN NATURE

Abstract
The positions of atoms in materials can be explored most directly by diffraction of X-rays. This was demonstrated 1912 for crystals by Laue, Friedrich and Knipping /1/. The positions of atoms in polymers could be analysed in a similar way by transforming the intensity of scattered X-rays or neutrons into detailed structural information. Words such as short range order, medium range order, clusters, micelles, mesophases or amorphous phases, semi-crystalline or liquid-crystalline materials may be used. New definitions such as alignments, nodules, inclinations and meander-cubes appear. Another kind of research applies mathematical language : beginning with the results by Laue /2/, the reciprocal space notation by Ewald /3/ and the idea of the same a-priori probability function for all atoms in the noncrystalline state by Debye /4/, the theory of the "ideal paracrystal" was published in 1950 /5/. Laue's idea of lattices is blended with Debye's a-priori probability function : The three lattice cell vectors [MATH]_k each have a priori three relative variances g_ki in the three directions [MATH], e.g. [MATH].