Novel aspects of the real paracrystal

Abstract

A revision of the mathematical concept of paracrystals is proposed. Hermann's [Z. Electrochem. (1940), 46, 425-436] 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 α* law. Hence, a missing corner-stone of colloid science is established.