The small angle X-ray scattering from ideal “supermolecular pseudo-crystals”

The small angle X-ray scattering intensity I (S) from an ideal “supermolecular pseudo-crystal” was calculated under the following conditions: 1) all its edges are in parallel with the coordinates of some steric curved system of coordinates; 2) all the boundary surfaces are in parallel with those of the same system of coordinates; 3) the density distribution inside the pseudo-crystal is described by the product of three functions, each of which depends only on one of the curved coordinates, and the distribution is the average within the volume; it is also large enough to permit the change from a discrete distribution of the electron density (at peaks where the atoms are situated) to a continuous one. A specific case of the “supermolecular crystal” is the ideal pseudo-crystal, a pseudo-crystalline layer lattice, a fibril with bent crystals, and also the Hausemann macro-lattice. The general formulae for calculating I (S) have been obtained in a form suitable for changing to various concrete models.