Generalisation of P.P. Ewald's intensity function for microparacrystals in colloids and their superstructures

Abstract

The expectation value of the diffraction of an ensemble of paracrystals defined by statistically distributed point defects within their lattices can be calculated by means of the correlation function of bounded point lattices with the help of their shape function. The result is a convolution product of their shape factor S²(b) with a lattice peak function Z(b) defined by a three-dimensional convolution polynomial. S²(b) depends on Z(b) because of the alpha * law. For crystals the convolution product ZS² degenerates to P.P. Ewald's (1940) intensity function. All existing objections against the theory of paracrystals fail because they do not take into account this shape factor nor the alpha * law!.