Diffraction by one-dimensional paracrystals and perturbed lattices

A detailed comparison of the one-dimensional paracrystalline and perturbed lattice models of disordered crystals, and their diffraction, is made. If noncumulative (thermal) disorder is added to the paracrystalline model, then the two models and their diffraction patterns are similar but not identical because of their different intersite statistics. However, they are identical in the limiting cases of either strong or weak correlations. Calculation of diffraction patterns shows that, with an appropriate choice of parameters, the two models give essentially identical diffraction for small crystallites and very similar diffraction for larger crystallites. An empirical relationship is derived between parameters of the two models such that they give similar diffraction patterns.