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 n oncumulative (thermal) disorder is added to the paracrystalline model, then the two models and their diffraction patterns are similar but not identica l because of their different intersite statistics. However, they are identi cal in the limiting cases of either strong or weak correlations. Calculatio n of diffraction patterns shows that, with an appropriate choice of paramet ers, the two models give essentially identical diffraction for small crysta llites and very similar diffraction for larger crystallites. An empirical r elationship is derived between parameters of the two models such that they give similar diffraction patterns.