X-ray intensity statistics of approximately centrosymmetric structures

Abstract

The joint probability distribution of X-ray structure factors of a non-centrosymmetric structure (true structure) and that of a centrosymmetric structure (assumed model) from which it deviates slightly, are given. These are characterised by a parameter D=<cos2πH.Δr_j> where Δr_j are the deviations of the N atoms from the centrosymmetric arrangements. The limiting forms of the distribution for D=0, and D=1 are respectively the acentric and centric distributions of Wilson. Intermediate values of D characterise different degrees of centrosymmetry of the structure. The parallelism of the results to another "approximately centrosymmetric" situation (Srinivasan, Indian J. Pure Appl. Phys., 1965, 3, 187), is pointed out.