Effects of symmetry and atomic heterogeneity on X-ray intensities – a case of hypercentric distribution*

Abstract

Abstract A series expansion distribution function of the structure amplitude |F| has been used to calculate the generalised cumulative distribution function Nn (z) for a hypercentric crystal with n centres of symmetry. Modified expressions for moments have been derived considering the effect of hypercentrosymmetry for three different space groups P[unk], P2/m and Pmmm, which also take into account the effect of atomic heterogeneity in the crystal. The resultant change from the corresponding Wilson-type distribution is illustrated with the help of a hypothetical example and the effects of expansion terms have been discussed.