The fourth central moment of an X-ray diffraction profile from an aggregate of distorted crystallites has been expressed by Mitra (1964a) as a function of the crystallite size, strain and strain gradients in the specimen. While the usual methods of line profile analysis yield information regarding either the apparent strain or the rms strain, the present study provides additional information regarding strain distribution in the form of strain derivatives and rms displacements of atoms over a given distancet in the direction of study. The strain parameters like 〈ee′〉, 〈ee″〉 have been obtained from fourth moment of the strain profile against range plots. The strain parameters thus obtained have subsequently been used to determine the rms displacements of the atoms. Alloys of copper and zinc at different stages of cold working and annealing have been studied by this method. The results have been discussed in the light of dislocation distribution, polygonisation and grain growth as well as distortion waves in the distorted crystals.

An expression for the fourth moment of the line profile in terms of several strain derivatives and the possibility of measuring the ‘wavelength’ of crystal distortions (λ) for any sinusoidally varying component of the strain are available. The experimental means for evaluating such strain derivatives in the expression for the fourth moment was earlier described. A numerical method for evaluating this wavelength and its subsequent use to determineλ in several samples ofα-brass is presented here. The data used are taken from the earlier paper of the authors. An attempt has been made to interpret the values ofλ and their changes with cold working and annealing in terms of lattice strain.

The reasons and conditions for applicability of the Cauchy distribution law for crystal structure factor components are discussed. It is shown that the standardized structure factors of centrosymmetric crystals are quite prone to be Cauchy distributed for crystals having planar molecules in their unit cells.