An X-ray analysis of stacking disorder in kaolinite by fourth moment

Abstract

Mathematically, it is well established that besides the Fourier coefficients, the natural characteristics of any distribution are its moments. The use of the second moment, called variance, as a measure of line broadening has already gained wide popularity because of its several merits relative to other empirically devised parameters. In recent decades, the fourth moment has been recognized as an important parameter; its theoretical significance has been discussed by Mitra (1964), who developed the moment range function for the estimation of crystallite size and distortion in cold-worked metal. However, owing to the requirements of high degree of accuracy of intensity measurement coupled with cumbersome calculations, this parameter did not find much general application. Modern diffractometers and sophisticated computers have helped ease the problem and in recent years several workers (Kagan & Snovidov, 1965; Kulshreshtha et al., 1971; Mukherjee, 1981) have successfully used this parameter for defect analysis in various non-ideal forms of materials.