Profile analysis for microcrystalline properties by the Fourier and other methods

TLDR: The use of the Fourier, variance and related methods in general requires that the diffraction lines are well resolved and it is thus restricted to materials with high symmetry or which exhibit a high degree of preferred orientation as discussed by the authors.

Abstract: In the 1960s the Fourier and variance methods superseded the use of the FWHM and integral breadth in detailed studies of microcrystalline properties. Provided that due allowance is made in the analysis for systematic errors, particularly the effects of truncation of diffraction line profiles at a finite range, these remain the best methods for characterising crystallite size and shape, microstrains and other imperfections in cases where accuracy is important. However, the application of the Fourier, variance and related methods in general requires that the diffraction lines are well resolved and it is thus restricted to materials with high symmetry or which exhibit a high degree of preferred orientation. Most materials, on the other hand, including many of technological importance, have complex patterns with severe overlapping of peaks. The introduction of pattern-decomposition methods, whereby a suitable model is fitted to the total diffraction pattern to give profile parameters for individual lines, means that microcrystalline properties can now be studied for any crystalline material or mixture of substances. The use of the FWHM and integral breadth has been given a new lease of life; though the information is less detailed than is given by the Fourier and variance methods and systematic errors are in general greater, self-consistent estimates of crystallite size and microstrains are obtained.