Crystallite shape and the Fourier analysis of diffraction line profiles

The relation between the column distribution as determined from the Fourier analysis of diffraction line profiles and the overall size distribution is examined for mixtures of crystallites of uniform shape, but differing in size. It is concluded that for such systems Fourier analyses of a number of profiles can lead to information on the nature of the shape, but that very careful measurements will be necessary to generate useful information on the nature of the distribution of sizes. While the detailed application of the results of this model may be limited, more general consequences seem to be that (a) there is normally no superficial resemblance between the Fourier column distribution and the true size distribution and (b) information on the latter can only be extracted with difficulty from Fourier analyses.