The use of the Voigt function for the analysis of the integral breadths of broadened X‐ray diffraction line profiles forms the basis of a rapid and powerful single‐line method of crystallite‐size and strain determination which is easy to apply. To avoid graphical methods or interpolation from tables, empirical formulae of high accuracy are used and an estimation of errors is presented, including the influence of line‐profile asymmetry. The method is applied to four practical cases of size‐strain broadening: (i) cold‐worked nickel, (ii) a nitrided steel, (iii) an electrodeposited nickel layer and (iv) a liquid‐quenched AlSi alloy.

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In the 1960s the Fourier and variance methods superseded the use of the FWHM and integral breadth in detailed studies of microcrystalline properties.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.At present the most promising technique for analysing the breadths obtained from pattern decomposition is the Voigt method applied to all lines of a diffraction pattern. When reliable data for two or more orders of reflections are available, a multiple-line analysis can be used to separate the contributions to line breadths from crystallite size and strain. For other reflections a single-line approach is used, though this can introduce an angle-dependent systematic error.

A revision is presented of the original description by Warren [X-ray Diffraction, (1969), pp. 275±298. Massachusetts: Addison-Wesley] of the intensity distribution of powder-pattern re¯ections from f.c.c. metal samples containing stacking and twin faults. The assumptions (in many cases unrealistic) that fault probabilities need to be very small and equal for all fault planes and that the crystallites in the sample have to be randomly oriented have been removed. To elucidate the theory, a number of examples are given, showing how stacking and twin faults change the shape and position of diffraction peaks. It is seen that signi®cant errors may arise from Warren's assumptions, especially in the peak maximum shift. Furthermore, it is explained how to describe powder-pattern re¯ections from textured specimens and specimens with non-uniform fault probabilities. Finally, it is discussed how stacking-and twin-fault probabilities (and crystallite sizes) can be determined from diffraction line-pro®le measurements.