Existing knowledge about Scherrer constants is reviewed and a summary is given of the interpretation of the broadening arising from small crystallites. Early work involving the half‐width as a measure of breadth has been completed and Scherrer constants of simple regular shapes have been determined for all low‐angle reflections (h2 + k2 + l2≤ 100) for four measures of breadth. The systematic variation of Scherrer constant with hkl is discussed and a convenient representation in the form of contour maps is applied to simple shapes. The relation between the `apparent' crystallite size, as determined by X‐ray methods, and the `true' size is considered for crystallites having the same shape. If they are of the same size, then the normal Scherrer constant applies, but if there is a distribution of sizes, a modified Scherrer constant must be used.

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.

The results of both a line-broadening study on a ceria sample and a size-strain round robin on diffraction line-broadening methods, which was sponsored by the Commission on Powder Diffraction of the International Union of Crystallography, are presented. The sample was prepared by heating hydrated ceria at 923 K for 45 h. Another ceria sample was prepared to correct for the effects of instrumental broadening by annealing commercially obtained ceria at 1573 K for 3 h and slowly cooling it in the furnace. The diffraction measurements were carried out with two laboratory and two synchrotron X-ray sources, two constant-wavelength neutron and a time-of-flight (TOF) neutron source. Diffraction measurements were analyzed by three methods: the model assuming a lognormal size distribution of spherical crystallites, Warren-Averbach analysis and Rietveld refinement. The last two methods detected a relatively small strain in the sample, as opposed to the first method. Assuming a strain-free sample, the results from all three methods agree well. The average real crystallite size, on the assumption of a spherical crystallite shape, is 191 (5) Å . The scatter of results given by different instruments is relatively small, although significantly larger than the estimated standard uncertainties. The Rietveld refinement results for this ceria sample indicate that the diffraction peaks can be successfully approximated with a pseudo-Voigt function. In a common approximation used in Rietveld refinement programs, this implies that the size-broadened profile cannot be approximated by a Lorentzian but by a full Voigt or pseudo-Voigt function. In the second part of this paper, the results of the round robin on the size-strain line-broadening analysis methods are presented, which was conducted through the participation of 18 groups from 12 countries. Participants have reported results obtained by analyzing data that were collected on the two ceria samples at seven instruments. The analysis of results received in terms of coherently diffracting, both volume-weighted and area-weighted apparent domain size are reported. Although there is a reasonable agreement, the reported results on the volume-weighted domain size show significantly higher scatter than those on the area-weighted domain size. This is most likely due to a significant number of results reporting a high value of strain. Most of those results were obtained by Rietveld refinement in which the Gaussian size parameter was not refined, thus erroneously assigning size-related broadening to other effects. A comparison of results with the average of the three-way comparative analysis from the first part shows a good agreement.

The Voigt function provides a rapid and easily applied method for interpreting the breadths of diffraction profiles in terms of specimen defects and for studying absorption or emission spectra. In the past, approximate methods have usually involved the assumption that the constituent profiles are either Cauchy (Lorentzian) or Gaussian, but a better representation of the experimental data is given by the convolution of these functions. The method is illustrated by analysis of the Cu K0t emission profile and of crystallite-size broadening in nickel powder.

The powder diffraction method, by using conventional X-ray sources, was devised independently in 1916 by Debye and Scherrer in Germany and in 1917 by Hull in the United States. The technique developed steadily and, half a century later, the 'traditional' applications, such as phase identification, the determination of accurate unit-cell dimensions and the analysis of structural imperfections, were well established. There was then a dramatic increase of interest in powder methods during the 1970s, following the introduction by Rietveld in 1967 of his powerful method for refining crystal structures from powder data. This has since been used extensively, initially by using neutron data and later with X-rays, and it was an important step towards extracting 3-dimensional structural information from 1-dimensional powder diffraction patterns, in order to study the structure of crystalline materials. Similarly, techniques which do not involve structural data have been introduced for modelling powder diffraction patterns, to extract various parameters (position, breadth, shape, etc.) which define the individual reflections. These are used in most applications of powder diffraction and are the basis of new procedures for characterizing the microstructural properties of materials. Many subsequent advances have been based on this concept and powder diffraction is now one of the most widely used techniques available to materials scientists for studying the structure and microstructure of crystalline solids. It is thus timely to review progress during the past twenty years or so.Powder data have been used for the identification of unknown materials or mixtures of phases since the late 1930s. This is achieved by comparison of experimental data with standard data in crystallographic databases. The technique has benefited substantially from the revolution in the development of storage media during the last decade and from the introduction of fast search/match algorithms. Phase identification sometimes precedes a quantitative analysis of compounds present in a sample and powder diffraction is frequently the only approach available to the analyst for this purpose. A new development in quantitative analysis is the use of the Rietveld method with multi-phase refinement.A major advance in recent years has occurred in the determination of crystal structures ab initio from powder diffraction data, in cases where suitable single crystals are not available. This is a consequence of progress made in the successive stages involved in structure solution, e.g. the development of computer-based methods for determining the crystal system, cell dimensions and symmetry (indexing) and for extracting the intensities of Bragg reflections, the introduction of high resolution instruments and the treatment of