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.

With the assumption that both size‐ and strain‐broadened profiles of the pure‐specimen function are described with a Voigt function, it is shown that the analysis of Fourier coefficients leads to the Warren–Averbach method of separation of size and strain contributions. The analysis of size coefficients shows that the `hook' effect occurs when the Cauchy content of the size‐broadened profile is underestimated. The ratio of volume‐weighted and surface‐weighted domain sizes can change from ~1.31, for the minimum allowed Cauchy content, to 2, when the size‐broadened profile is given solely by a Cauchy function. If the distortion Subscripts coefficient is approximated by a harmonic term, mean‐square strains decrease linearly with increasing the averaging distance. The local strain is finite only in the case of purely Gaussian strain broadening, because strains are then independent of averaging distance.

The size‐broadened profile given by the lognormal and gamma size distributions of spherical crystallites is considered. An analytical approximation for the size‐broadened profile is derived that can be analytically convolved with the strain‐broadened and instrumental‐broadened profiles. The method is tested on two CeO2 powders; one shows `super‐Lorentzian' profiles that were successfully modelled under the assumption of a broad lognormal size distribution. It is shown that the Voigt function, as a common model for a size‐broadened profile, fails for both very narrow and broad size distributions. It is argued that the size‐broadened line profile is not very sensitive to variations in size distribution and that an apparent domain size or even column‐length distribution function can correspond to significantly different size distributions.