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.

Apatite-type lanthanum silicates of general formula La9.33+2x/3(SiO4)6O2+x have appeared recently as a new promising class of oxide ion conductors with potential applications as electrolytes for solid oxide fuel cells (SOFCs). They have been shown to demonstrate relatively high oxide ion conductivity at moderate temperatures as well as at low oxygen partial pressures. In this paper, the diffusion pathways and the conduction mechanism of oxide ions in these phases are reinvestigated. This is done by means of atomic scale computer modeling techniques with both semiempirical and bond valence methods. Our results support that oxide ion conduction along the c-axis proceeds by an interstitial mechanism. They also support the presence of interstitial sites located within the conduction channel. However, contrarily to recent research, it is shown that the channel oxide ions are involved in the conduction process by a push−pull type mechanism. This mechanism brings into play a cooperative movement of both two adjacent interstitial oxide ions forming a complex defect and the channel oxide ions. This complex defect is shown to move along the c-axis via a nonlinear pathway different from the conduction path proposed in literature to date. The calculated migration energy of this mechanism is found to be equal to 0.32 eV, which compares well with activation energy measured along the c-axis for Nd9.33(SiO4)6O2 single crystals.