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.

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The orthorhombic and rhombohedral structures of ferroelectric potassium niobate have been determined by neutron diffraction measurements on powdered crystals, using the profile refinement technique to analyse the data. In the orthorhombic phase at 22 "C the atomic displacements along [Oll] from the cubic perovskite positions are 6(K) = -0.006 + SA, 6(Nb) = 0,070A, S ( 0 , ) = -0.138 + 6 A and 6(0,,) 6(0,,,) = -0,125 + 4A. In the rhombohedral phase at 230K, the displacements are along [lll]; 6(K) = -0,013 i 32A, 6(Nb) = 0.078A and 6(0,) = 6(0,,) = S(O,,,) = -0,140 + 4A. As a check on the profile technique, the tetragonal structure was redetermined, and good agreement obtained with the previous single-crystal work, with displacements along [OOl] of S(K) = -0,014 + 26A, 6(Nb) = 0.063A, S ( 0 , ) = -0.117 + 4 A and 6(0,,) = 6(0,,,) = 0099 + 3A. All of these transitions result from the condensation at q = 0 of soft modes in which almost rigid oxygen octahedra vibrate against the potassium and niobium atoms. Our results account for the observed changes in the spontaneous polarization of potassium niobate, and demonstrate the power of the profile refinement technique for the investigation of structural phase transitions.

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The perovskite structure of the relaxor PbMg,,,Nb,,,O, (PMN) is studied using x-ray and neutron powder diffraction data. The static diffuse scattering (SDS) observed in the diffraction patterns at low temperatures is interpreted using a two-phase Rietveld analysis. The structural model is based on a long-range structure with an average cubic symmetry, and a short-range order due to atomic shifts involved by the formation of polar regions. The two-phase model provides a good improvement in reliability factors. The correlation length and thecoexistence of different phases at low temperatures are discussed.