Rietveld refinement round robin. I. Analysis of standard X-ray and neutron data for PbSO₄

Abstract

The Commission on Powder Diffraction of the International Union of Crystallography has undertaken an intercomparison of Rietveld refinements performed with two 'standard' PbSO4 powder diffraction patterns: a conventional (two-wavelength) X-ray pattern collected on a Bragg-Brentano diffractometer with Cu Ks radiation and a constant-wavelength neutron pattern collected on the D1A diffractometer at the Institut Laue-Langevin. The aims of this project were: (i) to evaluate a cross section of currently used Rietveld refinement software; (ii) to examine the range and effect of various strategies of Rietveld refinement; (iii) to assess the precision and accuracy (spread) of the parameters derived by Rietveld analysis. 23 participants provided 18 refinements with the X-ray data and 20 refinements with the neutron data, using 11 different Rietveld-analysis programs. Analysis of the submitted results shows that refinement strategies play a large part in determining the detailed outcome of a Rietveld refinement. The wide variation in the values of the agreement indices obtained in these studies of the same data sets highlights the need for standardization both of the refinement procedures and of the type of data included tn the algorithms used for assessing the fit. The major factors limiting the accuracy of the derived PbSO4 crystal structure parameters were: (i) use of insufficiently flexible peak shape and/or background functions; (ii) elimination of the high-angle diffraction data from the refinement; (iii) inclusion of an insufficiently wide range of diffraction angles on either side of the centroid of each peak during the step intensity calculation; and, additionally for X-rays, (iv) simultaneous release of the O-atom site-occupancy and displacement parameters. Rietveld analysis of the PbSO4 X-ray powder diffraction data provided atomic coordinates and isotropic displacement parameters for the Pb and S atoms that are precise (i.e. have small e.s.d.s) and are in reasonable agreement with the values derived from a singlecrystal study (viz the spread of coordinates is over the range 0.007-0.042 A). On the other hand, the 'light' 0021-8898/92//050589-22506. 00 O-atom parameters show relatively poor precision and have a disconcertingly wide spread of values about the weighted mean (viz 0.12-0.19A for the coordinates). Despite the much lower intrinsic resolution of the neutron data (i.e. peak widths some four times those of the X-ray data), the coordinates and anisotropic displacement parameters obtained for the Pb and O atoms are very precise and have a relatively narrow distribution about the single-crystal results, namely 0.004-0.020 A for the coordinates. The range of coordinates determined from the neutron data for the relatively 'light' S atom is correspondingly larger, namely 0.024-0.043 A, about equivalent to that obtained from the X-ray data. In general, and as expected, the e.s.d.s from the Rietveld analyses are substantially smaller than the observed inter-refinement variation of the unit-cell dimensions...

Intensity enhancement in asymmetric diffraction with parallel-beam synchrotron radiation

“…The samples used in the present experiments were powders of the National Institute of Standards and Technology (NIST) standard reference material (SRM) 640b Si, NIST SRM 674 CeO 2 and monoclinic ZrO 2 distributed by the Commission on Powder Diffraction (CPD) as one of the standard samples for the Rietveld Refinement Round Robin (Hill, 1992).…”

THE COMPRESSIONAL BEHAVIOR OF P4/n VESUVIANITE

“…It is to be noted, however, that the difference between the cell parameters measured at room pressure with the two different experimental setups is much higher than the estimated standard deviation. This difference reflects the actual precision of the Rietveld refinement procedure, which is reported to be generally lower than that which would appear from the estimated standard deviations alone (Hill 1992). The cell parameters at various pressures are reported in Table 2.…”

Effects of crystalline growth on structural and luminescence properties of Ca(10−3x)Eu2x(PO4)6F2 nanoparticles fabricated by using a microwave driven hydrothermal process

“…The used procedure (both datacollection and refinement strategy) corresponded to the general guidelines for structure refinement using the Rietveld method (whole-profile) formulated by the International Union of Crystallography Commission on Powder Diffraction 31,32 . The initial structural parameters of fluorapatite, Ca 10 (PO 4 ) 6 F 2 , were taken from 35 .…”