The estimation of standard deviations in powder diffraction Rietveld refinements

Scott, H. G.

doi:10.1107/s0021889883010195

Cited by 99 publications

(48 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The corresponding mean neutron 9~ value for the O-atom coordinates is 4.1, leading to a difference between the e.s.d, and probable error of only a factor of two. These values are typical of the differences generally encountered in Rietveld-analysis results (Young, 1980;Scott, 1983;Hill & Madsen, 1986) and also of those observed in systematic single-crystal studies Coppens et al, 1984).…”

Section: Atomic Coordinatesmentioning

confidence: 59%

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

Hill¹

1992

J Appl Crystallogr

View full text Add to dashboard Cite

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...

show abstract

Section: Atomic Coordinatesmentioning

confidence: 59%

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

Hill¹

1992

J Appl Crystallogr

View full text Add to dashboard Cite

show abstract

“…'s are critical to the correct interpretation of small differences (e.g. oxidation states, occupancy parameters or unusual bond lengths that might indicate unusual chemistry), the reader is referred to the papers by Prince (1981Prince ( , 1993, Scott (1983), Hill & Flack (1987), Hill & Madsen (1987), Antoniadis et al (1990), Be Â rar (1992) and Cox & Papoular (1996).…”

Section: Estimated Standard Deviationsmentioning

confidence: 99%

Rietveld refinement guidelines

et al. 1999

View full text Add to dashboard Cite

A set of general guidelines for structure re®nement using the Rietveld (whole-pro®le) method has been formulated by the International Union of Crystallography Commission on Powder Diffraction. The practical rather than the theoretical aspects of each step in a typical Rietveld re®nement are discussed with a view to guiding newcomers in the ®eld. The focus is on X-ray powder diffraction data collected on a laboratory instrument, but features speci®c to data from neutron (both constant-wavelength and time-of-¯ight) and synchrotron radiation sources are also addressed. The topics covered include (i) data collection, (ii) background contribution, (iii) peak-shape function, (iv) re®nement of pro®le parameters, (v) Fourier analysis with powder diffraction data, (vi) re®nement of structural parameters, (vii) use of geometric restraints, (viii) calculation of e.s.d.'s, (ix) interpretation of R values and (x) some common problems and possible solutions.

show abstract

“…More importantly, it is clear that the e.s.d. 's reflect mainly random experimental errors, neglecting the effect of systematic errors arising due to model inadequacy (Scott, 1983;Young, 1993). For all these reasons, it is obvious that the e.s.d.…”

Section: Estimated Errorsmentioning

confidence: 99%

Adaptation of the Rietveld Method for the Characterization of the Lamellar Microstructure of Polymers

Dupont¹,

Jonas²,

Legras³

1997

J Appl Cryst

View full text Add to dashboard Cite

This paper describes a variant of the Rietveld refinement procedure applied to the characterization by X-ray scattering of disordered and small crystals as found in semicrystalline polymers. The program essentially focuses on the profile of the reflections and allows one to obtain the size, unit-cell parameters and lattice distortions (atomic displacements and paracrystallinity) of crystals in isotropic samples. The detailed influence of instrumental aberrations on the scattering is also considered. To illustrate the usefulness of the method, results obtained on PEEK [poly(ether-ether-ketone)] samples, cold-crystallized at various temperatures are presented. As the crystallization temperature increases, a closer packing of the chains in the (100) direction, a decrease in paracrystallinity along (100) and a thickening of the crystalline lamellae ((001) direction) are observed. The lamellae are strongly microfragmented perpendicularly to the chain axis, resulting in coherently diffracting regions of sizes between 700 and 2000 nm 3 only.

show abstract

The estimation of standard deviations in powder diffraction Rietveld refinements

Cited by 99 publications

References 0 publications

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

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

Rietveld refinement guidelines

Adaptation of the Rietveld Method for the Characterization of the Lamellar Microstructure of Polymers

Contact Info

Product

Resources

About

The estimation of standard deviations in powder diffraction Rietveld refinements

Cited by 99 publications

References 0 publications

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

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

Rietveld refinement guidelines

Adaptation of the Rietveld Method for the Characterization of the Lamellar Microstructure of Polymers

Contact Info

Product

Resources

About

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

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