Least-squares structure refinement based on profile analysis of powder film intensity data measured on an automatic microdensitometer

Malmros, Gunnar; Thomas, Josh

doi:10.1107/s0021889877012680

Cited by 157 publications

(74 citation statements)

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“…The procedure for refinement of a two-component system follows exactly that used for the single-component case: see Rietveld (1969) and Malmros & Thomas (1977), hereafter: MT. The combined data file is created in a preparation program where all pertinent input information needed for the individual components is supplied in sequence.…”

Section: The Analysis Methodsmentioning

confidence: 99%

“…There is also a widespread need for experimental techniques for performing structural studies where single-phase powder cannot be obtained. It is clear that the full-profile analysis procedure of Rietveld (1969) can find an application in both fields; particularly the technique as applied to microdensitometermeasured Guinier-H~igg X-ray powder film data (Malmros & Werner, 1973;Malmros & Thomas, 1977;Berg & Werner, 1977). The latter method has the great advantage that it requires extremely small amounts of powder (down to 0-2 mg) and, in as much as it takes full account of overlap, it makes optimal use of the data available.…”

Section: Introductionmentioning

confidence: 99%

“…

AbstractFull-profile analysis of microdensitometer-measured Guinier-H~igg X-ray powder film data (strictly monochromatized Cu K~I radiation) [see Malmros & Thomas (1977). J. Appl.

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confidence: 99%

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Quantitative analysis of multicomponent powders by full-profile refinement of Guinier–Hägg X-ray film data

Werner¹,

Salomé²,

Malmros³

1979

J Appl Cryst

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Full-profile analysis of microdensitometer-measured Guinier-H~igg X-ray powder film data (strictly monochromatized Cu K~I radiation) [see Malmros & Thomas (1977). J. Appl. Cryst. 10,[7][8][9][10][11] is here extended to treat a multicomponent system where two of the components are refinable. The method is demonstrated for the case of: (a) ~-Bi203/KC1 (standard), and (b) CaF2/SiO2 (s-quartz) together with a Mg(OH)2 matrix. In (a), a weight ratio BizO3/KCI of 1:1 gave an experimental result of 0-96(9):1. In (b), a number of admixtures have been studied in the range 1-60 wt% SiO2 all with 10 wt % CaF2. The agreement between weight ratios and profile refinement results suggests that the formal temperature factors function as effective absorption correction parameters. It is thus shown that approximate quantitative analysis is feasible from Guinier-H~igg diffraction data without any previously determined calibration curve. Moreover, the method permits the use of all available overlapping data in the refinement of a structure without needing to exclude data from known impurities [see Waltersson, Werner & Wilhelmi (1977). Cryst. Struct. Commun. 6,[231][232][233][234][235].This feature is likely to prove the most common application of the method.

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Section: The Analysis Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantitative analysis of multicomponent powders by full-profile refinement of Guinier–Hägg X-ray film data

Werner¹,

Salomé²,

Malmros³

1979

J Appl Cryst

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“…Dramatic expansion in the use of the method followed construction of the first wave of h;gh-resolution single-wavelength (Hewat, 1975) and time-of-flight (Jorgensen & Rotella, 1982) neutron powder diffractometers. Extension to conventional X-ray data (Malmros & Thomas, 1977;Young, Mackie & Von Dreele, 1977;Wiles & Young, 1981) provided the catalyst for its increased usage in the wider crystallographic community, while the most recent new application has involved the use of X-rays from synchrotron sources (Cox, Hastings, Thomlinson & Prewitt, 1983;Parrish, Hart & Huang, 1986).…”

Section: Introductionmentioning

confidence: 99%

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

Hill¹

1992

J Appl Cryst

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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...

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“…Reviews of this technique have been given by Cheetham & Taylor (1977) and, more recently, by Albinati & Willis (1982). There is now also considerable interest in structure refinement from X-ray powder diffraction patterns and a number of papers (Malmros & Thomas, 1977;Young, Mackie & Von Dreele, 1977;Khattak & Cox, 1977;Wiles & Young, 1981;Young & Wiles, 1982) have discussed applications of Rietveld refinement to X-ray diffraction. The methods tried, unfortunately, have so far met with only limited success, the major problem being in obtaining an adequate description of the peak shape of the diffraction line and its variation with Bragg angle.…”

Section: Introductionmentioning

confidence: 99%

X-ray Rietveld refinement using Debye–Scherrer geometry

Thompson¹,

Wood²

1983

J Appl Crystallogr

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A procedure for Rietveld refinement from DebyeScherrer X-ray diffraction patterns is described, in which the effects of instrumental aberrations on the peak shapes and positions are calculated and incorporated into the refinement model. These aberrations, neglected in previous Rietveld refinement programs, can produce severe systematic errors in both the structural and non-structural parameters derived. Results presented from four materials (SiO2, AIPO4, AI20 3, LiTaO3) are in good agreenent with singlecrystal values and are an improvement over those previously obtained by X-ray powder diffraction.

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Least-squares structure refinement based on profile analysis of powder film intensity data measured on an automatic microdensitometer

Cited by 157 publications

References 5 publications

Quantitative analysis of multicomponent powders by full-profile refinement of Guinier–Hägg X-ray film data

Quantitative analysis of multicomponent powders by full-profile refinement of Guinier–Hägg X-ray film data

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

X-ray Rietveld refinement using Debye–Scherrer geometry

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Least-squares structure refinement based on profile analysis of powder film intensity data measured on an automatic microdensitometer

Cited by 157 publications

References 5 publications

Quantitative analysis of multicomponent powders by full-profile refinement of Guinier–Hägg X-ray film data

Quantitative analysis of multicomponent powders by full-profile refinement of Guinier–Hägg X-ray film data

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

X-ray Rietveld refinement using Debye–Scherrer geometry

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