Application of the pattern-fitting structure-refinement method of X-ray powder diffractometer patterns

Young, R. A.; Mackie, P. E.; Dreele, Robert B. Von

doi:10.1107/s0021889877013466

Cited by 181 publications

(77 citation statements)

References 13 publications

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“…As pointed out by Young, Mackie & Von Dreele (1977), this method yields very precise lattice parameters for each phase, and if coupled with an appropriate instrument calibration curve (Howard, 1988), the method can provide accurate parameters. The resultant lattice parameters can often be used with published determinative curves relating composition or ordering to unit-cell size.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Quantitative phase analysis using the Rietveld method

Bish¹,

Howard²

1988

J Appl Crystallogr

918

516

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Quantitative phase analysis of multicomponent mixtures using X-ray powder diffraction data has been approached with a modified version of the Rietveld computer program of Wiles & Young [ J. Appl. Cryst. (1981), 14, 149-151]. This new method does not require measurement of calibration data nor the use of an internal standard; however, the approximate crystal structure of each phase of interest in a mixture is necessary. The use of an internal standard will allow the determination of total amorphous phase content in a mixture. Analysis of synthetic mixtures yielded high-precision results, with errors generally less than 1.0% absolute. Since this technique fits the complete diffraction pattern, it is less susceptible to primary extinction effects and minor amounts of preferred orientation. Additional benefits of this technique over traditional quantitative analysis methods include the determination of precise cell parameters and approximate chemical compositions, and the potential for the correction of preferred orientation and microabsorption effects.

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Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Quantitative phase analysis using the Rietveld method

Bish¹,

Howard²

1988

J Appl Crystallogr

918

516

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“…O programa utiliza um algoritmo baseado no ajuste por mínimos quadrados para refinar um modelo estrutural teórico em relação a difratogramas reais. Uma extensa bibliografia sobre o assunto pode ser encontrada, porém não é objetivo deste trabalho o aprofundamento teórico na técnica, que pode ser consultada nas diversas referências apresentadas [1][2][3][4][5][6].…”

Section: Introductionunclassified

Determinação de fase vítrea em bauxitas refratárias

Pascoal¹,

Machado

Pandolfelli

2002

Cerâmica

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ResumoA refratariedade e a resistência ao choque térmico dos materiais estão intrinsecamente ligadas às fases que os compõem, de modo que a identificação destas fases através da técnica de difração de raios X é atualmente imprescindível para a completa caracterização de matérias-primas de produtos cerâmicos. Em 1969, H. M. Rietveld desenvolveu um software de refinamento por mínimos quadrados que permite a completa caracterização cristalográfica de um material mono ou multifásico. Apesar de possuir mais de trinta anos, a técnica ainda não é utilizada de maneira regular na análise quantitativa de matérias-primas naturais. O presente estudo busca utilizar o método de Rietveld em conjunto com outras metodologias, na quantificação da fase vítrea de bauxitas refratárias, analisando as vantagens e limitações desta técnica, bem como os resultados obtidos. Foram escolhidas a partir da literatura quatro técnicas cuja proposta comum é a determinação da fase vítrea em refratários e/ou outras classes de cerâmicas utilizando-se o método de Rietveld como base teórica. Uma quinta técnica, denominada dissolução química, foi utilizada como meio de comparação. Os resultados ilustram que, apesar dos esforços, nenhuma das técnicas estudadas pode ser utilizada de forma rápida e principalmente confiável para a determinação da quantidade de fase vítrea em refratários. Palavras-chave: matérias-primas, refratários, caracterização química. Abstract

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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 Crystallogr

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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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Application of the pattern-fitting structure-refinement method of X-ray powder diffractometer patterns

Cited by 181 publications

References 13 publications

Quantitative phase analysis using the Rietveld method

Quantitative phase analysis using the Rietveld method

Determinação de fase vítrea em bauxitas refratárias

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

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Application of the pattern-fitting structure-refinement method of X-ray powder diffractometer patterns

Cited by 181 publications

References 13 publications

Quantitative phase analysis using the Rietveld method

Quantitative phase analysis using the Rietveld method

Determinação de fase vítrea em bauxitas refratárias

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

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