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Parametric Rietveld refinement.

Stinton GW, Evans JS - J Appl Crystallogr (2007)

Bottom Line: In this paper the method of parametric Rietveld refinement is described, in which an ensemble of diffraction data collected as a function of time, temperature, pressure or any other variable are fitted to a single evolving structural model.Parametric refinement offers a number of potential benefits over independent or sequential analysis.It can lead to higher precision of refined parameters, offers the possibility of applying physically realistic models during data analysis, allows the refinement of 'non-crystallographic' quantities such as temperature or rate constants directly from diffraction data, and can help avoid false minima.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Chemistry, University of Durham, UK.

ABSTRACT
In this paper the method of parametric Rietveld refinement is described, in which an ensemble of diffraction data collected as a function of time, temperature, pressure or any other variable are fitted to a single evolving structural model. Parametric refinement offers a number of potential benefits over independent or sequential analysis. It can lead to higher precision of refined parameters, offers the possibility of applying physically realistic models during data analysis, allows the refinement of 'non-crystallographic' quantities such as temperature or rate constants directly from diffraction data, and can help avoid false minima.

No MeSH data available.


Parametric Rietveld refinement of Rb[MnCr(CN)6].xH2O. Observed data in are red, calculated in blue. Data have been offset in 2θ and intensity for clarity. The difference surface is plotted in pink.
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fig4: Parametric Rietveld refinement of Rb[MnCr(CN)6].xH2O. Observed data in are red, calculated in blue. Data have been offset in 2θ and intensity for clarity. The difference surface is plotted in pink.

Mentions: In an initial round of parametric refinement, the Si cell parameter was expressed as a fixed quantity in terms of equation (3) and a 2θ correction polynomial and sample height offset refined from all 64 data sets simultaneously; parameters describing an overall pseudo-Voigt peak shape were also refined for each phase. In this process, a total of 1747 parameters were refined (19 overall parameters: 3 terms of a calibration polynomial, a height offset between sample and holder and 5 overall peak shape parameters per phase; 27 parameters per individual data set: 15 background terms, 2 scale factors, 2 cell parameters, an isotropic overall temperature factor for Si and the sample, 5 hkl peak intensities for the Al Pawley fit, and the sample height of the Al holder). Coefficients of the 2θ calibration polynomial were then fixed and parametric Rietveld refinement performed using a single parameter to describe the sample height offset and with the Si cell allowed to refine freely. An overall R wp of 9.05% was obtained with higher temperature refinements showing slightly worse agreement factors than for free refinements. Allowing Al peak shapes for each data set to refine independently led to an overall R wp = 8.925%, individual R wp values for each data set that varied smoothly with temperature, and smooth changes in peaks shape values; these minor variations are presumably caused by small changes in sample height with temperature. The parametric R factor is essentially the same as the average of those obtained by independent refinements. Fig. 4 ▶ shows the equivalent of a standard Rietveld plot for the parametric refinement.


Parametric Rietveld refinement.

Stinton GW, Evans JS - J Appl Crystallogr (2007)

Parametric Rietveld refinement of Rb[MnCr(CN)6].xH2O. Observed data in are red, calculated in blue. Data have been offset in 2θ and intensity for clarity. The difference surface is plotted in pink.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2483475&req=5

fig4: Parametric Rietveld refinement of Rb[MnCr(CN)6].xH2O. Observed data in are red, calculated in blue. Data have been offset in 2θ and intensity for clarity. The difference surface is plotted in pink.
Mentions: In an initial round of parametric refinement, the Si cell parameter was expressed as a fixed quantity in terms of equation (3) and a 2θ correction polynomial and sample height offset refined from all 64 data sets simultaneously; parameters describing an overall pseudo-Voigt peak shape were also refined for each phase. In this process, a total of 1747 parameters were refined (19 overall parameters: 3 terms of a calibration polynomial, a height offset between sample and holder and 5 overall peak shape parameters per phase; 27 parameters per individual data set: 15 background terms, 2 scale factors, 2 cell parameters, an isotropic overall temperature factor for Si and the sample, 5 hkl peak intensities for the Al Pawley fit, and the sample height of the Al holder). Coefficients of the 2θ calibration polynomial were then fixed and parametric Rietveld refinement performed using a single parameter to describe the sample height offset and with the Si cell allowed to refine freely. An overall R wp of 9.05% was obtained with higher temperature refinements showing slightly worse agreement factors than for free refinements. Allowing Al peak shapes for each data set to refine independently led to an overall R wp = 8.925%, individual R wp values for each data set that varied smoothly with temperature, and smooth changes in peaks shape values; these minor variations are presumably caused by small changes in sample height with temperature. The parametric R factor is essentially the same as the average of those obtained by independent refinements. Fig. 4 ▶ shows the equivalent of a standard Rietveld plot for the parametric refinement.

Bottom Line: In this paper the method of parametric Rietveld refinement is described, in which an ensemble of diffraction data collected as a function of time, temperature, pressure or any other variable are fitted to a single evolving structural model.Parametric refinement offers a number of potential benefits over independent or sequential analysis.It can lead to higher precision of refined parameters, offers the possibility of applying physically realistic models during data analysis, allows the refinement of 'non-crystallographic' quantities such as temperature or rate constants directly from diffraction data, and can help avoid false minima.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Chemistry, University of Durham, UK.

ABSTRACT
In this paper the method of parametric Rietveld refinement is described, in which an ensemble of diffraction data collected as a function of time, temperature, pressure or any other variable are fitted to a single evolving structural model. Parametric refinement offers a number of potential benefits over independent or sequential analysis. It can lead to higher precision of refined parameters, offers the possibility of applying physically realistic models during data analysis, allows the refinement of 'non-crystallographic' quantities such as temperature or rate constants directly from diffraction data, and can help avoid false minima.

No MeSH data available.