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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.


(a) The Si cell parameter from independent refinement of data sets and (b) from parametric fitting. In each case the solid line represents equation (3). (c) A histogram of the offset between refined and ideal Si cell parameters. (d) Superposition of the sample cell parameter obtained by the two methods. In each graph, open symbols represent independent fitting, and closed symbols represent parametric fitting. For ease of comparison, both individual and parametric fitting refinement values used the 2θ correction polynomial derived from parametric fitting.
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fig5: (a) The Si cell parameter from independent refinement of data sets and (b) from parametric fitting. In each case the solid line represents equation (3). (c) A histogram of the offset between refined and ideal Si cell parameters. (d) Superposition of the sample cell parameter obtained by the two methods. In each graph, open symbols represent independent fitting, and closed symbols represent parametric fitting. For ease of comparison, both individual and parametric fitting refinement values used the 2θ correction polynomial derived from parametric fitting.

Mentions: Fig. 5 ▶ shows the Si and sample cell parameters obtained by this protocol compared with free refinements. While the overall trends in behaviour are comparable, the scatter on data points from parametric fitting is considerably lower than from independent refinements. Average standard uncertainties on Si cell parameters are 0.00028 Å from individual refinements and 0.00017 Å from parametric fitting; for the sample values are 0.0008 Å and 0.0003 Å, respectively. The significantly narrower spread of values is also shown in Fig. 5 ▶(c), which shows deviations of refined values from those of equation (3) for the two refinements.


Parametric Rietveld refinement.

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

(a) The Si cell parameter from independent refinement of data sets and (b) from parametric fitting. In each case the solid line represents equation (3). (c) A histogram of the offset between refined and ideal Si cell parameters. (d) Superposition of the sample cell parameter obtained by the two methods. In each graph, open symbols represent independent fitting, and closed symbols represent parametric fitting. For ease of comparison, both individual and parametric fitting refinement values used the 2θ correction polynomial derived from parametric fitting.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig5: (a) The Si cell parameter from independent refinement of data sets and (b) from parametric fitting. In each case the solid line represents equation (3). (c) A histogram of the offset between refined and ideal Si cell parameters. (d) Superposition of the sample cell parameter obtained by the two methods. In each graph, open symbols represent independent fitting, and closed symbols represent parametric fitting. For ease of comparison, both individual and parametric fitting refinement values used the 2θ correction polynomial derived from parametric fitting.
Mentions: Fig. 5 ▶ shows the Si and sample cell parameters obtained by this protocol compared with free refinements. While the overall trends in behaviour are comparable, the scatter on data points from parametric fitting is considerably lower than from independent refinements. Average standard uncertainties on Si cell parameters are 0.00028 Å from individual refinements and 0.00017 Å from parametric fitting; for the sample values are 0.0008 Å and 0.0003 Å, respectively. The significantly narrower spread of values is also shown in Fig. 5 ▶(c), which shows deviations of refined values from those of equation (3) for the two refinements.

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.