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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.


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Temperature dependence of (a) Si cell parameter [open diamonds derived from experimental dilatometry data; solid line from equation (3)] and (b) Al2O3 cell parameters (solid lines) used in this work. (c) The difference in thermal expansion, here plotted as V(T)/V(293.15 K), allows a direct measure of temperature.
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fig2: Temperature dependence of (a) Si cell parameter [open diamonds derived from experimental dilatometry data; solid line from equation (3)] and (b) Al2O3 cell parameters (solid lines) used in this work. (c) The difference in thermal expansion, here plotted as V(T)/V(293.15 K), allows a direct measure of temperature.

Mentions: In the case of Al2O3, thermal expansion data have been collated by Toulakien and by Taylor (Taylor, 1984 ▶; Toulakian et al., 1977 ▶). We have chosen to take Taylor’s expression for the temperature dependence of cell parameters [equation (4)]. The x 0 values quoted differ from those of Taylor but yield cell parameters at 295 K consistent with those reported by Cline for NIST SRM676 (NIST, 1991 ▶). Note that Taylor’s expression uses temperature in °C not K: For non-ambient work, if the thermal expansion of the internal standard were precisely known, it could be used to calibrate experimental temperature (see below). This process can, however, be prone to significant errors since a small systematic error in cell parameter can lead to a large error in temperature determination. For this reason, we prefer to employ two internal standards at high temperature; one with low expansion (e.g. Si) and one with high (e.g. Al2O3). Since systematic errors in cell determination of each standard will be similar, one can use the differential thermal expansion to determine temperature (Fig. 2 ▶ c); the ratio of cell volumes, or difference in the two curves of Fig. 2 ▶(c), providing a direct measure of temperature.


Parametric Rietveld refinement.

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

Temperature dependence of (a) Si cell parameter [open diamonds derived from experimental dilatometry data; solid line from equation (3)] and (b) Al2O3 cell parameters (solid lines) used in this work. (c) The difference in thermal expansion, here plotted as V(T)/V(293.15 K), allows a direct measure of temperature.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig2: Temperature dependence of (a) Si cell parameter [open diamonds derived from experimental dilatometry data; solid line from equation (3)] and (b) Al2O3 cell parameters (solid lines) used in this work. (c) The difference in thermal expansion, here plotted as V(T)/V(293.15 K), allows a direct measure of temperature.
Mentions: In the case of Al2O3, thermal expansion data have been collated by Toulakien and by Taylor (Taylor, 1984 ▶; Toulakian et al., 1977 ▶). We have chosen to take Taylor’s expression for the temperature dependence of cell parameters [equation (4)]. The x 0 values quoted differ from those of Taylor but yield cell parameters at 295 K consistent with those reported by Cline for NIST SRM676 (NIST, 1991 ▶). Note that Taylor’s expression uses temperature in °C not K: For non-ambient work, if the thermal expansion of the internal standard were precisely known, it could be used to calibrate experimental temperature (see below). This process can, however, be prone to significant errors since a small systematic error in cell parameter can lead to a large error in temperature determination. For this reason, we prefer to employ two internal standards at high temperature; one with low expansion (e.g. Si) and one with high (e.g. Al2O3). Since systematic errors in cell determination of each standard will be similar, one can use the differential thermal expansion to determine temperature (Fig. 2 ▶ c); the ratio of cell volumes, or difference in the two curves of Fig. 2 ▶(c), providing a direct measure of temperature.

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.


Related in: MedlinePlus