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Powder diffraction in Bragg-Brentano geometry with straight linear detectors.

Kriegner D, Matěj Z, Kužel R, Holý V - J Appl Crystallogr (2015)

Bottom Line: An easy approach to limit the resolution-degrading effects is presented.The presented algorithm selects an adaptive range of channels of the linear detector at low angles, resulting in increased resolution.Using this algorithm a well behaved resolution function is obtained in the full angular range, whereas using the full linear detector the resolution function varies within one pattern, which hinders line-shape and Rietveld analysis.

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Affiliation: Department of Condensed Matter Physics, Charles University in Prague, Ke Karlovu 5, 121 16 Prague 2, Czech Republic.

ABSTRACT

A common way of speeding up powder diffraction measurements is the use of one- or two-dimensional detectors. This usually goes hand in hand with worse resolution and asymmetric peak profiles. In this work the influence of a straight linear detector on the resolution function in the Bragg-Brentano focusing geometry is discussed. Because of the straight nature of most modern detectors geometrical defocusing occurs, which heavily influences the line shape of diffraction lines at low angles. An easy approach to limit the resolution-degrading effects is presented. The presented algorithm selects an adaptive range of channels of the linear detector at low angles, resulting in increased resolution. At higher angles the whole linear detector is used and the data collection remains fast. Using this algorithm a well behaved resolution function is obtained in the full angular range, whereas using the full linear detector the resolution function varies within one pattern, which hinders line-shape and Rietveld analysis.

No MeSH data available.


Related in: MedlinePlus

Defocusing length  and blurring B versus goniometer angle θ and distance from the detector centre d. (a) shows the angular dependence of the defocusing length for several positions on the detector. (b) shows the variation of  on the detector for fixed goniometer position. The inset shows a zoom to the high-angle curve. (c) shows the angular dependence of the blurring, while (d) shows the variation of B along the detector for certain fixed angles. (c) and (d) are shown for variable slits (full lines) and fixed slits (dashed lines). The parameters used for the calculations are  mm, ° and  for the fixed-slit case and  mm in the case of variable slits.
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fig2: Defocusing length and blurring B versus goniometer angle θ and distance from the detector centre d. (a) shows the angular dependence of the defocusing length for several positions on the detector. (b) shows the variation of on the detector for fixed goniometer position. The inset shows a zoom to the high-angle curve. (c) shows the angular dependence of the blurring, while (d) shows the variation of B along the detector for certain fixed angles. (c) and (d) are shown for variable slits (full lines) and fixed slits (dashed lines). The parameters used for the calculations are  mm, ° and for the fixed-slit case and  mm in the case of variable slits.

Mentions: In order to obtain a proper line shape for the full angular range, we consider how the defocusing length ( in Fig. 1 ▶a) changes with the goniometer angle θ and varies for different positions on the detector. From geometrical considerations it follows that the defocusing is We further define the more relevant blurring width B, which specifies the width into which the scattered signal is blurred on the detector (Fig. 1 ▶a). B depends not only on the detector distance but also on the irradiated sample length S. For an irradiated sample length S small enough in comparison with the detector distance () one obtains This means that the blurring is different in the case of fixed or variable slits, which results in either variable or constant S, respectively. If one works with fixed slits, resulting in a change of the irradiated sample length with the goniometer angle, one has to consider that S depends on θ as Here we use the beam footprint on the sample as approximated in the work by Słowik & Zięba (2001 ▶), which uses the primary beam divergence α (indicated in Fig. 1 ▶a). The size of the sample is used to limit the maximum illuminated length at low angles. Fig. 2 ▶ shows how the defocusing length and the blurring vary with the goniometer angle and position on the detector. The defocusing length rapidly increases at low goniometer angles as expected and changes approximately linearly for different positions on the detector as suggested by equation (3). The blurring, however, has a more elaborate dependence on the goniometer angle in the case of a variable-slit system (full lines in Figs. 2 ▶c and 2 ▶d). For the upper part of the detector it decreases at low angles owing to the small projected size of the sample, while it diverges for the lower parts of the detector. This divergence is due to the fact that parts of the detector reach below the sample horizon and therefore the defocusing length is ill defined. In the case of a fixed-slit system (dashed lines in Figs. 2 ▶c and 2 ▶d) the blurring has a similar angular dependence to the defocusing length.


Powder diffraction in Bragg-Brentano geometry with straight linear detectors.

Kriegner D, Matěj Z, Kužel R, Holý V - J Appl Crystallogr (2015)

Defocusing length  and blurring B versus goniometer angle θ and distance from the detector centre d. (a) shows the angular dependence of the defocusing length for several positions on the detector. (b) shows the variation of  on the detector for fixed goniometer position. The inset shows a zoom to the high-angle curve. (c) shows the angular dependence of the blurring, while (d) shows the variation of B along the detector for certain fixed angles. (c) and (d) are shown for variable slits (full lines) and fixed slits (dashed lines). The parameters used for the calculations are  mm, ° and  for the fixed-slit case and  mm in the case of variable slits.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4379442&req=5

fig2: Defocusing length and blurring B versus goniometer angle θ and distance from the detector centre d. (a) shows the angular dependence of the defocusing length for several positions on the detector. (b) shows the variation of on the detector for fixed goniometer position. The inset shows a zoom to the high-angle curve. (c) shows the angular dependence of the blurring, while (d) shows the variation of B along the detector for certain fixed angles. (c) and (d) are shown for variable slits (full lines) and fixed slits (dashed lines). The parameters used for the calculations are  mm, ° and for the fixed-slit case and  mm in the case of variable slits.
Mentions: In order to obtain a proper line shape for the full angular range, we consider how the defocusing length ( in Fig. 1 ▶a) changes with the goniometer angle θ and varies for different positions on the detector. From geometrical considerations it follows that the defocusing is We further define the more relevant blurring width B, which specifies the width into which the scattered signal is blurred on the detector (Fig. 1 ▶a). B depends not only on the detector distance but also on the irradiated sample length S. For an irradiated sample length S small enough in comparison with the detector distance () one obtains This means that the blurring is different in the case of fixed or variable slits, which results in either variable or constant S, respectively. If one works with fixed slits, resulting in a change of the irradiated sample length with the goniometer angle, one has to consider that S depends on θ as Here we use the beam footprint on the sample as approximated in the work by Słowik & Zięba (2001 ▶), which uses the primary beam divergence α (indicated in Fig. 1 ▶a). The size of the sample is used to limit the maximum illuminated length at low angles. Fig. 2 ▶ shows how the defocusing length and the blurring vary with the goniometer angle and position on the detector. The defocusing length rapidly increases at low goniometer angles as expected and changes approximately linearly for different positions on the detector as suggested by equation (3). The blurring, however, has a more elaborate dependence on the goniometer angle in the case of a variable-slit system (full lines in Figs. 2 ▶c and 2 ▶d). For the upper part of the detector it decreases at low angles owing to the small projected size of the sample, while it diverges for the lower parts of the detector. This divergence is due to the fact that parts of the detector reach below the sample horizon and therefore the defocusing length is ill defined. In the case of a fixed-slit system (dashed lines in Figs. 2 ▶c and 2 ▶d) the blurring has a similar angular dependence to the defocusing length.

Bottom Line: An easy approach to limit the resolution-degrading effects is presented.The presented algorithm selects an adaptive range of channels of the linear detector at low angles, resulting in increased resolution.Using this algorithm a well behaved resolution function is obtained in the full angular range, whereas using the full linear detector the resolution function varies within one pattern, which hinders line-shape and Rietveld analysis.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Condensed Matter Physics, Charles University in Prague, Ke Karlovu 5, 121 16 Prague 2, Czech Republic.

ABSTRACT

A common way of speeding up powder diffraction measurements is the use of one- or two-dimensional detectors. This usually goes hand in hand with worse resolution and asymmetric peak profiles. In this work the influence of a straight linear detector on the resolution function in the Bragg-Brentano focusing geometry is discussed. Because of the straight nature of most modern detectors geometrical defocusing occurs, which heavily influences the line shape of diffraction lines at low angles. An easy approach to limit the resolution-degrading effects is presented. The presented algorithm selects an adaptive range of channels of the linear detector at low angles, resulting in increased resolution. At higher angles the whole linear detector is used and the data collection remains fast. Using this algorithm a well behaved resolution function is obtained in the full angular range, whereas using the full linear detector the resolution function varies within one pattern, which hinders line-shape and Rietveld analysis.

No MeSH data available.


Related in: MedlinePlus