Photon Factory Activity Report 2004 #22 Part B (2005)
Instrumentation and Technique

4B2/2003G029

Symmetrisation of synchrotron X-ray powder diffraction peak profiles
Takashi IDA*, Hisashi HIBINO
Ceramics Research Laboratory, Nagoya Institute of Technology, Asahigaoka, Tajimi, Gifu 507-0071,
Japan
Introduction
We have previously reported the mathematicalexpressions of the axial divergence aberration for thepowder X-ray diffractometer on the beam-line BL-4B2 at
the Photon Factory [1]. We have also suggested that
instrumental peak shift, line broadening and deformationin peak shape can be removed by our originally developed
deconvolution procedure applying non-linear abscissa
mapping method [2].
However, there were somedifficulties in application of the method to the datameasured with the multiple-detector diffractometer on
BL-4B2, because (i) profile of strong peaks are affected bylosses in counting devices, (ii) instrumental functions may
be varied between different detectors, and (iii) the axial
divergence aberration function has a singularity at a
certain diffraction angle. Recently, we have developed anadvanced method for correction of counting losses [3] andalso a Fourier connection method automatically adjusting
difference between segmented intensity data supplied by
the multiple-detector systems [4]. In this study, we havedeveloped a practical algorithm to avoid numericalinstability at the singularity point, and automatically
restore the observed profiles to be symmetric. The
method is applied to the powder diffraction intensity datafrom standard ZnO powder (NIST SRM674).
MethodTreatment of singularity in instrumental function
Axial divergence aberration function for highresolution powder diffractometer with the analyser Bragg
angle of ΘA has singularity at the diffraction angle of 2θ =2ΘA+π/2, where the function coincides with the Diracdelta function [1]. The centre 2θ region near thesingularity where the width of the aberration function issmaller than one-tenth of the sampling interval (0.005º)
was separated and kept unchanged. The rest of data on
both sides of the centre region were treated by thedeconvolution, and merged to the center data. The
segmentation, deconvolution and combination process
could be completed automatically with a simple algorithm.

Experimental and analysis
ZnO powder was filled into a 0.5 mmφ glass capillary
and the diffraction intensity data were collected by amultiple-arm measurement at the wavelength of 0.13 nm.
The diffraction data were treated by a whole-patterndeconvolution method and it has been confirmed that all

the diffraction peak profiles have become symmetric. The
integrated intensities of the symmetrised peak profiles
were extracted by a simple individual profile fitting
method applying symmetric peak profile functions. The
crystal structure of ZnO was refined by a conventional
least-squares method for integrated peak intensities. The
Rietveld method or whole-pattern fitting methods were
not used for the structure refinement.
Results
Structure refinement
The refined structure parameters are listed in table 1.
The structure parameters determined by the current
method are in good agreement within experimental errors
with the data refined from single-crystal diffraction data.
Table 1: Refined structure parameters
This
Abrahams
Albertson
Work(1969) [5](1989) [6]singlesinglepowder/Specimen/
crystal/crystal/synchrotron
beamlaboratory
neutronX-raysource
X-ray
No. of42
141394reflectionsa (Å)
3.24987(18)3.24990(4)c (Å)
5.20650(3)5.220660(6)0.3819(1)0.3825(14)0. 3827(8)z(O)
0.0080(3)U(Zn)
0. 0086(9)U(O)
0. 0073(4)0. 0079(2)U11(Zn)0.0094(4)0. 0080(4)U33(Zn)0.0056(4)0.0065(11)U11(O)
0.0064(4)0.0095(21)U33(O)
R(%)
0.85
3.78
2.31

References[1] T. Ida et al., J. Appl. Cryst. 34, 144 (2001).
[2] T. Ida & H. Toraya, J. Appl. Cryst. 36, 181 (2003).
[3] T. Ida & H. Iwata, J. Appl. Cryst. 38, 46 (2005).
[4] T. Ida, submitted to J. Appl. Cryst.
[5] S. C. Abrahams et al. Acta Cryst. B 25, 1233 (1969).
[6] J. Albertsson et al. Acta Cryst B 45, 34 (1989)* ida.takashi@nitech.ac.jp

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