Accurate determination of X-ray energies using powder diffraction

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Abstract

We report synchrotron energy determinations using the powder diffraction patterns of Si (640b) and LaB6 (660) standard reference powders at a number of energies between 5 and 20 keV. The fitted peak positions of all peaks recorded on image plates were used in each energy determination. Several sources of systematic error were investigated and their connection led to physically reasonable and consistent fitting parameters. The energies were determined to better than 0.025% at all energies. Our procedure shows that the use of the accurately known lattice parameters of standard materials makes it possible to determine X-ray energies without involving the full panoply of the Rietveld technique (which involves the crystal structure, crystal perfection, particle size, preferred orientation and other parameters affecting the full powder diffraction pattern).

Introduction

Synchrotron radiation sources provide a continuum of X-ray energies. The ability to monochromate the beam to a particular energy with a very narrow energy width has greatly broadened the field of X-ray spectroscopy. Powder diffraction is a widely used technique at synchrotrons and is often used to determine energy. While single crystals often have narrower diffraction peaks and a more accurate final determination of the X-ray energy under ideal conditions, powder diffraction techniques can quickly measure the full powder pattern. Determining energy from the entire powder pattern, rather than from selected peaks, provides information about key systematic errors. By using all of the peaks and using the entire energy range, the different errors can be readily separated.

Powder patterns of the Si (SRM640b) and LaB6 (SRM660) standard powders (unsorted as to particle size) were recorded using image plates at 23 energies between 5 and 20 keV. The 640 and 660 series are the most accurate powder standards available: a0=5.430940(11)Å for silicon 640b (Parrish et al., 1999) and a0=4.15695(6)Å for lanthanum hexaboride 660 (Rasberry et al., 1989). The diffraction pattern was recorded in 8 mm wide strips on six X-ray image plates mounted in Big Diff, a large cylindrical diffraction chamber with the Debye–Scherrer geometry (Barnea et al., 1992). The glass capillary tubes filled with the powders were spun to average over crystal orientations. Radioactive fiducials on the perimeter of the diffraction chamber gave a calibrated signature for the plate locations.

The energies were used as part of the X-ray extended range technique to measure the mass attenuation coefficient of pure elemental samples of silver, copper and gold (Chantler et al., 2001, Chantler et al., 2003).

Section snippets

Analysis of the diffraction pattern

Diffraction peaks were fitted with a nonlinear least squares fit of a lorentzian convolved with a slit on a quadratic background. Peak centroids were determined to a precision between 0.001 and 0.0001. Reduced χr2 values varied from 1 to 10 for a typical energy, owing to background noise and structure, and occasionally due to the effect of nearby peaks.

Analysis has been automated, so that all peaks were indexed and fitted for energy. In past studies (Chantler et al., 2004), peaks have often

Conclusion

By matching the powder diffraction spectrum using fitted peak centroids, the energy of the synchrotron X-ray beam was successfully determined to high precision. The accuracy of the determination was increased by fitting all of the diffraction peaks consistently, in a robust and automated procedure. Systematic errors were investigated using the powder patterns obtained at the various energies. Fitted parameters were found to have consistent, physically meaningful values in all the energy

Acknowledgements

The authors acknowledge the experimental team and the local ANBF staff, particularly James Hester, as well as funding from the ASRP and ARC.

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