A new model for the description of X-ray diffraction from mosaic crystals for ray-tracing calculations

Abstract

This paper presents the development of a new reflection model for describing X-ray diffraction from mosaic crystals. In contrast to the well established diffraction model of Zachariasen [Zachariasen (1994), Theory of X-ray Diffraction in Crystals. Mineola: Dover Publications], it gives additional information on the spatial reflection behaviour and not just on the depthintegrated reflectivity of the crystal material. The new reflection model enables a concrete description of mosaic crystal performance in an arbitrary X-ray spectrometer configuration. Multiple reflections inside the crystal are described by splitting the calculation into a discrete number of reflections. Hence, the influence of each number of reflections is investigated, leading to a laterally resolved solution for the reflectivity. In addition, the model can use a mosaicity of arbitrary shape. This is important because the present work uses a Lorentzian-shaped mosaicity instead of a Gaussian one, which is usually the case in the most widely used simulation programs. A comparison between the new model and that of Zachariasen is performed, and it predicts a similar integrated reflectivity with a deviation lower than 0.7%. Further, a ray-tracing simulation with multiple reflections based on the new model is compared with a measurement, showing a deviation of lower than 5%.

Experimental determination of line energies, line widths and relative transition probabilities of the Gadolinium L x-ray emission spectrum

“…The Bragg crystal is a 40 µm thick highly annealed pyrolytic graphite (HAPG) sheet mounted on a full-cylinder Zerodur substrate. HAPG has been subject to detailed characterizations with respect to its use as dispersive elements [18] as well as its diffraction properties [19]. HAPG is a modified material similar to highly oriented pyrolytic graphite which has been proven to be a promising material for x-ray optics [20][21][22][23].…”

A laboratory spectrometer for high throughput X-ray emission spectroscopy in catalysis research

“…4 together with the result of an experimental determination, which followed the procedure described by Anklamm. 14,16 The spectral broadening of this spectrometer is dominated by the intrinsic broadening of the crystal. Thus, the spectral resolving power is close to the maximum achievable.…”

“…25 While the values of mosaicity and reflectivity agree across published experimental results, measured values for the Darwin width are sparse and considerably scatter. 23 We use the value given by Ice and Sparks 15 because it produced the best match of estimates of the spectral resolution and of simulations 16 in comparison with measurements. The manufacturers recommend to use 3.354 Å as a value for the interlayer distance.…”

“…We checked these equations by comparing to more elaborate simulations 16 and experiments. For high resolution optics, where the contribution of the Darwin broadening dominates, they provide good estimates for the spectral resolution.…”

Recent progress in the performance of HAPG based laboratory EXAFS and XANES spectrometers

“…Our in-house soware allows for the prediction of the performance of such HAPG-optics with good accuracy and thus for the optimization of their design. 18 In this paper, new optics tailored for EXAFS and XANES experiments are presented, respectively. The XANES optic is optimized for maximum spectral resolving power.…”