Institute of Experimental Physics, Slovak Academy of Science, Watsonova 45, 04001 Košice, Slovakia
The systematic study of reciprocal space resolution of two-dimensional X-ray diffraction (2D XRD) setup implemented at the P21.2 beamline is presented. Beam size, sample thickness and sample-to-detector distance were identified as key parameters, mostly affecting reciprocal space resolution. Few series of 2D XRD patterns were taken on powder LaB6 standard sample with a monochromatic photon beam having energy of 81.84 keV. Beamsize (square profile) was set to four distinct sizes 0.1, 0.3, 0.5 and 1.0 mm. Sample thickness was set to 0.4, 1.0, 1.5 and 2.0 mm. Sample-to-detector distance was changed from 460 to 1800 mm. Scattered photons were acquired by 2D detector VAREX XRD4343CT (2880 x 2800 pixels, pixel size 150 μm x 150 μm, 16 bit intensity resolution). Altogether 144 patterns were acquired and used in analysis. Each 2D XRD pattern was azimuthally integrated, and its peak profiles were analyzed with pseudo-Voigt function. Instrument resolution function, i.e. variation of the peak full-width at half-maximum with Bragg angle 2θ was investigated as a function of the beam size, sample thickness and sample-to-detector distance.
The Instrument resolution function (IRF) in X ray Diffraction (XRD) describes how the instrument itself influences the shape and width of the diffraction peaks. This function is crucial because it determines the inherent limitations of the instrument in terms of resolving power, affecting the accuracy and precision of the XRD measurements. The IRF is affected by several experimental parameters such as i) X ray source characteristics (degree of monochromaticity, source shape and size), ii) beam optics and collimation (beam divergence), iii) sample geometry (sample size, shape, alignment and positioning), iv) detector parameters (pixel size, detector distance from the sample), v) instrument geometry (goniometer precision, slit widths). All these imperfections and limitations associated with the real experimental setup contribute to the broadening of the experimentally observed diffraction profiles Iobs(2θ). The P21.2 beamline at PETRA III [1] is a high-performance beamline designed for a variety of advanced scientific experiments, particularly in the fields of material science, chemistry, and biology. Accurate determination of the instrument resolution function (IRF) is crucial for interpreting experimental data correctly. This study aims to characterize the IRF of the P21.2 beamline, providing insights into its performance and potential applications.
To determine the IRF, we conducted a series of measurements using a combination of standard calibration LaB6 sample [2] and advanced detection techniques. The methodology involved: 1) Performing a set of calibration measurements with the LaB6 reference material using an experimental setup with a 2D detector on the P21.2 instrument of the PETRA III synchrotron source at DESY Hamburg. Calibration measurements were done with symmetrically varying parameters such as sample thickness, the photon beam cross section and the distance between the sample and 2D detector. 2) Analysis of acquired 2D diffraction patterns to characterize the angular resolution of the P21.2 instrument depending on the changing parameters. 3) Proposed a theoretical model based on the kinetic theory of diffraction and verification of its agreements with experimental data using a Monte Carlo simulation.
The IRF curves shifted towards lower values with increasing SDD, independent of the sample thickness and beam size. For a given beam size and SDD, there is almost no variation of the IRF with the sample thickness. For a given sample thickness and SDD, the IRF shifts towards lower values with decreasing beam size. With decreasing beam size and sample thickness, the noise level in the IRF increases due to lower photon statistics and smaller scattering volume. Subsequently a simple theoretical model describing the single point scattering process based on kinematic theory of diffraction was proposed. Monte Carlo simulations of this model showed very good agreement with the experimental data. In spite the proposed model did not consider all the parameters that determine the angular resolution of the P21.2 instrument (e.g. divergence of the photon beam), the achieved agreement with the experimental results confirms the correctness of the assumptions of our mode.