![]() ![]() Therefore, with the (2 + 3) setup at the I07 beamline (Nicklin et al., 2016 ), it is necessary to integrate the two-dimensional data collected by the area detector into a one-dimensional pattern. Such refinement is usually performed on PXRD patterns where the intensity is plotted as a function of 2 θ. A significant step forward in the analysis of PXRD data was the Rietveld method (Rietveld, 1966, 1967 Young, 1993 van Laar & Schenk, 2018 ). The phenomena involved in PXRD are well known and have been extensively studied in the past century. Furthermore, the relatively high resolution of the instrument (compared with bench-top diffractometers) enhances the study and the identification of multi-phase systems. The control over the grazing-incidence angle and thus over the X-ray penetration depth enables the study of layered materials and buried interfaces. ![]() This experimental setup is thus well suited for a wide range of sample types with an extended face, such as thin polycrystalline films on substrates. In this scenario, the major benefit of the (2 + 3) diffractometer is control over the orientation of the sample and of the detector (and thus of the scattering vector), which enables convenient investigations of specimen textures and preferred orientations. Although this setup was originally designed for single-crystal SXRD, it can also be used in PXRD and in grazing-incidence X-ray diffraction (GIXRD) by rotating the detector about the diffractometer center in longitudinal and equatorial 2 θ scans, across the Debye–Scherrer cones. ![]() The (2 + 3) diffractometer was presented by Vlieg (1997 ) and its combination with an area detector was explored by Schlepütz et al. In surface X-ray diffraction (SXRD), an experimental setup composed of a (2 + 3) diffractometer and an area detector is used at some beamlines. PXRD data quality improves significantly when synchrotron X-ray beams are employed, which provide a high photon flux, enhanced collimation, tunable energies and a superior angular resolution. Quantitative analyses of PXRD data enable access to information such as size, strain and stress of the crystallites, the number of different phases in multi-phase materials, and atomic and unit-cell parameters. It has proved to be a fundamental tool for phase identification and structure determination of materials. Since the early studies by Debye & Scherrer (1916 ), powder X-ray diffraction (PXRD) has become a well established characterization technique. Some of the limitations with respect to texture, refraction and instrumental resolution are also discussed, as is the kind of information that one can hope to obtain. This paper presents the angle calculations and correction factors required to calculate meaningful intensities for 2 θ scans with a (2 + 3)-type diffractometer and an area detector. Although the underlying physics is known, converting the data is time consuming and the appropriate corrections are dispersed across several publications, often not with powder diffraction in mind. There are, however, very few examples where the measured intensity is directly used, such as for profile/Rietveld refinement, as is common with other powder diffraction data. Such diffractometers typically scan in directions not possible on a conventional laboratory diffractometer, which gives enhanced control of the scattering vector relative to the sample orientation. Unlike in high-energy powder diffraction, only a fraction of the powder rings is typically measured, and the data consist of many detector images across the 2 θ range. X-ray diffractometers primarily designed for surface X-ray diffraction are often used to measure the diffraction from powders, textured materials and fiber-texture samples in 2 θ scans. ![]()
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