This work presents a new method of synthesizing the reflection profile, based on the calculation of Fourier coefficients of instrumental functions. The classification and construction of Fourier coefficients are effected, in a general way, from the analysis of the possible paths of beams in the diffractometer. Relationships were obtained which made it possible to synthesize the line profiles in different experimental conditions. The possibility of calculating the reflection profiles of a standard (annealed BaF2) without introducing varying profile parameters is shown. Better results in describing the reflection profiles have been obtained than by applying the Pearson VII function with varying profile parameters.
Small-angle X-ray scattering (SAXS) is a well-established, versatile technique for the analysis of nanoscale structures and dimensions, e.g., in liquid dispersions, thin solid objects or powder samples. When combined with wide-angle X-ray scattering (WAXS), complementary information about the atomic structure can be obtained. SAXS experiments traditionally require dedicated instruments to achieve the desired angular resolution, sensitivity, stability, and speed of measurement. Here we demonstrate how a multi-functional laboratory goniometer platform, as widely being used for powder X-ray diffraction and for a variety of related techniques, can be configured with pre-aligned X-ray modules that enable advanced SAXS/WAXS experiments, without compromising the exceptional versatility of the instrument. Line and point collimation setups, as well as quick and easy switching between them, are readily possible. Key components are a detachable, evacuated beam path and a high-resolution, low-noise hybrid pixel area detector, in combination with a hardware interface design that allows to configure the instrument with different X-ray modules without the need for re-alignment. Software for SAXS data reduction and analysis was developed. The good SAXS/WAXS performance and the derived analytical results were verified on various test samples, such as gold nanoparticles, colloidal silica, liposomes, dilute protein solutions, and solid polymer samples. It is believed that this novel approach to SAXS/WAXS instrumentation will help to make this powerful structure analysis technique more widely accessible and affordable for multi-user laboratories.
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