A fast X-ray-diffraction-based method for the determination of crystal size distributions (FXD-CSD)

Abstract

A procedure for a fast X-ray-diffraction-based crystal size distribution analysis, named FXD-CSD, is presented. The method enables the user, with minimal sample preparation, to determine the crystal size distribution (CSD) of crystalline powders or polycrystalline materials, derivedviaan intensity scaling procedure from the diffraction intensities of single Bragg spots measured in spotty diffraction patterns with a two-dimensional detector. The method can be implemented on any single-crystal laboratory diffractometer and any synchrotron-based instrument with a fast-readout two-dimensional detector and a precise sample scanning axis. The intensity scaling is achievedviathe measurement of areferencesample with known CSD under identical conditions; the only other prerequisite is that the structure (factors) of bothsampleandreferencematerial must be known. The data analysis is done with a software package written in Python. A detailed account is given of each step of the procedure, including the measurement strategy and the demands on the spottiness of the diffraction rings, the data reduction and the intensity corrections needed, and the data evaluation and the requirements for the reference material. Using commercial laboratory X-ray equipment, several corundum crystal size fractions with precisely known CSD were measured and analysed to verify the accuracy and precision of the FXD-CSD method; a comparison of known and deduced CSDs shows good agreement both in mean size and in the shape of the size distribution. For the used material and diffractometer setup, the crystal size application range is one to several tens of micrometres; this range is highly material and X-ray source dependent and can easily be extended on synchrotron sources to cover the range from below 0.5 µm to over 100 µm. FXD-CSD has the potential to become a generally applicable method for CSD determination in the field of materials science and pharmaceutics, including development and quality management, as well as in various areas of fundamental research in physics, chemistry, chemical engineering, crystallography, the geological sciences and bio-crystallization. It can be used also underin situconditions for studying crystal coarsening phenomena, and delivers precise and accurate CSDs, permitting experimental tests of various theories developed to predict their evolution.