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A mathematical framework is presented to represent turbostratic disorder in materials like carbon blacks, smectites and twisted n‐layer graphene. In particular, the set of all possible disordered layers, including rotated, shifted and curved layers, forms a stochastic sequence governed by a hidden Markov model. The probability distribution over the set of layer types is treated as an element of a Hilbert space and, using the tools of Fourier analysis and functional analysis, expressions are developed for the scattering cross sections of a broad class of disordered materials. [ABSTRACT FROM AUTHOR]

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, derived via an 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 achieved via the measurement of a reference sample with known CSD under identical conditions; the only other prerequisite is that the structure (factors) of both sample and reference material 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 under in situ conditions for studying crystal coarsening phenomena, and delivers precise and accurate CSDs, permitting experimental tests of various theories developed to predict their evolution. [ABSTRACT FROM AUTHOR]

A novel X-ray diffraction based method is presented, capable of determining volume-based crystal size distribution ( CSD) of polycrystalline materials and crystalline powders with unprecedented sampling statistics; the method is named fast X-ray diffraction crystal size distribution analysis ( FXD- CSD). FXD- CSD can be performed with standard laboratory X-ray diffractometers equipped with a position sensitive detector and uses a software package written in Python for the data analysis. FXD- CSD is a destruction-free and generally applicable method to establish CSDs of polycrystalline materials as well as powders for sizes well below 1 μm up to about 100 μm; it even allows for studies of samples enclosed in complex environments, e.g., for in situ measurements in a furnace or in a pressure cell. To show the capability of the method the microstructural evolution of four alumina substrates with different time-spans of sintering (4, 8, 16, and 24 hour at 1600°C) is investigated via FXD- CSD and SEM imaging. The corresponding CSDs and average grain sizes are determined, results obtained by FXD- CSD and the line-intersection methods are compared and clear evidence for the presence of abnormal grain growth ( AGG) during sintering is shown. From three tested probability density functions ( PDF) describing the CSDs a log-normal PDF fits best to the volume based CSDs; the method provides size distributions with unprecedented precision opening the way to a systematic and meaningful comparison between theoretically predicted and observed CSDs. [ABSTRACT FROM AUTHOR]

Bragg intensities can be used to analyse crystal size distributions in a method called FXD‐CSD, which is based on the fast measurement of many Bragg spots using two‐dimensional detectors. This work presents the Python‐based software and its graphical user interface FXD‐CSD‐GUI. The GUI enables user‐friendly data handling and processing and provides both graphical and numerical crystal size distribution results. [ABSTRACT FROM AUTHOR]

A calibration protocol to quantify the compositional information of gas hydrates using Raman spectroscopy is proposed. Structure I pure CH4-, CO2- and C2H6-hydrates in their deuterated and hydrogenated forms with known cage occupancies were investigated by Raman spectroscopy. Raman scattering cross sections of CH4 in the large and small cages were found to be very similar, but not identical. Some C2H6 bands of C2H6-hydrate were tentatively reassigned or newly reported and assigned. Our results show that the relative cross sections of guest vibrational modes in the deuterated hydrate are in agreement with those in the hydrogenated hydrate, whereas they are considerably different from those in fluid phase. Using our Raman quantification factors, the relative cage occupancies can now be determined more reliably in CH4-hydrates. Moreover, with additional assumptions, the absolute cage occupancies, the bulk guest composition and hydration number of pure or mixed gas hydrates become accessible by Raman spectroscopy. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2155-2167, 2013 [ABSTRACT FROM AUTHOR]