We present a simple analytical formalism based on the Lorentz-Scherrer equation and Bernoulli statistics for estimating the fraction of crystallites (and the associated uncertainty parameters) contributing to all finite Bragg peaks of a typical powder pattern obtained from a static polycrystalline sample. We test and validate this formalism using numerical simulations, and show that they can be applied to experiments using monochromatic or polychromatic (pink-beam) radiation. Our results show that enhancing the sampling efficiency of a given powder diffraction experiment for such samples requires optimizing the sum of the multiplicities of reflections included in the pattern along with the wavelength used in acquiring the pattern. Utilizing these equations in planning powder diffraction experiments for sampling efficiency is also discussed.
DOCUMENT
Vibrational and structural properties of lead-free piezoelectric (1-x)Na0.5Bi0.5TiO3–xCaTiO3 (0 < x < 1.00) solid solutions have been investigated using Raman spectroscopy and X-ray diffraction. Different anomalies were detected and analyzed taking into consideration the phase transition from rhombohedral to orthorhombic phase at room temperature. All Raman bands were interpreted through the variation in the peak positions (frequency) and the corresponding half-widths at half maximum (HWHM) as a function of x. XRD used as a complementary technique to Raman spectroscopy, showed that the rhombohedral – orthorhombic phase transition went gradually through an intermediate phase consisting of a mixture of rhombohedral (R3c) and orthorhombic (Pnma) structures and that the fraction of orthorhombic phase increased with CT composition. The results show that the morphotropic phase boundary (MPB) is located between 0.09 and 0.15.
DOCUMENT
Light scattering is a fundamental property that can be exploited to create essential devices such as particle analysers. The most common particle size analyser relies on measuring the angle-dependent diffracted light from a sample illuminated by a laser beam. Compared to other non-light-based counterparts, such a laser diffraction scheme offers precision, but it does so at the expense of size, complexity and cost. In this paper, we introduce the concept of a new particle size analyser in a collimated beam configuration using a consumer electronic camera and machine learning. The key novelty is a small form factor angular spatial filter that allows for the collection of light scattered by the particles up to predefined discrete angles. The filter is combined with a light-emitting diode and a complementary metal-oxide-semiconductor image sensor array to acquire angularly resolved scattering images. From these images, a machine learning model predicts the volume median diameter of the particles. To validate the proposed device, glass beads with diameters ranging from 13 to 125 µm were measured in suspension at several concentrations. We were able to correct for multiple scattering effects and predict the particle size with mean absolute percentage errors of 5.09% and 2.5% for the cases without and with concentration as an input parameter, respectively. When only spherical particles were analysed, the former error was significantly reduced (0.72%). Given that it is compact (on the order of ten cm) and built with low-cost consumer electronics, the newly designed particle size analyser has significant potential for use outside a standard laboratory, for example, in online and in-line industrial process monitoring.
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