Method of calculating the coherent scattering power of crystals with unknown atomic arrangements and its application in the quantitative phase analysis

Quantitative phase analysis is one of the major applications of X-ray powder diffraction. The essential principle of quantitative phase analysis is that the diffraction intensity of a component phase in a mixture is proportional to its abundance. Nevertheless, the diffraction intensities of the component phases cannot be compared with each other directly since the coherent scattering power per unit cell (or chemical formula) of each component phase is usually different. The coherent scattering power per unit cell of a crystal is well represented by the sum of the squared structure factors, which cannot be calculated directly when the crystal structure data is unavailable. Presented here is a way to approximate the coherent scattering power per unit cell based solely on the unit cell parameters and the chemical contents. This approximation is useful when the atomic coordinates for one or more of the phases in a sample are unavailable. An assessment of the accuracy of the approximation is presented. This assessment indicates that the approximation will likely be within 10% when X-ray powder diffraction data is collected over a sufficient portion of the measurable pattern.

Psilocybin: crystal structure solutions enable phase analysis of prior art and recently patented examples

Psilocybin {systematic name: 3-[2-(dimethylamino)ethyl]-1H-indol-4-yl dihydrogen phosphate} is a zwitterionic tryptamine natural product found in numerous species of fungi known for their psychoactive properties. Following its structural elucidation and chemical synthesis in 1959, purified synthetic psilocybin has been evaluated in clinical trials and has shown promise in the treatment of various mental health disorders. In a recent process-scale crystallization investigation, three crystalline forms of psilocybin were repeatedly observed: Hydrate A, Polymorph A, and Polymorph B. The crystal structure for Hydrate A was solved previously by single-crystal X-ray diffraction. This article presents new crystal structure solutions for the two anhydrates, Polymorphs A and B, based on Rietveld refinement using laboratory and synchrotron X-ray diffraction data, and density functional theory (DFT) calculations. Utilizing the three solved structures, an investigation was conducted via Rietveld method (RM) based quantitative phase analysis (QPA) to estimate the contribution of the three different forms in powder X-ray diffraction (PXRD) patterns provided by different sources of bulk psilocybin produced between 1963 and 2021. Over the last 57 years, each of these samples quantitatively reflect one or more of the hydrate and anhydrate polymorphs. In addition to quantitatively evaluating the composition of each sample, this article evaluates correlations between the crystal forms present, corresponding process methods, sample age, and storage conditions. Furthermore, revision is recommended on characterizations in recently granted patents that include descriptions of crystalline psilocybin inappropriately reported as a single-phase `isostructural variant.' Rietveld refinement demonstrated that the claimed material was composed of approximately 81% Polymorph A and 19% Polymorph B, both of which have been identified in historical samples. In this article, we show conclusively that all published data can be explained in terms of three well-defined forms of psilocybin and that no additional forms are needed to explain the diffraction patterns.

Exploring the structural, optical and photoluminescent properties of (1-x)NiCo2O4/xPbS nanocomposites for optoelectronic applications

(1-x)NiCo2O4/xPbS (0≤x≤0.2) nanocomposite samples were synthesized using the hydrothermal and thermolysis procedures. The different phases developed in the obtained nanocomposite samples were accurately determined using the x-ray diffraction technique equipped with a line-detector. The percentage of the formed phases (NiCo2O4 (NCO), PbS, PbSO4), structural and microstructure parameters were determined using Rietveld quantitative phase analysis. The transmission electron microscope (TEM) images and Rietveld analysis reveal almost isotropic particle size in the nano range with a very narrow size distribution. The obtained phase percentages of PbS and PbSO4 are smaller than nominated values (x) suggesting dissolving of some Pb and S ions in NCO which then confirmed by the analysis of Fourier-transform infrared (FTIR) spectra of nanocomposite samples. The absorption spectra are modified upon doping NCO with PbS. The optical band gaps of the nanocomposites increase as the amount of PbS is increased. The effect of alloying on extinction coefficient, refractive index, dielectric constant, optical conductivity, the intensity, and emitted color from the photoluminescence of the nanocomposite samples are also studied. The refractive index values of NCO and NCO-PbS nanocomposite samples exhibit normal dispersions. The photoluminescent measurements reveal that NCO-PbS nanocomposites could emit a violet color. The improvement in the values of the non-linear optical (NLO) parameters of pristine NCO at high frequencies or the nanocomposite samples at low frequencies, nominated them to be used in NLO photonic applications.

Phosphorus Substitution Preference in Ye’elimite: Experiments and Density Functional Theory Simulations

Density functional theory (DFT) simulation has been recently introduced to understand the doping behavior of impurities in clinker phases. P-doped ye’elimite, a typical doping clinker phase, tends to form when phosphogypsum is used to manufacture calcium sulfoaluminate cement (CSA) clinkers. However, the substitution mechanism of P has not been uncovered yet. In this study, the influence of different doping amounts of P on the crystalline and electronic structure of ye’elimite was investigated using backscattered scanning electron microscopy–energy X-ray dispersive spectroscopy, X-ray diffraction tests, Rietveld quantitative phase analysis, and DFT simulations. Furthermore, the substitution preference of P in ye’elimite was revealed. Our results showed that increasing the doping amount of P increased the impurity contents in CSA clinkers, transforming the ye’elimite crystal system from the orthorhombic to the cubic system and decreasing the interplanar spacing of ye’elimite. Based on the calculation results of the defect formation energies, additional energies were required for P atoms to substitute Ca/Al atoms compared with those required for P atoms to substitute S atoms in both orthorhombic and cubic systems of ye’elimite. Combined calculation results of the bond length–bond order and partial density of states showed that the doped P atoms preferably substituted S atoms; the second possible substituted atoms were Al atoms, while there was only a slight possibility for substitution of Ca atoms. The substitution of P atoms for S atoms can be verified based on the elemental distribution in P-doped ye’elimite and the increasing residual CaSO4 contents. The transition of the crystal system and a decrease in the interplanar spacing for ye’elimite can also prove that the substitution of P atoms for Al atoms occurred substantially.

Synthesis and Formation Process of a Typical Doped Solid-Solution Ye’elimite (Ca3.8Na0.2Al5.6Fe0.2Si0.2SO16): Experiments and Kinetic Analysis

Ye’elimite is a dominant phase in calcium sulfoaluminate cement, which is a promising alternative type of cementitious binder. Ca3.8Na0.2Al5.6Fe0.2Si0.2SO16 (abbreviated as ss-C4A3$) is a kind of typical doped solid-solution ye’elimite. In this study, the formation process of ss-C4A3$ was investigated. Clinkers of ss-C4A3$ were sintered at various temperatures for different holding times. X-ray diffraction tests and Rietveld quantitative phase analysis were conducted to determine the phase compositions of the clinkers. Meanwhile, the formation process of ss-C4A3$ was analyzed by kinetic theory. The results show that solid reactions between intermediate phases (calcium aluminate phases) and anhydrite mainly resulted in the formation of ss-C4A3$. In the conditions of 1150–1250 °C, ss-C4A3$ tended to be formed and stable until 4 h. However, when the sintering temperature was 1300 °C, the ss-C4A3$ decreased to generate calcium aluminate phases after 2 h. Compared to other kinetic models, the three-dimensional diffusion model mostly conformed with the formation process of ss-C4A3$, and the fitting results obtained by the Jander model exhibited the highest correlation coefficients. The activation energy of ss-C4A3$ formation equaled 285.6 kJ/mol, which was smaller than that of stoichiometric ye’elimite.

The Features of X-Ray Phase Analysis of Rocks with Complex Mineral Composition

The article presents the results of identification and quantitative analysis of the phase composition, fine structure parameters of minerals in carbonate and terrigenous rocks by the use of modern X-ray diffraction (XRD) analysis. To make the XRD analysis, we optimized the modes of x-ray pattern shooting by changing the radius of the goniometer, the system of primary and secondary slits, Soller slits, and the system of detecting the low-content minerals. In processing the obtained x-ray patterns, we considered the size and defects of the crystal grains, the crystallographic mode of arrangements, atomic population of the crystal lattice, the Debye-Waller factor and the instrumental line broadening by the use of the Caliotti function for LaB6. So we determined the type and content of minerals, estimated the period of the crystal lattice, the size of the coherent scattering domains and micro-distortion crystal lattice of the mineral. We compared the obtained data on the presence and quantitative content of minerals with the data of X-ray fluorescence (XRF) analysis and scanning electron microscopy (SEM). Based on the obtained data, reference intensity ratio (RIR) coefficients were selected for a number of minerals typically contained in core materials for quantitative phase analysis by the use of the corundum number method.

Quantitative phase analysis of Bi2Sr2CaCu2O8+x and competing intergrowth and co-crystallizing phases via a Rietveld refinement study

The Rietveld refinement technique has been used to determine the extent of intergrowth of the Bi2Sr2CuO6+x phase and co-crystallization of competing phases in the high-temperature superconductor Bi2Sr2CaCu2O8+x (Bi-2212). The refinement was done on powder diffractograms obtained on powders made by grinding single crystals of Bi2Sr2CaCu2O8+x grown using two different self-flux techniques, namely the pressure technique and the regrowth technique, and ground for either 2 min or 2 h. The Rietveld programs JANA and FULLPROF were used for the refinement and both gave consistent results. The Bi and Sr atom positions were refined in the average structure of centrosymmetric space group Bbmb. To incorporate Bi-atom modulation and extract information about the modulation vector, refinement was done in the centrosymmetric space group N^{Bbmb}_{1\overline 11}(Bbmb(0γ1)). The b* component of the modulation vector decreases with a decrease in the superconducting transition temperature in the pressure-technique sample compared with the regrowth sample, suggesting a better alignment of the CuO2 planes with respect to the Bi–O planes in the pressure-technique sample. All the samples exhibit a strong preferred orientation effect. Values of the March–Dollase parameters corresponding to the preferred orientation function were obtained. Brindley absorption contrast factors t ϕ were also calculated, together with the effect of microabsorption on the number of phases present in each sample. Rietveld refinements incorporating all the factors resulted in excellent values for the goodness-of-fit parameters for all the samples, with the lowest value of 2.08 for the pressure-technique sample ground for 2 min. Additionally, the powders corresponding to the pressure-technique crystals have no co-crystallizing phase and ∼94% of the Bi-2212 phase, suggesting that crystals grown by the pressure technique are of extremely good quality, much better than those grown by the regrowth flux technique.

Factors Influencing Mullite Formation in Refractory Grog

The mineral mullite has many outstanding refractory properties. The content of aluminum oxide in the raw material is the basic factor influencing the content of mullite in the final product. Depending on Al2O3 content, silica-alumina materials can be divided into fireclay and high-alumina with the Al2O3 content of 45 % and more. The study describes the influence of raw material, the influence of homogenization of raw material and influence of firing temperature on the mullite formation in fireclay refractory material. Three kinds of refractory clay with different chemical composition were used as raw material for fireclay grog production. Three kinds of homogenization and three different temperatures were studied as factors influencing mullite formation. Powder X-ray diffraction was used to determine mullite content in material. Quantitative phase analysis was conducted by the Rietveld method. Mullite crystals morphology was observed by scanning electron microscopy.

Dependence of Magnetic Properties with Structural/Microstructural Parameters of Ball-milled Fe15Co2P3 Powder Mixture

This research work aims to investigate the mechanically alloyed Fe15Co2P3. Parametric Rietveld refinement method, of the obtained X-ray patterns, was performed for qualitative and quantitative phase analysis, structural, microstructural and mechanical properties. The ball-milled powder mixture crystallized within the face-centred cubic α-Fe(P) solid solution in equilibrium with Co75Fe25 phase. The crystallite size decreases reaching 100 and 200 nm respectively after 3h of milling. The highest values of the dislocation density, microstain and stored energy are registered for the α-Fe(P) solid solution. The studied mechanical properties manifest the brittle nature of the α-Fe(P) solid solution compared to the Co75Fe25 phase. The squareness ratio Mr/Ms and the coercivity values of the milled powders increase with increasing milling time and reach steady state after 2 h. The hysteresis loss energy and maximum permeability reach minimal values of 45*10− 4 W/m3 and 49*10− 3 H/m respectively, after 1 h of milling at the opposite of the switching field distribution.

Corrosion Assessment of a Weathering Steel Bridge Structure after 30 Years of Service

The first steel with improved resistance towards atmospheric corrosion, the so-called weathering steel, was patented in the USA in 1933 and was initially used for coal railway cars, and after that, in building and bridge engineering. Weathering steels show higher corrosion resistance than carbon steels in many types of atmosphere due to their ability to form a compact, stable, adherent and protective patina during the time of exposure. Morphological evaluation of the appearance of the corrosion product layer, together with phase analysis of its components, can enable determination of the type of patina and the degree of protection of the steel. To support the visual assessment of a patina, a check based on the qualitative and quantitative phase analysis of its components may be carried out, and the PAI (Protective Ability Index) can be calculated. The estimation of the corrosion processes on original Polish-made weathering steel (12HNNbA) was carried out on a 30-year-old bridge in Poland. There are some structural problems within the deck derived not only from corrosion but also steel cracking, both inside and outside the boxes, at different heights. Fourteen representative samples of patina were analysed and their phase structures were determined by the X-ray powder diffraction method. The PAIs were determined and analysed.