Sample transparency aberration in Bragg–Brentano geometry affected by interference with opaque and translucent sample holders has been formulated. The formulation for an opaque sample holder should be classified to 5 cases, depending on the apparent diffraction angle, beam width, specimen width, and specimen thickness. The cumulants of the aberration function for a translucent sample holder with an arbitrary linear attenuation coefficient can numerically be evaluated by a Gauss–Legendre quadrature. The use of a function defined by the convolution of truncated exponential and rectangular functions has been tested as the model for the aberration function. A double deconvolutional treatment (DCT) designed to cancel the effects of the first and third order cumulants of the aberration function has been applied to the XRD data of Si standard powder, NIST SRM640d. The diffraction peak profile in the data treated by the DCT method certainly shows improved symmetry. The main features of the symmetrized peak profile in the DCT data have been simulated by instrumental and specimen parameters. It is suggested that the current analytical method could be utilized for texture analysis, if the manufacturer of an XRD instrument should supply a more accurate information about the instrument.

The magnetostrictive response of a Terfenol-D pellet was measured via a laboratory-based X-ray diffractometer. X-ray diffraction patterns were collected from the pellet sample with and without the presence of an applied magnetic field (~30 mT) generated by placing a large magnet under the pellet. A standard reference material, Silicon 640c, was employed as an internal standard. Magnetostriction values of 323 and 227 ppm Δl/l were determined for the (104) and (110) indexed peaks, respectively, assuming a rhombohedral structure for Terfenol-D. A threshold noise level value of ~20 to 30 ppm Δl/l was suggested based on before/after measurements in the absence of the applied field. No clear evidence of domain wall rotation was detected via changes in relative intensities of diffraction peaks in the presence of the applied magnetic field.

Using a variety of analytical tools, the mineralogy of the sands and dunes at several public beaches along the coastline near Marshfield, Massachusetts was examined. X-ray powder diffraction analyses combining Rietveld methods, orientation analyses, and clustering techniques were primarily used for mineral identification. The results of the analyses point to the underlying geology, a history of glaciation, and erosion of the underlying bedrock and rocks. The sands could be termed “continental” sands since they reflect the composition of the underlying bedrock. The averaged bulk (>1%) mineral composition of the Marshfield beaches and coastal dunes is very similar and similar to other reported mineralogical analyses of Massachusetts and many New England beaches. Quartz and the alkali feldspars, microcline, and albite, comprise ~90% of dune and beach samples. These are usually followed by muscovite and clinochlore, and varieties of amphibole. Higher albite concentrations and a few characteristic minor phases (i.e., epidote) differentiate this sand from others in the region. When analyzing rocks and rock berms present on all beaches, the mineralogy is much more complex and reflects historic glacial till coverage and glacial retreat, combined with modern erosion and storm impact

Data mining for materials science and structure prediction is growing rapidly. Such an approach relies a lot on the available published and unpublished crystal structure. In this contribution, we are using the experimental pattern reported in the PDF entry 00-058-0728 for the experimental data used to solve the previously unreported crystal structure of RbCdVO4. Contrary to the reported literature, the title compound crystallizes in the monoclinic system P21 with Z = 4. The lattice parameters are a = 12.53678(16) Å, b = 5.82451(7) Å, c = 12.47733(17) Å, β = 105.6169(10)°, and V = 877.47(2) Å3. Its crystal structure type is new and quite complex as it exhibits 28 atoms in the asymmetric unit.

In the present study, the High Score Plus software (Malvern Panalytical, 2014), combined with the PDF-4+ database release 2023 (ICDD, 2018), was used to perform phase identification from all the powder XRD data sets of 0.5 g by weight of the crystalline deposits from various units of refineries and gas plants. Subsequently, the Rietveld method with the generalized spherical harmonic description for preferred orientation correction [Von Dreele (1997). Journal of Applied Crystallography 30: 517–25; Sitepu (2002). Journal of Applied Crystallography 35: 274–77; Sitepu et al., (2005). Journal of Applied Crystallography 38: 158–67; Sitepu (2009). Powder Diffraction 24: 315–26] were used to determine texture and crystal structure refinement of scale deposits (calcite – CaCO3) from the boiler equipment at a gas plant and quantitative phase analysis of (i) iron oxide corrosion products from the boiler tube, (ii) synthetic mixtures of 87.0 wt% by weight of barite (BaSO4), 10.0 wt% by weight of hematite (Fe2O3), and 3.0 wt% by weight of quartz (SiO2), (iii) iron oxide corrosion products from the affected equipment parts in a refinery, (iv) vanadium oxide (V2O5), sodium vanadium oxide (NaV2O5), sodium vanadium sulfate hydrate (Na2V(SO4)2⋅H2O), and mackinawite (FeS) compounds found in the ash deposits from an external surface of the boiler tubes in a refinery, and (v) iron sulfide corrosion products found at the affected equipment in the sulfur recovery unit. The results revealed that the phase identification of powder XRD data is an excellent tool to determine the nature, source, and formation mechanism of crystalline deposits – part of the scale and corrosion products formed by the processes in the various units of refineries and gas plants. The quantitative Rietveld analysis results serve to guide the engineers at the refinery and gas plants to overcome the problems by applying the right procedures. For example, for iron oxide corrosion products, at a high temperature, magnetite will coat the iron/steel to prevent oxygen reaching the underlying metal. At low temperature, lepidocrocite formed and with time it transformed into the most stable goethite. Akaganeite is formed in marine environments. Additionally, for iron sulfide corrosion products, pyrophoric iron sulfide (pyrrhotite – FeS) results from the corrosive action of sulfur compounds (H2S) and moisture on the iron (steel). Additionally, for the crystalline ash samples from an external surface of the boiler tubes in a refinery, if sodium and vanadium compounds appear, the fuel oil is poor. For the boiler crystalline deposits, if a hematite phase appears, it means that the boiler feed water contains dissolved oxygen; and if the metallic copper appears among the crystalline deposits, it indicates erosion in the boiler tubes, and therefore, special precaution is required to prevent the plating out of copper during cleaning operations. Finally, for crystalline deposits from the steam drum equipment at the sulfur recovery unit, if magnetite has a high quantity, it indicates the presence of dissolved oxygen in the boiler feed water.

We present a versatile method to generate asymmetric profiles and use it to create Gaussian-like, Cauchy-like, and Pseudo-Voigt-like profiles in terms of elementary functions. Furthermore, this method guarantees that the position and magnitude of the global maximum are independent of the asymmetry parameter, which substantially facilitates the convergence of an optimizer when fitting the peaks to real data. This investigation shows that the method developed here exhibits favorable practical properties and is particularly well suited for various applications where asymmetric peak profiles are observed. For example, in X-ray diffraction (XRD) measurements, the use of asymmetric profiles is essential for obtaining accurate outcomes. This is because diffractometers can introduce asymmetry into the diffraction peaks due to factors such as axial divergence in the beam path. By taking this asymmetry into account during the modeling process, the resulting data obtained can be corrected for instrumental effects. The results of the study show that the evaluation of XRD using nearly defect-free LaB6 allows a precise characterization of the peak broadening caused by the diffractometer itself. Additional size-strain effects of ZnO are determined by considering the asymmetric peak profile of the diffractometer.

The crystal structure of flumethasone has been solved and refined using synchrotron X-ray powder diffraction data, and optimized using density functional theory techniques. Flumethasone crystallizes in space group P21 (#4) with a = 6.46741(5), b = 24.91607(20), c = 12.23875(11) Å, β = 90.9512(6)°, V = 1971.91(4) Å3, and Z = 4 at 298 K. The crystal structure consists of O–H⋯O hydrogen-bonded double layers of flumethasone molecules parallel to the ac-plane. The powder pattern has been submitted to ICDD for inclusion in the Powder Diffraction File™ (PDF®).

Isaac Newton spent some four decades researching “chymistry,” the early modern equivalent of our chemistry. Although his laboratory notebooks survive, his experimental goals remain obscure to the present day. Our work reveals that Newton was engaged in fruitful chemical research even by modern standards. Replication of his experiments, involving Newton’s “vitriol” (from his “liquor of antimony,” NH4Cl, HNO3, and Sb2S3) and verdigris (Cu(CH3COO)2), produced a variety of NH4+-, Cl−-, SO4−2-, NO3−-, and Cu-containing crystallization products. We analyzed these products using powder X-ray diffraction (XRD) (Cu Kα radiation) and Rietveld refinement, which revealed a complex mixture of (NH4)2Cu(SO4)2(H2O)6, NH4NO3, NH4Cl, (NH4)2CuCl4(H2O)2, and (NH4)[Cu(NH3)2Cl3]⋅2H2O. The XRD data also consistently showed a suite of peaks unmatched by any phase in the PDF-5 database. A crystal of the unknown product was analyzed using single-crystal X-ray methods (Mo Kα radiation), revealing a previously unknown compound, (NH4)2[Cu2Cl2(C2H3O2)4]·2NH4Cl, with space group Pmna and room-temperature unit-cell parameters of a = 14.550(3) Å, b = 8.850(1) Å, and c = 9.116(2) Å. The inclusion of this phase in the Rietveld refinements yielded a satisfactory fit. Our ongoing replications of Newton’s crystallization experiments reveal that his research produced a complex, unusual suite of phases, including the aforementioned previously unknown compound.

The crystal structure of etrasimod has been solved and refined using synchrotron X-ray powder diffraction data and optimized using density functional theory techniques. Etrasimod crystallizes in space group P1 (#1) with a = 10.6131(5), b = 10.7003(5), c = 11.1219(8) Å, α = 72.756(2), β = 76.947(2), γ = 77.340(1)°, V = 1159.28(6) Å3, and Z = 2 at 298 K. The crystal structure contains O▬H⋯O hydrogen-bonded etrasimod dimers, which lie in layers approximately parallel to the (2,0,−1) plane. The amino group of each molecule forms an intramolecular N▬H⋯O hydrogen bond to the carbonyl group of the adjacent carboxylic acid group. The powder pattern has been submitted to ICDD for inclusion in the Powder Diffraction File™ (PDF®).

Phase characterization with selected area electron diffraction (SAED) represents a significant challenge when the pattern contains a substantial number of diffraction spots arranged in concentric but incomplete rings. This is a common situation when the crystallites are neither large enough to form a single crystal pattern nor sufficiently small and numerous to form continuous Debye-Scherrer rings. In such circumstances, it is often extremely difficult to distinguish between reflections belonging to a specific phase or to identify reflections that originate from secondary phases. To facilitate the process of phase identification for these kinds of multiphase samples, a macro script with the recursive acronym FINDS (FINDS Identifies Non-matrix Diffraction Spots) was developed on the ImageJ/FIJI platform. The program allows the user to mark diffraction spots of known phases by superimposed rings, making it easy to identify and address additional reflections between them. In addition to the full functionality of calculating and plotting the diffraction ring patterns of the known phases in different styles and colors, FINDS also provides tools for locating spot positions and determining the corresponding d-values of the reflections of interest. The effectiveness of this approach and of the developed program in assisting the process of phase identification with SAED patterns of multiphase samples is demonstrated by two representative examples. The macro code of FINDS is published under GNU General Public License v3.0 or later at https://doi.org/10.5281/zenodo.13748483.

We report the lattice parameters and cell volume for cristobalite powder added at 35 wt% to Ba-Al-Silicate glass (CGI930) as reflowed bulk glass bars where the embedded cristobalite phase is constrained within the glass matrix. Analysis confirms that the room temperature lattice parameters and cell volume obtained for the bulk glass–ceramic are larger compared with single-phase cristobalite powders. The increased volume of the cristobalite phase in a glass matrix is driven by tensile stresses developed at the interface between the cristobalite and matrix glass phase, and this stress impacts the phase transition temperature and thermal hysteresis of the cristobalite phase. In situ high-temperature measurements confirm that the tetragonal to cubic α–β phase transformation of the cristobalite phase within the glass matrix is ~195 °C with complete suppression of hysteresis behavior. In contrast, bulk glass–ceramic material ground to a powder form displays the expected thermal hysteresis behavior and more comparable phase transition temperatures of 245 °C on heating and 220 °C on cooling. Isothermal holds at varying temperatures above or near the α–β phase transition suggest that the cristobalite phase does not undergo significant relaxation within the matrix phase to reduce accumulated stress imposed by the constraining matrix glassy phase.

The crystal structure of diroximel fumarate has been solved and refined using synchrotron X-ray powder diffraction data, and optimized using density functional theory techniques. Diroximel fumarate crystallizes in space group P-1 (#2) with a = 6.12496(15), b = 8.16516(18), c = 12.7375(6) Å, α = 85.8174(21), β = 81.1434(12), γ = 71.1303(3)°, V = 595.414(23) Å3, and Z = 2 at 298 K. The crystal structure consists of interleaved double layers of hook-shaped molecules parallel to the ab-plane. The side chains form the inner portion of the layers, and the rings comprise the outer surfaces. There are no classical hydrogen bonds in the structure, but 9 C▬H⋯O hydrogen bonds contribute to the crystal energy. The powder pattern has been submitted to ICDD for inclusion in the Powder Diffraction File™ (PDF®).

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.

We studied the spectral analysis of X-ray emission spectroscopy for lithium-ion battery materials during the disproportionation reaction driven by heat treatment. To improve the quantitative analysis of chemical states, we consider the contribution of unstable chemical states in the peak deconvolution. We first applied a linear combination fitting (LCF) to the residuals, assuming an asymmetric Lorentzian peak, which was obtained for the unstable chemical component. Since LCF requires a set of known spectra for peak deconvolution, we develop the LCF for spectral analysis, including unknown chemical states. Both quantification results show a similar trend in the temperature dependence of the heat treatment. With the latter method, we can quantify the samples, including unknown chemical compounds, even when that compound does not have a known X-ray emission spectrum.

Bimetallic Pt nanoparticles play a critical role in various applications, including catalysis, chemical production, fuel cells, and biosensing. In this study, we start with Au@Pt core–shell structure and investigate the evolution of these nanoparticles at elevated temperatures. Our in-situ X-ray diffraction study at elevated temperatures concluded that the onset of Au–Pt alloying occurs between 500 and 600 °C. At higher temperatures, the nanoparticles gradually approached the state of a solid solution, but the composition across the nanoparticles was not uniform even at 1,000 °C. Our results suggest that the alloyed nanoparticles at high temperatures are dominated by one solid solution but contain distinct regions with slightly different compositions.

The crystal structure of decoquinate has been solved and refined using synchrotron X-ray powder diffraction data and optimized using density functional theory techniques. Decoquinate crystallizes in space group P21/n (#14) with a = 46.8261(5), b = 12.94937(12), c = 7.65745(10) Å, β = 91.972(1), V = 4640.48(7) Å3, and Z = 8 at 295 K. The crystal structure consists of alternating layers of hydrocarbon chains and ring systems along the a-axis. Hydrogen bonds link the ring systems along the b-axis. The rings stack along the c-axis. The two independent decoquinate molecules have very different conformations, one of which is typical and the other has an unusual orientation of the decyl chain with respect to the hydroxyquinoline ring system, facilitating chain packing. The powder pattern has been submitted to the ICDD for inclusion in the Powder Diffraction File™ (PDF®).

The room-temperature X-ray powder diffraction data for bosentan monohydrate, an API used in the treatment of pulmonary arterial hypertension, is presented. Bosentan monohydrate is monoclinic, P21/c (No. 14), with unit cell parameters a = 12.4520(7) Å, b = 15.110(1) Å, c = 15.0849(9) Å, β = 95.119(5)°, V = 2827.0(3) Å3, Z = 4. All the diffraction maxima recorded were indexed and are consistent with the P21/c space group. The crystal structure of this material corresponds to the phase associated with Cambridge Structural Database entry NEQHEY, which was determined at 123 K. The successful Rietveld refinement, carried out with TOPAS-Academic, showed the single-phase nature of the material and the good quality of the data. A comprehensive analysis of intra- and intermolecular interactions corroborates that the structure is dominated by extensive hydrogen bonding, accompanied by C▬H⋯π and π⋯π interactions. Hirshfeld surface analysis and fingerprint plots indicate that the most important interactions are H⋯H and O⋯H/H⋯O in bosentan and the water molecule and C⋯H/H⋯C interactions in bosentan.

We developed a method called “component decomposition” to extract the pattern of each component of the sample from the multiple powder X-ray diffraction data. Using the component decomposition and the Direct Derivation Method™, we analyze the behavior of phase transitions of trehalose during the changes in temperature and humidity. Because we do not require databases or standard samples, this method is a powerful tool for the quantification of polymorphs in samples containing multiple polymorphs.

The crystal structure of benserazide hydrochloride Form I has been solved and refined using synchrotron X-ray powder diffraction data and optimized using density functional theory techniques. Benserazide hydrochloride Form I crystallizes in space group P21/n (#14) with a = 19.22983(15), b = 14.45066(10), c = 4.57982(2) Å, β = 93.6935(3), V = 1270.014(15) Å3, and Z = 4 at 295 K. The crystal structure contains pairs of hydrogen-bonded benserazide cations, which are hydrogen bonded to chloride anions, resulting in chains along the c-axis. In addition, O–H⋯Cl, N–H⋯O, O–H⋯N, and O–H⋯O hydrogen bonds link the cations and anions into a three-dimensional framework. The powder pattern has been submitted to ICDD® for inclusion in the Powder Diffraction File™ (PDF®).