The orthorhombic mineral moolooite, CuC2O4. nH2O, described by Clarke and Williams (1986) using Debye-Scherrer photographic data, has a fully-disordered stacking fault (FDSF) structure. Related monoclinic models have been reported for various synthesised samples based on Schmittler (1968). In the present study, synchrotron radiation diffraction data for moolooite and synthesised specimens have been examined with particular reference to crystallographic disorder. The moolooite data correspond to space group Pnnm, with a = 5.3064(2), b = 5.6804(2), c = 2.5630(1) Å; Vc = 77.26(1) Å3; and Z = 1; and the FDSF structure along the b-direction has been confirmed. The synthetic specimen data from the study indicate partial ordering, with space group P21/n; and the cell parameters for one specimen being a = 5.957(7), b = 5.611(5), c = 5.133(7) Å; β = 115.16(2)°; Vc = 155.27 Å3 and Z = 2. The level of zeolitic water in the materials has been considered using the approach of Schmittler based on thermogravimetry and pycnometry. The new data for natural topotype material correspond to CuC2O4.1.0H2O. It is postulated that the level of water for natural and synthetic specimens may be attributed to the conditions under which the material forms.

Additional crystallographic data are given for the recently reported mineral middlebackite, which has been described for discoveries at Iron Knob in South Australia and Passo di San Lugano near Trento, Italy. The material examined in the present study was from a third finding of the mineral, viz. from a quartz outcrop at Mooloo Downs Station in Western Australia within which it was co-located with the chemically- and structurally-related mineral moolooite, CuIIC2O4·nH2O, reported by Clarke and Williams (1986). In this study, the crystal structure was elucidated independently of the other studies using a combination of the a priori charge flipping and simulated annealing methods with synchrotron radiation diffraction (SRD) powder data. The principal crystal data for the Mooloo Downs material are: space group P21/c with lattice parameters a = 7.2659(18) Å, b = 5.7460(11) Å, c = 5.6806(11) Å, β = 104.588(3)°; Vc = 229.46(18) Å3; empirical formula CuII2C2O4(OH)2 with 2 formula units per unit cell; and calculated density = 3.605 g cm−3. The lattice parameters agree approximately with values given for the other studies, but not within the reported error estimates. The atom coordinates, interatomic distances, and angles for the Mooloo Downs material are compared with those from the other studies using single crystal data, with the values from all three studies agreeing approximately, but again not within the reported uncertainties. The crystal chemistry found for middlebackite received strong confirmation through the synthesis for the first time of di-copper oxalate di-hydroxide. Laboratory X-ray diffraction powder data for the synthetic form of the mineral from this study agree closely with the SRD data for the natural mineral.

The growing interest in the use of powder X-ray diffractometry for materials’ characterization has led to the introduction of relevant concepts (e.g. microstructure, strain, anisotropy, texture) to undergraduate teaching in engineering and science. In this concern, the study of polycrystalline materials underlays the use of appropriate software: free, licensed, proprietary, or commercial to assist research on structure determination, structure refinement, and microstructure characterization. Today with the easy access to personal computers, routines for powder diffractometry also becomes feasible to use for non-specialist. Therefore, it would be relevant that students with computing knowledge may decide to improve routines on such three tasks incorporating their own computational approaches. In this study, we show the development of a ready-to-use and open source program written in GNU-Octave (v4.2.1) focused on X-ray diffraction line-profile analysis. The programing language platform was chosen mainly because of two reasons: (1) there is no requirement for commercial licenses, meaning that both programing language and routines can be downloaded online, facilitating collaborative efforts between students, instructors, and developers, and (2) easy re-coding of evaluation strategies is always allowed through fast implementation of modules into the code. The code, IndexCub, features routines for background subtraction, whole profile smoothing, and Kα2 radiation removal, location of diffraction peaks positions, indexing for cubic specimens, multi peak separation of individual peaks, and evaluation of full-width at half-maximum and integral breadth values. Microstructure properties are characterized through the use of integral breadth methods (e.g. Williamson–Hall) and Fourier analysis (e.g. Warren–Averbach), and the anisotropy effects are incorporated introducing calculations of contrast factors. In terms of diffraction domain sizes, size distribution, and the lattice microstrain, the analysis of the microstructure is discussed along with examples for polycrystalline coarse-grained materials (NaCl), epitaxial film (Si), and thin-films (Au) specimens. The code facilitates the understanding of microstructure analysis by using theoretical approaches well established and in state-steady level.

In this paper, some results of neutron diffraction properties of the dispersive double-crystal Si(111) + Si(311) and Si(111) + Si(400) monochromator settings containing two bent perfect crystals but with the second one – analyzer in the strongly asymmetric diffraction geometry, are presented. For the sake of possible applications, both double crystal settings were tested in the orientation of the second crystal for the output beam compression geometry. Powder diffraction test was carried out on a α-Fe(211) pin of the diameter of 2 mm. Contrary to the Si(111) + Si(400) setting, an excellent resolution represented by full width at half maximum in the (Δd/d)-scale was obtained for the Si(111) + Si(311) double crystal monochromator in the parallel as well as in the antiparallel diffraction geometry.

Structural characterization and X-ray reference powder pattern determination have been conducted for the Co- and Zn-containing tridymite derivatives Ba(Co1−xZnx)SiO4 (x = 0.2, 0.4, 0.6, 0.8). The bright blue series of Ba(Co1−xZnx)SiO4 crystallized in the hexagonal P63 space group (No. 173), with Z = 6. While the lattice parameter “a” decreases from 9.126 (2) Å to 9.10374(6) Å from x = 0.2 to 0.8, the lattice parameter “c” increases from 8.69477(12) Å to 8.72200(10) Å, respectively. Apparently, despite the similarity of ionic sizes of Zn2+ and Co2+, these opposing trends are due to the framework tetrahedral tilting of (ZnCo)O4. The lattice volume, V, remains comparable between 626.27 Å3 and 626.017 (7) Å3 from x = 0 to x = 0.8. UV-visible absorption spectrum measurements indicate the band gap of these two materials to be ≈3.3 and ≈3.5 eV, respectively, therefore potential UV photocatalytic materials. Reference powder X-ray diffraction patterns of these compounds have been submitted to be included in the Powder Diffraction File (PDF).

Powder X-ray diffraction was used to monitor the solvent-free synthesis of two-dimensional (2D) metal–organic frameworks (MOFs) via mechanochemical methods. For four isophthalic acid-based, alkoxide-functionalized organic ligands, optimal milling times were found to vary from 12 to 48 min. This work confirms that mechanochemical synthesis routes can be utilized to afford highly-crystalline, 2D MOFs.

The crystal structures of (NH4)H2C6H5O7 and (NH4)3C6H5O7 have been determined using a combination of powder and single crystal techniques. The structure of (NH4)2HC6H5O7 has been determined previously by single crystal diffraction. All three structures were optimized using density functional techniques. The crystal structures are dominated by N-H⋅⋅⋅O hydrogen bonds, though O-H⋅⋅⋅O hydrogen bonds are also important. In (NH4)H2C6H5O7 very strong centrosymmetric charge-assisted O-H-O hydrogen bonds link one end of the citrate into chains along the b-axis. A more-normal O-H⋅⋅⋅O hydrogen bond links the other end of the citrate to the central ionized carboxyl group. In (NH4)2HC6H5O7, the very strong centrosymmetric O-H-O hydrogen bonds link the citrates into zig-zag chains along the b-axis. The citrates occupy layers parallel to the bc plane, and the ammonium ions link the layers through N-H⋅⋅⋅O hydrogen bonds. In (NH4)3C6H5O7, the hydroxyl group forms a hydrogen bond to a terminal carboxylate, and there is an extensive array of N-H⋅⋅⋅O hydrogen bonds. The energies of the density functional theory-optimized structures lead to a correlation between the energy of an N-H⋅⋅⋅O hydrogen bond and the Mulliken overlap population: E(N-H⋅⋅⋅O) (kcal/mole) = 23.1(overlap)½. Powder patterns of (NH4)H2C6H5O7 and (NH4)3C6H5O7 have been submitted to International Centre for Diffraction Data for inclusion in the powder diffraction file.

This work was undertaken in preparation for a survey to assess the exposure of carpenters to hazardous dust working in construction. Inhalable dust, in this industry, was expected to contain both crystalline mineral and amorphous phases (wood dust). The Rietveld method was applied to provide a simultaneous multicomponent analysis. To assess its performance, mixtures of aerosolised calcite, gypsum, quartz, kaolinite, and wood dust were collected onto quartz fibre filters (n = 41) using the Button inhalable sampler. Results obtained using Rietveld were compared with loaded mass and those from external standard calibrations. The measured content of a component in 14 samples was used as an internal standard by Rietveld to determine amorphous content (wood). The performance of the Rietveld and external standard methods was similar. The 95% confidence interval for the absolute differences between the two methods was 15%. Only one relative difference of more than 15% had a mass loading >0.5 mg. An approach for assessing the limits of detection with relative intensity ratios was applied and gave comparable values with the usual method using calibration coefficients from the external standard method. Rietveld is therefore a potentially useful multicomponent method for the measurement of dust aerosol to help better understand workers' exposures.

3-[1-[4-(2-Methylpropyl)phenyl]ethyl]-6-(4-fluorophenyl)-1,2,4-triazolo[3,4-b]-1,3,4-thiadiazole (C21H21FN4S) has been synthesized as a member of a series of triazolothiadiazoles having NSAIDs moieties with cytotoxic activity. The crystal structure of this new compound has been solved and refined using conventional laboratory X-ray powder diffraction data and optimized using density functional techniques. The final structure solution was achieved by Rietveld refinement using soft restraints on all non-H atom bond lengths and angles. This compound crystallizes in $P\bar{1}\;$ space group, with the unit cell parameters a = 5.5880(4) Å, b = 9.3074(7) Å, c = 19.497(4) Å, α = 99.311(10)°, β = 91.925(9)°, γ = 98.199(6)°, and V = 988.8(2) Å3. To complement and verify the structure solution of the compound, the density functional theory (DFT) calculations were performed by using the local density approximation and the generalized gradient approximation for exchange-correlation energy. In order to see the effect of the van der Waals interactions on the electronic structure, the relevant structure was also optimized with B3LYP-D2, PBE-D2, and optB88-vdW functionals. The refined crystal structure was confirmed by the DFT calculations. The best agreement with the experimental structure was achieved by optB88-vdW functional.

Apatite-type materials AI4AII6(BO4)6X2 have two unique cations sites AI and AII, which can host large mono-, di- tri- and tetra-valent cations. The average cation radii will affect the twist angle and lattice constants. However, there are few reports on the influence of B site substitutions on the twist angle and lattice parameters. It is believed that the lattice constant variation as a function of B site substitutions may not follow the same twist-angle model as proposed for A site. This work reports our results on the crystal chemistry of synthetic apatite Ca10(VxP1−xO4)6F2 obtained through the crystal structure characterization using Rietveld refinement and high-resolution transmission electron microscopy. The quantification of vanadium/phosphorus partitioning in BO4 tetrahedra showed that equilibrium with more than 70% substitution of phosphorous by vanadium was difficult to achieve unless longer annealing (about 1 week at 900 °C) was employed. In comparison with the apatites with different ionic radii at AI and AII sites, Ca10(VxP1−xO4)6F2 apatites with different ionic radii at B site show little twist angle variation for the whole series, which indicates that the dilation of unit cell constants is mainly because of the expansions of BO4 tetrahedra when A site cation is fixed.

Variation of structural parameters of dimethylammonium manganese formate [(CH3)2NH2]Mn[(HCOO)3] upon substitution by the transition elements Zn, Co, and Ni is studied by powder X-ray diffraction (PXRD) technique. These metal–organic framework (MOF) crystals were grown by solvothermal method. The PXRD patterns of all MOFs exhibited rhombohedral structure. PXRD patterns of MOFs were analyzed using Rietveld refinement method. While the parent Mn-MOF and Mn0.9Zn0.1MOF are found to have similar structural parameters, Co and Ni substituted Mn-MOFs have smaller structural parameters than that of parent Mn-MOF. The reason for this variation in the lattice parameters is explained based on the Shannon ionic radii.

This paper is devoted to the study of formation mechanism of metal solid solutions during the thermolysis of single-source precursors in Co–Pt systems with a wide range of superstructural ordering. It is shown that the thermal decomposition of [Pt(NH3)4][Co(C2O4)2(H2O)2]·2H2O salt in helium is critically different from that under hydrogen atmospheres. Thermal degradation under the helium atmosphere is followed by a gradual reduction of platinum and cobalt, and at each thermolysis temperature only one phase is present. At 380 °C an equiatomic Co0.50Pt0.50 solid solution is formed (a = 3.749 (4) Å, Fm−3m space group, V/Z = 13.17 Å3, crystallite size: 5–7 nm). When the precursor is decomposed under a hydrogen atmosphere, the process proceeds mainly through the simultaneous reduction of the platinum and cobalt atoms, and at each temperature section two metal phases are present. The formation of the close to equiatomic Co0.50Pt0.50 solid solution (a = 3.782 (4) Å, Fm−3m space group, V/Z = 13.52 Å3, crystallite size: 7–9 nm) occurs at 450 °C. The calculations of crystallite sizes are confirmed by transmission electron microscopy data.

The crystal structure of MoO2(O2)(H2O)·H2O has been solved using parallel tempering with the FOX software package and refined using synchrotron powder diffraction data obtained from beamline 08B1-1 at the Canadian Light Source. Rietveld refinement, performed with the software package GSAS, yielded monoclinic lattice parameters of a = 17.3355(5) Å, b = 3.83342(10) Å, c = 6.55760(18) Å, and β = 91.2114(27)° (Z = 4, space group I2/m). The structure is composed of double zigzag molybdate chains running parallel to the b-axis. The Rietveld refined structure was compared with density functional theory (DFT) calculations performed with CRYSTAL14, and shows comparable agreement with two DFT optimized structures of similar energy, which differ by the location of the molybdate coordinated water molecule. The true structure is likely a disordered combination of the two DFT optimized structures.

Structure and optical properties have been successfully determined for a series of niobium- and tantalum-containing layered alkaline-earth silicate compounds, Ba3(Nb6−xTax)Si4O26 (x = 0.6, 1.8, 3.0, 4.2, 5.4). The structure of this solid solution was found to be hexagonal P-62m (No. 189), with Z = 1. With x increases from 0.6 to 5.4, the lattice parameter a increases from 8.98804(8) to 9.00565(9) Å and c decreases from 7.83721(10) to 7.75212(12) Å. As a result, the volume decreases from 548.304(11) to 544.479(14) Å3. The (Nb/Ta)O6 distorted octahedra form continuous chains along the c-axis. These (Nb/Ta)O6 chains are in turn linked with the Si2O7 groups to form distorted pentagonal channels in which Ba ions were found. These Ba2+ ions have full occupancy and a 13-fold coordination environment with neighboring oxygen sites. Another salient feature of the structure is the linear Si–O–Si chains. When x in Ba3(Nb6−xTax)Si4O26 increases, the bond valence sum (BVS) values of the Ba sites increase slightly (2.09–2.20), indicating the size of the cage becoming progressively smaller (over-bonding). While SiO cages are also slightly smaller than ideal (BVS range from 4.16 to 4.19), the (Nb/Ta)O6 octahedral cages are slightly larger than ideal (BVS range from 4.87 to 4.90), giving rise to an under-bonding situation. The bandgaps of the solid solution members were measured between 3.39 and 3.59 eV, and the x = 3.0 member was modeled by density functional theory techniques to be 3.07 eV. The bandgaps of these materials indicate that they are potential candidates for ultraviolet photocatalyst.

History of the development of the reciprocal lattice is reviewed. The reciprocal lattice as an essential tool for the study of diffraction experiments by ordered structures and characterization of their structural properties is widely taught in any text of solid state or chemistry, but usually without discussion of its history. This article aims to give a coherent historical perspective on the reciprocal lattice. First, a basic introduction to the reciprocal lattice concept, its mathematical foundation and physical origin, and its relationship with the direct lattice is provided. Then a detailed chronicle of ideas leading to the concept of the reciprocal lattice is presented, including a review of the contributions of Gibbs, Ewald, and others. The polar lattice concept, the great ancestor of the reciprocal lattice, is presented.

A collection of 65 formulated tablets and capsules were analyzed for phase composition by full pattern matching powder diffraction methods. The collection contained 32 of the top 200 prescription drugs sold in 2016 as well as many high-volume prescriptions and over the counter drugs from prior years. The study was used to evaluate new methods of analysis as well as the efficacy of programs designed to collect references on high volume excipients and pharmaceuticals for inclusion in the Powder Diffraction File™. The use of full pattern matching methods as well as reference pattern additions of many common excipients enabled major phase excipient identification in all formulations. This included identification of crystalline, nanocrystalline, and amorphous ingredients because full pattern matching involved the use of characteristic coherent and incoherent scatter. Oftentimes identification of the major excipients significantly aided the clean identification of the active pharmaceutical ingredients (APIs) and their polymorphic form, even at low concentrations (1–10 wt. %). Overall 93% of the APIs were identified, most through a PDF® material reference, but also through patent cross-referencing and similarity analysis comparisons.

The crystal structures of cefdinir and cefdinir sesquihydrate have been solved and refined using synchrotron X-ray powder diffraction data, and optimized using density functional techniques. Cefdinir crystallizes in space group P21 (#4) with a = 5.35652(4), b = 19.85676(10), c = 7.57928(5) Å, β = 97.050(1) °, V = 800.061(6) Å3, and Z = 2. Cefdinir sesquihydrate crystallizes in space group C2 (#5) with a = 23.98775(20), b = 5.01646(3), c = 15.92016(12) Å, β = 109.4470(8) °, V = 1806.438(16) Å3, and Z = 4. The cefdinir molecules in the anhydrous crystal structure and sesquihydrate have very different conformations. The two conformations are similar in energy. The hydrogen bonding patterns are very different in the two structures, and the sesquihydrate is more stable than expected from the sum of the energies of cefdinir and cefdinir sesquihydrate, the result of additional hydrogen bonding. The powder patterns are included in the Powder Diffraction File™ as entries 00-066-1604 (cefdinir) and 00-066-1605 (cefdinir sesquihydrate).

Crystal structure and electronic structure of YMnO3 were investigated by X-ray diffraction and transmission electron microscopy related techniques. According to the density of states (DOS), the individual interband transitions to energy loss peaks in the low energy loss spectrum were assigned. The hybridization of O 2p with Mn 3d and Y 4d analyzed by the partial DOS was critical to the ferroelectric nature of YMnO3. From the simulation of the energy loss near-edge structure, the fine structure of O K-edge was in good agreement with the experimental spectrum. The valence state of Mn (+3) in YMnO3 was determined by a comparison between experiment and calculations.

The crystal structure of oxybutynin hydrochloride hemihydrate has been solved and refined using synchrotron X-ray powder diffraction data, and optimized using density functional techniques. Oxybutynin hydrochloride hemihydrate crystallizes in space group I2/a (#15) with a = 14.57266(8), b = 8.18550(6), c = 37.16842(26) Å, β = 91.8708(4)°, V = 4421.25(7) Å3, and Z = 8. The compound exhibits X-ray-induced photoreduction of the triple bond. Prominent in the layered crystal structure is the N–H⋅⋅⋅Cl hydrogen bond between the cation and anion, as well as O–H⋅⋅⋅Cl hydrogen bonds from the water molecule and hydroxyl group of the oxybutynin cation. C–H⋅⋅⋅Cl hydrogen bonds also contribute to the crystal energy, and help determine the conformation of the cation. The powder pattern is included in the Powder Diffraction File™ as entry 00-068-1305.

The General Structure Analysis System (GSAS)-II software package is a fully developed, open source, crystallographic data analysis system written almost entirely in Python. For powder diffraction, it encompasses the entire data analysis process beginning with 2-dimensonal image integration, peak selection, fitting and indexing, followed by intensity extraction, structure solution and ultimately Rietveld refinement, all driven by an intuitive graphical interface. Significant functionality of GSAS-II also can be scripted to allow it to be integrated into workflows or other software. For protein studies, it includes restraints on bond distances, angles, torsions, chiral volumes and coupled torsions (e.g. Ramachandran Φ/Ψ angles) each with graphical displays allowing visual validation. Each amino acid residue (and any ligands) can be represented by flexible rigid bodies with refinable internal torsions and optionally fully described TLS thermal motion. The least-squares algorithm invokes a Levenberg-Marquart minimization of a normalized double precision full matrix via Singular Value Decomposition providing fast convergence and high stability even for a large number of parameters. This paper will focus on the description of the flexible rigid body model of the protein and the details of the refinement algorithm.