The fluorite-related anion-excess β-Pb1−xFexF2+x (0.25 ≤ x ≤ 0.27) orthorhombic crystal structure is approached from powder diffraction data. A 1 × 1 × 2 fluorite supercell is found to describe the main aspects of the structure, which would have ideally the Pb3FeF9 formula (x = 0.25) (space group Cmmm, a = 5.9926(1), b = 5.5781(1), c = 11.5208(3) Å), and would include a complete [FeF4]∝−1 perovskite plane, orthogonal to the c axis. However, there is large Pb substitution (44%) on the perovskite Fe site as well as Fe substitution (∼25%) on one of the two main Pb sites. A strong relationship with the fully ordered crystal structure of Pb8MnFe2F24, which can be expressed as Pb1−xMxF2+2/3x (x = 0.273), is discussed, suggesting that both phases may have infinite [M3F14]∝ ribbons in common.

The structure of 3,4-diaminopyridin-1-ium dihydrogen phosphate, [C5H3(NH)(NH2)2]+ (H2PO4)−, is solved from conventional X-ray powder diffraction data in direct space (monoclinic unit cell with a = 16.0725(9) Å, b = 7.7301(3) Å, c = 14.6189(9) Å, β = 96.869(1)°, V = 1803.2(2) Å3, Z = 8, and space group I2/c), and optimized by energy minimization in the solid state. In the crystal structure of the title compound, dihydrogenphosphate tetrahedra are linked by strong hydrogen O-H…O bonds forming chains running parallel to the b-axis. Antiparallelly π–π stacked DAP cations form molecular columns in the spaces between the chains. Although the dominant interaction of the molecules with their surroundings is electrostatic, their bonding are further enhanced by N-H…O and C-H…O hydrogen bonds.

The capacity of goethite for CdII substitution has been explored in a series of synthetic samples prepared from FeIII and CdII nitrate solutions aged 21 days in alkaline media. The total metal content ([Fe]+[Cd]) was 0.071 M in all preparations. The samples have been characterized by chemical and X-ray diffraction analysis; the morphology of the solids is described. The cell parameters for all samples were obtained by the Rietveld fits to the X-ray diffraction data. Refined structures show that for samples prepared at the final molar ratio μCd≤5.50 (expressed as μCd=100×[Cd]/[Cd]+[Fe]), a (Cd, Fe)-goethite is the only crystalline product. In these samples, the unit cell parameters increased as a function of Cd concentration, indicating Cd incorporation in the structural frame. At the preparative ratio, μCd=7.03, the incorporation of Cd in the goethite structure is drastically reduced and a probable Cd-substituted hematite is formed together with the Fe,Cd-goethite.

An in situ time-resolved XRD system for hydrothermal reaction has been developed in order to investigate the phase evolution during autoclave process in autoclaved aerated concrete (AAC) formation. The system includes a novel autoclave cell for transmission XRD with thin beryllium windows, a two-dimensional photon-counting pixel array detector, and uses high energy X-rays from a synchrotron radiation source. The temperature and pressure inside the cell are extremely stable during hydrothermal reaction over the course of several hours. The system was utilized for the formation reaction of AAC. Phase evolution was clearly observed, including several intermediate phases, and detailed information on the structural changes during the hydrothermal reaction were obtained.

A new method, namely UACIEM, to extract reliable intensities of nonequivalent systematical overlapping reflections has been proposed and tested by simulated powder diffraction data from known crystal structures. Using both crystallographic and structural chemistry information, the method reconstructs diffraction intensities and solves a crystal structure through an iterative procedure. Our study shows that UACIEM is successful for cases where more than 30% of the total scattering power is located with precision from equivalent systematical overlapping reflections. The UACIEM process is not needed when equivalent systematical overlapping reflections are sufficient to reveal a crystal structure. UACIEM may fail in cases when: (i) only a small portion of the total scattering power (e.g., less than 7%) can be located, and (ii) most of the total scattering power (e.g., 95%) is located, but the atomic coordinates are not accurately known. The UACIEM method is superior to the simple equipartition methods for nonequivalent systematical overlapping reflections.

X-ray powder diffraction investigation of the new high temperature polymorphs beta- and gamma-CaTeO3 and gamma- and delta-CaTe2O5 and picnometric measurements of the room temperature phases of the two compounds have been carried out. The study led to the elucidation of their unit cell structures and assignment of entirely new lattice types and parameters to the room temperature phases of CaTeO3 and CaTe2O5 in contrast and supersession to the existing structural information. The results are as follows: CaTeO3 has only one stable phase at room temperature and temperatures up to 882 °C, i.e., α- and has a triclinic unit cell with a=4.132±0.003 Å, b=6.120±0.006 Å, c=12.836±0.013 Å, α=121.80°, β=99.72°, γ=97.26°. The first high temperature phase stable between 882 and 894 °C, i.e., β-CaTeO3, has a monoclinic lattice: a=20.577±0.007 Å, b=21.857±0.009 Å, c=4.111±0.002 Å, β=96.15°, while the next phase stable above 894 °C, i.e., γ-CaTeO3, has a hexagonal unit cell with parameters: a=14.015±0.0001 Å, c=9.783±0.001 Å, c/a=0.698. CaTe2O5 has one stable phase at temperatures up to 802 °C, i.e., α-CaTe2O5 with a monoclinic lattice and parameters: a=9.069±0.002 Å, b=25.175±0.007 Å, c=3.366±0.001 Å, β=98.29 °. The first high temperature phase stable in the range 802–845°, i.e., β-CaTe2O5, is monoclinic with unit cell parameters: a=4.146±0.001 Å, b=5.334±0.002 Å, c=6.105±0.002 Å, β=98.362 °; the next higher temperature phase stable over 845–857 °C, i.e., γ-CaTe2O5, has an orthorhombic unit cell with: a=8.638±0.001 Å, b=9.291±0.001 Å, c=7.862±0.001 Å and the highest temperature solid phase stable above 857 °C, i.e., δ-CaTe2O5 has a tetragonal unit cell with a=5.764±0.000 Å, c=32.074±0.020 Å, c/a=5.5637.

Heavy atoms dominate the X-ray scattering from many inorganic compounds like oxides and oxalates, and often only partial structures of these compounds can be obtained by X-ray powder diffraction data. Combining information from X-ray and neutron diffraction data is an advantage. Scattering contributions from the atoms are more evenly distributed in neutron diffraction data than in X-ray diffraction data. Neutron diffraction data can then be used to complete a structure partially solved with data from an X-ray diffraction pattern. Examples of heavy atom structures solved in the time period 1983–2004 using direct methods outlined above are presented.

The microstructural evolution of Fe–Mn–C austenitic steels, which exhibit outstanding high-ductile deformation in their plastic regions, was characterized by line-profile and texture analyses. The convolutional multiple whole profile fitting procedure was used for a line-profile analysis of 2θ−θ diffraction data to evaluate variations of crystallite size, dislocation density, and dislocation arrangement. A substantial refinement of the crystallite size proceeded at an early deformation stage. In addition, the dislocation density increased with an increase in the tensile strain. Texture evolution was characterized by the analysis of orientation distribution functions. Three texture components grew with an increase in the tensile strain. According to the pole figure describing the full width at half maximum (FWHM) distribution of the 220 reflection, the nontextured grains had more microstructural defects than the textured grains. To evaluate the microstructural defects in detail, the 220 reflection observed at each texture orientation was analyzed by the single-line-profile method. The crystallite size and dislocation density were almost comparable, irrespective of the kind of texture component. The crystallite size of the nontextured grains was also comparable to that of the textured grains, whereas the nontextured grains had a dislocation density several times that of the textured grains.

The title compound, ∣Na6Li1.6K0.4Cl2∣[Al6Si6O24]‐SOD, is similar to sodalite proper, but the introduction of Li and K into the structure creates a reduction in unit-cell volume and additional collapse of the framework tetrahedra. Refinement of an X-ray powder diffraction pattern of a multiphase material yielded for sodalite a lattice parameter of 0.88427 (2) nm, an Al–O–Si bond angle of 137.9(3°), and Al–O and Si–O bond lengths of 0.1730(5) nm and 0.1620(5) nm, respectively. The angle of the unique Al–O–Si bond corresponds well with the 138° obtained by 29Si solid-state magic-angle-spinning nuclear magnetic resonance spectroscopy. This characterization is important since the compound constitutes an essential part of a radioactive waste form intended for a high-level waste repository.

In the course of an investigation of cracks in certain magnesia floors containing the mineral chlorartinite [Mg2(CO3)(H2O)(OH)]Cl·H2O, the dehydration process of chlorartinite was carried out in high vacuum. The crystal structure of dehydrated chlorartinite [Mg2(CO3)(H2O)(OH)]Cl was refined from laboratory X-ray powder diffraction data using the Rietveld method [R3c, a=22.6791(5) Å, c=7.22336(14) Å, V=3217.52(11) Å3, Z=18, Rp=4.13%, Rwp=5.82%]. Dehydrated chlorartinite exhibits the same type of 3D honeycomb zeolite-like crystal structure with large channels as the hydrated form. Compared to the hydrated form, the channels of dehydrated chlorartinite are empty because of the removal of all non-coordinating water molecules with the cell volume shrinking by 4.0%, leading to a more distorted environment of the magnesium atoms.

Phase composition estimates by X-ray powder diffraction and Rietveld analysis are becoming more widely used in the cement industry. The ASTM C01.23 Compositional Analysis subcommittee developed test method C 1365, “Standard Test Method for Determination of the Proportion of Phases in Portland Cement and Portland-Cement Clinker Using X-Ray Powder Diffraction Analysis.” A round-robin analysis involving 11 laboratories was initiated to assess the precision and bias of this approach and to develop guidelines for Rietveld analysis of hydraulic cements. Four cements were prepared using NIST SRM clinkers spiked with known amounts of one or more of the following minerals: gypsum, bassanite, anhydrite, and calcite. Specimens were provided with instructions that laboratories analyze the whole cement, collect data in triplicate, and repack the specimen for each run. The results of the round robin were used to estimate interlaboratory and intralaboratory precision and bias of phase abundance determinations. The results show an improvement over previous cement round-robin studies utilizing traditional internal-standard-based, peak-area-measurement methods.