Particle statistics in quantitative X-ray diffractometry relates to the number of particles (crystallites) contributing to the diffracted intensity for a given line. Variations in line intensity between replicate preparations of the same sample arise from statistical variations in the number of diffracting particles. The uncertainty in line intensity, and hence in quantitative estimates of analyte concentration, is termed the particle statistics error. A theoretical estimate of the error for stationary samples qives σPS=ξ[μ*〈v〉/c]1/2, where μ* is the mass absorption coefficient of the mixture, and 〈v〉 and c are the mean particle volume and mass concentration respectively of the analyte. The factor ξ is a function mainly of diffractometer geometry, but also contains contributions from rocking angle and reflection multiplicity. For measurements of the (112) quartz line with a Philips PW1050 vertical goniometer with 2o divergence slit and 0.3 mm receiving slit, ξ was calculated to be 116 g1/2 cm−5/2 for stationary samples. Three close-cut size fractions of quartz were prepared at various concentrations in a calcium carbonate matrix. Replicate preparations were measured and the standard deviation obtained as a function of particle volume and concentration. After correction for other contributing errors, including counting statistics and thermal fluctuations, the experimental value ξ=122±10 g1/2 cm−5/2 was obtained. The effect of sample spinning is considered briefly and predicted to reduce σPS by a factor of about 5. Experimentally, a reduction in σPS of about this order is observed, but the effect is rather variable.

X-ray diffraction pattern from cotton fiber (dch32) grown in the Karnataka state of India has been recorded. Fiber was found to contain 17 Bragg reflections, of which 11 are broadened because of crystal size and intrinsic strain influences. Contributions to integrated intensities from intrinsic strain in the fiber have been estimated using line profile analysis. A molecular model was first constructed with standard bond lengths and angles using helical symmetry and layer-line spacings observed in the X-ray pattern. The model was then refined against observed X-ray data using the linked atom least squares (LALS) method. The refinement has been done with and without the intrinsic strain correction to find the extent of structural changes. These changes have been quantified in terms of bond angles, bond lengths, and torsion angles. Young’s modulus has been estimated for these fibers using the results of line profile analysis, and a broad agreement with the reported physical measurements has been obtained.

Samples of single-phase Sr2FeMoO6 were successfully prepared by solid-state reaction with long sintering times. The crystal structures of the Sr2FeMoO6 samples were determined from X-ray powder diffraction data using the Rietveld refinement method. The structure results obtained by the Rietveld refinements show that an increase in the total sintering time of the solid-state reaction is an effective method to obtain single Sr2FeMoO6 phase and to improve the ordering of Fe and Mo cations (or reducing antisite defects) in the double-perovskite structure. The volume of the tetragonal unit cell of Sr2FeMoO6 contracts slightly after successive sintering treatments. The averaged Fe-O and Mo-O bond lengths as well as the tilt between the FeO6 and the MoO6 octahedra decrease with increasing total sintering time. Our results suggest that the detected subtle changes in crystal structure, such as bond lengths and bond angles between the Fe and Mo cations and oxygen, in the ordered double-perovskite structure may be responsible for the large effects on previously reported transport and magnetic properties of an oxide metal.

Advances in instrumentation, software applications, and database content have all contributed to improvements in pharmaceutical analyses by powder diffraction methods in the 21st century. When compared to the globally harmonized United States Pharmacopeia General Chapter <941>, “Characterization of Crystalline and Partially Crystalline Solids by X-ray Powder Diffraction”, many historic problems in pharmaceutical analysis have been addressed by combinations of improved methods and instrumentation. Major changes in the last 20 years include (i) a dramatic lowering in detection capability and detection limits, (ii) enhanced capabilities for dynamic measurements such as in situ analyses under a variety of conditions, and (iii) the ability to identify and characterize nanomaterials, non-crystalline, and amorphous materials by both coherent and incoherent scattering profiles.

The General Structure and Analysis Software II (GSAS-II) package is an all-new crystallographic analysis package written to replace and extend the capabilities of the universal and widely used GSAS and EXPGUI packages. GSAS-II was described in a 2013 article, but considerable work has been completed since then. This paper describes the advances, which include: rigid body fitting and structure solution modules; improved treatment for parametric refinements and equation of state fitting; and small-angle scattering data reduction and analysis. GSAS-II offers versatile and extensible modules for import and export of data and results. Capabilities are provided for users to select any version of the code. Code documentation has reached 150 pages and 17 web-tutorials are offered.

Twenty-four coal samples representing the four major rank types were analyzed by the X-ray RIM methodology which includes mass absorption analysis by X-ray transmission and quantitative X-ray powder diffraction. Twenty-three separate mineral species were observed in the samples, many of which could be quantified in the whole coal analysis. Several mineral species at levels of 5 weightpercent or less were observed only in the ashed scans. Some dehydration and reconstitution reactions were observed in the ashing process, including the combination of organically bound alkaline-earth elements and sulfur to form bassanite and magnesium sulfates. Quartz and kaolinite dominated the silicate mineral portion of the mineralogy, whereas calcite and siderite represented the carbonate; pyrite with associated sulfate oxidation products were generally present as well. The X-ray transmission studies were successful in estimating the carbonaceous matter in the whole coal samples and comparison of the chemical oxides derived from the X-ray data with direct analyses from the Penn State data sheets revealed good correlations, although significant departures occurred for some species and a systematic underestimation of aluminum oxide from the X-ray clay peaks was observed. This study suggests that the RIM procedure can be applied to coal mineral and amorphous component analysis on a routine basis.

Indexed X-ray powder diffraction data are reported for the homologous compound (ZnO)5(In1−xYx)2O3. The structures of (ZnO)5In2O3 and of (ZnO)5(In1−xYx)2O3 were refined by the Rietveld technique on the basis of the space group R3¯m. Refined unit cell dimensions are a=3.3285(1) Å, c=58.127(2) Å, V=557.71(3) Å3, Dx=6.11 g/cm3, Rwp=10.52, RB=8.56 for (ZnO)5In2O3, and a=3.3505(1) Å, c=57.863(1) Å, V=562.53(2) Å3, Dx=5.97 g/cm3, Rwp=9.05, RB=6.94 for (ZnO)5(In0.8Y0.2)2O3. The structure of (ZnO)5In2O3 was shown to be isostructural with (ZnO)5LuFeO3. Y3+ ions were determined to be arranged at the 3a-metal sites substituting for In3+ ions.

ID11 is a multi-purpose high-energy beamline at the European Synchrotron Radiation Facility (ESRF). Owing to the high-energy X-ray source (up to 140 keV) and flexible, high-precision sample mounting which allows small sample–detector distances to be achieved, experiments such as total scattering in transmission geometry are possible. This permits the exploration of a wide Q range and so provides high real-space resolution. A range of samples (glasses and crystalline powders) have been measured at 78 keV, first putting the detector as close as possible to the sample (~10 cm), and then moving it vertically and laterally with respect to the beam in order to have circular and quarter circle sections of diffraction rings, with consequent Q MAX at the edge of the detector of about 16 and 28 Å−1, respectively. Data were integrated using FIT2D, and then normalized and corrected with PDFgetX3. Results have been compared to see the effects of Q-range and counting statistics on the atomic pair distribution functions of the different samples. A Q of at least 20 Å−1 was essential to have sufficient real-space resolution for both type of samples while statistics appeared more important for glass samples rather than for crystalline samples.

The crystal structure of the perovskite phase KCaF3 has been redetermined at 4.2 and 300 K using powder neutron diffraction collected at the highest resolution. At both temperatures the phase was found to be orthorhombic in space group Pnma, with lattice parameters a=0.622 879(5) nm, b=0.870 031(7) nm, c=0.611 210(5) nm at 4.2 K, and a=0.621 488(6) nm, b=0.876 360(8) nm, c=0.616 481(6) nm at 300 K. The CaF6 octahedron is regular at both temperatures with octahedral rotations of 9.6° and 13.2° for the in-phase and anti-phase tilts, respectively, at 4.2 K. No evidence was found to support the recent revision of the space group from Pnma to the monoclinic space group B21∕m.

Mechanical sensitivity of energetic materials is discussed as a function of particle size and lattice defects. Therefore an approach is made to quantify and characterize lattice defects of the energetic powders RDX and HMX using X-ray diffraction. The mechanical properties of these cyclic nitramines are supposed to be dominated by different defect mechanisms—deformation twinning and dislocation slip. The energetic powders and the line-shape standard SRM 660a (NIST) were measured on a Bragg-Brentano diffractometer D5000 (Bruker-AXS), and the diffraction patterns were evaluated by Rietveld- and peak-profile analysis using Williamson-Hall plots. Additionally, preparing samples as thin powder layers was tested in order to reduce line broadening due to low absorption. The investigations reveal interesting details. Characteristic line broadening was found for RDX and HMX pointing to a comparably higher microstrain in HMX. Anisotropic line broadening was found for RDX and discussed in terms of strain fields of dislocations.

Total reflection X-ray fluorescence analysis (TXRF) is an established technique for trace element analysis in various sample types. Restricted in the past to expensive large-scale systems, in this study the capability of a benchtop system for trace element analysis is reported. By analysing various heavy metals in raw and digested sewage as well as mercury in recycling glass, the suitability of the TXRF system for these kinds of applications could be proven. Based on this data, the benefits, disadvantages, and restrictions of the benchtop system in comparison to other trace element techniques like inductively coupled plasma optical emission spectroscopy (ICP-OES) and atomic adsorption spectroscopy (AAS) are evaluated.

A general expression is proposed for the peak profile produced by a system of simple-shape crystalline domains (sphere, cube, tetrahedron, octahedron) whose size is dispersed according to a gamma distribution. The analytical expression obtained is particularly suited to “on the fly” pattern simulation or profile fitting for nanocrystalline materials. An advantage of using the proposed profile expression is that it always corresponds to a physically meaningful, though a priori fixed, size distribution, whereas the traditionally employed Voigtian profiles can produce unphysical negative size distributions for certain combinations of profile parameters. The peak profile depends on the distribution mean and variance instead of the more common empirical parameters of peak width and shape.

The microstructure of materials is generally, macroscopically, anisotropic and/or inhomogeneous. Traditional diffraction analyses do not take into account this anisotropy and/or inhomogeneity of microstructural features. Thus obtained results can be incomplete, ambiguous, or even erroneous. In this work instrumental requirements (application of parallel beam diffractometers with X-ray lenses or X-ray mirrors and parallel-plate collimators in the laboratory and at synchrotron beam lines) and methodological approaches for the diffraction analysis of anisotropic and inhomogeneous microstructures have been discussed and have been illustrated on the basis of two experimental examples: analysis of the anisotropic nature of the structural imperfection of a sputterdeposited Ti3Al layer and analysis of the anisotropic and inhomogeneous elastic grain interaction in a sputter-deposited Ni layer.

The application of the Rietveld method to quantify mineral components of bauxite and lateritic samples was carried out in order to determine the ability of the method to obtain accurate mineralogical abundances for these materials. The method was initially applied to synthetic mixtures using both Cu and Co Kα radiations, and it was shown that Rietveld-derived data compared favourably with the weighed compositions. Application to two types of natural bauxite resulted in a high correlation between Rietveld predicted values and those calculated by proportioning peak intensities with chemical assays. The use of the whole pattern rather than selected peak intensities gives greater accuracy, confirmed by a strong correlation between derived oxide concentrations from XRF assays. Accuracy and precision were improved by the determination of isomorphous substitution of aluminum in goethite and hematite by refinement of unit cell dimensions. Importantly, the ability of the Rietveld program to successfully model several goethites with different levels of isomorphous substitution improved the correlation between predicted and calculated values. In addition, crystallinity and crystallite size that influence the reactivity of the mineral components can be derived from refined peak profiles.

Trigonal rare-earth dioxymonocyanamides Ln2O2CN2 (Ln=Dy, Ho, Er, Tm, Yb) were synthesized by the modified solid-state metathesis (SSM) method, in which Ln2O3 and melamine C3N6H6 were mixed and heated at 850 °C in vacuumed silica ampoules. Possible chemical reaction pathways are proposed. X-ray diffraction (XRD) patterns of Ln2O2CN2 were refined using the Rietveld method. Compounds Ln2O2CN2 crystallize in the trigonal system with space group P3m1, Z=1, and cell parameters of a and c varying from 3.7267(1) to 3.6407(1) Å and from 8.1848(3) to 8.1152(3) Å, respectively, as Ln atoms change from Dy to Yb. These compounds have stacking structures of Ln2O22+ and CN22− layers, similar to those of previously reported compounds Ln2O2CN2 (Ln=Ce, Pr, Nd, Sm, Eu, Gd). The presence of CN22− ions has been confirmed by infrared spectroscopy, with two characteristic peaks in the vicinity of 651 and 2075 cm−1.

Fifteen reference patterns of oxides, nitrides, borides, carbides, silicides, and sulfides are included in this report. The general methods of producing these X-ray powder diffraction reference patterns are described in this Journal, Vol. 1, No. 1, pg. 40(1986).

Samples were mixed with one or two internal standards: silicon (SRM640a), silver, tungsten, or fluorophlogopite (SRM675). Expected 2θ values for these internal standards are specified in the methods described (ibid.). Data were measured with a computer controlled diffractometer. The POWDER-PATTERN system of computer programs was used to locate peak positions, to calibrate the patterns, and to perform indexing and least-squares cell refinement. A check on the overall internal consistency of the data was also provided by a computer program.

Intensities were measured as peak heights above background and were read manually from strip charts. To minimize preferred orientation effects, the powders were passed through a 400 mesh sieve and were mixed with an amorphous diluent material, glass powder. Samples were prepared by side-drifting the mixture into the holder or by dusting a thin layer on a glass slide coated with a thin smear of silicone grease.

The support and interest of the ICDD in this project is gratefully acknowledged. The expert guidance of R. Roth of the Ceramics Division on material synthesis and the careful review of the manuscript by S. Block of the Ceramics Division and A. D. Mighell of the Reactor Division are fully appreciated. Acknowledgement is also extended to D. Minor for performing sample analysis by using SEM. In the production of these standard powder patterns, the ability to search NBS CRYSTAL DATA has proven invaluable.

The crystal structures of Mek[Fe(CN)6];l·mH2O where Me = Cu, Ni and Co, have been refined from X-ray (CuKa) powder diffraction data by means of Rietveld analyses in space group . The Fe and Me ions are octahedrally coordinated by C and N atoms respectively, forming three-dimensional bimetallic networks with the CN-groups as bridging ligands. The Me(l) sites (k = 2, l=1) and the Fe sites (k = 3, l = 2) are partially occupied. Water oxygens were placed in alternative, empty metal sites.

A Rietveld refinement of powder X-ray diffraction data of BiSbO4 is reported. The refined lattice parameters are a =5.4690(2), b =4.8847(3), c = 11.8252(6) Å, and β = 101.131(3)°. The powder data are compared with the PDF patterns designated BiSbO4 (30-177) and SbBiO4 (7-191).

A first attempt to differentiate goethite- and hematite-based natural materials, used for several purposes during the Late Palaeolithic in the Lessini Mountains (Italy), is here proposed. All raw materials were collected from known geological sites within a distance of about 20 km from archaeological excavations (Tagliente and Fumane caves) where ochre fragments were found. X-ray powder diffraction allowed the mineralogical composition of samples collected from carbonate and volcanic geological host and parent rocks to be inferred; in addition, a preliminary distinction based on the different mineral assemblages, on the presence of distinctive mineral phases and on the degree of crystallinity of some compounds such as hematite, became possible. The acquired data thus represent a sort of preliminary inventory for provenance studies on archaeological samples originating in the same region, for which ancillary micro-analytical and geochemical techniques are planned.

GSAS instrument parameters are tabulated for a variety of laboratory and synchrotron diffractometers to give users an idea of the typical ranges of profile parameters when they generate their own instrument parameter files. For modern high-resolution laboratory diffractometers, the parameters fall in the ranges 0<U<3, V=0, 0<W<4, 1<X<3, 0<Y<3, 1<asym<3, and 0<S/L<0.03. For synchrotron diffractometers, the parameters fall in the ranges 0<U<1.2, −1<V<0, 0<W<1, 0<X<1, 0<Y<1, 0<asym<0.5, 0<S/L<0.001, and 0<H/L<0.007. FULLPROF equivalents are also reported. The factors which are convoluted together to generate the instrument profile are described.