A method to obtain both one-dimensional powder diffraction intensities I(2θ) and statistical uncertainties σ(2θ) from the data collected with a flat two-dimensional X-ray detector is proposed. The method has been applied to analysis of the diffraction data of fine quartz powder recorded with synchrotron X-ray. The profile and magnitude of the estimated uncertainties σ(2θ) have shown that the effects of propagation of the errors in 2θ are dominant as the uncertainties about the observed intensity values I(2θ). The powder diffraction intensity data I(2θ), including nine reflection peaks have been analyzed by the Rietveld method incorporating the experimentally estimated uncertainties σ(2θ). The observed I(2θ) data have been reproduced with a symmetric peak profile function (R wp = 0.84 %), and no significant peak shifts from calculated locations have been detected as compared with the experimental errors. The optimized values of the lattice constants of the quartz sample have nominally been estimated at a = 4.9131(4) Å and c = 5.4043(2) Å, where the uncertainties in parentheses are evaluated by the Rietveld optimization based on the estimated uncertainties σ(2θ) for intensities I(2θ). It is likely that reliability of error estimation about unit-cell dimensions has been improved by this analytical method.

In recent years considerable success has been achieved in the development of detectors for the localization of ionizing radiation. One dimensional position sensitive detectors have a number of uses in nuclear physics and in biological studies utilizing small-angle scattering. Detectors are now capable of providing position information of high resolution with a high count rats capability and a simple readout system. We report here on the feasibility of employing a position sensitive proportional counter (PSPC) for the measurement of residual stresses with X-rays.

Comparisons of the accuracy and time of data accumulation between a scintillation detector and a PSPC have been performed on stress relieved, shot peened steel specimens, and specimens deformed in tension.

The ability of obtaining the entire profile at once is somewhat offset by the lower efficiency of the PSPC when compared to a scintillation detector, but this is counteracted by the fact that motion of the detector is eliminated with the PSPC, It will be shown that a PSPC system provides a speed of data accumulation currently not available in any other way, while still remaining a versatile and accurate method.

A new X-ray diffraction pattern for the compound cerium oxygen apatite, Ce4.67[SiO4]3O is suggested. The compound was prepared by the solid state reaction of the oxides, CeO2 and SiO2 and has a hexagonal crystal structure with the lattice constants a = 9.6578 Å and c = 7.1187 Å. The sample of the most recent PDF pattern 31-0336* (Visser, 1978) for this compound is believed to be contaminated with significant quantities of N owing to the fact that it was prepared by mixing Ce2O3 and Si3N4 and its very close resemblance to the pattern displayed in the PDF 33-0333 given for the cerium “nitrogen” apatite, Ce5[SiO4]3N.

X-ray powder diffraction data for CuGa0.15In0.85Se2 and CuGa0.50In0.50Se2 are reported. Indexing of the X-ray diffraction powder pattern and the Rietveld refinement confirmed that these compounds crystallize in the tetragonal crystal system, with space group I-42d (No. 122) and lattice parameters of a=5.7528(2) Å and c=11.5225(3) Å for CuGa0.15In0.85Se2 and a=5.6847(1) Å and c=11.2817(1) Å for CuGa0.50In0.50Se2. The CuGaxIn1−xSe2 system presents the chalcopyrite type crystal structure (CuFeS2) and corresponds to two stacked zinc-blende unit cells. The metal atoms Cu, In, and Ga are regularly ordered in the unit cell. Every Se atom is tetrahedrally bonded to two Cu and two In and Ga atoms.

A new and improved sample holder for use with powder X-ray diffractometry has been developed. This holder is made from a semiconductor grade silicon single crystal cut perpendicular to the [911] axis, i.e., Si (911). This crystal meets most of the basic requirements of an ideal zero background plate, with practically no interference lines. The pattern obtained, by using this crystal as background plate, is very clean, and even very low-intensity Bragg reflections of samples can be detected easily.

The subject of the paper is the old and well-known linear least squares method for determining the lattice dimension of a crystalline phase from the peak locations of a powder diffraction pattern. Approximations, limits, and extensions of the method are discussed with reference to the assignment of hkl indices to an experimental multiphase pattern.

A method for the correction of peak position for the Seemann-Bohlin X-ray diffractometer, useful for practical application, is presented. The position of diffraction peaks is largely influenced by both the displacement of specimen from the diffractometer circle and the shift of the X-ray tube focus. The described correction method has been used for investigation of thin layers, especially for the precise determination of both lattice parameter and stresses in thin films. The application of the method is illustrated on samples of TiN and ZrN coatings deposited on steel substrates and additionally covered with a thin film of Si or Ta or TaC powder used as an internal standard.

Sr0.5Zr2(AsO4)3 arsenate was prepared and structurally characterized by powder X-ray diffraction and by Raman and infrared spectroscopies. Its structure, which belongs to the Nasicon-type family, was refined by the Rietveld method in the R-3 space group, from X-ray powder diffraction data. The hexagonal unit-cell parameters were determined to be ah=8.965(2) Å, ch=23.955(6) Å, V=1667.43(6) Å3, and Z=6. The structure is formed by an ionic three-dimensional network of AsO4 tetrahedra and ZrO6 octahedra linked by corners with Sr2+ ions occupying half of the M1 sites in an ordered manner. Raman and infrared spectra were recorded and assignments of the stretching and bending vibrations of the AsO43− tetrahedra were made. The number of the peaks observed is in good agreement with that predicted by the factor-group analysis of the R-3 space group.

A provisional setup for X-ray microprobe experiments at 35 keV is described. It is based on compound refractive lenses (CRLs) for nanofocusing and a Vortex silicon drift detector with 2 mm sensor thickness for increased sensitivity at high energies. The Microprobe experiment (PETRA III) generally uses Kirkpatrick-Baez mirrors for submicrometer focusing in the energy range of 5–21 keV. However, various types of scanning X-ray microscopy experiments require higher excitation energies. The CRL optics were characterized by X-ray ptychography and X-ray fluorescence (XRF) knife edge scans on a siemens star pattern and showed beam sizes down to 110 nm. The performance of the new setup for microscopic X-ray diffraction (XRD)–XRF scanning X-ray microscopy measurements at 35 keV is demonstrated on a cross-section of a painting fragment.

X-ray diffraction data revealed that the initial SiO2/Ag nanocomposite, manufactured in a chemical synthesis process, is mainly composed of silica in amorphous phase (95.5 wt.%), crystalline Ag with a cubic structure (Fm-3m) and cristobalite (SiO2) with a tetragonal structure (P41212) in the amount of 4.2 and 0.3 wt.%, respectively. High-temperature diffraction data revealed high stability of the SiO2/Ag composite up to 1000 °C. High-temperature X-ray diffraction measurements revealed phase cristallization temperatures of silica at 1060 °C for cristobalite and 1080 °C for tridymite as well as temperature of silver evaporation starting from the composite (ca. 1000 °C). Infrared spectroscopy data confirmed the presence of amorphous matrix with embedded silver ions and crystalline compounds in the form of cristobalite and tridymite without silver after thermal treatment.

The phase identification of a polycrystalline mixture by X-ray powder diffraction data is often requested for studying materials interesting to different scientific and technological fields: chemistry, pharmaceutics, mineralogy, archeometry, forensic science, etc. The availability of user friendly computer programs, able to carry out qualitative phase analysis in efficient and possibly automatic way, is extremely useful to the scientific community involved in powder diffraction. QUALX2.0, the evolution of QUALX, is a freely distributed software for qualitative phase analysis. Based on the traditional search–match method, it is able to manage both a commercial database (PDF-2 maintained by ICDD), and a freely available database (POW_COD generated by the structure information contained in the Crystallography Open Database). QUALX2.0 is continuously improved in terms of computing and graphic tools. Correspondingly, the database POW_COD is suitably modified to make efficient the operations of search. The search–match approach can be facilitated by the use of restraints, when available, involving the chemical composition, the kind of compound(s) (e.g., organic, inorganic, etc.), the symmetry (space group, crystal system), the unit-cell parameters and/or volume, the crystal properties (measured and/or calculated crystal density, crystal color). An outline of the main features of QUALX2.0 and an example of application is described.

Linezolid (LZD) is one of the first commercially available synthetic oxazolidinone antibiotics and is widely used for the treatment of multidrug-resistant Gram-positive bacterial infection. LZD was found to have five polymorphic forms. The most stable and commercialized polymorphs are known as forms II and IV. Trace content of form II in LZD form IV will cause to transition LZD form IV to II rapidly. Powder X-ray diffraction (PXRD) methods were evaluated for the determination of the polymorphic content of the drug substance and drug product. The estimated limit of detection values of the single peak method for LZD polymorph form II in drug substance and tablet formulation were 0.4 and 0.6%, respectively, while the limit of detection value of Rietveld Refinement (full-profile fitting) evaluated LZD polymorph form II in drug substance was 0.2%. The results clearly show that levels <1 wt.% (in active pharmaceutical ingredients) and 2 wt.% (in tablets) LZD form II in form IV can be detected and quantified by PXRD. Validation of the analytical method proved that the method is repeatable, sensitive, and accurate.

Calibration of powder diffraction experiments using area detectors is essential to extract high quality one-dimensional powder diffraction pattern. Precise calibration necessitates a sensible characterization of the Debye-Scherrer rings formed on the detector plane. An algorithm, designed and developed to automate this process, is described in this paper. All the parameters required for an experimental calibration are extracted using robust pattern recognition techniques. Several image preprocessing methods are employed, reducing the computational cost but retaining high signal quality. A modified version of a one-dimensional Hough transformation is used to determine the final parameters of the ellipses. After extraction, the parameters are optimized using nonlinear least squares fit. The presented algorithm is insensitive to image artefacts and was successfully applied to a large number of calibration images. The performance of the algorithm is demonstrated by the comparison of results obtained from the presented automatic calibration method and an existing manual method.

Sm(OH)2NO3, was prepared by hydrolysis of the corresponding nitrate, leading to a product which is insoluble in water. IR-spectroscopy showed a comparison with the analogous Gd-compound. The temperature of decomposition to SmONO3 is below 573 K. The structure was refined by the Rietveld technique in space group P21, (Z=2), a=6.3852(3) Å, b=3.7784(2) Å, c=7.7402(3) Å, β=97.572(3)°, V=185.11 Å3, Rp=4.9, Rwp=6.3, RB=4.0. The compound is isotypic with Ln(OH)2NO3 (Ln=Pr,Nd,Gd). Infrared spectra and thermal decomposition data are also given for the Gd phase.

In the course of our research on normal alkanols, the crystal structure of 1-pentanol has been solved by applying Patterson-search methods to laboratory powder X-ray diffraction data recorded on a curved position-sensitive detector (CPS120) at 183 K. The crystal structure was refined with the rigid-body Rietveld least-squares method. The cell is monoclinic, space group P21∕c, Z=4, and the cell parameters are a=15.592(9) Å, b=4.349(1) Å, c=9.157(1) Å, β=104.7(7)°, V=600.6(3) Å3. There is one molecule in the asymmetric unit with the O–H bond in gauche conformation with respect to the alkyl skeleton. Packing is defined by the hydrogen bonds linking the 1-pentanol molecules along zigzag chains parallel to b.

For residual stress evaluation in complex substrate-coating systems, energy-dispersive (ED) diffraction with energies up to 100 keV can be applied to analyze the near interface residual stress state in the substrate, because the high energy white beam penetrates the coating completely. By the example of an Al2O3/TiCN on WC coating system we have studied the feasibility for using the coating reflections being stored in the ED diffraction patterns together with the substrate diffraction lines to analyze the residual stress state in individual sublayers of which the coating system consists. The results indicate that the ED method is suitable to detect even steep intralayer stress gradients, if the diffraction conditions are adapted to the coating geometry.

In situ laboratory-based and in situ synchrotron X-ray diffraction techniques were employed to study quantitatively the strain-induced austenite-to-martensite (A–M) transformation in thermally cycled (TC) superelastic NiTi alloys. The propagation of the A–M interfaces and the evolution of the microstructure were traced during uniaxial tensile loading. It was shown that the TC material exhibits localized transformation via the propagation of transformation bands. The amount of the martensite phase depends approximately linearly on the applied strain. Analysis of the broadening of the austenite diffraction lines indicates the presence of highly deformed austenite grains within the transformation bands. Analysis of the austenite diffraction-line shifts indicates that the overall lattice strain in the (retained) austenite in the transformation bands differs from that of the austenite in the adjacent untransformed regions.

Multilayer optics is one of the widely applied optics for conditioning an X-ray beam in the region of X-ray diffraction. Multilayer optics offers a well-balanced performance. The beam conditioned by a multilayer optic is characterized by low divergence, good spectrum purity, and high intensity. This article will start with a short historical note of the development of X-ray multilayer and a summary on the basic performance characteristics of X-ray multilayer, then move on to the discussion on the design principle of one- and two-dimensional optics. Both parallel beam optics and focusing optics will be addressed. As examples, selected applications of multilayer optics are also briefly discussed. Finally, the main problems associated with the application of multilayer optics are identified and the future developments are discussed.

A quantitative simultaneous determination method by X-ray powder diffractometry is described for calcium sulfate and calcium carbonate in airborne dusts. In order to eliminate the mutual interference among diffraction peaks, and to avoid the presence of the hydration isomers of calcium sulfate, dust samples were heated at 350°C for 2 h. To reduce the errors due to the difference-in crystallinity between the standard materials and the samples, the synthesized calcium sulfate anhydrate (anhydrite) was heated to such an extent that the half-width of the 002,020 peak was identical with that of the anhydrite in pretreated dust samples. Standard calcium carbonate (calcite) was ground until the half-width and the orientation index of the 104 peak of calcite was identical with that of the calcite in dust samples. Linear calibration curves were obtained throughout the range of 0 ∼ 30 wt% for anhydrite and the range of 0 ∼ 10 wt% for calcite, respectively. The determination limits were 0.2 wt% for anhydrite and 0.3 wt% for calcite. Relative standard deviations were 3.4 % for 8.0 wt% of anhydrite and 1.8% for 5.4 wt% of calcite. The present method is applicable to determination of calcium sulfate and calcium carbonate in actual dust samples.

A novel type X-ray detector, called PILATUS, has been developed at the Paul Scherrer Institut in Switzerland during the last decade. PILATUS detectors are two-dimensional hybrid pixel array detectors, which operate in single-photon counting mode. PILATUS detectors feature a very wide dynamic range (1:1 000 000), very short readout time (<3.0 ms), no readout noise, and very high counting rate (>2×106counts/s/pixel). In addition, a lower energy threshold can be set in order to suppress fluorescence background from the sample, thus a very good signal-to-noise ratio is achieved. The combination of these features for area detectors is unique and thus the PILATUS detectors are considered to be the next generation X-ray detectors. The basic building block of all the detectors is the PILATUS module having an active area of 83.8×33.5 mm2. The PILATUS 100K is a complete detector system with one module. PILATUS detector systems can have other configurations, including large area systems consisting of 20 to 60 modules that can cover up to an area of 431×448 mm2. Such large systems are mainly used for macromolecular structure determination, such as protein crystallography and small angle X-ray scattering. The PILATUS 100K detector can be easily adapted to many systems; the single-module detector is integrated to an in-house X-ray diffraction (XRD) system. Examples of XRD measurements with the PILATUS 100K detector are given.