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.

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.

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).

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 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.

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 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.

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.

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 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.

A software for the calculation of diffraction elastic constants (DEC) for materials both with and without preferred orientation was developed. All grain-interaction models that can use the crystallite orientation distribution function (ODF) are incorporated, including Kröner, Hill, inverse Kröner, and Reuss. The functions of the software include: reading the ODF in common textual formats, pole figure calculation, calculation of DEC for different (hkl,φ,ψ), calculation of anisotropic bulk constants from the ODF, calculation of macro-stress from lattice strain and vice versa, as well as mixture ratios of (hkl) of overlapped reflections in textured materials.

The Debye temperature of wurtzite aluminum nitride (AlN) was determined by the Rietveld refinement method based on the room-temperature X-ray powder diffraction data. The refined lattice parameters are a = 3.11139(1) Å, c = 4.978 43(3) Å; the refined positional parameter for N is z = 0.384 59(33) Å; and the refined temperature factors of Al and N were 0.442(12) Å2 and 0.559(33) Å2, respectively. Using this refined temperature factor, the Debye temperature was evaluated as 971 K through the Debye approximation.

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.

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 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.

The absorption of X-rays in a heterogeneous material depends on the linear absorption coefficients and volume fractions of the components, and on die geometrical peculiarities of their distribution. The latter is called the microabsorption effect, it can be separated into a bulk and a surface contribution. Within the framework of a well-defined stochastic structure model, the bulk contribution to the microabsorption is calculated for arbitrary random multiphase systems in terms of dependence on volume fractions and mean chord lengths of particles. Expressions are derived which are suitable for eliminating the experimental errors of scattering intensities caused by the bulk contribution of microabsorption.

If only one wavelengtii of radiation is used, the mean chord lengths of the phases of the sample must be determined by other experimental techniques. A method is proposed to overcome this difficulty by using two or more wavelengths of radiation; this correction procedure works without the knowledge of the particle sizes of the phases.

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.

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.

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.