Synchrotron X-ray diffraction images are increasingly used to characterize not only structural and microstructural features of polycrystalline materials, but also crystal preferred orientation distributions. Diffraction data can be analyzed quantitatively and efficiently with the Rietveld method and here the detailed procedure is reported from the experiment to the calibration of the two-dimensional detector and full analysis of the sample. In particular, we emphasize the advantage of doing the calibration inside the Rietveld least-squares fitting instead of a preliminary graphical calibration. Then the procedure is described to quantify crystal preferred orientations with the Rietveld method implemented in software “Materials Analysis Using Diffraction”. The process is illustrated for a US “nickel” coin, a 75 at.% copper 25 at.% nickel alloy with face-centered cubic structure and a strong cube texture.

The Powder Diffraction File (PDF) X-ray diffraction pattern for SnO2 (cassiterite, syn), determined in the early 1950's at the National Bureau of Standards, was evaluated using the NBS*AIDS83 editorial review program and a calculated powder pattern. Systematic errors in d-spacings and relative intensities were attributed to the lack of an iterative least-squares refinement of unit cell parameters, to inadequate precision in reporting d-spacings, to poor sensitivity to high angle reflections, and to detector dead time. A new SnO2 pattern was prepared and used to illustrate criteria for evaluation of powder patterns. An R-Factor for quantifying agreement between observed and calculated relative intensities was utilized. The systematic errors in the earlier pattern occurred at higher angles and did not hinder its usefulness for identification purposes.

Powder diffraction pattern of SP-1 graphite has been obtained using synchrotron X-ray diffraction. Unit cell dimensions were calculated using a least-squares analysis that refined to a |Δ2θ°| of no more than 0.007. A hexagonal cell was determined with a space group of P63/mmc (194), a=2.4617(2) and c=6.7106 (4) Å. The Smith/Synder figure of merit is 167 based upon 11 peaks, which indicates that the quality of this data set is superior to the existing PDF card for graphite, 41-1487. It is also emphasized that the interlayer spacing of graphite should be 3.355(1) Å. Using GAS and EXPGUI codes, a new set of calculated powder diffraction data based upon the interlayer spacing of 3.555 Å is generated. A comparison with the current calculated card, 75-1621, has also been made.

CeO2 transforms to an orthorhombic PbCl2-type structure at a pressure of about 31 GPa. The phase transition is accompanied by a 9.8% volume contraction. The bulk modulus of the low-pressure fluorite-type structure is 236(4) GPa. Comparisons are made with the high-pressure behaviour of UO2 and ThO2.

A novel approach to the determination of crystallite size and lattice strain by means of Total Pattern Analysis is described. Parameters to define the position, magnitude, breadth and shape of individual peaks are obtained by an adaptation of the pattern fitting program of Sonneveld and Visser (J. Appl. Cryst. 8, 1–7, 1975). A rapid assessment of the nature of the specimen broadening is given by a Williamson-Hall Plot. This leads to a more detailed study of line breadths by, for example, Voigt analysis applied to several orders of reflections or to single lines. Preliminary results are given for the application of this procedure to ‘size only’ and ‘size-strain’ samples of ZnO.

Rietveld neutron powder profile analysis of the (Na1−xKx)0.5Bi0.5TiO3 (NKBT) series (x=0, 0.2, 0.4, 0.5, 0.6, 0.8, 1.0) is reported over the temperature range 293–993 K. A detailed characterization of the structures and phase transitions occurring across this series as a function of temperature has been made. Room-temperature refinements have revealed a rhombohedral phase, space group R3c for x=0, 0.2, and 0.4, which exhibits an antiphase, a−a−a− oxygen tilt system with parallel cation displacements along [111]p. An intermediate zero-tilt rhombohedral phase, space group R3m possessing cation displacements along [111]p, has been established for x=0.5 and 0.6. At the potassium-rich end of the series at x=0.8 and 1.0, a tetragonal phase, space group P4mm is observed possessing cation displacements along [001]. At the sodium-rich end of the series for x=0.2, the unusual tetragonal structure with space group P4bm is seen for Na0.5Bi0.5TiO3 which possesses a combination of in-phase a0a0c+ tilts and antiparallel cation displacements along the polar axis. Temperature-induced phase transitions are reported and structural modifications are discussed.

Powder diffraction data for semiconductor and metallic states of vanadium dioxide are presented. The structures are refined by Rietveld methods using a monoclinic cell (a = 5.7529Å, b = 4.5263Å, c = 5.3825Å, β = 122.61°) and space group P21/c for the room temperature data, and a tetragonal cell (a =4.5540Å, c = 2.8557Å) and space group P42/mnm for data collected at 400 K. The similarity between the corresponding X-ray diffraction patterns is discussed. The transition process from the monoclinic to tetragonal phase is investigated and initial evidence for the coexistence of phases over a small temperature range is presented.

In this paper we describe the capabilities for texture measurements of the new neutron time-of-flight diffractometer HIPPO at the Los Alamos Neutron Science Center. The orientation distribution function (ODF) is extracted from multiple neutron time-of-flight histograms using the full-pattern analysis first described by Rietveld. Both, the well-established description of the ODF using spherical harmonics functions and the WIMV method, more recently introduced for the analysis of time-of-flight data, are available to routinely derive the ODF from HIPPO data. At ambient conditions, total count time of less than one hour is ample to collect sufficient data for texture analysis in most cases. The large sample throughput for texture measurements at ambient conditions possible with HIPPO requires a robust and reliable, semi-automated data analysis. HIPPO’s unique capabilities to measure large quantities of ambient condition samples and to measure texture at temperature and uni-axial stress are described. Examples for all types of texture measurements are given

PyFAI is an open-source Python library for Fast Azimuthal Integration which provides 1D- and 2D-azimuthal regrouping with a clean programming interface and tools for calibration. The library is suitable for interactive use in Python. In optimising the speed of the algorithms there has been no compromise on the accuracy compared to reference software. Fast integrations are obtained by the combination of an algorithm ensuring that each pixel from the detector provides a direct contribution to the final diffraction pattern and an OpenCL implementation that can use graphics cards for acceleration. This contribution describes how the algorithms were modified to work better in parallel.

A new quantitative X-ray powder diffraction (QXRPD) method has been developed to analyze polyphase crystalline mixtures. The unique approach employed in this method is the utilization of the full diffraction pattern of a mixture and its reconstruction as a weighted sum of diffraction patterns of the component phases. To facilitate the use of the new method, menu-driven interactive computer programs with graphics have been developed for the VAX series of computers. The analyst builds a reference database of component diffraction patterns, corrects the patterns for background effects, and determines the appropriate reference intensity ratios. This database is used to calculate the weight fraction of each phase in a mixture by fitting its diffraction pattern with a least-squares best-fit weighted sum of selected database reference patterns.

The new QXRPD method was evaluated using oxides found in ceramics, corrosion products, and other materials encountered in the laboratory. Experimental procedures have been developed for sample preparation and data collection for reference samples and unknowns. Prepared mixtures have been used to demonstrate the very good results that can be obtained with this method.

Two-dimensional X-ray diffraction refers to X-ray diffraction applications with two-dimensional detector and corresponding data reduction and analysis. The two-dimensional diffraction pattern contains far more information than a one-dimensional profile collected with the conventional diffractometer. In order to take advantage of two-dimensional diffraction, new theories and approaches are necessary to configure the two-dimensional X-ray diffraction system and to analyze the two-dimensional diffraction data. This paper is an introduction to some fundamentals about two-dimensional X-ray diffraction, such as geometry convention, diffraction data interpretation, and advantages of two-dimensional X-ray diffraction in various applications, including phase identification, stress, and texture measurement.

Cristobalite and tridymite are distinct forms of crystalline silica which, along with quartz, are encountered in industrial operations and industrial products. Because the International Agency for Research on Cancer has designated “crystalline silica” as an IARC Group 2A (probable carcinogen) and quartz and cristobalite as a Group 1 (carcinogen), it is important to properly identify and quantify the silica phase in all materials used in production and encountered in products. Opal is a form of hydrated silica which is also encountered in industry. Although some forms of opal mimic cristobalite and tridymite, they are not truly crystalline. The term “silica” in the industrial sense is used to mean any material whose composition is SiO2 whether it is crystalline or noncrystalline. Some people also consider silica to include hydrated SiO2. There are many forms of SiO2 which have both long-range and short-range order and are recognized as crystalline phases among which are quartz, cristobalite, and tridymite. The hydrated silicas, on the other hand, pose an enigma. Only a few forms show sufficient long-range and short-range order to be considered crystalline. The mineral silhydrite is an example. Opal in all its forms lacks sufficient order to be considered crystalline. Even opal-C, which produces a X-ray pattern similar to the diffraction pattern of cristobalite, lacks not only sufficient order to be considered crystalline but also contains water in the structural make-up. This paper discusses a classification and nomenclature for these forms which is critical to proper regulation. It also reviews the recent literature on tridymite, cristobalite, and opal, and provides an extensive bibliography. Modern studies have shown that opal-A is disordered, but opal-CT and opal-C contain ordered domains that mimic stacked sequences of cristobalite and tridymite sheets such that X-ray patterns show features similar to the crystalline cristobalite and tridymite. There is debate on whether the ordered regions have lost the water that characterizes the opals. In fact, heating studies have shown that all opals show changes on heating characteristic of materials that lose water in the process. The TEM evidence showing domains in the range 10–30 nm in a matrix of disordered opal suggest that the proper term for this system is paracrystalline analogous to inorganic and organic polymers.

Patterns useful for identification are obtained by automated diffractometer methods. The lattice constants from the experimental work are refined by least-squares methods; reflections are assigned hkℓ indices consistent with space group extinctions. Relative intensities, calculated densities, literature references, and other relevant data are included.

High-precision unit-cell parameters for the TiO2 polymorphs anatase and rutile at temperatures between 300 and 575 K have been determined using Rietveld analysis of synchrotron powder XRD data. Polynomial models were used to express the tetragonal unit-cell parameters as a function of absolute temperature, with a (anatase)=1.759 37×10−8×T2+6.418 16×10−6×T+3.779 84, c (anatase)=6.6545×10−8×T2+4.0464×10−5×T+9.4910, V (anatase)=2.237 58×10−6×T2+1.027 77×10−3×T+135.602, a (rutile)=−6.636 42×10−11×T3+1.005 01×10−7×T2−1.009 9310−5×T+4.586 34, c (rutile)=−4.115 50×10−11×T3+6.405 94×10−8×T2+4.675 61×10−7T+2.951 81, and V (rutile)=−2.7790×10−9×T3+4.2386×10−6×T2−3.3551×10−4×T+62.100. The polynomial expressions were used to calculate linear (α) and volume (β) thermal expansion coefficients of anatase and rutile between 300 and 575 K. At 298.15 K, these values were αa=4.46943×10−6 K−1, αc=8.4283×10−6 K−1, and β=17.3542×10−6 K−1 for anatase, and αa=6.99953×10−6 K−1, αc=9.36625×10−6 K−1, and β=28.680×10−6 K−1 for rutile.

Synchrotron X-ray diffraction images are increasingly used to characterize crystallographic preferred orientation distributions (texture) of fine-grained polyphase materials. Diffraction images can be analyzed quantitatively with the Rietveld method as implemented in the software package Materials Analysis Using Diffraction. Here we describe the analysis procedure for diffraction images collected with high energy X-rays for a complex, multiphase shale, and for those collected in situ in diamond anvil cells at high pressure and anisotropic stress.

Preferred orientation or texture is a common feature of experimental powder patterns. The mathematics of two commonly used models for preferred orientation—the March-Dollase and the generalized spherical-harmonic models—is reviewed. Both models were applied individually to neutron powder data from uniaxially pressed molybdite (MoO3) and calcite (CaCO3) powders in Rietveld analyses, as well as the as-received powders. The structural refinement results are compared to single-crystal structures. The results indicate that reasonable refinement of crystal structures can be obtained using either the March model or generalized spherical-harmonic description. However, the generalized spherical-harmonic description provided better Rietveld fits than the March model for the molybdite and calcite. Therefore, the generalized spherical-harmonic description is recommended for correction of preferred orientation in neutron diffraction analysis for both crystal structure refinement and phase composition analysis. Subsequently, the generalized spherical-harmonic description is extended to crystal structure refinement of annealed and the aged polycrystalline Ni-rich Ni50.7Ti49.30 shape memory alloys.

A Bi2O3 compound which is unknown to date has been synthesized at 800 °C on a BeO substrate. α-Bi2O3 at 800 °C undergoes a phase transition to a metastable new compound named ω-Bi2O3 which in turn transforms to stable δ-Bi2O3 at 900 °C. X-ray powder diffraction data were collected, indexed, and refined in order to obtain a unit cell (probable space group P1¯: a=7.2688(4), b=8.6390(6), c=11.9698(8) Å, α=87.713(6), β=93.227(6), γ =86.653(4)°. This compound is of interest for the thick films circuits and sensors technology.

Rietveld quantitative X-ray diffraction analysis of the fly ash Standard Reference Materials (SRMs) issued by the National Institute of Standards and Technologies was performed. A rutile (TiO2) internal standard was used to enable quantitation of the glass content, which ranged from 65% to 78% by weight. The GSAS Rietveld code was employed. Precision was obtained by performing six replicates of an analysis, and accuracy was estimated using mixtures of fly ash crystalline phases and an amorphous phase. The three low-calcium (ASTM Class F) fly ashes (SRM 1633b, 2689 and 2690) contained four crystalline phases: quartz, mullite, hematite, and magnetite. SRM 1633b also contained a detectable level of gypsum, which is not common for this type of fly ash. The high-calcium (ASTM Class C) fly ash, SRM 2691, had eleven crystalline phases and presented a challenge for the version of GSAS employed, which permits refinement of only nine crystalline phases. A method of analyzing different groups of nine phases and averaging the results was developed, and tested satisfactorily with an eleven-phase simulated fly ash. The results were compared to reference intensity ratio method semiquantitative analyses reported for most of these SRMs a decade ago.

Commercial atomoxetine hydrochloride crystallizes in the orthorhombic space group P212121 (#19), with a = 7.362 554(12), b = 13.340 168(27), c = 16.701 887(33) Å, V = 1640.421(5) Å3, and Z = 4. The structure was solved and refined using synchrotron powder diffraction data, and Rietveld and density functional techniques. The most prominent feature of the structure is zigzag chains of N–H···Cl hydrogen bonds along the a-axis. The powder pattern has been submitted to the ICDD for inclusion in future releases of the Powder Diffraction File™.

Graphite oxide (GO) is generated by treating graphite with strong oxidizers. GO retains the structure of graphite, but does so with a larger and irregular basal plane spacing. The oxidation of graphite results in the formation of epoxide groups, as well as C–OH and COOH groups. It is the presence of some of these moieties that allows GO to be dispersed in water, allowing for its use in waterborne formulations. Although GO does not possess the electrical properties of single-sheet graphene, it can be swelled in water, which allows for intercalation of hydrophilic polymer between GO sheets, resulting in a composite that can be coated to produce a continuous film. After coating it may be possible to chemically convert GO to a reduced graphite oxide (r-GO) with improved electrical conductivity. X-ray diffraction (XRD) is ideally suited to evaluate GO–polymer composite samples for evidence of intercalation or exfoliation of GO. Examples of GO–polymer analysis by XRD are presented, along with results that demonstrate the effect of relative humidity (RH) on neat GO. Knowing the ambient RH during XRD data collection was found to be important to correctly assess the extent of polymer intercalation within the GO lattice.