Debye Scherrer Geometry Research Articles

Specimen-displacement correction for powder X-ray diffraction in Debye-Scherrer geometry with a flat area detector.

The effect of small changes in the speci-men-to-detector distance on the unit-cell parameters is examined for synchrotron powder diffraction in Debye-Scherrer (transmission) geometry with a flat area detector. An analytical correction equationis proposed to fix the shift in 2θ values due to speci-men capillary displacement. This equationdoes not require the use of an internal reference material, is applied during the Rietveld refinement step, and is analogous to the speci-men-displacement correction equations for Bragg-Brentano and curved-detector Debye-Scherrer geometry experiments, but has a different functional form. The 2θ correction equationis compared with another speci-men-displacement correction based on the use of an internal reference material in which new integration and calibration parameters of area-detector images are determined. Example data sets showing the effect of a 3.3 mm speci-men displacement on the unit-cell parameters for 25°C CeO2, including both types of displacement correction, are described. These experiments were performed at powder X-ray diffraction beamlines at the National Synchrotron Light Source II at Brookhaven National Laboratory and the Advanced Photon Source at Argonne National Laboratory.

PAINEIRA beamline at Sirius: an automated facility for polycrystalline XRD characterization

Herein we outline the design of the Paineira beamline – a beamline dedicated to powder X-ray diffraction at the new Brazilian synchrotron source (Sirius). The optical layout optimizes the high photon brightness of the fourth-generation synchrotron light source generated by an undulator. The heavy-duty diffractometer operating in Debye-Scherrer geometry has two detector setups: a multi-analyser crystal for high-resolution and an arc-shaped area detector covering 100° in scattering angle (2θ). The beamline is optimized by carrying out high-throughput measurements with the possibility of rapid setup changes to in-situ and operando measurement conditions. Paineira beamline is under construction and will open new opportunities for materials science, catalysis, energy materials, and geoscience research with synchrotron XRD in Brazil.

Focal construct geometry for high-intensity x-ray diffraction from laser-shocked polycrystalline.

An increasing number of dynamic experiments, especially those involving laser drive, are employing in situ x-ray diffraction as a probe to interrogate structure evolution between states of matter under extreme pressure and temperature. We present an alternative configuration, focal construct geometry, for in situ x-ray diffraction to measure the structure and evolution of dynamically compressed polycrystalline materials on a laser platform. This configuration makes full use of the isotropically emitted He-α x rays by employing an annular (or semi-annular) collimator rather than a regular pinhole collimator and thus increases the flux of incident x rays reaching the sample as well as the intensity of the diffracted x rays, enabling the detection of a diffraction pattern with less laser energy. Its effectiveness and applicability are validated against the conventional Debye-Scherrer geometry through direct molecular dynamics simulations and x-ray diffraction simulations for two representative shock-induced phase transition events, solid-solid and solid-liquid (or melting). This configuration reproduces all the Debye-Scherrer diffraction profiles in good accuracy and demonstrates superior efficiency in utilizing the isotropic x-ray source and harvesting diffracted x rays while preserving the angular resolution.

Pushing data quality for laboratory pair distribution function experiments.

Over the last decade, some studies with laboratory pair distribution function (PDF) data emerged. Yet, limited Qmax or instrumental resolution impeded in-depth structural refinements. With more advanced detector technologies, the question arose how to design novel PDF equipment for laboratories that will allow decent PDF refinements over r = 1-70 Å. It is crucial to reflect the essential requirements, namely, monochromatic X-rays, suppression of air scattering, instrumental resolution, and overall measurement times. The result is a novel PDF setup based on a STOE STADI P powder diffractometer in transmission-/Debye-Scherrer geometry with monochromatic Ag Kα1 radiation, featuring a MYTHEN2 4K detector covering a Q range of 0.3-20.5 Å-1. PDF data are collected in a moving PDF mode within 6 h. Structural signatures of liquids can be satisfactorily resolved in the PDF as shown for the ionic liquid hmimPF6. The high instrumental resolution is mirrored in low qdamp values determined from LaB6 measurements. PDF data from a powder sample of ca. 7 nm TiO2 nanoparticles were successfully refined over up to 70 Å with goodness-of-fit values Rw < 0.22 (respectively Rw = 0.18 over 30 Å), thanks to the low background and high instrumental resolution, hereby enlarging the accessible r range by several tens of Angstroms compared to previous laboratory PDF studies.

Comparison Study of Internal Stress Measured by Diffraction Mapping and Calculation Using FEM

The measuring of internal stress has not only a great scientific aspect, but is particularly important for nondestructive description of component or products in industry. It is expected that exceeding of local mechanical limits in the material can have catastrophic consequences. In this paper is mapped the deformation field of amorphous material under the nanoindenter tip using diffraction in Debye-Scherrer geometry. Using the FEM analysis, it was modeled the deformation field in such material. There is a great match in between measured and calculated data. The result is pointing out on large limits of internal stresses measuring by conventional standard methods.

Phase equilibria in Ce–Cu–C ternary system at 400 °С and 600 °С

Phase equilibria in Ce–Cu–C system at 600 °С and 400 °С have been studied using X-ray powder diffraction analysis and energy dispersive spectroscopy in the concentration ranges 0–40.0 at. and 40.0–100 at. % Ce respectively. The samples were prepared by arc melting under Ti-getter-purified argon atmosphere on a water cooled copper hearth using a nonconsumable tungsten electrode. The alloys were annealed in evacuated quartz glass ampoules at 600 °С and 400 °С for 6 and 12 weeksrespectively. The alloys are active on air. The crystal structure refinement of binary compounds was performed using WinCSD program package. Powder XRD data was obtained with a STOE STADI P (MoK α1 ) powder diffractometer (Debye-Scherrer geometry). Metallographic qualitative and quantitative compositional analyses of the polished samples were performed by EDX with REMMA-102-02 scanning electron microscope. Seven binary compounds – CeCu 6 , CeCu 5 , CeCu 4 , CeCu 2 , CeCu, α-CeC 2 , Ce 2 C 3 – have been confirmed to occur at 400 °С and 600 °С. They do not solute a third component C or Cu according to the X-ray structure and EDX analyses. No binary compounds occur in Cu–C system at 600 °С. No ternary compounds have been detected in the ternary system both at 400 °С and 600 °С. Probably, they may exist at higher temperatures and pressures. CeCu 4 binary compound has not been synthesized at 600 °С. Cerium and copper amount (19(2):81(2) at. %) has been measured by means of EDX technique. A more detailed investigation of CeCu 4 will be provided after the synthesis of well crystallized alloy. Cerium and copper amount was confirmed in the phases for other alloys by means of EDX technique. The results were in agreement with compositions of binary compounds. Keywords : ternary system, phase equilibria, rare earth carbides, crystal structure.

Multipurpose synchrotron spectrometer of the Kurchatov Institute: Part 3. Diffraction in Debye–Scherrer geometry

The performance of a multipurpose synchrotron spectrometer is diversified by installing additional equipment for the studies of diffraction in the Debye–Scherrer geometry. The design of X-ray optics and technical characteristics of the spectrometer are described. Diffraction patterns for polycrystals detected in both the forward and backward hemispheres are illustrated.

High-throughput powder diffraction measurement system consisting of multiple MYTHEN detectors at beamline BL02B2 of SPring-8.

In this study, we developed a user-friendly automatic powder diffraction measurement system for Debye-Scherrer geometry using a capillary sample at beamline BL02B2 of SPring-8. The measurement system consists of six one-dimensional solid-state (MYTHEN) detectors, a compact auto-sampler, wide-range temperature control systems, and a gas handling system. This system enables to do the automatic measurement of temperature dependence of the diffraction patterns for multiple samples. We introduced two measurement modes in the MYTHEN system and developed new attachments for the sample environment such as a gas handling system. The measurement modes and the attachments can offer in situ and/or time-resolved measurements in an extended temperature range between 25 K and 1473 K and various gas atmospheres and pressures. The results of the commissioning and performance measurements using reference materials (NIST CeO2 674b and Si 640c), V2O3 and Ti2O3, and a nanoporous coordination polymer are presented.

Aberration corrections for non-Bragg–Brentano diffraction geometries

The construction of peak intensity, profile and displacement aberration functions based on the geometry of a powder diffraction measurement allows for physically realistic corrections to be applied in Rietveld modelling through a fundamental parameters approach. Parallel-beam corrections for asymmetric reflection and Debye–Scherrer geometry are summarized, and corrections for thin-plate transmission are derived and validated. Geometrically correct implementations of preferred orientation models are also summarized.

The contributions of Albert W. Hull to X-ray powder diffraction at one hundred years of his landmark publication

One hundred years ago X-ray powder diffraction, one of the premier techniques used in the characterization of materials, was invented. Its origins can be traced to two landmark contributions presented to the scientific community in 1916. They are the better known and celebrated work carried out by Paul Scherrer under the guidance of Peter W. Debye, at the University of Göttingen, Germany, and the lesser known work of Albert W. Hull performed at the Research Laboratory of the General Electric Company, Schenectady, NY, USA. The great contributions of Scherrer and Debye have been prominently recognized. They are presented in many textbooks and in technical and scientific articles published in the area of characterization of materials using powder diffraction techniques. The camera designed by them, later called “the Debye–Scherrer camera”, was used extensively for many years and the experimental setup (“the Debye–Scherrer geometry”) is still used today. On the other hand, the work performed by Hull has not been adequately appreciated and remembered. In this communication, an account of his contributions to X-ray powder diffraction and to crystallography is presented at 100 years of his landmark publication, which appeared in the first issue of Physical Review of 1917.

X-ray powder diffraction of high-absorption materials at the XRD1 beamline off the best conditions: Application to (Gd, Nd)5Si4 compounds

Representative compounds of the new family of magnetic materials Gd5−xNdxSi4 were analyzed by X-ray diffraction at the XRD1 beamline at Laboratório Nacional de Luz Síncrotron. To reduce X-ray absorption, thin layers of the powder samples were mounted outside the capillaries and measured in Debye–Scherrer geometry as usual. The XRD analyses and the magnetometry results indicate that the behavior of the magnetic transition temperature as a function of Nd content may be directly related to the average of the four smallest interatomic distances between different rare earth sites of the majority phase of each compound. The quality and consistency of the results show that the XRD1 beamline is able to perform satisfactory XRD experiments on high-absorption materials even off the best conditions.

Facile usage of a MYTHEN 1K with a Huber 5021 diffractometer and angular calibration inoperandoexperiments

A facile usage of a MYTHEN 1K detector with a Huber 5021 six-circle diffractometer is described in detail. A mechanical support has been custom designed for the first time to combine the MYTHEN 1K detector with a point detector, which can be used as a reference point for each individual pixel of the MYTHEN 1K during measurements. The MYTHEN 1K is mounted on the arm of the 2θ circle of the Huber diffractometer with an intrinsic angular resolution of ∼0.0038°, and its pitch angle can be automatically adjusted with an accuracy of 0.0072°. Standard procedures are discussed for its calibration. Programs have been written in theSPECenvironment for simultaneous data conversion, integration and acquisition. The X-ray powder diffraction patterns of standard samples were measured in the Debye–Scherrer geometry and matched well with those of references. The angular shift due to sample-to-center displacement in the `flat-plate transmission' geometry, which is frequently employed inoperandoexperiments, has been successfully investigated and can be efficiently corrected. Oneoperandoexperiment using the MYTHEN 1K is presented. This work provides a straightforward procedure to use the MYTHEN 1K detector properly in Debye–Scherrer geometry, and could facilitate its application at other synchrotron facilities.

Quantification of amorphous phases in the silt fraction of Mexican pre-Hispanic adobe earth bricks

This study is focused on quantifying the amorphous phases in soil-related material samples by quantitative phase analysis (QPA) with a carefully designed methodological strategy in the X-ray diffraction sample measurement and in the refinement procedure. The configuration applied was Debye–Scherrer geometry with Mo Kα radiation which, together with meticulous instrumental profile modelling using an LaB6 standard, allowed the refinement of a minimum of sample-related parameters. This method was applied to two micro-samples of adobe earth bricks from The Great Pyramid of Cholula, Mexico, and one local soil micro-sample containing several amorphous and semi-crystalline phases such as allophane, volcanic glass and opal. The results obtained by the QPA method, complemented by elemental particle induced X ray emission (PIXE) spectrometry analysis, were compared with a silicon chemical environment analysis by 29Si MAS-NMR. An average amorphous content of 40 wt% was calculated with the QPA/PIXE results, which is in agreement within 10% with the NMR experiments. Consequently, the methodology proposed could be of interest for further studies of cultural heritage geomaterials, which usually contain amorphous phases in their composition and allow only micro-sampling.

Microstructure analysis of complex CuO/ZnO@carbon adsorbers: what are the limits of powder diffraction methods?

Activate carbon impregnated with a mixture of copper oxide and zinc oxide performs well as active adsorber for NO2 removal in automotive cabin air filters. The oxide-loaded activated carbon exhibits superior long-term stability in comparison to pure activated carbon as has been shown in previous studies. The carbon material was loaded only with 2.5 wt% of each metal oxide. Characterization of the oxide nanoparticles within the pores of the activated carbon is difficult because of the rather low concentration of the oxides. Therefore, a systematic study was performed to evaluate the limits of line profile analysis of X-ray powder diffraction patterns. The method allows evaluation of crystalline domain size distributions, crystal defect concentrations and twinning probabilities of nanoscopic materials. Here, the analysis is hampered by the presence of several phases including more or less amorphous carbon. By using physical mixtures of defined copper oxide and zinc oxide particles with activated carbon, potential errors and limits could be identified. The contribution of the activated carbon to the scattering curve was modeled with a convolution of an exponential decay curve, a Chebyshev polynomial, and two Lorentzian peaks. With this approach, domain size distributions can be calculated that are shifted only by about 0.5-1.0 nm for very low loadings (≤4 wt%). Oxide loadings of 4 wt% and 5 wt% allow very reliable analyses from diffraction patterns measured in Bragg-Brentano and Debye-Scherrer geometry, respectively. For the real adsorber material, mean domain sizes have been calculated to be 2.8 nm and 2.4 nm before and after the NO2 removal tests.

Combined Hydrodynamic and Diffraction Simulations of Femtosecond X-ray Scattering from Laser-Shocked Crystals

We describe a simple hydrocode based on a two-step integration scheme that models the evolution of elastic and plastic strains in crystals subject to rapid laser-shock loading. By monitoring the elastic strains during plastic flow we track the rotation and spacing of lattice planes within the polycrystalline sample, and can thus predict the signal that would be produced by x-ray diffraction in a variety of experimental geometries. By employing a simple Taylor-Orowan dislocation model we simulate diffraction patterns in a Debye-Scherrer geometry to track the orthogonal strain states within a laser-shocked sample. The yielding rate is approximately matched to those observed in multi-million atom molecular dynamics (MD) simulations, allowing movies to be made of the diffraction images that would be seen in a real experimental geometry, and illustrating the pertinent experimental requirements, including target texture. Judicious choice of geometry allows clear demarcation of the initial elastic response of the target to be made from the subsequent plastic relaxation. We discuss the simulations in the context of the novel experimental capabilities that have recently become available with the advent of 4th generation light sources, which allow single-shot diffraction with sub-100-fsec resolution.

Low-temperature Debye–Scherrer powder diffraction on Beamline I11 at Diamond

A bespoke capillary sample holder is described that attaches to the cold head of a commercially manufactured (PheniX) closed-cycle helium cryostat originally intended for flat-plate geometry. The new holder allows high-resolution synchrotron powder diffraction data to be collected from samples in Debye–Scherrer geometry over the temperature range 11–295 K. To demonstrate that high-quality powder data can be obtained using this new sample holder, structural refinement (Rietveld) and thermal expansion results measured from reference samples (Si and Al) are presented.

Quantitative analysis of turbostratically disordered nontronite with a supercell model calibrated by the PONKCS method

Two calibration-based quantitative X-ray diffraction (XRD) models for turbostratically disordered Bulong nontronite, the PONKCS (partial or no known crystal structure) approach and the supercell structural model, were compared in terms of the accuracy and refinement error from Rietveld quantitative phase analysis. The PONKCS approach achieved improved nontronite quantitative results with synchrotron diffraction patterns compared with those achieved with laboratory XRD data as a result of better data quality and the use of Debye–Scherrer geometry with significantly reduced preferred orientation effects. The introduction of a peak shape modifier (spherical harmonics) to correct the quantification result is mainly useful for laboratory XRD patterns containing nontronite collected from Bragg–Brentano geometry with appreciable preferred orientation effects. A novel calibration approach for the nontronite supercell model was developed, based on the Rietveld quantitative formula in theTOPASsymbolic computation system. The calibrated supercell model achieved better accuracy (deviation within 1 wt%) and lower refinement error than the PONKCS approach because the physically based description of turbostratic disorder requires fewer refinable parameters than the PONKCS approach. The drawbacks and limitations of the supercell approach are also discussed.

Spatial distribution of the absorption factor for an infinite cylindrical sample used with a two-dimensional area detector

Specialized software has been developed to calculate the absorption factor for the infinite-cylinder transmission Debye–Scherrer geometry (including inclined beams) to be used with two-dimensional area powder pattern registration. The diffracted beams are defined by the direction cosines in the laboratory Cartesian coordinate system. Modern two-dimensional area detectors have a large number of pixels, so an interpolation is made by the triangulation procedure to save computer time. The absorption correction is allowed for so that the intensity in each pixel is reduced on the same scale and the final diffraction-angle-dependent intensity,I(2θ), does not require any further absorption correction.

Lattice parameter determination using a curved position-sensitive detector in reflection geometry and application to Smx/2Ndx/2Ce1–xO2–δceramics

X-ray diffractometers with curved position-sensitive (CPS) detectors have become popular for their ability to perform fast data collection over a wide 2θ range, enabling kinetics studies of chemical reactions and measurement of other time-resolved solid-state phenomena. While the effect of sample displacement onhkl-specific apparent lattice parameters has been explored for a transmission-mode Debye–Scherrer geometry, such effects for a reflection-mode Debye–Scherrer geometry are not yet well understood. The reflection-mode Debye–Scherrer geometry for CPS detectors is unique in the sense that the angle for the incident X-ray beam is kept fixed with respect to the normal of a flat diffracting sample, while the diffracted beams are measured at multiple angles with respect to the sample normal. An efficient method for precise lattice parameter determination using linear extrapolation of apparent lattice parameters calculated from differenthkldiffraction peaks is proposed for such geometries. The accuracy involved with this method is investigated for an Si powder standard. The extrapolation method is then applied to develop an empirical relationship between composition (x) and the lattice parameter (ao) of Smx/2Ndx/2Ce1−xO2−δceramics for solid oxide fuel cell electrolytes. In this system, the empirical relationship betweenxandaois compared with a previous theoretical prediction.

Time-resolved studies of the order–disorder phase transformations in rare-earth–transition metal intermetallics with 2-17 stoichiometry

High-temperature order–disorder transformations in R2T17 and R2T17-M-C intermetallics with R = Pr, Sm, Dy, Tb; T = Co, Fe; and M = Zr, Nb were studied utilizing time-resolved synchrotron x-ray diffraction at the Advanced Photon Source (APS) at the U.S. Department of Energy’s Argonne National Laboratory (Argonne, IL). High-energy synchrotron radiation provides intense, highly penetrating x-rays, which are ideal for in situ studies of phase transformations. Alloying additions are used to stabilize formation of metastable phases; their influence on order recovery was investigated. The experimental setup utilized Debye–Scherrer geometry; specimens were heated at a rate of 10 K/min. Full-profile diffraction patterns collected every 10 s were refined in sequence using the Rietveld method to track changes of lattice parameters and phase assemblages during heating. Sharp changes observed in the evolution of temperature-dependent lattice parameters suggested formation of ordered structure via nucleation and growth. Both 2-17 polymorphs co-existed in light and heavy rare-earth systems at high temperatures. The presence of alloying additions in the solid solution greatly influenced long-range order formation.