On the resolution function for powder diffraction with area detectors

In a powder diffraction experiment the resolution function defines the instrumental contribution to the peak widths as a function of the Bragg angle. The Caglioti formula is frequently applied to model the instrumental broadening and used in structural refinement. The parameters in the Caglioti formula are linked to physically meaningful parameters for most diffraction geometries. However, this link is lost for the now very popular powder diffraction geometry using large 2D area detectors. Here we suggest a new physical model for the instrumental broadening specifically developed for powder diffraction data measured with large 2D area detectors. The model is verified using data from two synchrotron diffraction beamlines with the Pilatus2M and MAR345 detectors. Finally, a functional form is proposed to replace the Caglioti formula for this geometry in the Rietveld method and profile refinements.

Dynamical effects in the integrated X-ray scattering intensity from imperfect crystals in Bragg diffraction geometry. II. Dynamical theory

The analytical expressions for coherent and diffuse components of the integrated reflection coefficient are considered in the case of Bragg diffraction geometry for single crystals containing randomly distributed microdefects. These expressions are analyzed numerically for the cases when the instrumental integration of the diffracted X-ray intensity is performed on one, two or three dimensions in the reciprocal-lattice space. The influence of dynamical effects, i.e. primary extinction and anomalously weak and strong absorption, on the integrated intensities of X-ray scattering is investigated in relation to the crystal structure imperfections.

A polarization-switch effect of silicon crystals under multiple-beam diffraction geometry

On the basis of rigorous dynamical-theory calculations, a complete X-ray polarization-switch effect of silicon crystals at the exact multiple-beam diffraction condition is demonstrated. The underlying physical mechanism of this unique phenomenon can be revealed using a simple multiple-wave propagation and interference model. The constructive and destructive interference of the multiple detoured-diffraction beams along the direction of the primary diffracted beam directly leads to the complete polarization switch. This phenomenon can be realized using both synchrotron and laboratory X-ray sources at many discrete wavelengths, and used to design a novel crystal-based polarizer to achieve a 90° polarization rotation.

Investigation of multiple Bragg reflections and their possible exploitation

This paper summarizes recent results of an exhaustive experimental study of multiple Bragg reflections accompanying allowed as well as forbidden reflections. The multiple reflection observations were carried out in the frame of Bragg diffraction optics experiments on cylindrically bent perfect single crystals. It has been found that depending on the thickness and curvature of the crystal slabs and the diffraction geometry (reflection, transmission), many strong multiple reflections can be excited which can also be used as a source of highly monochromatic and highly collimated beams for further experiments requiring extremely high resolution.

Dynamical effects in the integrated X-ray scattering intensity from imperfect crystals in Bragg diffraction geometry. I. Semi-dynamical model

The analytical expressions for the coherent and diffuse components of the integrated reflection coefficient are considered in the case of asymmetric Bragg diffraction geometry for a single crystal of arbitrary thickness, which contains randomly distributed Coulomb-type defects. The possibility to choose the combinations of diffraction conditions optimal for characterizing defects of several types by accounting for dynamical effects in the integrated coherent and diffuse scattering intensities, i.e. primary extinction and anomalous absorption, has been analysed based on the statistical dynamical theory of X-ray diffraction by imperfect crystals. The measured integrated reflectivity dependencies of the imperfect silicon crystal on azimuthal angle were fitted to determine the diffraction parameters characterizing defects in the sample using the proposed formulas in semi-dynamical and semi-kinematical approaches.

3D grain reconstruction from laboratory diffraction contrast tomography

A method for reconstructing the three-dimensional grain structure from data collected with a recently introduced laboratory-based X-ray diffraction contrast tomography system is presented. Diffraction contrast patterns are recorded in Laue-focusing geometry. The diffraction geometry exposes shape information within recorded diffraction spots. In order to yield the three-dimensional crystallographic microstructure, diffraction spots are extracted and fed into a reconstruction scheme. The scheme successively traverses and refines solution space until a reasonable reconstruction is reached. This unique reconstruction approach produces results efficiently and fast for well suited samples.

A middle energy-bandwidth X-ray monochromator for high-flux synchrotron diffraction: revisiting asymmetrically cut silicon crystals

To supply the growing demand for high photon flux in synchrotron science including surface diffraction, a middle energy-bandwidth monochromator covering the 10−4 to 10−3 range has been adapted by applying an asymmetric diffraction geometry to a cryogenically cooled silicon 111 double-crystal monochromator used as a standard for the undulator source at SPring-8. The asymmetric geometry provides a great advantage with its ability to configure flux gains over a wide energy range by simply changing the asymmetry angle, while the angular divergence of the exit beam remains unchanged. A monolithic design with three faces has been employed, having one symmetrically cut and another two asymmetrically cut surfaces relative to the same atomic plane, maintaining cooling efficiency and the capability of quickly changing the reflection surface. With the asymmetric geometry, an X-ray flux greater than 1014 photons s−1 was available around 12 keV. A maximum gain of 2.5 was obtained relative to the standard symmetric condition.

Dispersive double bent crystal monochromators Si(111) + Si(311) and Si(111) + Si(400) with a strongly asymmetric diffraction geometry of the analyzer for powder diffractometry

In this paper, some results of neutron diffraction properties of the dispersive double-crystal Si(111) + Si(311) and Si(111) + Si(400) monochromator settings containing two bent perfect crystals but with the second one – analyzer in the strongly asymmetric diffraction geometry, are presented. For the sake of possible applications, both double crystal settings were tested in the orientation of the second crystal for the output beam compression geometry. Powder diffraction test was carried out on a α-Fe(211) pin of the diameter of 2 mm. Contrary to the Si(111) + Si(400) setting, an excellent resolution represented by full width at half maximum in the (Δd/d)-scale was obtained for the Si(111) + Si(311) double crystal monochromator in the parallel as well as in the antiparallel diffraction geometry.

A new diffractometer for diffuse scattering studies on the ID28 beamline at the ESRF

A new diffractometer is now available to the general user community at the ESRF. The new diffractometer is a side station of the high-resolution inelastic X-ray scattering spectrometer on beamline ID28 and is located in the same experimental hutch. Both instruments can be operated simultaneously. The new diffractometer combines a fast and low-noise hybrid pixel detector with a variable diffraction geometry. The beam spot on the sample is 50 µm × 50 µm, where focusing is achieved by a combination of Be lenses and a KB mirror. Wavelengths from 0.5 to 0.8 Å can be used for the diffraction experiments. The setup is compatible with a variety of sample environments, allowing studies under non-ambient conditions. The diffractometer is optimized to allow a rapid survey of reciprocal space and diffuse scattering for the identification of regions of interest for subsequent inelastic scattering studies, but can also be employed as a fully independent station for structural studies from both powder and single-crystal diffraction experiments. Several software packages for the transformation and visualization of diffraction data are available. An analysis of data collected with the new diffractometer shows that the ID28 side station is a state-of-the-art instrument for structural investigations using diffraction and diffuse scattering experiments.