Asymmetric Diffraction Geometry Research Articles

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.

Applied strain effect to the luminosity and divergence of neutron monochromator with fully asymmetric diffraction

The effect of applied strain on the luminosity and divergence of neutron monochromator with fully asymmetric diffraction geometry will be reported. The monochromator used silicon single crystal with 200 x 30 x 4 mm3, which has the parallel face of the crystal to the planes (220). The plain used for this monochromator was (311), which has a 31.5 degree to the (220) face. Fully asymmetric diffraction geometry had been fulfilled with the take-of-angle of the monochromator at 63 degrees. Four lines are bending system used for applying the strain to the crystal, which remote-controlled by computer. The 0, 25, 50, 75, 100, 125, 150, 175, 200 microStrain (uStrain) applied the monochromator crystal respectively. Diffracted neutron from the monochromator was monitored by using a neutron camera for evaluating the luminosity and divergence of the beam. The wavelength of the monochromatized beam was calibrated by using a Nickel rod.

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.

Magnifying effect by neutron diffraction on cylindrically bent perfect crystal (BPC) of Si in fully asymmetric diffraction geometry

Low absorption of neutrons in Si crystal enables using the fully asymmetric diffraction geometry (FAD) of the single crystal slab in which neutron beam can pass inside a rather long distance more than ten centimetres. A practical exploitation of this property can be namely in the case of bent perfect crystals when due to the homogeneous deformation a neutron beam can meet, on the path, the diffraction condition only once and its attenuation is mainly brought about by absorption or incoherent scattering. In this paper a large one dimensional magnifying property of the FAD geometry of the cylindrically bent perfect crystal slab of Si is demonstrated. This property can be used in high resolution small angle neutron scattering as well as in neutron imaging.

Neutron diffraction studies of a double-crystal (+n,-m) setting containing a fully asymmetric diffraction geometry (FAD) of a bent perfect crystal (BPC)

In this paper, some results of neutron diffraction properties of the double-crystal Si(111) + Si(311) setting containing two bent perfect crystals, but with the second one – analyzer in the fully asymmetric diffraction geometry are presented. Both fully asymmetric diffraction geometries, with the output beam compression as well as the output beam expansion, were tested for the sake of possible applications.

Neutron Diffraction Studies of a Fully Asymmetric Diffraction Geometry of a Bent Perfect Crystal with the Output Beam Compression

Neutron Diffraction Studies of a Fully Asymmetric Diffraction Geometry of a Bent Perfect Crystal with the Output Beam Compression P. Mikulaa,∗, M. Vrana, J. Saroun, V. Em and J. Capek Nuclear Physics Institute ASCR, v.v.i., 25068 Řež, Czech Republic National Research Centre “Kurchatov Institute”, Moscow, 123182, Russia Faculty of Mathematics and Physics, Charles University, 12116 Prague, Czech Republic

Comparison of double crystal (+n,-m) and (+n,+m) settings containing a fully asymmetric diffraction geometry of a bent perfect crystal with the output beam expansion

In this paper neutron diffraction properties of the dispersive double crystal (+n,-m) and (+n,+m) settings containing the bent perfect crystal Si(220) in symmetric diffraction geometry and the bent perfect crystal Si(311) in the fully asymmetric diffraction geometry with the output beam expansion are studied and compared. It has been found that the properties, namely, the width of the output double diffracted beam, of both settings strongly depends on the relative combination of curvatures of Si(311) crystal slab with respect to the curvature of the Si(220) one. Moreover, after the beam expansion the fully asymmetric diffraction geometry provides in both cases a highly collimated and highly monochromatic beam of a rather large cross-section of several square centimetres. Application possibilities, of such a beam, namely for neutron phase contrast radiography will be discussed.

Whole powder pattern decomposition - An application for the evaluation of residual stress states in consideration of steep stress gradients

The whole powder pattern decomposition procedure is an established tool for the analysis of diffraction patterns with overlapping reflections. Its adapted application to data obtained in asymmetric diffraction geometry was shown to yield depth-resolved results of biaxial residual stress states, e.g. of thin film materials. Yet, with increasing coating thickness and in presence of pronounced stress gradients, this approach overestimates the magnitudes of the residual stresses present. The current work aims at overcoming this by including the variations in X-ray penetration depth encountered during the experiment into the applied refinement strategy. A proof of concept is obtained by measuring stress states in molybdenum thin films as a model material using the proposed approach in comparison to classical X-ray residual stress evaluation techniques.

Neutron diffraction studies of a high resolution double crystal (+n,-m) setting containing Si(220) and Si(311) bent perfect crystals in symmetric and fully asymmetric diffraction geometry, respectively

In this paper studies of neutron diffraction properties of the double crystal (+n,-m) setting containing Si(220) and Si(311) bent perfect crystals (BPC) in symmetric and fully asymmetric diffraction (FAD) geometry with the output beam expansion (OBE), respectively, are presented. Namely, our attention was focused on the properties of the FAD geometry of the BPC Si(311) crystal slab. It has been found that after a beam expansion this FAD geometry can provide a monochromatic beam of a rather large cross-section and of very small divergence with some possible application use.

Neutron diffraction studies of a double-crystal (+n,–m) setting containing a fully asymmetric diffraction geometry of a bent perfect crystal with output beam expansion

The neutron diffraction properties of a double-crystal (+n,−m) setting, which contains a bent perfect Si(311) crystal in the fully asymmetric diffraction (FAD) geometry with output beam expansion and a bent perfect Si(220) crystal in the symmetric diffraction geometry, are presented. Generally, there are two possibilities for the FAD geometry: either with output beam compression or with output beam expansion. In this case, attention has been focused on the latter. The properties of the (+n,−m) double-bent-crystal arrangement of a bent perfect crystal FAD Si(311) geometry, in combination with a bent Si(220) crystal slab in the symmetric diffraction geometry, were studied. It was found that, after beam expansion, this FAD geometry can provide a monochromatic beam of rather large cross section but very small divergence.

X-ray diffraction study of residual elastic stress and microstructure of near-surface layers in nickel-titanium alloy irradiated with low-energy high-current electron beams

In the work, we compare quantitative estimates of residual stresses in nickel-titanium (NiTi) alloy surface layers after electron beam treatment. The quantitative estimates to be compared were taken using X-ray diffraction (XRD) techniques with symmetric and asymmetric Bragg diffraction geometries. A method of quantitative X-ray diffraction estimation of residual stresses in materials with gradient changes in microstructure and physical properties, including elastic moduli, is described. It is found that in a NiTi specimen with one side irradiated by a low-energy high-current electron beam, the maximum residual elastic stresses σ ≈550MPa are localized in the modified surface layer (melted by the electron beam and rapidly quenched), whereas the residual elastic stresses in the underlying layer with initial B2 structure are no greater than ∼100MPa. It is for this reason that stress-induced B19′ martensite is formed in the material layer beneath the modified layer.

Structural evolution of Pd-capped Mg thin films under H2 absorption and desorption cycles

In this paper we present a study on the relation between the evolution, upon successive H2 cycling, of the crystalline order and the H2 sorption properties of Pd-capped textured Mg thin films grown on Si and glass substrates. Using an asymmetric diffraction geometry suitable for thin films, it is found that: i) hydrogen desorption can be achieved at low temperatures exposing the samples to air and ii) already upon one hydrogen absorption–desorption cycle, the original texture is lost. Moreover metal-to-insulator transition following magnesium hydride formation is observed through spectrophotometry. However, cycling results in being detrimental to film properties, mainly due to the Pd cap degradation and correlated processes.

Anin situmethod for the study of strain broadening using synchrotron X-ray diffraction

A tensonometer for stretching metal foils has been constructed for the study of strain broadening in X-ray diffraction line profiles. This device, which is designed for use on powder diffractometers and was tested on Station 2.3 at Daresbury Laboratory, allowsin situmeasurements to be performed on samples under stress. It can be used for data collection in either transmission or reflection modes using either symmetric or asymmetric diffraction geometries. As a test case, measurements were carried out on an 18 µm-thick copper foil experiencing strain levels of up to 5% using both symmetric reflection and symmetric transmission diffraction. All the diffraction profiles displayed peak broadening and asymmetry which increased with strain. The measured profiles were analysed by the fundamental-parameters approach using theTOPASpeak-fitting software. All the observed broadened profiles were modelled by convoluting a refineable diffraction profile, representing the dislocation and crystallite size broadening, with a fixed instrumental profile predetermined using high-quality LaB6reference powder. The deconvolution process yielded `pure' sample integral breadths and asymmetry results which displayed a strong dependence on applied strain and increased almost linearly with applied strain. Assuming crystallite size broadening in combination with dislocation broadening arising from f.c.c.a/2〈110〉{111} dislocations, the variation of mechanical property with strain has been extracted. The observation of both peak asymmetry and broadening has been interpreted as a manifestation of a cellular structure with cell walls and cell interiors possessing high and low dislocation densities.

Imaging defects in strained-silicon thin films by glancing-incidence x-ray topography

X-ray topographical images from thin (⩽50nm) strained-Si films grown on relaxed, planarized crystalline SiGe-on-Si (001) virtual substrates have been imaged by glancing-incidence monochromatic x-ray topography. This extremely asymmetric diffraction geometry, utilizing (311) diffraction planes, can limit penetration into the sample to as little as 6nm and allows separate images from the thin strained-Si film, the SiGe layer, and the base Si wafer to be recorded at different angles above the critical angle. Strain fields from the misfit dislocations in the SiGe layer penetrate the Si wafer and act as a template for the defect structure of the strained-Si films, even after an ex situ planarization step was inserted during the growth of the SiGe layer. This defect structure remains in the strained-Si film throughout the fabrication of strained-Si-on-insulator substrates.

Direct comparison of plastically deformed Ge mosaic crystal and bent perfect Si crystal for neutron monochromatization

The results of direct comparison of some monochromator properties of plastically deformed (mosaic) Ge single crystal with cylindrically bent perfect crystal (BPC) of Si are presented. Using a double-crystal diffractometer and α o=20′ collimation of the incident polychromatic beam we compared monochromatic beam current at the sample position for the take off angles of 40°, 50° and 60°. The comparison was carried out on the diffraction planes (3 1 1) M when the monochromators operated at nearly the same asymmetric diffraction geometry. For the sake of comparison of their resolution properties, Fe(1 1 0) and Fe(2 1 1) diffraction profiles of the beam scattered by a solid and well annealed α-Fe polycrystalline sample are also presented. It has been found that under these specific experimental conditions often used for residual strain scanning, the focusing bent Si crystal is a good cheap alternative to the flat mosaic Ge monochromator.

On the possibility of using bent perfect crystals in TOF neutron scattering devices

A silicon bent perfect crystal in fully asymmetric diffraction (FAD) geometry in combination with a linear position-sensitive detector can be effectively used for high-resolution analysis of a beam scattered by a sample. The results of the first promising time of flight (TOF) experimental tests of λ scanning carried out with the FAD of cylindrically bent Si slabs of different cuts are presented. The length and the homogeneous curvature of the crystal determine the range of Δλ/λ of about 10-2 that could be investigated with the accuracy of δk/k≈10-4. The obtained experimental results indicate that the FAD geometry of the bent Si slab in combination with a one-dimensional position-sensitive detector could be a good candidate for a high-resolution analyzer at some of the TOF instruments.

Asymmetric diffraction geometry of the bent crystal monochromator - A way to improve the properties of strain diffractometers

The possibility to advantageously exploit the asymmetric diffraction geometry of bent perfect crystals was studied with the aim of further increasing the detector signal and/or resolution of the strain diffractometer in Studsvik. It was proved that, in the case of strain diffractometers, the asymmetric diffraction geometry of the bent perfect crystal monochromator with output-beam extension can be considerably superior to the asymmetric geometry with output-beam compression usually used in powder diffractometry.

Mosaicity of GaN Epitaxial Layers: Simulation and Experiment

High-resolution X-ray diffraction has been used to analyze GaN epilayers with varying coalescence thickness which were grown by MOVPE on (0001) oriented sapphire. The decrease of the density of edge type threading dislocations with increasing coalescence thickness causes a marked difference in the mosaicity of the samples. As the defects form along the grain boundaries, this corresponds to an increase in lateral coherence length with increasing coalescence thickness. The lateral coherence length has been obtained from simulations of reciprocal lattice points of off-axis Bragg reflections, measured in asymmetric diffraction geometry.

Analysis of carbon fibers and carbon composites by asymmetric X-ray diffraction technique

The effect of annealing on the microstructure of three sets of carbon fibers and their composites with a phenol-formaldehyde matrix was investigated by X-ray diffraction. An asymmetric diffraction geometry with parallel beam optics was used to get more information in comparison with conventional diffraction experiments. It was found that the microstructure of the samples is improved after annealing up to 2800°C in terms of the following parameters: the narrowing of the orientation distribution function of (00l) planes by a factor between 2 and 3 was observed, and this effect of the annealing ordering is more pronounced for the composites than for the fibers alone. The degree of graphitization increases by annealing, which is reflected in the decrease of the interplanar distance of (002) planes from about 3.51 Å to 3.40 Å, without any significant difference between the fibers and composites. The line broadening due to microstrains and small size effects is also strongly reduced by the annealing but the asymmetric shape of 100 and 110 reflections suggests that the layer stacking is still turbostratic.