Laue Spots Research Articles

High-quality single crystal growth and magnetic property of Mn4Ta2O9

A large-size single crystal of Mn4Ta2O9 with ∼3.5 mm in diameter and ∼65 mm in length was successfully grown for the first time by a newly designed one-step method based on the optical floating zone technique. Both the clear Laue spots and sharp XRD Bragg reflections suggest the high quality of the single crystal. In Mn4Ta2O9 single crystal, an antiferromagnetic phase transition was observed below Néel temperature 102 K along c axis, which is similar to the isostructural compound Mn4Nb2O9, but differs from the isostructural Co4Nb2O9. Relative dielectric constant at 30 kOe suggests that no magnetoelectric coupling exists in Mn4Ta2O9.

Deformation behaviour of [001] oriented MgO using combined in-situ nano-indentation and micro-Laue diffraction

We report a coupled in-situ micro-Laue diffraction and nano-indentation experiment, with spatial and time resolution, to investigate the deformation mechanisms in [001]-oriented single crystal MgO. Crystal plasticity finite element modelling was applied to aid interpretation of the experimental observations of plasticity. The Laue spots showed both rotation and streaking upon indentation that is typically indicative of both elastic lattice rotation and plastic strain gradients respectively in the material. Multiple facets of streaking of the Laue peaks suggested plastic slip occurring on almost all the {101}-type slip planes oriented 45° to the sample surface with no indication of slip on the 90° {110} planes. Crystal plasticity modelling also supported these experimental observations. Owing to asymmetric slip beneath the indenter, as predicted by modelling results and observed through Laue analysis, sub-grains were found to nucleate with distinct misorientation. With cyclic loading, the mechanical hysteresis behaviour in MgO is revealed through the changing profiles of the Laue reflections, driven by reversal of plastic strain by the stored elastic energy. Crystal plasticity simulations have also shown explicitly that in subsequent loading cycles after first, the secondary slip system unloads completely elastically while some plastic strain of the primary slip reverses. Tracking the Laue peak movement, a higher degree of lattice rotation was seen to occur in the material under the indent, which gradually decreased moving laterally away. With the progress of deformation, the full field elastic strain and rotation gradients were also constructed which showed opposite lattice rotations on either sides of the indent.

Characterization of microscopic deformation in Cu-Al-Mn superelastic alloy by in situ Laue diffraction study using white X-ray microbeam

In this study, in situ white X-ray microbeam diffraction experiments were conducted to investigate the microscopic deformation behavior of a Cu-Al-Mn superelastic alloy during tensile testing. Local deformation both at a grain scale and an intragranular scale was revealed by analyzing Laue spot streaking that occurred within a grain and in some grains with different orientations. The streaking measured within a grain under tensile load showed inhomogeneous behavior because of an inhomogeneous martensitic transformation. Moreover, the effect was dependent on grain orientation. In a grain with a high Schmid factor, a large dispersion in the 2θ diffraction angle of Laue spots was observed due to significant Laue spot streaking, which can be attributed to that grain's favored martensitic transformation.

Relating Residual Stress and Substructural Evolution During Tensile Deformation of an Aluminum-Manganese Alloy

Interrupted tensile tests were coupled with ex situ measurements of residual stress and microtexture. The residual stress quantification involved measurements of six independent Laue spots and conversion of the interplanar spacings to the residual stress tensor. A clear orientation-dependent residual stress evolution emerged from the experiments and the numerical simulations. For the orientations undergoing negligible changes in ρ GND (density of geometrically necessary dislocation), the residual stress developments appeared to be governed by the elastic stiffness of the grain clusters. For the others, the evolution of the residual stress and ρ GND exhibited a clear orientation-dependent scaling.

Accuracy of stress measurement by Laue microdiffraction (Laue-DIC method): the influence of image noise, calibration errors and spot number.

Laue microdiffraction, available at several synchrotron radiation facilities, is well suited for measuring the intragranular stress field in deformed materials thanks to the achievable submicrometer beam size. The traditional method for extracting elastic strain (and hence stress) and lattice orientation from a microdiffraction image relies on fitting each Laue spot with an analytical function to estimate the peak position on the detector screen. The method is thus limited to spots exhibiting ellipsoidal shapes, thereby impeding the study of specimens plastically deformed. To overcome this difficulty, the so-called Laue-DIC method introduces digital image correlation (DIC) for the evaluation of the relative positions of spots, which can thus be of any shape. This paper is dedicated to evaluating the accuracy of this Laue-DIC method. First, a simple image noise model is established and verified on the data acquired at beamline BM32 of the European Synchrotron Radiation Facility. Then, the effect of image noise on errors on spot displacement measured by DIC is evaluated by Monte Carlo simulation. Finally, the combined effect of the image noise, calibration errors and the number of Laue spots used for data treatment is investigated. Results in terms of the uncertainty of stress measurement are provided, and various error regimes are identified.

Single-shot full strain tensor determination with microbeam X-ray Laue diffraction and a two-dimensional energy-dispersive detector.

The full strain and stress tensor determination in a triaxially stressed single crystal using X-ray diffraction requires a series of lattice spacing measurements at different crystal orientations. This can be achieved using a tunable X-ray source. This article reports on a novel experimental procedure for single-shot full strain tensor determination using polychromatic synchrotron radiation with an energy range from 5 to 23 keV. Microbeam X-ray Laue diffraction patterns were collected from a copper micro-bending beam along the central axis (centroid of the cross section). Taking advantage of a two-dimensional energy-dispersive X-ray detector (pnCCD), the position and energy of the collected Laue spots were measured for multiple positions on the sample, allowing the measurement of variations in the local microstructure. At the same time, both the deviatoric and hydrostatic components of the elastic strain and stress tensors were calculated.

Creating von Laue patterns in crystal scattering with partially coherent sources

When spatially coherent radiation is diffracted by a crystalline object, the field is scattered in specific directions, giving rise to so-called von Laue patterns. We examine the role of spatial coherence in this process. Using the first-order Born approximation, a general analytic expression for the far-zone spectral density of the scattered field is obtained. This equation relates the coherence properties of the source to the angular distribution of the scattered intensity. We apply this result to two types of sources. Quasihomogeneous Gaussian Schell-model sources are found to produce von Laue spots whose size is governed by the effective source width. Delta-correlated ring sources produce von Laue rings and ellipses instead of point-like spots. In forward scattering, polychromatic ellipses are created, whereas in backscattering striking, overlapping ring patterns are formed. We show that both the directionality and the wavelength-selectivity of the scattering process can be controlled by the state of coherence of the illuminating source.

Using coupled micropillar compression and micro-Laue diffraction to investigate deformation mechanisms in a complex metallic alloy Al13Co4

In this study, we have used in-situ micro-Laue diffraction combined with micropillar compression of focused ion beam milled Al13Co4 complex metallic alloy to investigate the evolution of deformation in Al13Co4. Streaking of the Laue spots shows that the onset of plastic flow occurs at stresses as low as 0.8 GPa, although macroscopic yield only becomes apparent at 2 GPa. The measured misorientations, obtained from peak splitting, enable the geometrically necessary dislocation density to be estimated as 1.1 × 1013 m−2.

Application of a pnCCD for energy-dispersive Laue diffraction with ultra-hard X-rays

In this work the spectroscopic performance of a pnCCD detector in the ultra-hard energy range between 40 and 140 keV is tested by means of an energy-dispersive Laue diffraction experiment on a GaAs crystal. About 100 Bragg peaks were collected in a single-shot exposure of the arbitrarily oriented sample to white synchrotron radiation provided by a wiggler at BESSY II and resolved in a large reciprocal-space volume. The positions and energies of individual Laue spots could be determined with a spatial accuracy of less than one pixel and a relative energy resolution better than 1%. In this way the unit-cell parameters of GaAs were extracted with an accuracy of 0.5%, allowing for a complete indexing of the recorded Laue pattern. Despite the low quantum efficiency of the pnCCD (below 7%), experimental structure factors could be obtained from the three-dimensional data sets, taking into account photoelectric absorption as well as Compton scattering processes inside the detector. The agreement between measured and theoretical kinematical structure factors calculated from the known crystal structure is of the order of 10%. The results of this experiment demonstrate the potential of pnCCD detectors for applications in X-ray structure analysis using the complete energy spectrum of synchrotron radiation.

Fast GPU-based absolute intensity determination for energy-dispersive X-ray Laue diffraction

This paper presents a novel method for fast determination of absolute intensities in the sites of Laue spots generated by a tetragonal hen egg-white lysozyme crystal after exposure to white synchrotron radiation during an energy-dispersive X-ray Laue diffraction experiment. The Laue spots are taken by means of an energy-dispersive X-ray 2D pnCCD detector. Current pnCCD detectors have a spatial resolution of 384 × 384 pixels of size 75 × 75 μm2 each and operate at a maximum of 400 Hz. Future devices are going to have higher spatial resolution and frame rates.The proposed method runs on a computer equipped with multiple Graphics Processing Units (GPUs) which provide fast and parallel processing capabilities. Accordingly, our GPU-based algorithm exploits these capabilities to further analyse the Laue spots of the sample. The main contribution of the paper is therefore an alternative algorithm for determining absolute intensities of Laue spots which are themselves computed from a sequence of pnCCD frames. Moreover, a new method for integrating spectral peak intensities and improved background correction, a different way of calculating mean count rate of the background signal and also a new method for n-dimensional Poisson fitting are presented.We present a comparison of the quality of results from the GPU-based algorithm with the quality of results from a prior (base) algorithm running on CPU. This comparison shows that our algorithm is able to produce results with at least the same quality as the base algorithm. Furthermore, the GPU-based algorithm is able to speed up one of the most time-consuming parts of the base algorithm, which is n-dimensional Poisson fitting, by a factor of more than 3. Also, the entire procedure of extracting Laue spots' positions, energies and absolute intensities from a raw dataset of pnCCD frames is accelerated by a factor of more than 3.

Determination of deviatoric elastic strain and lattice orientation by applying digital image correlation to Laue microdiffraction images: the enhanced Laue-DIC method

A new method of determining the deviatoric elastic strain and lattice orientation from Laue microdiffraction images is presented. Standard data treatment methods can suffer from the difficulty of precisely pinpointing the positions of diffraction peaks on two-dimensional Laue images. In a previous article, digital image correlation (DIC) was introduced for the treatment of Laue images, leading to the so-called Laue-DIC method. This performed better than the standard method in terms of the deviatoric elastic strain increment and relative rotation from one lattice to another, particularly when the shape of the Laue spots departs from regular ellipsoids. The present work intends to push forward the Laue-DIC method, aiming to determine the deviatoric elastic strain and lattice orientation, as well as the calibration parameters. The performance of this new method, named enhanced Laue-DIC, is assessed by modeling the spot displacements and accounting for random fluctuations relevant for typical experimental conditions. When the enhanced Laue-DIC method is applied to the case of anin situdeformed Si crystal, the obtained standard deviation of local stress is of the order of 1–2 MPa, while the calibration parameters are optimized to high accuracy.

Correlating sampling and intensity statistics in nanoparticle diffraction experiments

In a previous article [Öztürk, Yan, Hill & Noyan (2014). J. Appl. Cryst. 47, 1016–1025] it was shown that the sampling statistics of diffracting particle populations within a polycrystalline ensemble depended on the size of the constituent crystallites: broad X-ray peak breadths enabled some nano-sized particles to contribute more than one diffraction spot to Debye–Scherrer rings. Here it is shown that the equations proposed by Alexander, Klug & Kummer [J. Appl. Phys. (1948), 19, 742–753] (AKK) to link diffracting particle and diffracted intensity statistics are not applicable if the constituent crystallites of the powder are below 10 nm. In this size range, (i) the one-to-one correspondence between diffracting particles and Laue spots assumed in the AKK analysis is not satisfied, and (ii) the crystallographic correlation between Laue spots originating from the same grain invalidates the assumption that all diffracting plane normals are randomly oriented and uncorrelated. Such correlation produces unexpected results in the selection of diffracting grains. For example, three or more Laue spots from a given grain for a particular reflection can only be observed at certain wavelengths. In addition, correcting the diffracted intensity values by the traditional Lorentz term, 1/cos θ, to compensate for the variation of particles sampled within a reflection band does not maintain fidelity to the number of poles contributing to the diffracted signal. A new term, cos θB/cos θ, corrects this problem.

Laue-DIC: a new method for improved stress field measurements at the micrometer scale.

A better understanding of the effective mechanical behavior of polycrystalline materials requires an accurate knowledge of the behavior at a scale smaller than the grain size. The X-ray Laue microdiffraction technique available at beamline BM32 at the European Synchrotron Radiation Facility is ideally suited for probing elastic strains (and associated stresses) in deformed polycrystalline materials with a spatial resolution smaller than a micrometer. However, the standard technique used to evaluate local stresses from the distortion of Laue patterns lacks accuracy for many micromechanical applications, mostly due to (i) the fitting of Laue spots by analytical functions, and (ii) the necessary comparison of the measured pattern with the theoretical one from an unstrained reference specimen. In the present paper, a new method for the analysis of Laue images is presented. A Digital Image Correlation (DIC) technique, which is essentially insensitive to the shape of Laue spots, is applied to measure the relative distortion of Laue patterns acquired at two different positions on the specimen. The new method is tested on an in situ deformed Si single-crystal, for which the prescribed stress distribution has been calculated by finite-element analysis. It is shown that the new Laue-DIC method allows determination of local stresses with a strain resolution of the order of 10(-5).

High-quality single crystal growth and spin flop of multiferroic Co4Nb2O9

A single crystal of Co4Nb2O9 about 7mm in diameter and 55mm in length was successfully grown by an optical floating zone method. X-ray powder diffraction (XRD) indicates that it has a single phase corundum-type structure. Clear Laue spots and sharp XRD peaks confirm the good quality and crystallographic orientations. Below TN, magnetization of Co4Nb2O9 along a axis shows dramatically different behaviors between H=1kOe and 20kOe, suggesting a spin flop occurs along a axis. Ma(H) curve at 5K shows a change of slope at a critical magnetic field of 7.5kOe for triggering the spin flip.

Single Molecule Motion Map of GLIC by Diffracted X-Ray Tracking

GLIC is a proton-gated bacterial ion channel from Gloeobacter violaceus and is a member of pentameric ligand-gated ion channels. Recently structural information of GLIC in open (acidic pH) and closed state (neutral pH) has become available (1,2), and the gating mechanism is discussed based on the structural information. However the dynamic information of each state in physical point of view is not available. Here we used the diffracted X-ray tracking (DXT) method (3) to detect the motion of the extracellular or transmembrane domain of GLIC. DXT has been considered as a powerful technique in biological science for detecting atomic-scale dynamic motion of the target protein at the single molecular level at several tens of microseconds time resolution. The dynamics of a single protein can be monitored through trajectory of a Laue spot from a nanocrystal which was attached to the target protein immobilized on the substrate surface (4,5).DXT observation was performed at BL40XU in SPring-8 Japan and showed that tilting motion of the transmembrane domain of GLIC and both tilting and twisting motions of the extracellular domain of GLIC were enhanced in open state (acidic pH). The detailed information on dynamic will be discussed.[1] N. Bocquet et al., Nature 457:111 (2009)[2] L. Sauguet et al., PNAS 111:966 (2014)[3] Y.C. Sasaki et al., Phys. Rev. E 62:3843 (2000)[4] H. Sekiguchi et al, PLOS ONE 8:e64176 (2013)[5] H. Sekiguchi et al, Scientific Reports 4:6384 (2014)

Fast GPU-based spot extraction for energy-dispersive X-ray Laue diffraction

This paper describes a novel method for fast online analysis of X-ray Laue spots taken by means of an energy-dispersive X-ray 2D detector. Current pnCCD detectors typically operate at some 100 Hz (up to a maximum of 400 Hz) and have a resolution of 384 × 384 pixels, future devices head for even higher pixel counts and frame rates.The proposed online data analysis is based on a computer utilizing multiple Graphics Processing Units (GPUs), which allow for fast and parallel data processing. Our multi-GPU based algorithm is compliant with the rules of stream-based data processing, for which GPUs are optimized. The paper's main contribution is therefore an alternative algorithm for the determination of spot positions and energies over the full sequence of pnCCD data frames. Furthermore, an improved background suppression algorithm is presented.The resulting system is able to process data at the maximum acquisition rate of 400 Hz. We present a detailed analysis of the spot positions and energies deduced from a prior (single-core) CPU-based and the novel GPU-based data processing, showing that the parallel computed results using the GPU implementation are at least of the same quality as prior CPU-based results. Furthermore, the GPU-based algorithm is able to speed up the data processing by a factor of 7 (in comparison to single-core CPU-based algorithm) which effectively makes the detector system more suitable for online data processing.

A new method for polychromatic X-ray μLaue diffraction on a Cu pillar using an energy-dispersive pn-junction charge-coupled device.

μLaue diffraction with a polychromatic X-ray beam can be used to measure strain fields and crystal orientations of micro crystals. The hydrostatic strain tensor can be obtained once the energy profile of the reflections is measured. However, this remains a challenge both on the time scale and reproducibility of the beam position on the sample. In this review, we present a new approach to obtain the spatial and energy profiles of Laue spots by using a pn-junction charge-coupled device, an energy-dispersive area detector providing 3D resolution of incident X-rays. The morphology and energetic structure of various Bragg peaks from a single crystalline Cu micro-cantilever used as a test system were simultaneously acquired. The method facilitates the determination of the Laue spots' energy spectra without filtering the white X-ray beam. The synchrotron experiment was performed at the BM32 beamline of ESRF using polychromatic X-rays in the energy range between 5 and 25 keV and a beam size of 0.5 μm × 0.5 μm. The feasibility test on the well known system demonstrates the capabilities of the approach and introduces the "3D detector method" as a promising tool for material investigations to separate bending and strain for technical materials.

A tunable multicolour `rainbow' filter for improved stress and dislocation density field mapping in polycrystals using X-ray Laue microdiffraction

White-beam X-ray Laue microdiffraction allows fast mapping of crystal orientation and strain fields in polycrystals, with a submicron spatial resolution in two dimensions. In the well crystallized parts of the grains, the analysis of Laue-spot positions provides the local deviatoric strain tensor. The hydrostatic part of the strain tensor may also be obtained, at the cost of a longer measuring time, by measuring the energy profiles of the Laue spots using a variable-energy monochromatic beam. A new `rainbow' method is presented, which allows measurement of the energy profiles of the Laue spots while remaining in the white-beam mode. It offers mostly the same information as the latter monochromatic method, but with two advantages: (i) the simultaneous measurement of the energy profiles and the Laue pattern; (ii) rapid access to energy profiles of a larger number of spots, for equivalent scans on the angle of the optical element. The method proceeds in the opposite way compared to a monochromator-based method, by simultaneously removing several sharp energy bands from the incident beam, instead of selecting a single one. It uses a diamond single crystal placed upstream of the sample. Each Laue diffraction by diamond lattice planes attenuates the corresponding energy in the incident spectrum. By rotating the crystal, the filtered-out energies can be varied in a controlled manner, allowing one to determine the extinction energies of several Laue spots of the studied sample. The energies filtered out by the diamond crystal are obtained by measuring its Laue pattern with another two-dimensional detector, at each rotation step. This article demonstrates the feasibility of the method and its validation through the measurement of a known lattice parameter.

High quality FeSb2 single crystal growth by the gradient freeze technique

A single crystal of FeSb2 about 5mm in diameter and 10mm in length with a tapering spire was grown by the gradient freeze technique combining the Bridgman technique and flux method using Sb-rich melts in sealed quartz ampoules. X-ray powder diffraction pattern of single crystal FeSb2 indicates that it is a single phase marcasite structure. Clear Laue spots and scanning electron microscopy photographs indicate good quality and uniform of the FeSb2 single crystal. Magnetic susceptibility of FeSb2 along b-axis does not show the diamagnetic to paramagnetic crossover, indicating the intrinsic susceptibility of FeSb2 determined on large single crystals differs from that of the smaller samples prepared by other techniques. The new method of gradient freeze is of great significance for the single crystal growth of FeSb2 like materials with a peritectic point.

Assessment of Plastic Deformation Induced by Indentation on a Large Grain on Inconel 600 Using Synchrotron Polychromatic X-ray Microdiffraction

A synchrotron-based three-dimensional (3-D) Laue technique called Differential Aperture X-ray microscopy (DAXM) was used to investigate plastic deformation of Inconel 600 induced by indentation. The DAXM technique is capable of probing up to 60 to 100 μm into the Ni alloy, with micron resolution. A conical indenter was used to generate an indent on a large surface grain on Inconel 600. The DAXM Laue images from the uppermost grain exhibited pronounced streaking and splitting of Laue spots, which increased as the grain boundary was approached. Splitting of the Laue patterns correlates with subgrain or dislocation cell formation. A significant amount of dislocation cell formation was found within the 1-μm voxels probed by DAXM. A change in total angle of 8.79 deg was determined for the uppermost grain from the diffraction data from depths 4 to 28 μm, with an average misorientation angle of 2.15 deg between the dislocation cells. The next grain having a different crystallographic orientation continued to rotate in the same direction as the uppermost grain due to the large plastic deformation.