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Bragg coherent diffraction imaging of iron diffusion into gold nanocrystals

Understanding how diffusion takes place within nanocrystals is of great importance for their stability and for controlling their synthesis. In this study, we used the strain sensitivity of Bragg coherent diffraction imaging (BCDI) to study the diffusion of iron into individual gold nanocrystals in situ at elevated temperatures. The BCDI experiments were performed at the I-07 beamline at Diamond Light Source, UK. The diffraction pattern of individual gold nanocrystals was measured around the (11-1) Bragg peak of gold before and after iron deposition as a function of temperature and time. Phase retrieval algorithms were used to obtain real space reconstructions of the nanocrystals from their measured diffraction patterns. Alloying of iron with gold at sample temperatures of 300 °C–500 °C and dealloying of iron from gold at 600 °C were observed. The volume of the alloyed region in the nanocrystals was found to increase with the dose of iron. However, no significant time dependence was observed for the structure following each iron deposition, suggesting that the samples reached equilibrium relatively quickly. The resulting phase distribution within the gold nanocrystals after the iron depositions suggests a contraction due to diffusion of iron. Furthermore, our results show that BCDI is a useful technique for studying diffusion in three dimensions and alloying behaviour in individual crystalline grains.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A large interlaboratory electron diffraction study of monolayer graphene

Standardisation of data collection and analysis is essential to enable commercialisation of 2D materials in a wide range of technologies. Selected area electron diffraction (SAED) in the transmission electron microscope (TEM) is one of the key methods for distinguishing monolayer from bilayer and few-layer graphene by comparing the 1st and 2nd order diffraction spot intensities. Yet there are many factors that can affect the reliability of data collection and interpretation, causing the measurement of monolayer samples to deviate from the literature boundary condition of $I_{\{\bar{2}110\}}$$/$$I_{\{1\bar{1}00\}}$ < 1 for monolayer graphene (1LG). Here we present the results of a large interlaboratory SAED comparison study, where 15 international laboratories measured and analysed nominally identical samples of chemical vapour deposited graphene. Large variations were observed in the measured ratios of diffraction spot intensities, with the largest variance associated with poor quality SAED data resulting from inadequate specimen handling and storage. To inform the reliable determination of monolayer thickness from SAED patterns we provide a description of best practice for specimen handling, TEM operation, data collection and analysis. This work was undertaken within VAMAS Technical Working Area 41: Graphene and related 2D materials—Project 9, the results of which have been directly incorporated into ISO/TS 21356–2 for the characterisation of graphene sheets. We find that when this methodology is followed, 1LG can be distinguished from bilayer or thicker material with high confidence where analysis of a single SAED pattern gives $I_{\{\bar{2}110\}}$$/$$I_{\{1\bar{1}00\}}$ < 1.2, even in the absence of precise specimen tilting.

2D materials↗

Adaptive sampling for accelerating neutron diffraction-based strain mapping *

Abstract Neutron diffraction is a useful technique for mapping residual strains in dense metal objects. The technique works by placing an object in the path of a neutron beam, measuring the diffracted signals and inferring the local lattice strain values from the measurement. In order to map the strains across the entire object, the object is stepped one position at a time in the path of the neutron beam, typically in raster order, and at each position a strain value is estimated. Typical dwell times at neutron diffraction instruments result in an overall measurement that can take several hours to map an object that is several tens of centimeters in each dimension at a resolution of a few millimeters, during which the end users do not have an estimate of the global strain features and are at risk of incomplete information in case of instruments outages. In this paper, we propose an object adaptive sampling strategy to measure the significant points first. We start with a small initial uniform set of measurement points across the object to be mapped, compute the strain in those positions and use a machine learning technique to predict the next position to measure in the object. Specifically, we use a Bayesian optimization based on a Gaussian process regression method to infer the underlying strain field from a sparse set of measurements and predict the next most informative positions to measure based on estimates of the mean and variance in the strain fields estimated from the previously measured points. We demonstrate our real-time measure-infer-predict workflow on additively manufactured steel parts—demonstrating that we can get an accurate strain estimate even with 30%–40% of the typical number of measurements—leading the path to faster strain mapping with useful real-time feedback. We emphasize that the proposed method is general and can be used for fast mapping of other material properties such as phase fractions from time-consuming point-wise neutron measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Multi-angle Precession Electron Diffraction (MAPED): A Versatile Approach to 4D-STEM Precession

Precession of a converged beam during acquisition of a 4D-STEM dataset improves strain, orientation, and phase mapping accuracy by averaging over continuous angles of illumination. Precession experiments usually rely on integrated systems, where automatic alignments lead to fast, high-quality results. The dependence of these experiments on specific hardware and software is evident even when switching to nonintegrated detectors on a precession tool, as experimental set-up becomes challenging and time-consuming. Here, we introduce multi-angle precession electron diffraction (MAPED): a method to perform electron diffraction by collecting sequential 4D-STEM scans at different incident beam tilts. The multiple diffraction datasets are averaged together postacquisition, resulting in a single dataset that minimizes the impact of the curvature and orientation of the Ewald sphere relative to the crystal under study. Our results demonstrate that even four additional tilts improved measurement of material properties, namely strain and orientation, as compared to single-tilt 4D-STEM experiments. We show the versatility and flexibility of our MAPED approach with data collected on a number of microscopes with different hardware configurations and a variety of detectors.

4D-STEM↗

Inherent issues regarding the use of in situ x-ray diffraction measurements to determine temperature in shock-compressed metals

Temperature determination in shock compressed solids constitutes an important and long-standing scientific need. Since the reduction of Bragg diffracted peaks due to temperature increase, using the Debye-Waller factor, is well established, we examined the use of this approach to determine temperatures in shock compressed gold and platinum by representing the shocked state as a superposition of density and temperature changes. Comparison of the calculated and measured diffraction peaks did not show good agreement, because x-ray diffraction (XRD) profiles in the shock compressed state are not governed solely by density and temperature changes. XRD results are also influenced measurably by shock wave induced microstructural changes. Our results demonstrate that contributions from microstructural changes need to be incorporated and modeled in the theoretical analysis to use XRD measurements for reliable temperature determination in shock compressed solids.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Investigation of the commensurate magnetic structure in the heavy-fermion compound CePt 2 In 7 using magnetic resonant x-ray diffraction

In this paper, we investigated the magnetic structure of the heavy-fermion compound CePt 2 In 7 below T N = 5.34 (2) K using magnetic resonant x-ray diffraction at ambient pressure. The magnetic order is characterized by a commensurate propagation vector k 1/2 = (1/2, 1/2, 1/2) with spins lying in the basal plane. Our measurements did not reveal the presence of an incommensurate order propagating along the high-symmetry directions in reciprocal space but cannot exclude other incommensurate modulations or weak scattering intensities. The observed commensurate order can be described equivalently by either a single-k structure or by a multi-k structure. Furthermore we explain how a commensurate-only ordering may explain the broad distribution of internal fields observed in nuclear quadrupolar resonance experiments [Sakai et al., Phys. Rev. B 83, 140408 (2011)] that was previously attributed to an incommensurate order. We also report powder x-ray diffraction showing that the crystallographic structure of CePt 2 In 7 changes monotonically with pressure up to P = 7.3 GPa at room temperature. The determined bulk modulus B 0 = 81.1 (3) GPa is similar to those of the Ce-115 family. Broad diffraction peaks confirm the presence of pronounced strain in polycrystalline samples of CePt 2 In 7 . Lastly, we discuss how strain effects can lead to different electronic and magnetic properties between polycrystalline and single crystal samples.

36 MATERIALS SCIENCE↗

Neutron diffraction and μ SR studies of two polymorphs of nickel niobate NiNb 2 O 6

Neutron diffraction and muon spin relaxation (μSR) studies are presented in this paper for the newly characterized polymorph of NiNb 2 O 6 (β-NiNb 2 O 6 ) with space group P4 2 /n and μSR data only for the previously known columbite structure polymorph with space group Pbcn. The magnetic structure of the P4 2 /n form was determined from neutron diffraction using both powder and single-crystal data. Powder neutron diffraction determined an ordering wave vector → k=( 1 / 2 , 1 / 2 , 1 / 2 ). Single-crystal data confirmed the same → k vector and showed that the correct magnetic structure consists of antiferromagnetically coupled chains running along the a or b axis in adjacent Ni 2+ layers perpendicular to the c axis, which is consistent with the expected exchange interaction hierarchy in this system. The refined magnetic structure is compared with the known magnetic structures of the closely related trirutile phases, NiSb 2 O 6 and NiTa 2 O 6 . μSR data finds a transition temperature of T N ~15K for this system, while the columbite polymorph exhibits a lower T N =5.7(3) K. Our μSR measurements also allowed us to estimate the critical exponent of the order parameter β for each polymorph. We found β =0.25(3) and 0.16(2) for the β and columbite polymorphs, respectively. The single-crystal neutron scattering data give a value for the critical exponent β =0.28(3) for β-NiNb 2 O 6 , in agreement with the μSR value. While both systems have β values less than 0.3, which is indicative of reduced dimensionality, this effect appears to be much stronger for the columbite system. Finally, in other words, although both systems appear to be well described by S=1 spin chains, the interchain interactions in the β polymorph are likely much larger.

36 MATERIALS SCIENCE↗

Path length dependent neutron diffraction peak shifts observed during residual strain measurements in U–8 wt% Mo castings

This study reports an angular diffraction peak shift that scales linearly with the neutron beam path length traveled through a diffracting sample. This shift was observed in the context of mapping the residual stress state of a large U–8 wt% Mo casting, as well as during complementary measurements on a smaller casting of the same material. If uncorrected, this peak shift implies a non-physical level of residual stress. A hypothesis for the origin of this shift is presented, based upon non-ideal focusing of the neutron monochromator in combination with changes to the wavelength distribution reaching the detector due to factors such as attenuation. The magnitude of the shift is observed to vary linearly with the width of the diffraction peak reaching the detector. Consideration of this shift will be important for strain measurements requiring long path lengths through samples with significant attenuation. This effect can probably be reduced by selecting smaller voxel slit widths.

36 MATERIALS SCIENCE↗

Alignment of sample position and rotation during in situ synchrotron X-ray micro-diffraction experiments using a Laue cross-correlation approach

Laue micro-diffraction has proven to be able to reveal material properties at the sub-grain scale for many polycrystalline materials and is now routinely available at several synchrotron facilities, providing an approach for nondestructive three-dimensional probing of the microstructures and mechanical states of materials. However, for in situ experiments, maintaining the positioning of the sample throughout the experiment, to achieve a good alignment of the characterized volumes, is a challenging issue. The aim of the present work is to address this problem by developing an approach based on digital image correlation of focused-beam Laue diffraction patterns. The method uses small changes in the diffraction signal as a focused X-ray beam is scanned over a surface region to allow corrections to be made for both sample lateral movement and rotation. The method is demonstrated using a tensile deformation experiment on an Al sample with 2.5 µm average grain size. The results demonstrate an accuracy of 0.5 µm for sample position registration and a precision in sample rotation of ~0.01°. Finally, the proposed method is fast to implement and does not require the use of additional surface markers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part I

This two-part article series provides a generalized description of the scattering geometry of Bragg coherent diffraction imaging (BCDI) experiments, the shear distortion effects inherent in the 3D image obtained from presently used methods and strategies to mitigate this distortion. Part I starts from fundamental considerations to present the general real-space coordinate transformation required to correct this shear, in a compact operator formulation that easily lends itself to implementation with available software packages. Such a transformation, applied as a final post-processing step following phase retrieval, is crucial for arriving at an undistorted, correctly oriented and physically meaningful image of the 3D crystalline scatterer. As the relevance of BCDI grows in the field of materials characterization, the available sparse literature that addresses the geometric theory of BCDI and the subsequent analysis methods are generalized here. This geometrical aspect, specific to coherent Bragg diffraction and absent in 2D transmission CDI experiments, gains particular importance when it comes to spatially resolved characterization of 3D crystalline materials in a reliable nondestructive manner. This series of articles describes this theory, from the diffraction in Bragg geometry to the corrections needed to obtain a properly rendered digital image of the 3D scatterer. Part I of this series provides the experimental BCDI community with the general form of the 3D real-space distortions in the phase-retrieved object, along with the necessary post-retrieval correction method. Part II builds upon the geometric theory developed in Part I with the formalism to correct the shear distortions directly on an orthogonal grid within the phase-retrieval algorithm itself, allowing more physically realistic constraints to be applied. Taken together, Parts I and II provide the X-ray science community with a set of generalized BCDI shear-correction techniques crucial to the final rendering of a 3D crystalline scatterer and for the development of new BCDI methods and experiments.

36 MATERIALS SCIENCE↗

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II

X-ray Bragg coherent diffraction imaging (BCDI) has been demonstrated as a powerful 3D microscopy approach for the investigation of sub-micrometre-scale crystalline particles. The approach is based on the measurement of a series of coherent Bragg diffraction intensity patterns that are numerically inverted to retrieve an image of the spatial distribution of the relative phase and amplitude of the Bragg structure factor of the diffracting sample. This 3D information, which is collected through an angular rotation of the sample, is necessarily obtained in a non-orthogonal frame in Fourier space that must be eventually reconciled. To deal with this, the approach currently favored by practitioners (detailed in Part I) is to perform the entire inversion in conjugate non-orthogonal real- and Fourier-space frames, and to transform the 3D sample image into an orthogonal frame as a post-processing step for result analysis. In this article, which is a direct follow-up of Part I, two different transformation strategies are demonstrated, which enable the entire inversion procedure of the measured data set to be performed in an orthogonal frame. The new approaches described here build mathematical and numerical frameworks that apply to the cases of evenly and non-evenly sampled data along the direction of sample rotation ( i.e. the rocking curve). The value of these methods is that they rely on the experimental geometry, and they incorporate significantly more information about that geometry into the design of the phase-retrieval Fourier transformation than the strategy presented in Part I. Finally, two important outcomes are (1) that the resulting sample image is correctly interpreted in a shear-free frame and (2) physically realistic constraints of BCDI phase retrieval that are difficult to implement with current methods are easily incorporated. Computing scripts are also given to aid readers in the implementation of the proposed formalisms.

36 MATERIALS SCIENCE↗

Combining synchrotron X-ray diffraction, mechanistic modeling and machine learning for in situ subsurface temperature quantification during laser melting

Laser melting, such as that encountered during additive manufacturing, produces extreme gradients of temperature in both space and time, which in turn influence microstructural development in the material. Qualification and model validation of the process itself and the resulting material necessitate the ability to characterize these temperature fields. However, well established means to directly probe the material temperature below the surface of an alloy while it is being processed are limited. To address this gap in characterization capabilities, a novel means is presented to extract subsurface temperature-distribution metrics, with uncertainty, from in situ synchrotron X-ray diffraction measurements to provide quantitative temperature evolution data during laser melting. Temperature-distribution metrics are determined using Gaussian process regression supervised machine-learning surrogate models trained with a combination of mechanistic modeling (heat transfer and fluid flow) and X-ray diffraction simulation. The trained surrogate model uncertainties are found to range from 5 to 15% depending on the metric and current temperature. The surrogate models are then applied to experimental data to extract temperature metrics from an Inconel 625 nickel superalloy wall specimen during laser melting. The maximum temperatures of the solid phase in the diffraction volume through melting and cooling are found to reach the solidus temperature as expected, with the mean and minimum temperatures found to be several hundred degrees less. The extracted temperature metrics near melting are determined to be more accurate because of the lower relative levels of mechanical elastic strains. However, uncertainties for temperature metrics during cooling are increased due to the effects of thermomechanical stress.

36 MATERIALS SCIENCE↗

Automated pipeline processing X-ray diffraction data from dynamic compression experiments on the Extreme Conditions Beamline of PETRA III

Presented and discussed here is the implementation of a software solution that provides prompt X-ray diffraction data analysis during fast dynamic compression experiments conducted within the dynamic diamond anvil cell technique. It includes efficient data collection, streaming of data and metadata to a high-performance cluster (HPC), fast azimuthal data integration on the cluster, and tools for controlling the data processing steps and visualizing the data using the DIOPTAS software package. This data processing pipeline is invaluable for a great number of studies. The potential of the pipeline is illustrated with two examples of data collected on ammonia–water mixtures and multiphase mineral assemblies under high pressure. The pipeline is designed to be generic in nature and could be readily adapted to provide rapid feedback for many other X-ray diffraction techniques, e.g. large-volume press studies, in situ stress/strain studies, phase transformation studies, chemical reactions studied with high-resolution diffraction etc.

97 MATHEMATICS AND COMPUTING↗

Pixel detectors for diffraction-limited storage rings

Dramatic advances in synchrotron radiation sources produce ever-brighter beams of X-rays, but those advances can only be used if there is a corresponding improvement in X-ray detectors. With the advent of storage ring sources capable of being diffraction-limited (down to a certain wavelength), advances in detector speed, dynamic range and functionality is required. While many of these improvements in detector capabilities are being pursued now, the orders-of-magnitude increases in brightness of diffraction-limited storage ring sources will require challenging non-incremental advances in detectors. This article summarizes the current state of the art, developments underway worldwide, and challenges that diffraction-limited storage ring sources present for detectors.

47 OTHER INSTRUMENTATION↗

Dynamic crystal rotation resolved by high-speed synchrotron X-ray Laue diffraction

Dynamic compression experiments are performed on single-crystal Si under split Hopkinson pressure bar loading, together with simultaneous high-speed (250–350 ns resolution) synchrotron X-ray Laue diffraction and phase-contrast imaging. A methodology is presented which determines crystal rotation parameters, i.e. instantaneous rotation axes and angles, from two unindexed Laue diffraction spots. Two-dimensional translation is obtained from dynamic imaging by a single camera. High-speed motion of crystals, including translation and rotation, can be tracked in real time via simultaneous imaging and diffraction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Bragg coherent diffraction imaging and metrics for radiation damage in protein micro-crystallography

The proliferation of extremely intense synchrotron sources has enabled ever higher-resolution structures to be obtained using data collected from smaller and often more imperfect biological crystals. Synchrotron beamlines now exist that are capable of measuring data from single crystals that are just a few micrometres in size. This provides renewed motivation to study and understand the radiation damage behaviour of small protein crystals. Reciprocal-space mapping and Bragg coherent diffractive imaging experiments have been performed on cryo-cooled microcrystals of hen egg-white lysozyme as they undergo radiation damage. Several well established metrics, such as intensity-loss and lattice expansion, are applied to the diffraction data and the results are compared with several new metrics that can be extracted from the coherent imaging experiments. Individually some of these metrics are inconclusive. However, combining metrics, the results suggest that radiation damage behaviour in protein micro-crystals differs from that of larger protein crystals and may allow them to continue to diffract for longer. As a result, a possible mechanism to account for these observations is proposed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Observation of the shock-induced β-Sn to b.c.t.-Sn transition using time-resolved X-ray diffraction

Time-resolved X-ray diffraction measurements have been carried out here on dynamically compressed Sn up to a maximum pressure of ~13 GPa at the European Synchrotron Radiation Facility. The phase transition from β-Sn to body-centered tetragonal (b.c.t.) Sn has been observed using synchrotron X-ray diffraction for the first time undergoing shock compression and release. Following maximum compression, the sample releases to lower pressures for several nanoseconds until the reverse transition occurs. The data are in good agreement with previous shock boundaries that indicate that the β-Sn phase is stable ~2 GPa higher than the static boundary upon compression and the b.c.t.-Sn phase is stable ~1 GPa lower upon release. The transition to the high-pressure phase reveals a loss of texture in the X-ray diffraction data from the `quasi' single-crystal β-Sn structure to a more powder-like Debye–Scherrer ring.

36 MATERIALS SCIENCE↗

Analysis of XFEL serial diffraction data from individual crystalline fibrils

Serial diffraction data collected at the Linac Coherent Light Source from crystalline amyloid fibrils delivered in a liquid jet show that the fibrils are well oriented in the jet. At low fibril concentrations, diffraction patterns are recorded from single fibrils; these patterns are weak and contain only a few reflections. Methods are developed for determining the orientation of patterns in reciprocal space and merging them in three dimensions. This allows the individual structure amplitudes to be calculated, thus overcoming the limitations of orientation and cylindrical averaging in conventional fibre diffraction analysis. The advantages of this technique should allow structural studies of fibrous systems in biology that are inaccessible using existing techniques.

36 MATERIALS SCIENCE↗