High‐energy transmission Laue micro‐beam X‐ray diffraction: a probe for intra‐granular lattice orientation and elastic strain in thicker samples

An understanding of the mechanical response of modern engineering alloys to complex loading conditions is essential for the design of load‐bearing components in high‐performance safety‐critical aerospace applications. A detailed knowledge of how material behaviour is modified by fatigue and the ability to predict failure reliably are vital for enhanced component performance. Unlike macroscopic bulk properties (e.g. stiffness, yield stress, etc.) that depend on the average behaviour of many grains, material failure is governed by `weakest link'‐type mechanisms. It is strongly dependent on the anisotropic single‐crystal elastic–plastic behaviour, local morphology and microstructure, and grain‐to‐grain interactions. For the development and validation of models that capture these complex phenomena, the ability to probe deformation behaviour at the micro‐scale is key. The diffraction of highly penetrating synchrotron X‐rays is well suited to this purpose and micro‐beam Laue diffraction is a particularly powerful tool that has emerged in recent years. Typically it uses photon energies of 5–25 keV, limiting penetration into the material, so that only thin samples or near‐surface regions can be studied. In this paper the development of high‐energy transmission Laue (HETL) micro‐beam X‐ray diffraction is described, extending the micro‐beam Laue technique to significantly higher photon energies (50–150 keV). It allows the probing of thicker sample sections, with the potential for grain‐level characterization of real engineering components. The new HETL technique is used to study the deformation behaviour of individual grains in a large‐grained polycrystalline nickel sample during in situ tensile loading. Refinement of the Laue diffraction patterns yields lattice orientations and qualitative information about elastic strains. After deformation, bands of high lattice misorientation can be identified in the sample. Orientation spread within individual scattering volumes is studied using a pattern‐matching approach. The results highlight the inability of a simple Schmid‐factor model to capture the behaviour of individual grains and illustrate the need for complementary mechanical modelling.     

Energy resolution of the CdTe‐XPAD detector: calibration and potential for Laue diffraction measurements on protein crystals

The XPAD3S‐CdTe, a CdTe photon‐counting pixel array detector, has been used to measure the energy and the intensity of the white‐beam diffraction from a lysozyme crystal. A method was developed to calibrate the detector in terms of energy, allowing incident photon energy measurement to high resolution (approximately 140 eV), opening up new possibilities in energy‐resolved X‐ray diffraction. In order to demonstrate this, Laue diffraction experiments were performed on the bending‐magnet beamline METROLOGIE at Synchrotron SOLEIL. The X‐ray energy spectra of diffracted spots were deduced from the indexed Laue patterns collected with an imaging‐plate detector and then measured with both the XPAD3S‐CdTe and the XPAD3S‐Si, a silicon photon‐counting pixel array detector. The predicted and measured energy of selected diffraction spots are in good agreement, demonstrating the reliability of the calibration method. These results open up the way to direct unit‐cell parameter determination and the measurement of high‐quality Laue data even at low resolution. Based on the success of these measurements, potential applications in X‐ray diffraction opened up by this type of technology are discussed.     

Micro‐beam Laue alignment of multi‐reflection Bragg coherent diffraction imaging measurements

Multi‐reflection Bragg coherent diffraction imaging has the potential to allow three‐dimensional (3D) resolved measurements of the full lattice strain tensor in specific micro‐crystals. Until now such measurements were hampered by the need for laborious, time‐intensive alignment procedures. Here a different approach is demonstrated, using micro‐beam Laue X‐ray diffraction to first determine the lattice orientation of the micro‐crystal. This information is then used to rapidly align coherent diffraction measurements of three or more reflections from the crystal. Based on these, 3D strain and stress fields in the crystal are successfully determined. This approach is demonstrated on a focused ion beam milled micro‐crystal from which six reflections could be measured. Since information from more than three independent reflections is available, the reliability of the phases retrieved from the coherent diffraction data can be assessed. Our results show that rapid, reliable 3D coherent diffraction measurements of the full lattice strain tensor in specific micro‐crystals are now feasible and can be successfully carried out even in heavily distorted samples.     

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.     

共振光子晶体中Laue孤子传播的动力学行为

从理论上研究了Laue孤子传播的动力学行为，并通过数值模拟验证了这些行为.结果表明，由于非线性衍射，入射脉冲会分裂产生四种模式，其中产生的Laue孤子的传播行为与一般共振介质中孤子的传播行为相似.     

Study of the influence of higher—order Laue zones on the exit wavefunction

Based on an analytical expression of electron dynamical diffraction derived recently,the exit wavefunctions of nonperiodic samples have been calculated.The results have shown that the amplitude and phase obtained by the analytical expression were in good agreement with those obtained using the multi-slice method.Besides,the influence of the higher-order Laue zone on the wavefunction for different sample thickness was studied in detail and the results showed that the exit wavefunction is dominated by the zero-order Laue zone.When the sample is very thin,the influence of the higher-order Laue zone should be considered.     

二维X射线衍射及其应用研究进展

介绍了三维、一维和二维X射线衍射的有关概念,给出二维X射线衍射的定义:在X射线衍射实验中使用二维探测器,并对由二维探测器记录的二维象、二维衍射花样的数据进行处理分析和解释的X射线衍射方法称为二维X射线衍射术。之后,分四部分综述二维X射线衍射(2D-XRD)和散射及其应用的进展。1)单晶样品的二维衍射包括经典的劳厄法定向和用二维探测器(带衰减底片组件、CCD和IP等)的劳厄法测定晶体结构的单晶样品现代二维衍射术;2)随后,评述多晶样品二维衍射的衍射几何、实验装置,以及在物相鉴定、应力测定和织构测定方面应用的方法和基本公式;3)二维小角散射(2D-SAXS)也作了简介。4)把一维和二维衍射术作了较全面的比较和综合评论。     

二维X射线衍射及其应用研究进展

介绍了三维、一维和二维X射线衍射的有关概念,给出二维X射线衍射的定义:在X射线衍射实验中使用二维探测器,并对由二维探测器记录的二维象、二维衍射花样的数据进行处理分析和解释的X射线衍射方法称为二维X射线衍射术。之后,分四部分综述二维X射线衍射(2D-XRD)和散射及其应用的进展。1)单晶样品的二维衍射包括经典的劳厄法定向和用二维探测器(带衰减底片组件、CCD和IP等)的劳厄法测定晶体结构的单晶样品现代二维衍射术;2)随后,评述多晶样品二维衍射的衍射几何、实验装置,以及在物相鉴定、应力测定和织构测定方面应用的方法和基本公式;3)二维小角散射(2D-SAXS)也作了简介。4)把一维和二维衍射术作了较全面的比较和综合评论。     

晶体X射线劳厄衍射分束特性研究

本文基于X射线衍射动力学分析了劳厄晶体的分束特性,模拟了晶体吸收和入射光角发散对于透射光和衍射光摇摆曲线的影响,定量给出晶体衍射面内角调节范围和晶体加工厚度对于劳厄衍射分束比的调制.在实验中,采用分析晶体和分束晶体的消色散配置限制入射光角发散的影响,实现300μm厚Si(220)晶体面内角调节劳厄衍射分束的精确测量,并得到300μm, 400μm和500μm厚度Si晶体分束比的调节范围,实现了透射光和衍射光强度的定量调制.     

劳厄对晶体衍射的发现

介绍了劳厄提出晶体衍射思想的科学背景及当时的实验过程,并探讨在劳厄发现晶体衍射的过程中其科学思想的形成及X射线晶体衍射的发现带给我们的启示及影响．     

热处理引起3C-ZnS结构转变的X-射线衍射分析

为了论证层错是硫化锌晶体中交流电致发光的一个必要条件,我们把3C-ZnS单晶体在1100℃热处理后引入了层错.同时,我们对热处理前后的结构,用劳埃背反射法和文献[8、13]推导的公式进行了分析.结果表明,沿3C-结构<111>四个等价方向都可以产生无序、孪晶和2H-结构,而且当热处理时间足够长时,结构转变趋向于一个<111>方向.这些实验结果,在有关的文献中尚未见到.     

Point focusing with flat and wedged crossed multilayer Laue lenses

Point focusing measurements using pairs of directly bonded crossed multilayer Laue lenses (MLLs) are reported. Several flat and wedged MLLs have been fabricated out of a single deposition and assembled to realise point focusing devices. The wedged lenses have been manufactured by adding a stress layer onto flat lenses. Subsequent bending of the structure changes the relative orientation of the layer interfaces towards the stress‐wedged geometry. The characterization at ESRF beamline ID13 at a photon energy of 10.5 keV demonstrated a nearly diffraction‐limited focusing to a clean spot of 43 nm × 44 nm without significant side lobes with two wedged crossed MLLs using an illuminated aperture of approximately 17 µm × 17 µm to eliminate aberrations originating from layer placement errors in the full 52.7 µm × 52.7 µm aperture. These MLLs have an average individual diffraction efficiency of 44.5%. Scanning transmission X‐ray microscopy measurements with convenient working distances were performed to demonstrate that the lenses are suitable for user experiments. Also discussed are the diffraction and focusing properties of crossed flat lenses made from the same deposition, which have been used as a reference. Here a focal spot size of 28 nm × 33 nm was achieved and significant side lobes were noticed at an illuminated aperture of approximately 23 µm × 23 µm.     

巧妙的构想大胆的创新——劳厄与X射线衍射的实验

通过劳厄对X射线衍射的实验构想,来展现他的思维方法的独创性,从中得到对我们的科学研究工作的启迪.     

LEED studies on stepped W surfaces

Steps on single crystal surfaces have been shown to cause changes of various physical properties and to influence the behaviour towards chemical reactions. A proper knowledge of the step structure is required for the understanding of these phenomena. The following investigation concentrates on a detailed evaluation of the LEED patterns of various stepped tungsten surfaces. A formula is given for determining the terrace width of ordered step arrays from any diffraction order. Step height, step orientation, terrace width and the sample orientation have been deduced from the LEED patterns and the experimental errors involved are being discussed. The step height can be determined within 1% and the terrace width within 1 to 3% depending on the step density. It is concluded that the determination of the sample orientation as obtained from the LEED pattern is at least as precise as by using the Laue X-ray back reflection technique.     

The RATIO method for time‐resolved Laue crystallography

A RATIO method for analysis of intensity changes in time‐resolved pump–probe Laue diffraction experiments is described. The method eliminates the need for scaling the data with a wavelength curve representing the spectral distribution of the source and removes the effect of possible anisotropic absorption. It does not require relative scaling of series of frames and removes errors due to all but very short term fluctuations in the synchrotron beam.     

劳厄弯晶光学特性的光线追迹研究

基于X射线几何衍射的晶层模型,编写了用于柱面弯曲劳厄晶体的光线追迹软件.程序主体用C语言编写,在VC++环境下运行.利用程序分别对衍射光方向和能量带宽两方面不同的项目进行追迹,通过模拟结果与理论计算和实验结果的对比,显示出很好的一致性,从而验证了程序在追迹衍射光衍射方向变化和能量变化方面的正确性.利用该光线追迹软件,追...     

2D Laue focusing of X-ray radiation by a double-crystal system

The theory of the dynamic 2D focusing of an X-ray wave upon its Laue diffraction by a system of two bent crystals is developed. The reflecting planes of the crystals are perpendicular to their surfaces. 2D focusing is shown to be highly sensitive to the bending radius of the crystals and to the difference in their thicknesses. The effect of astigmatism on 2D Laue focusing is described, and conditions for stigmatic focusing are found. One-dimensional focusing inside the crystals is discussed. The spectral characteristics of a double-crystal 2D-focusing spectrometer are considered.     

On the Theory of X-Ray Diffractional Laue Focusing on Two Bent Crystals

The Laue focusing of a spherical x-ray wave onto dynamical diffraction by a double-bent crystal system is studied. The geometrical equations of two-dimensional Laue focusing and the intensity distribution formula are derived. A high sensitivity of the two-dimensional Laue focusing to the crystal thickness and bending radii difference is revealed. It is shown that this sensitivity can be used to control the crystal thickness with accuracy up to 100 and bending radii up to 10^-2 m. The focusing process of the spherical wave inside crystals as well as in vacuum is investigated. The possibility of using the two-crystal Laue system as a lens for x-ray microscopy is studied. The spectral characteristics of a twice-diffracted wave are discussed. The spectral resolution is demonstrated to be 10⁶.     

Initial electron back-scattered diffraction observations of cerium

The first electron back-scattered diffraction Kikuchi patterns and grain orientation maps were captured for pure n-phase (fcc) Ce. The sample preparation technique used for electron back-scattered diffraction orientation mapping of this surface-reactive metal included ion sputtering the surface using a scanning Auger microprobe followed by vacuum transfer of the sample from the scanning Auger microprobe to the scanning electron microscope. The effect of ion sputtering on the microstructure as well as preliminary electron back-scattered diffraction microstructural characterization is presented. Based on the sputtering data, the room-temperature diffusivity of O in n-Ce was estimated.     

Design and performance of an X‐ray scanning microscope at the Hard X‐ray Nanoprobe beamline of NSLS‐II

A hard X‐ray scanning microscope installed at the Hard X‐ray Nanoprobe beamline of the National Synchrotron Light Source II has been designed, constructed and commissioned. The microscope relies on a compact, high stiffness, low heat dissipation approach and utilizes two types of nanofocusing optics. It is capable of imaging with ～15 nm × 15 nm spatial resolution using multilayer Laue lenses and 25 nm × 26 nm resolution using zone plates. Fluorescence, diffraction, absorption, differential phase contrast, ptychography and tomography are available as experimental techniques. The microscope is also equipped with a temperature regulation system which allows the temperature of a sample to be varied in the range between 90 K and 1000 K. The constructed instrument is open for general users and offers its capabilities to the material science, battery research and bioscience communities.