Microstructures and micromechanical behaviors of high -entropy alloys investigated by synchrotron X-ray and neutron diffraction techniques: A review

High-entropy alloys(HEAs)possess outstanding features such as corrosion resistance,irradiation resistance,and good mechan-ical properties.A few HEAs have found applications in the fields of aerospace and defense.Extensive studies on the deformation mech-anisms of HEAs can guide microstructure control and toughness design,which is vital for understanding and studying state-of-the-art structural materials.Synchrotron X-ray and neutron diffraction are necessary techniques for materials science research,especially for in situ coupling of physical/chemical fields and for resolving macro/microcrystallographic information on materials.Recently,several re-searchers have applied synchrotron X-ray and neutron diffraction methods to study the deformation mechanisms,phase transformations,stress behaviors,and in situ processes of HEAs,such as variable-temperature,high-pressure,and hydrogenation processes.In this review,the principles and development of synchrotron X-ray and neutron diffraction are presented,and their applications in the deformation mechanisms of HEAs are discussed.The factors that influence the deformation mechanisms of HEAs are also outlined.This review fo-cuses on the microstructures and micromechanical behaviors during tension/compression or creep/fatigue deformation and the application of synchrotron X-ray and neutron diffraction methods to the characterization of dislocations,stacking faults,twins,phases,and intergrain/interphase stress changes.Perspectives on future developments of synchrotron X-ray and neutron diffraction and on research directions on the deformation mechanisms of novel metals are discussed.

Numerical Study on the Effect of Gap Diffraction on the Hydrodynamic Performance of A Floating Breakwater

Two-dimensional(2D)flume experiments are useful in investigating the performances of floating breakwaters(FBs),including hydrodynamic performances,motion responses,and mooring forces.Designing a reasonable gap between the flume wall and the FBs is a critical step in 2D flume tests.However,research on the effect of the gap on the accuracy of 2D FB experimental results is scarce.To address this issue,a numerical wave tank is developed using CFD to estimate the wave-FB interaction of a moored dual-cylindrical FB,and the results are compared to experimental data from a previously published work.There is good agreement between them,indicating that the numerical model is sufficiently accurate.The numerical model is then applied to explore the effect of gap diffraction on the performance of FBs in2D experiments.It was discovered that the nondimensional gap length L_(Gap)/W_(Pool)should be smaller than 7.5%to ensure that the relative error of the transmission coefficient is smaller than 3%.The influence of the gap is also related to the entering wave properties,such as the wave height and period.

Deformation behavior of Mg-Y-Ni alloys containing different volume fraction of LPSO phase during tension and compression through in-situ synchrotron diffraction

The deformation behavior of the as-extruded Mg-Y-Ni alloys with different volume fraction of long period stacking ordered(LPSO)phase during tension and compression was investigated by in-situ synchrotron diffraction.The micro-yielding,macro-yielding,tension-compression asymmetry and strain hardening behavior of the alloys were explored by combining with deformation mechanisms.The micro-yielding is dominated by basal slip of dynamic recrystallized(DRXed)grains in tension,while it is dominated by extension twinning of non-dynamic recrystallized(non-DRXed)grains in compression.At macro-yielding,the non-DRXed grains are still elastic deformed in tension and the basal slip of DRXed grains in compression are activated.Meanwhile,the LPSO phase still retains elastic deformation,but can bear more load,so the higher the volume fraction of hard LPSO phase,the higher the tensile/compressive macro-yield strength of the alloys.Benefiting from the low volume fraction of the non-DRXed grains and the delay effect of LPSO andγphases on extension twinning,the as-extruded alloys exhibit excellent tension-compression symmetry.When the volume fraction of LPSO phase reaches∼50%,tension-compression asymmetry is reversed,which is due to the fact that the LPSO phase is stronger in compression than in tension.The tensile strain hardening behavior is dominated by dislocation slip,while the dominate mechanism for compressive strain hardening changes from twinning in theα-Mg grains to kinking of the LPSO phase with increasing volume fraction of LPSO phase.The activation of kinking leads to the constant compressive strain hardening rate of∼2500 MPa,which is significantly higher than the tensile strain hardening rate.

Intensity correlation properties of x-ray beams split with Laue diffraction

Beam splitting is one of the main approaches to achieving x-ray ghost imaging, and the intensity correlation between diffraction beam and transmission beam will directly affect the imaging quality. In this paper, we investigate the intensity correlation between the split x-ray beams by Laue diffraction of stress-free crystal. The analysis based on the dynamical theory of x-ray diffraction indicates that the spatial resolution of diffraction image and transmission image are reduced due to the position shift of the exit beam. In the experimental setup, a stress-free crystal with a thickness of hundredmicrometers-level is used for beam splitting. The crystal is in a non-dispersive configuration equipped with a double-crystal monochromator to ensure that the dimension of the diffraction beam and transmission beam are consistent. A correlation coefficient of 0.92 is achieved experimentally and the high signal-to-noise ratio of the x-ray ghost imaging is anticipated.Results of this paper demonstrate that the developed beam splitter of Laue crystal has the potential in the efficient data acquisition of x-ray ghost imaging.

Analytical Method for the Wave Diffraction of Asymmetrically Arranged Breakwaters

The layout forms of several breakwater structures can be generalized as asymmetrical arrangements in actual engineering.However,the problem of wave diffraction around asymmetrically arranged breakwaters has not been adequately investigated.In this study,we propose an analytical method of wave diffraction for regular waves passing through asymmetrically arranged breakwaters,and we use the Nyström method to obtain the analytical solution numerically.We compared the results of this method with those of previous analytical solutions and with numerical results to demonstrate the validity of our approach.We also provided diffraction coefficient diagrams of breakwaters with different layout forms.Moreover,we described the analytical expression for the problem of diffraction through long-wave incident breakwaters and presented an analysis of the relationship between the diffraction coefficients and the widths of breakwater gates.The analytical method presented in this study contributes to the limited literature on the theory of wave diffraction through asymmetrically arranged breakwaters.

Surface diffraction beamline at the SSRF

BL02U2 of the Shanghai Synchrotron Radiation Facility is a surface diffraction beamline with a photon flux of 5.5×10^(12) photons/s at 10 keV and a beam size of 160µm×80µm at the sample site.It is dedicated to studying surfaces(solid-vacuum,solid-gas)and interfaces(solid-solid,solid-liquid,and liquid-liquid)in nanoscience,condensed matter,and soft matter systems using various surface scattering techniques over an energy range of 4.8-28 keV with transmission and reflection modes.Moreover,BL02U2 has a high energy resolution,high angular resolution,and low beam divergence,which can provide excellent properties for X-ray diffraction experiments,such as grazing incident X-ray diffraction,X-ray reflectivity,crystal truncation rods,and liquid X-ray scattering.Diversity of in situ environments can also be provided for the samples studied.This paper describes the setup of the new beamline and its applications in various fields.

A Novel High Temperature Apparatus for in situ Synchrotron X-ray Diffraction Studies of Molten Salt

This study demonstrates the design and application of a novel high temperature rotatory apparatus for insitu synchrotron X-ray diffraction studies of molten salts,facilitating investigation into the interaction between various structural materials and molten salts.The apparatus enables accurate detection of every phase change during hightemperature experiments,including strong reaction processes like corrosion.Molten salts,such as chlorides or fluo⁃rides,together with the structure materials,are inserted into either quartz or boron nitride capillaries,where X-ray diffraction pattern can be continuously collected,as the samples are heated to high temperature.The replacement re⁃action,when molten ZnCl2 are etching Ti3AlC2,can be clearly observed through changes in diffraction peak intensity as well as expansion in c-axis lattice parameter of the hexagonal matrix,due to the larger atomic number and ionic ra⁃dius of Zn2+.Furthermore,we investigated the high-temperature corrosion process when GH3535 alloy is in FLiNaK molten salt,and can help to optimize its stability for potential applications in molten salt reactor.Additionally,this high temperature apparatus is fully compatible with the combined usage of X-ray diffraction and Raman technique,providing both bulk and surface structural information.This high temperature apparatus has been open to users and is extensively used at BL14B1 beamline of the Shanghai Synchrotron Radiation Facility.

Direct observation of shock-induced phase transformation in polycrystalline iron via in situ x-ray diffraction

Phase transition of polycrystalline iron compressed along the Hugoniot is studied by combining laser-driven shock with in situ x-ray diffraction technique.It is suggested that polycrystalline iron changes from an initial body-centered cubic structure to a hexagonal close-packed structure with increasing pressure(i.e.,a phase transition fromαtoε).The relationship between density and pressure for polycrystalline iron obtained from the present experiments is found to be in good agreement with the gas-gun Hugoniot data.Our results show that experiments with samples at lower temperatures under static loading,such as in a diamond anvil cell,lead to higher densities measured than those found under dynamic loading.This means that extrapolating results of static experiments may not predict the dynamic responses of materials accurately.In addition,neither the face-centered cubic structure seen in previous molecular-dynamics simulations or twophase coexistence are found within our experimental pressure range.

Direct visualization of laser-driven dynamic fragmentation in tin by in situ x-ray diffraction

We present a novel method for investigating laser-driven dynamic fragmentation in tin using in situ X-ray diffraction.Our experimental results demonstrate the feasibility of the method for simultaneously identifying the phase and temperature of fragments through analysis of the diffraction pattern.Surprisingly,we observe a deviation from the widely accepted isentropic release assumption,with the temperature of the fragments being found to be more than 100 K higher than expected,owing to the release of plastic work during dynamic fragmentation.Our findings are further verified through extensive large-scale molecular dynamics simulations,in which strain energies are found to be transferred into thermal energies during the nucleation and growth of voids,leading to an increase in temperature.Our findings thus provide crucial insights into the impact-driven dynamic fragmentation phenomenon and reveal the significant influence of plastic work on material response during shock release.

Diffraction deep neural network-based classification for vector vortex beams

The vector vortex beam(VVB)has attracted significant attention due to its intrinsic diversity of information and has found great applications in both classical and quantum communications.However,a VVB is unavoidably affected by atmospheric turbulence(AT)when it propagates through the free-space optical communication environment,which results in detection errors at the receiver.In this paper,we propose a VVB classification scheme to detect VVBs with continuously changing polarization states under AT,where a diffractive deep neural network(DDNN)is designed and trained to classify the intensity distribution of the input distorted VVBs,and the horizontal direction of polarization of the input distorted beam is adopted as the feature for the classification through the DDNN.The numerical simulations and experimental results demonstrate that the proposed scheme has high accuracy in classification tasks.The energy distribution percentage remains above 95%from weak to medium AT,and the classification accuracy can remain above 95%for various strengths of turbulence.It has a faster convergence and better accuracy than that based on a convolutional neural network.

Tailoring electron vortex beams with customizable intensity patterns by electron diffraction holography

An electron vortex beam(EVB) carrying orbital angular momentum(OAM) plays a key role in a series of fundamental scientific researches, such as chiral energy-loss spectroscopy and magnetic dichroism spectroscopy. So far, almost all the experimentally created EVBs manifest isotropic doughnut intensity patterns. Here, based on the correlation between local divergence angle of electron beam and phase gradient along azimuthal direction, we show that free electrons can be tailored to EVBs with customizable intensity patterns independent of the carried OAM. As proof-of-concept, by using computer generated hologram and designing phase masks to shape the incident free electrons in the transmission electron microscope, three structured EVBs carrying identical OAM are tailored to exhibit completely different intensity patterns. Furthermore, through the modal decomposition, we quantitatively investigate their OAM spectral distributions and reveal that structured EVBs present a superposition of a series of different eigenstates induced by the locally varied geometries. These results not only generalize the concept of EVB, but also demonstrate an extra highly controllable degree of freedom for electron beam manipulation in addition to OAM.

Dispersion Relations in Diffraction in Time

In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, g(x′)=±Sgn(x′)g(x′), which defines the property of being a truncated functions at the origin. On the other hand, we prove that the wave-function of a generalized diffraction in time problem is just the Fourier-transform of a truncated function. Consequently, the existence of dispersion relations for the diffraction in time wave-function follows. We derive these explicit dispersion relations.

The Crystal Structure Study of CaSrFe0.75Co0.75Mn0.5O6−δ by Neutron Diffraction

The crystal structure of CaSrFe0.75Co0.75Mn0.5O6−δ is investigated through neutron diffraction techniques in this study. The material is synthesized using a solid-state synthesis method at a temperature of 1200˚C. Neutron diffraction data is subjected to Rietveld refinement, and a comparative analysis with X-ray diffraction (XRD) data is performed to unravel the structural details of the material. The findings reveal that the synthesized material exhibits a cubic crystal structure with a Pm-3m phase. The neutron diffraction results offer valuable insights into the arrangement of atoms within the lattice, contributing to a comprehensive understanding of the material’s structural properties. This research enhances our knowledge of CaSrFe0.75Co0.75Mn0.5O6−δ, with potential implications for its applications in various technological and scientific domains.

Tracking the phase transformation and microstructural evolution of Sn anode using operando synchrotron X-ray energy-dispersive diffraction and X-ray tomography

Tin(Sn)holds great promise as an anode material for next-generation lithium(Li)ion batteries but suffers from massive volume change and poor cycling performance.To clarify the dynamic chemical and microstructural evolution of Sn anode during lithiation and delithiation,synchrotron X-ray energydispersive diffraction and X-ray tomography are simultaneously employed during Li/Sn cell operation.The intermediate Li-Sn alloy phases during de/lithiation are identified,and their dynamic phase transformation is unraveled which is further correlated with the volume variation of the Sn at particle-and electrode-level.Moreover,we find that the Sn particle expansion/shrinkage induced particle displacement is anisotropic:the displacement perpendicular to the electrode surface(z-axis)is more pronounced compared to the directions(x-and y-axis)along the electrode surface.This anisotropic particle displacement leads to an anisotropic volume variation at the electrode level and eventually generates a net electrode expansion towards the separator after cycling,which could be one of the root causes of mechanical detachment and delamination of electrodes during long-term operation.The unraveled chemical evolution of Li-Sn and deep insights into the microstructural evolution of Sn anode provided here could guide future design and engineering of Sn and other alloy anodes for high energy density Li-and Na-ion batteries.

Diffraction deep neural network based orbital angular momentum mode recognition scheme in oceanic turbulence

Orbital angular momentum(OAM)has the characteristics of mutual orthogonality between modes,and has been applied to underwater wireless optical communication(UWOC)systems to increase the channel capacity.In this work,we propose a diffractive deep neural network(DDNN)based OAM mode recognition scheme,where the DDNN is trained to capture the features of the intensity distribution of the OAM modes and output the corresponding azimuthal indices and radial indices.The results show that the proposed scheme can recognize the azimuthal indices and radial indices of the OAM modes accurately and quickly.In addition,the proposed scheme can resist weak oceanic turbulence(OT),and exhibit excellent ability to recognize OAM modes in a strong OT environment.The DDNN-based OAM mode recognition scheme has potential applications in UWOC systems.

Thermal expansivity of geikielite and ilmenite utilizing in-situ synchrotron X-ray diffraction at high temperature

The unit-cell parameters and volumes of geikielite(MgTiO_(3))and ilmenite(FeTiO_(3))were investigated at high temperatures up to 700 K and ambient pressure,using in-situ angle-dispersive synchrotron X-ray diffraction.No phase transition was detected over the experimental temperature range.Using(Berman in J Petrol29:445-522,1988.10.1093/petrology/29.2.445)equations to fit the temperature-volume data,the volumetric thermal expansion coefficients at ambient conditions(α_(V0))of MgTiO_(3) and FeTiO_(3) were obtained as follows:2.55(6)×10^(-5)K^(-1)and 2.82(10)×10^(-5)K^(-1),respectively.We infer that the larger effective ionic radius of Fe^(2+)(Ⅵ)(0.78 A)than that of Mg^(2+)(Ⅵ)(0.72?)renders FeTiO_(3)has a larger volumetric thermal expansivity than MgTiO_(3).Simultaneously,the refined axial thermal expansion coefficients under ambient conditions areα_(a0)=0.74(3)×10^(-5)K^(-1)andα_(c0)=1.08(5)×10^(-5)K^(-1)for the aaxis and c-axis of MgTiO_(3),respectively,andα_(a0)=0.95(5)×10^(-5)K^(-1)andα_(c0)=0.92(12)×10^(-5)K^(-1)for the aaxis and c-axis of FeTiO_(3),respectively.The axial thermal expansivity of MgTiO_(3) is anisotropic,but that of FeTiO_(3) is nearly isotropic.We infer that the main reason for the different axial thermal expansivity between MgTiO_(3) and FeTiO_(3) is that the thermal expansion mode of the Mg-O bond in MgTiO_(3) is different from that of the Fe-O bonds in FeTiO_(3).

Analysis and Prediction of Effect of Turning Marks Diffraction on Image Quality of Optical System

Single-point diamond turning (SPDT) is widely used in the machining of infrared materials and metal-based mirrors. Diamond tips can scratch material, replicate the shape of the tip, and create annular turning marks on optical surfaces, which can have unpredictable adverse effects on imaging. In order to predict the effect of turning marks diffraction on the degradation of imaging quality, a model of the influence of SPDT processing parameters on the reduction of system imaging MTF under the influence of ideal grating turning marks diffraction was established. The results show that the depth of the turning mark will lead to the decline of MTF, especially the low frequency information. Finally, a method is proposed to reduce the effect of turning marks diffraction through changing the processing parameters. .

基于衍射透镜接收的激光雷达特性分析及测试

在激光雷达系统设计中,光学系统的优化与设计是一个重要的研究方向,本文利用衍射光学元件(DOE)的设计自由度高和色散大等优势,将DOE用于激光雷达接收端,同时实现聚焦和滤光作用,降低了光学系统复杂度。本文基于DOE的原理,仿真分析了DOE的光学特性,并且以DOE作为激光雷达的光学接收端,完成了激光雷达测距实验,证明了DOE同时具有聚焦作用和窄带滤光作用,实验结果与仿真基本一致。本文利用DOE在激光雷达中的优势,实现激光雷达的轻量化、集成化和高效化。

广角衍射光学元件的优化设计

为进一步研究入射角度的增大对衍射光学元件(diffractive optical element,DOE)衍射效率及微结构高度等参数的影响,分析了入射角度和周期宽度对带宽积分平均衍射效率的影响。基于扩展标量衍射理论,建立了DOE的微结构高度与入射角度和周期宽度的数学模型,提出了工作在一定入射角度范围内,基于复合带宽积分平均衍射效率(comprehensive polychromatic integral diffraction efficiency,CPIDE)最大化实现设计波长和微结构高度等结构参数的优化设计方法。以工作在红外波段的DOE为例进行分析。结果表明:当相对周期宽度为20,入射角度范围为0°~40°时,该DOE的CPIDE为94.15%,微结构高度为1.3396mm。该设计方法可以实现广角DOE的优化设计。

基于Mathematica的平行光斜入射光栅衍射的模拟和可视化研究

光栅衍射作为大学物理的重要教学内容和教学难点,由于其理论推导和数学表达形式复杂,学生难以形成清晰的物理图像,导致课堂教学效果不理想。教材中仅对光垂直入射光栅时的衍射特性进行了讨论,但平行光斜入射光栅时的衍射特性却未被充分探讨,且这一领域的研究仍然有限。本文首先应用光的衍射理论推导出了平行光斜入射条件下单缝衍射和光栅衍射的光强分布表达形式,将单缝衍射和光栅衍射的研究由垂直入射推广到斜入射的情况。然后,应用Mathematica软件中的强大的交互式界面Manipulate,结合Initialization和Limit命令,对平行光斜入射情况下的单缝衍射和光栅衍射的光强分布进行了系统的模拟和仿真,分别绘制出单缝衍射的相对光强分布、多缝干涉的相对光强分布、光栅衍射的相对光强分布和衍射条纹分布情况。通过可视化过程,使学生深刻地理解光栅衍射的光强分布是单缝衍射和多缝干涉共同作用的结果,单缝衍射提供了光强分布的包络,而多缝干涉则决定了衍射条纹的具体亮暗变化,将抽象的光的衍射现象形象直观地动态演示出来,这有助于学生建立清晰的物理图像,深刻地理解单缝衍射和光栅衍射,极大地提高教学效果。