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.

Effect of power-law nonlinearity on PT-symmetric optical system with fourth-order diffraction

Gaussian-type soliton solutions of the nonlinear Schr?dinger(NLS)equation with fourth order dispersion,and power law nonlinearity in the novel parity-time(TP)-symmetric quartic Gaussian potential are derived analytically and numerically.The exact analytical expressions of the solutions are obtained in the first two-dimensional(1D and 2D)power law NLS equations.By means of the linear stability analysis,the effect of power law nonlinearity on the stability of Gauss type solitons in different nonlinear media is carried out.Numerical investigations do confirm the stability of our soliton solutions in both focusing and defocusing cases,specially around the propagation parameters.

Fourth-order phase-field modeling for brittle fracture in piezoelectric materials

Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

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.

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.

Pluggable multitask diffractive neural networks based on cascaded metasurfaces

Optical neural networks have significant advantages in terms of power consumption,parallelism,and high computing speed,which has intrigued extensive attention in both academic and engineering communities.It has been considered as one of the powerful tools in promoting the fields of imaging processing and object recognition.However,the existing optical system architecture cannot be reconstructed to the realization of multi-functional artificial intelligence systems simultaneously.To push the development of this issue,we propose the pluggable diffractive neural networks(P-DNN),a general paradigm resorting to the cascaded metasurfaces,which can be applied to recognize various tasks by switching internal plug-ins.As the proof-of-principle,the recognition functions of six types of handwritten digits and six types of fashions are numerical simulated and experimental demonstrated at near-infrared regimes.Encouragingly,the proposed paradigm not only improves the flexibility of the optical neural networks but paves the new route for achieving high-speed,low-power and versatile artificial intelligence systems.

ALMOST SURE GLOBAL WELL-POSEDNESS FOR THE FOURTH-ORDER NONLINEAR SCHR?DINGER EQUATION WITH LARGE INITIAL DATA

We consider the fourth-order nonlinear Schr?dinger equation(4NLS)(i?t+εΔ+Δ2)u=c1um+c2(?u)um-1+c3(?u)2um-2,and establish the conditional almost sure global well-posedness for random initial data in Hs(Rd)for s∈(sc-1/2,sc],when d≥3 and m≥5,where sc:=d/2-2/(m-1)is the scaling critical regularity of 4NLS with the second order derivative nonlinearities.Our proof relies on the nonlinear estimates in a new M-norm and the stability theory in the probabilistic setting.Similar supercritical global well-posedness results also hold for d=2,m≥4 and d≥3,3≤m<5.