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.

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.

Time-resolved ultra-small-angle X-ray scattering beamline(BL10U1)at SSRF

The construction of a new beamline,BL10U1,was completed at the Shanghai synchrotron radiation facility in 2020.This multipurpose beamline was designed to provide X-ray scattering techniques such as ultra-small-angle X-ray scattering(USAXS),small-angle X-ray scattering(SAXS),wide-angle X-ray scattering,and microfocus SAXS(μSAXS)for a broad user community.To realize fast time-resolved USAXS experiments,the beamline adopted an in-vacuum undulator with a total length of 1.6 m as the photon source.An in-house cryogenic-cooled double multilayer monochromator was installed to deliver a photon flux of approximately 10^(13) photons/s at a photon energy of 10 keV.The three-year successful operation of this beamline demonstrated that the monochromator operated smoothly,as expected.BL10U1 has three end stations in succession:USAXS end station,μSAXS end station,and end station for industrial applications.The minimum scattering vector q~0.0042 nm^(-1) at 10 keV can be achieved at the USAXS end station equipped with a 28 m-long and 1.8 m-diameter vacuum flight tube.At theμSAXS end station,a beam spot of less than 10×8μm was achieved for micro-SAXS experiments.In contrast,in situ experimental instruments up to 5 m high and 8 m wide can be mounted at the industrial application end station,which offers industrial scientists the opportunity to use their large industrial equipment.BL10U1 opens up a new capability to investigate phenomena such as non-equilibrium and dynamic processes of materials with a wide length scale from angstroms to micrometers with millisecond time resolution.In this paper,we also report beamline design considerations and commissioning results.

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.

Diffraction separation by plane-wave prediction filtering

Seismic data processing typically deals with seismic wave reflections and neglects wave diffraction that affect the resolution. As a general rule, wave diffractions are treated as noise in seismic data processing. However, wave diffractions generally originate from geological structures, such as fractures, karst caves, and faults. The wave diffraction energy is much weaker than that of the reflections. Therefore, even if wave diffractions can be traced back to their origin, their energy is masked by that of the reflections. Separating and imaging diffractions and reflections can improve the imaging accuracy of diffractive targets. Based on the geometrical differences between reflections and diffractions on the plane-wave record; that is, reflections are quasi-linear and diffractions are quasi-hyperbolic, we use plane-wave prediction fltering to separate the wave diffractions. First, we estimate the local slope of the seismic event using plane- wave destruction filtering and, then, we predict and extract the wave reflections based on the local slope. Thus, we obtain the diffracted wavefield by directly subtracting the reflected wavefield from the entire wavefield. Finally, we image the diffracted wavefield and obtain high-resolution diffractive target results. 2D SEG salt model data suggest that the plane-wave prediction filtering eliminates the phase reversal in the plane-wave destruction filtering and maintains the original wavefield phase, improving the accuracy of imaging heterogeneous objects.

Evaluation on residual stresses of silicon-doped CVD diamond films using X-ray diffraction and Raman spectroscopy

The effect of silicon doping on the residual stress of CVD diamond films is examined using both X-ray diffraction (XRD) analysis and Raman spectroscopy measurements. The examined Si-doped diamond films are deposited on WC-Co substrates in a home-made bias-enhanced HFCVD apparatus. Ethyl silicate (Si(OC2H5)4) is dissolved in acetone to obtain various Si/C mole ratio ranging from 0.1% to 1.4% in the reaction gas. Characterizations with SEM and XRD indicate increasing silicon concentration may result in grain size decreasing and diamond [110] texture becoming dominant. The residual stress values of as-deposited Si-doped diamond films are evaluated by both sin2ψ method, which measures the (220) diamond Bragg diffraction peaks using XRD, with ψ-values ranging from 0° to 45°, and Raman spectroscopy, which detects the diamond Raman peak shift from the natural diamond line at 1332 cm-1. The residual stress evolution on the silicon doping level estimated from the above two methods presents rather good agreements, exhibiting that all deposited Si-doped diamond films present compressive stress and the sample with Si/C mole ratio of 0.1% possesses the largest residual stress of ~1.75 GPa (Raman) or ~2.3 GPa (XRD). As the silicon doping level is up further, the residual stress reduces to a relative stable value around 1.3 GPa.

In-situ quantitative monitoring of fatigue crack using fastest time of flight diffraction method

Due to the cyclic loading and longtime exposure under extreme environment conditions, fatigue cracks often generate in the aircraft metal structures, i.e. wing skin, fuselage skin, strigners, pylons. These cracks could cause severe damages to the aircraft structures. Thus the position and size monitoring of fatigue cracks in the metal structures is very important to manufacturers as well as maintenance personnel for significantly improving the safety and reliability of aircraft. Much progress has been made for crack position monitoring in the past few years. However, the crack size monitoring is still very challenging. Fastest time of flight diffraction （FTOFD） method was developed to monitor both the position and size of a crack. FTOFD method uses an integrated sensor network to activate and receive ultrasonic waves in a structure. Diffraction waves will be generated when the ultrasonic waves pass a crack. These diffraction waves are received and analyzed to get the position and size of the crack. The experiment results show that the monitored size of the simulated crack is very close to the real size of the crack, and for frequencies of 350 and 400 kHz, the monitoring errors are both smaller than 5%.

Thermal expansion of kyanite at ambient pressure:An X-ray powder diffraction study up to 1000℃

The thermal expansion coefficients of kyanite at ambient pressure have been investigated by an X-ray powder diffraction technique with temperatures up to 1000 ℃. No phase transition was observed in the experimental temperature range. Data for the unit-cell parameters and temperatures were fitted empirically resulting in the following thermal expansion coefficients： αa = 5.8（3） × 10^-5, αb = 5.8 （1）× 10^-5, αc = 5.2（1）× 10^-5, and αv = 7.4（1） × 10^-3 ℃ 1 in good agreement with a recent neutron powder diffraction study. On the other hand, the variation of the unit-cell angles α, β and γ of kyanite with increase in temperature is very complicated, and the agreement among all studies is poor. The thermal expansion data at ambient pressure reported here and the compression data at ambient temperature from the literature suggest that, for the kyanite lattice, the most and least thermally expandable directions correspond to the most and least compressible directions, respectively.

Ware Diffraction from A Vertical Cylinder with Two Uniform Columns and Porous Outer Wall

Based on a linens model of the pressure difference between two sides of a porous wall and the fluid velocity inside it, an analytic solution is established for wave diffraction from a cylinder with an outer pore us column and an Inner solid column. Numerical experiments are carried out to examine the effects of the wave force on a porous low-column cylinder and the wave elevations outside and inside the cylinder due to the pore us character of the outer column and the ratio between the radii of the inner and outer columns. The numerical results show that the increase in the coefficient of porosity of the outer column of a double column cylinder will reduce the wave elevation around the cylinder and the wave load on it. The radius of the inner column does not affect too much the wave elevation around the cylinder and the total force on the cylinder.

Diffraction of plane SH waves by a semi-circular cavity in half-space

This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.