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.

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.

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.

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 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.

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.

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. .

Single order soft X-ray diffraction with quasi-random radius pinhole array spectroscopic photon sieves

A novel single order diffraction grating in the soft X-ray region, called quasi-random radius pinhole array spectro- scopic photon sieves （QRSPS）, is proposed in this paper. This new grating is composed of pinholes on a substrate, whose radii are quasi-random, while their centers are regular. Analysis proves that its transmittance function across the grating bar is similar to that of sinusoidal transmission gratings. Simulation results show that the QRSPS can suppress higher-order diffraction effectively. And the QRSPS would still retain its characteristic of single order diffraction when we take the effect of X-ray penetration into account. These properties indicate that the QRSPS can be used in the soft X-ray spectra measurement.

High-Throughput Powder Diffraction Using White X-Ray Beam and a Simulated Energy-Dispersive Array Detector

High-throughput powder X-ray diffraction(XRD)with white X-ray beam and an energy-dispersive detector array is demonstrated in this work on a CeO;powder sample on a bending magnet synchrotron beamline at the Shanghai Synchrotron Radiation Facility(SSRF),using a simulated energy-dispersive array detector consisting of a spatially scanning silicon-drift detector(SDD).Careful analysis and corrections are applied to account for various experimental hardware-related and diffraction angle-related factors.The resulting diffraction patterns show that the relative strength between different diffraction peaks from energy-dispersive XRD(EDXRD)spectra is consistent with that from angle-resolved XRD(ARXRD),which is necessary for analyzing crystal structures for unknown samples.The X-ray fluorescence(XRF)signal is collected simultaneously.XRF counts from all pixels are integrated directly by energy,while the diffraction spectra are integrated by d-spacing,resulting in a much improved peak strength and signal-to-noise(S/N)ratio for the array detector.In comparison with ARXRD,the diffraction signal generated by a white X-ray beam over monochromic light under the experimental conditions is about 104 times higher.The full width at half maximum(FWHM)of the peaks in q-space is found to be dependent on the energy resolution of the detector,the angle span of the detector,and the diffraction angle.It is possible for EDXRD to achieve the same or even smaller FWHM as ARXRD under the energy resolution of the current detector if the experimental parameters are properly chosen.

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.

Investigation of Peak Separation for X-ray Diffraction Profiles of Spinodal Decomposition by a Kind of Optimized Voigt Function

The intensity and position of sidebands (satellites) on both sides of main diffraction peak in a great number of X-ray diffraction profiles of alloys always change with progress of aging. The sidebands position is determined by a newly optimized Voigt function in present investigation. Furthermore, for Cu-4 wt pet Ti alloy aged at 400℃ for 720 min and 1080 min, after introducing the weight factor of above two satellites intensity, the relative error between the fitting curves and X-ray diffraction profiles is less than 0.185%, which is more precise than the previously calculating result.

Quantitative damage imaging using Lamb wave diffraction tomography

In this paper, we investigate the diffraction tomography for quantitative imaging damages of partly through-thickness holes with various shapes in isotropic plates by using converted and non-converted scattered Lamb waves generated nu- merically. Finite element simulations are carried out to provide the scattered wave data. The validity of the finite element model is confirmed by the comparison of scattering directivity pattern （SDP） of circle blind hole damage between the finite element simulations and the analytical results. The imaging method is based on a theoretical relation between the one-dimensional （1D） Fourier transform of the scattered projection and two-dimensional （2D） spatial Fourier transform of the scattering object. A quantitative image of the damage is obtained by carrying out the 2D inverse Fourier transform of the scattering object. The proposed approach employs a circle transducer network containing forward and backward projections, which lead to so-called transmission mode （TMDT） and reflection mode diffraction tomography （RMDT）, respectively. The reconstructed results of the two projections for a non-converted SO scattered mode are investigated to illuminate the influence of the scattering field data. The results show that Lamb wave diffraction tomography using the combination of TMDT and RMDT improves the imaging effect compared with by using only the TMDT or RMDT. The scattered data of the converted A0 mode are also used to assess the performance of the diffraction tomography method. It is found that the circle and elliptical shaped damages can still be reasonably identified from the reconstructed images while the reconstructed results of other complex shaped damages like crisscross rectangles and racecourse are relatively poor.

Crystallographic Characteristic of Intermetallic Compounds in Al-Si-Mg Casting Alloys Using Electron Backscatter Diffraction

The Al-Si-Mg alloy which can be strengthened by heat treatment is widely applied to the key components of aerospace and aeronautics. Iron-rich intermetallic compounds are well known to be strongly influential on mechanical properties in Al-Si-Mg alloys. But intermetallic compounds in cast Al-Si-Mg alloy intermetallics are often misidentified in previous metallurgical studies. It was described as many different compounds, such as AlFeSi, Al8Fe2Si, Al5（Fe, Mn）3Si2 and so on. For the purpose of solving this problem, the intermetallic compounds in cast Al-Si alloys containing 0.5% Mg were investigated in this study. The iron-rich compounds in Al-Si-Mg casting alloys were characterized by optical microscope（OM）, scanning electron microscope（SEM）, energy dispersive X-ray spectrometer（EDS）, electron backscatter diffraction（EBSD） and X-ray powder diffraction（XRD）. The electron backscatter diffraction patterns were used to assess the crystallographic characteristics of intermetallic compounds. The compound which contains Fe/Mg-rich particles with coarse morphologies was Al8FeMg3Si6 in the alloy by using EBSD. The compound belongs to hexagonal system, space group P6_2m, with the lattice parameter a=0.662 nm, c=0.792 nm. The β-phase is indexed as tetragonal Al3FeSi2, space group I4/mcm, a=0.607 nm and c=0.950 nm. The XRD data indicate that Al8FeMg3Si6 and Al3FeSi2 are present in the microstructure of Al-7Si-Mg alloy, which confirms the identification result of EBSD. The present study identified the iron-rich compound in Al-Si-Mg alloy, which provides a reliable method to identify the intermetallic compounds in short time in Al-Si-Mg alloy. Study results are helpful for identification of complex compounds in alloys.

X-ray Multiple Diffraction Topographic Imaging Technique For Growth History Study of Habit Modifying Impurity Doped Crystals

A novel crystal characterization instrument has been built up in which a combination of X-ray multiple diffraction and X-ray topography is applied to enabling the cross-correlation between micro-crystallographic symmetry and its spatial dependence in relation to lattice defects. This facility is used to examine, in a self-consistent manner, growth sector-dependant changes to both the crystallographic structure and the lattice defects associated with the action of habit-modifying additives in a number of representative crystal growth systems. In addition, the new instrument can be used to probe micro-crystallographic aspects(such as distortion to crystal symmetry) and relate these in a spatially resolved manner to the crystal defect structure in crystals doped with known habit modifiers.

Determination of Space Group Pncm of Prehnite Using Electron Diffraction Method

Space symmetry of prehnite, which occurs in cavities and veins within Skarn from the Tieshan iron mineral deposit,Daye,Hubei province,Central China,has been determined using selected area electron diffraction (SAED) and convergent-beam electron diffraction (CBED) on the submicrometer scale.Our results confirm that the natural prehnite may have the structure with symmetry Pncm.The unit-cell parameters of investigated prehnite (a=0.458nm,b=0.555nm,and c=1.853nm) have been calculated by using the multicrystal diffraction rings of gold,the internal standard.

A Basis for Causal Scattering Waves, Relativistic Diffraction in Time Functions

Relativistic diffraction in time wave functions can be used as a basis for causal scattering waves. We derive such exact wave function for a beam of Dirac and Klein-Gordon particles. The transient Dirac spinors are expressed in terms of integral defined functions which are the relativistic equivalent of the Fresnel integrals. When plotted versus time the exact relativistic densities show transient oscillations which resemble a diffraction pattern. The Dirac and Klein-Gordon time oscillations look different, hence relativistic diffraction in time depends strongly on the particle spin.

X-Ray and Neutron Diffraction Studies on Thermal Parameters of Thalous Bromide

Thermal parameters of TIBr were determined using both X-ray and neutron diffraction techniques. The data was analysed by Rietveld profile refinement procedure. From the neutron diffraction data, due to weak odd-order reflections, it was not possible to determine the individual thermal parameters. TheX-ray diffraction measurements yielded BT1=0.296(5) nm2 and BBr=0.162(5) nm2. The overall isotropic value, B was 0.252(7) nm2 which is in good agreement with B=0.230(8) nm2 obtained from present neutron diffraction measurements. The present values are also in good agreement with theoretical estimates obtained from the shell models.

Diffraction separation and imaging based on double sparse transforms

Reflection imaging results generally reveal large-scale continuous geological information,and it is difficult to identify small-scale geological bodies such as breakpoints,pinch points,small fault blocks,caves,and fractures,etc.Diffraction imaging is an important method to identify small-scale geological bodies and it has higher resolution than reflection imaging.In the common-offset domain,reflections are mostly expressed as smooth linear events,whereas diffractions are characterized by hyperbolic events.This paper proposes a diffraction extraction method based on double sparse transforms.The linear events can be sparsely expressed by the high-resolution linear Radon transform,and the curved events can be sparsely expressed by the Curvelet transform.A sparse inversion model is built and the alternating direction method is used to solve the inversion model.Simulation data and field data experimental results proved that the diffractions extraction method based on double sparse transforms can effectively improve the imaging quality of faults and other small-scale geological bodies.

Neutron powder diffraction and high-pressure synchrotron x-ray diffraction study of tantalum nitrides

Tantalum nitride （TAN） compact with a Vickers hardness of 26 GPa is prepared by a high-pressure and high- temperature （HPHT） method. The crystal structure and atom occupations of WC-type TaN have been investigated by neutron powder diffraction, and the compressibility of WC-type TaN has been investigated by using in-situ high-pressure synchrotron x-ray diffraction. The third-order Birch-Murnaghan equation of state fitted to the x-ray diffraction pressure- volume （P-V） sets of data, collected up to 41 GPa, yields ambient pressure isothermal bulk moduli of B0 = 369（2） GPa with pressure derivatives of B~ = 4 for the WC-type TaN. The bulk modulus of WC-type TaN is not in good agreement with the previous result （Bo = 351 GPa）, which is close to the recent theoretical calculation result （Bo = 378 GPa）. An analysis of the experiment results shows that crystal structure of WC-type TaN can be viewed as alternate stacking of Ta and N layers along the c direction, and the covalent Ta-N bonds between Ta and N layers along the c axis in the crystal structure play an important role in the incompressibility and hardness of WC-type TaN.