Diffraction Intensity Patterns Research Articles

Parameterization of magnetic vector potentials and fields for efficient multislice calculations of elastic electron scattering.

The multislice method, which simulates the propagation of the incident electron wavefunction through a crystal, is a well established method for analysing the multiple scattering effects that an electron beam may undergo. The inclusion of magnetic effects into this method proves crucial towards simulating enhanced magnetic interaction of vortex beams with magnetic materials, calculating magnetic Bragg spots or searching for magnon signatures, to name a few examples. Inclusion of magnetism poses novel challenges to the efficiency of the multislice method for larger systems, especially regarding the consistent computation of magnetic vector potentials A and magnetic fields B over large supercells. This work presents a tabulation of parameterized magnetic (PM) values for the first three rows of transition metal elements computed from atomic density functional theory (DFT) calculations, allowing for the efficient computation of approximate A and B across large crystals using only structural and magnetic moment size and direction information. Ferromagnetic b.c.c. (body-centred cubic) Fe and tetragonal FePt are chosen to showcase the performance of PM values versus directly obtaining A and B from the unit-cell spin density by DFT. The magnetic fields of b.c.c. Fe are well described by the PM approach while for FePt the PM approach is less accurate due to deformations in the spin density. Calculations of the magnetic signal, namely the change due to A and B of the intensity of diffraction patterns, show that the PM approach for both b.c.c. Fe and FePt is able to describe the effects of magnetism in these systems to a good degree of accuracy.

The Effect of Ethanol Solvent on Characterization of MAPbI<sub>3</sub> Perovskite

Methyl ammonium lead iodide CH3NH3PbI3 Perovskite was synthesized by a new method mixing between one and two steps, in addition, the ethanol solvent was used to dissolve CH3NH3I and compared with isopropanol solvent. The characterizations of synthesized perovskite samples included the structural properties, morphological characteristics and optical properties. The intensity and orientation in X-ray diffraction patterns appear clearly in ethanol solvent while disappearing at a peak at 12o due to the speed reaction of perovskite in this solvent. Additionally, the ethanol solvent increasing the grain size of perovskite which homogeneity of the surface morphology. the ethanol solvent cause a decrease in the wavelength of absorbance edge in addition to an increase in the energy bandgap value. Keywords: Ethanol Solvent, Perovskite, Photovoltaic Technologies, X-ray diffraction.

Development and application of a tender X-ray ptychographic coherent diffraction imaging system on BL27SU at SPring-8.

Ptychographic coherent diffraction imaging (CDI) allows the visualization of both the structure and chemical state of materials on the nanoscale, and has been developed for use in the soft and hard X-ray regions. In this study, a ptychographic CDI system with pinhole or Fresnel zone-plate optics for use in the tender X-ray region (2-5 keV) was developed on beamline BL27SU at SPring-8, in which high-precision pinholes optimized for the tender energy range were used to obtain diffraction intensity patterns with a low background, and a temperature stabilization system was developed to reduce the drift of the sample position. A ptychography measurement of a 200 nm thick tantalum test chart was performed at an incident X-ray energy of 2.500 keV, and the phase image of the test chart was successfully reconstructed with approximately 50 nm resolution. As an application to practical materials, a sulfur polymer material was measured in the range of 2.465 to 2.500 keV including the sulfur K absorption edge, and the phase and absorption images were successfully reconstructed and the nanoscale absorption/phase spectra were derived from images at multiple energies. In 3 GeV synchrotron radiation facilities with a low-emittance storage ring, the use of the present system will allow the visualization on the nanoscale of the chemical states of various light elements that play important roles in materials science, biology and environmental science.

Review of the direct derivation method: quantitative phase analysis with observed intensities and chemical composition data

The direct derivation (DD) method is a technique for quantitative phase analysis (QPA). It can be characterized by the use of the total sums of scattered/diffracted intensities from individual components as the observed data. The crystal structure parameters are required when we calculate the intensities of reflections or diffraction patterns. Intensity can, however, be calculated only with the chemical composition data if it is not of individual reflections but of a total sum of diffracted/scattered intensities for that material. Furthermore, it can be given in a form of the scattered intensity per unit weight. Therefore, we can calculate the weight proportion of a component material by dividing the total sum of observed scattered/diffracted intensities by the scattered intensity per unit weight. The chemical composition data of samples under investigation are known in almost all cases at the stage of QPA. Thus, a technical problem is how to separate the observed diffraction pattern of a mixture into individual component patterns. Various pattern decomposition techniques currently available can be used for separating the pattern of a mixture. In this report, the theoretical background of the DD method and various techniques for pattern decompositions are reviewed along with the examples of applications.

Polarization effects of X-ray monochromators modeled using dynamical scattering theory.

The difference in the diffracted intensity of the σ- and π-polarized components of an X-ray beam in powder diffraction has generally been treated according to equations based on dipole scattering, also known as kinematic X-ray scattering. Although this treatment is correct for powders and post-sample analyzers known to be of high mosaicity, it does not apply to systems configured with nearly perfect crystal incident-beam monochromators. Equations are presented for the polarization effect, based on dynamical diffraction theory applied to the monochromator crystal. The intensity of the π component relative to the σ component then becomes approximately proportional to |cos 2θm| rather than to cos22θm, where θm is the Bragg diffraction angle of the monochromator crystal. This changes the predicted intensities of X-ray powder diffraction patterns produced on instruments with incident-beam monochromators, especially in the regions far from 2θ = 90° in the powder pattern. Experimental data, based on well known standard reference materials, are presented, confirming that the dynamical polarization correction is required when a Ge 111 incident-beam monochromator is used. The dynamical correction is absent as an option in the Rietveld analysis codes with which the authors are familiar.

Quantitative pure-phase object reconstruction under single-shot Fourier measurement via deep learning

The phase retrieval problem, usually known as reconstructing an estimate of phase object from its diffraction intensity patterns, exists widely in the optical imaging field. In this paper, a deep convolutional neural network (CNN) framework is developed to accomplish the phase reconstruction given a single-shot Fourier measurement, without the requirement of prior knowledge (like nonnegativity and support constraints) or time-consuming iterations. A receptive field and input enhance learning-based design principle is applied to establish the neural network architecture. And a new loss function that combines the structural similarity (SSIM) index and the mean square error (MSE) is taken to further improve the network training. Quantitative (the average SSIM and relative MSE are ~ 0.9900 and 0.0012, respectively) and qualitative (SSIM, ranging from 0.87 to 0.95) phase reconstructions are achieved in the numerical simulation and experiment, respectively. Once the proposed network is well trained, it is convenient for the users to perform the phase reconstruction at a remarkably fast speed (~ 0.425 s). Moreover, our network is considerably robust to different noises and could be trained to additionally function as a denoiser in the phase retrieval process. In practice, the proposed method is able to build an accurate propagation model of the practical imaging system, and significantly enhance and improve the spatial resolution. With the great convenience and high accuracy of phase recovery, the proposed deep CNN framework may be helpful to solve the phase retrieval problem in Fourier imaging systems, like coherent diffraction imaging (CDI), X-ray imaging, and imaging through diffusers, etc.

Enhancing Multi-Distance Phase Retrieval via Unequal Interval Measurements

In the conventional methods of multi-distance phase retrieval, the diffraction intensity patterns are recorded at equal intervals, which can induce slow convergence or stagnation in the subsequent reconstruction process. To solve this problem, a measurement method with unequal intervals is proposed in this paper. The interval spacings between adjacent measurement planes are decreased gradually. A large gap accelerates retrieval progress, and a short span helps to recover detailed information. The proposed approach makes full use of the available measured dataset and simultaneously generates variations in diversity amplitude, which is a crucial issue for the techniques of multi-image phase retrieval. Both computational simulations and experiments are performed. The results demonstrate that this method can improve the convergence speed by 2 to 3 times and enhance the quality of reconstruction results in comparison to that of the conventional methods.

Diffraction on a Microbubble and the Morphology of the Silicon Surface Irradiated through Glycerol by a Pair of Femtosecond Laser Pulses

The effect of two successive laser pulses on silicon placed in glycerol has been studied experimentally and numerically with electromagnetic, hydrodynamic, and atomistic simulation programs. It has been shown that a microbubble in the liquid is formed on the surface after the first pulse; then, the second pulse whose width is comparable with the diameter of the microbubble is diffracted on this microbubble. The calculated diffraction pattern and light intensity distribution on the silicon surface indicate that the maximum intensity at the diffraction peaks can be noticeably higher than the intensity on the axis of the incident Gaussian beam. An increase in the intensity concentrated in one bright narrow ring around the microbubble results in the formation of a characteristic groove surrounded by ridges on silicon. The molecular dynamics simulation has shown that intense heating at the diffraction peak is responsible for the melting and displacement of the melt from the center of heating. This leads to the formation of grooves with ridges having a profile similar to that measured in the experiment.

Determination of nonlinear refractive index by an iterative phase retrieval method.

We present a simple and robust technique for measuring the nonlinear refractive index. The principle is based on an iterative phase retrieval algorithm with a pump-probe system. Different strong phase modulations are intentionally introduced into the probe beam, and corresponding diffraction intensity patterns are recorded. The recordings are used in the phase retrieval algorithm to reconstruct the pump-induced phase on the probe beam. The nonlinear refractive index is then extracted from the reconstructed phase. The reconstruction method offers a straightforward procedure and a simple lensless setup. Simulations validate the proposed method. The effects of different characteristics of the pump and probe beams on the quality of reconstructions are investigated. The obtained results demonstrate that the reconstructions are accurate even for the probe beams with complex-valued fields and non-Gaussian pump beams; it removes the requirement for smooth fields of the pump and probe beams. The validity of the method in noisy conditions is also shown.

High Pressure Effect on Structural and Electrochemical Properties of Anionic Redox-Based Lithium Transition Metal Oxides

Summary The richness of anionic redox chemistry in the solid state offers new opportunities and a possible paradigm shift in energy storage. The excess capacity that goes beyond conventional theoretical values is attributed to the anionic redox in Li-rich transition metal oxide cathodes for Li-ion batteries. Their electrochemical behavior is thermodynamically determined by structural evolution. To better understand the electrochemical dependence on structural factors, we have induced structural modifications in pristine and electrochemically activated Li1.144Ni0.136Co0.136Mn0.544O2 through high-pressure treatment. A unique cyclical change of structural reordering is observed in the anionic redox-activated material during operando pressure sweep, characterized by a periodic evolution of superlattice peak intensity in synchrotron X-ray diffraction patterns. During the structural reordering period, the bulk compressibility of the material decreases, even becoming negative. These insights elucidate the structural flexibility and metastability of anionic redox-based materials, which can undergo large compressions and structural modifications while delivering good electrochemical properties.

Hybrid Angular Gradient Phase Grating for Measuring the Orbital Angular Momentum of Perfect Optical Vortex Beams

We propose an effective method to measure the orbital angular momentum of a perfect optical vortex (POV) beam with a hybrid angular gradient phase grating (HAG-PG), which is a gradient grating with angular changing distribution. The HAG-PG performs the transformation from the POV to the dark stripes of the diffraction intensity patterns. From the number and the orientation of dark stripes of far-field diffraction patterns formed by the HAG-PG, the modulus of TC and sign of the incident POV beam can be determined. The high scalability of this method for being unrestricted by the Fourier plane and its adaptation for measuring the POV beams with different states are demonstrated by loading the HAG-PG hologram on a spatial light modulator. And the detection sensitivity of the POV beam can be significantly improved. The experimental results agree well with the theoretical simulations.

Quantitative electric field mapping of a p–n junction by DPC STEM

Local electromagnetic fields in a specimen is measured at high spatial resolutions using differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM). According to previous studies, DPC signals can be quantified by measuring the center of mass of the diffraction pattern intensity and/or performing a deconvolution method based on a phase contrast transfer function (PCTF). However, when using a segmented detector, the field strength has been considerably underestimated for a very thick specimen. The main cause of the underestimation is assumed to be inelastic scattering, mainly bulk plasmon scattering. In this study, we develop a method to remove this inelastic scattering effect from segmented detector DPC signals by modifying the PCTF deconvolution method. Field quantification results using this new technique are compared with those using pixelated detector DPC and electron holography, and all results indicated good agreement within an error margin.

Measuring high orbital angular momentum of vortex beams with an improved multipoint interferometer

A multipoint interferometer (MI), uniformly distributed point-like pinholes in a circle, was proposed to measure the orbital angular momentum (OAM) of vortex beams [Phys. Rev. Lett. 101, 100801 (2008)PRLTAO0031-900710.1103/PhysRevLett.101.100801], which can be used for measuring OAM of light from astronomical sources. This is a simple and robust method; however, it is noted that this method is only available for low topological charge because the diffracted intensity patterns for vortex beams with higher OAM will repeat periodically. Here, we propose an improved multipoint interferometer (IMI) for measuring the OAM of an optical vortex with high topological charge. The structure of our IMI is almost the same as the MI, but the size of each pinhole is larger than a point in the MI. Such a small change enables each pinhole to get more phase information from the incident beams; accordingly, the IMI can distinguish any vortex beams with different OAM. We demonstrate its viability both theoretically and experimentally.

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II

X-ray Bragg coherent diffraction imaging (BCDI) has been demonstrated as a powerful 3D microscopy approach for the investigation of sub-micrometre-scale crystalline particles. The approach is based on the measurement of a series of coherent Bragg diffraction intensity patterns that are numerically inverted to retrieve an image of the spatial distribution of the relative phase and amplitude of the Bragg structure factor of the diffracting sample. This 3D information, which is collected through an angular rotation of the sample, is necessarily obtained in a non-orthogonal frame in Fourier space that must be eventually reconciled. To deal with this, the approach currently favored by practitioners (detailed in Part I) is to perform the entire inversion in conjugate non-orthogonal real- and Fourier-space frames, and to transform the 3D sample image into an orthogonal frame as a post-processing step for result analysis. In this article, which is a direct follow-up of Part I, two different transformation strategies are demonstrated, which enable the entire inversion procedure of the measured data set to be performed in an orthogonal frame. The new approaches described here build mathematical and numerical frameworks that apply to the cases of evenly and non-evenly sampled data along the direction of sample rotation (i.e. the rocking curve). The value of these methods is that they rely on the experimental geometry, and they incorporate significantly more information about that geometry into the design of the phase-retrieval Fourier transformation than the strategy presented in Part I. Two important outcomes are (1) that the resulting sample image is correctly interpreted in a shear-free frame and (2) physically realistic constraints of BCDI phase retrieval that are difficult to implement with current methods are easily incorporated. Computing scripts are also given to aid readers in the implementation of the proposed formalisms.

Single exposure lensless subpixel phase imaging: optical system design, modelling, and experimental study.

Design and optimization of lensless phase-retrieval optical system with phase modulation of free-space propagation wavefront is proposed for subpixel imaging to achieve super-resolution reconstruction. Contrary to the traditional super-resolution phase-retrieval, the method in this paper requires a single observation only and uses the advanced Super-Resolution Sparse Phase Amplitude Retrieval (SR-SPAR) iterative technique which contains optimized sparsity based filters and multi-scale filters. The successful object imaging relies on modulation of the object wavefront with a random phase-mask, which generates coded diffracted intensity pattern, allowing us to extract subpixel information. The system's noise-robustness was investigated and verified. The super-resolution phase-imaging is demonstrated by simulations and physical experiments. The simulations included high quality reconstructions with super-resolution factor of 5, and acceptable at factor up to 9. By physical experiments 3 μm details were resolved, which are 2.3 times smaller than the resolution following from the Nyquist-Shannon sampling theorem.

Wilhelm Wien’s Photons Creating the BohEmian Pilot Wave for the Guiding of the Individual Huygens - de Broglie Particles on the Helical Path Governed by the Newton - Bohm Evolute (the Bohmian Pilot Wave) through the Young - Feynman Double - Slit Barrier.

In our approach we have combined knowledge of Old Masters (working in this field before the year 1905), New Masters (working in this field after the year 1905) and Dissidents under the guidance of Louis de Broglie and David Bohm. In our model the quantum particle is represented as the Huygens-de Broglie’s particle on the helical path (full wave) guided by the Newton-Bohm entangled helical evolute (Bohmian Pilot Wave). These individual Huygens - de Broglie particles in the Young - Feynman double - slit experiment react with Wilhelm Wien’s photons that are always present inside of the apparatus (Wien’s displacement law). Wilhelm Wien’s photons form collectively the Wien filter guiding the Huygens - de Broglie particles through the double - slit barrier towards a detector (BohEmian Pilot Wave). The interplay of those events creates the observed interference pattern. In the very well-known formula describing the intensity of double-slit diffraction patterns we have newly introduced the concept curvature κ of the Huygens - de Broglie particle and thus giving a physical interpretation for the Newton - Bohm guiding wave (the Bohmian Pilot Wave): for photons κ = π/λ, for electrons κ = 2π/λ. Moreover, we have introduced into that formula the expression λmax from the Wien’s displacement law to describe geometry of the double - slit barrier. We propose to modify the value λmax by the change of the system temperature. There is a second experimental possibility - we can insert into those slits filters to remove Wien’s photons while the Huygens - de Broglie particles continue towards a detector - we should observe the particle behavior. The similar situation might occur in the Mach - Zehnder interferometer. In this case the individual Huygens - de Broglie particle reacts in the first beam splitter with the Wien photon: the Huygens - de Broglie particle goes through one path while the Wien photon goes through the second path. In the second beam splitter they interact again and create the interference pattern on one detector. We can experimentally modify the resulting interference pattern in the Mach - Zehnder interferometer - by the temperature change of the system or by inserting filters to remove Wien’s photons from one or both paths. Can it be that Nature cleverly creates those interference patterns while the Bohmian pilot wave and the BohEmian pilot wave are hidden in plain sight? We want to pass this concept into the hands of Readers of this Journal better educated in the Mathematics and Physics.

Using Variant Selection to Facilitate Accurate Fitting of \u03b3\u2033 Peaks in Neutron Diffraction

γ″ diffraction peaks are hard to discern in neutron/X-ray diffraction patterns, hindering studies on the γ″-strengthened superalloys using in-situ diffraction. In this study, we propose a variant selection method to increase the intensity of γ″ peaks and to facilitate accurate fitting. The specific variants of γ″ are controlled by applying a 300 MPa tensile stress during aging at 790 °C for 5 hours. The interaction energy between the applied stress and the transformation strain of each γ″ variant differs, leading to an increase in the amount of the variants with a greater energy reduction at the expense of other variants. The enhanced variants result in greater γ″ peak intensities in neutron diffraction patterns, allowing both the Pawley refinement and single peak fitting to be performed. Lattice parameters of γ″ and γ phases, and lattice misfit between the two phases and volume fraction of γ″ are acquired. The uncertainties associated with the fitting maintain an acceptable level corresponding to 150 microstrains. The proposed variant selection method shows potential for studying the role of γ″ phase in Ni-base superalloys.

Phase retrieval exact solution based on structured window modulation without direct reference waves

Arising in coherent diffraction imaging (CDI), the phase retrieval problem is to reconstruct a complex object by measuring only diffraction intensity patterns. Existing approaches, such as iterative Fourier algorithm (IFA), transport intensity equation (TIE) methods and matrix optimisation, result in near-optimal solutions rather than exact solutions. This paper proposes an analytic method to get the exact phase retrieval solution without relying on direct reference waves. Based on structured template windows, the object far-field phase is solved analytically from the recorded Fourier intensities, from which the exact object reconstruction can be achieved. Sufficient conditions for obtaining exact phase retrieval solution are analysed rigorously and verified by numerical simulations, which also show the robustness of the method through simulations under noises, dynamic range, nonlinear response and bad alignment. A simple experimental result is provided to demonstrate the practical feasibility of the method. It achieves analytic phase retrieval for arbitrary complex-valued objects and may be applicable to quick phase imaging.

Смещение дифракционной картины при движении среды

Diffraction of waves of different physical nature is one of the most important and studied phenomena of nature in connection with its versatile use in devices and measuring techniques. The influence of media motion on the diffraction pattern attracted the attention of researchers in connection with the development of the theory of electrodynamics of moving media and continues to attract attention in connection with a number of unsolved problems of physics. In this paper we consider a model of the diffraction of waves on the slit and lattice, located on a movable substrate (medium). Analytical relations for the calculation of the diffraction pattern intensity distribution are obtained. The significant influence of the medium motion on the diffraction pattern is established. The position of the zero-order maximum does not depend on the motion of the medium, on the one hand, the distance between the diffraction maxima decreases, on the other hand increases, until they disappear. The conditions under which the motion of the medium leads to an asymmetrical appearance of the diffraction intensity distribution, which is not observed in a stationary medium, are established. Generalized conditions of diffraction minima are obtained taking into account the motion of the medium. Shows the effect of the direction of the velocity of motion of the medium on the intensity of the diffraction pattern.

Subsidiary and Principal Maxima in Multiple-Slit Interference

We present a theoretical study on the amplitudes and the linewidths of the subsidiary and principal maxima in multiple-slit interference patterns in the Fraunhofer regime. In the limit of a large slit number, we observe that the calculated amplitudes of the subsidiary maxima relative to the principal maximum are slightly different from the values presented in textbooks. We also present the calculation of the widths for the diffracted intensity patterns of the principal and the first several subsidiary maxima.