Diffraction Theory Research Articles

Can Raman Spectra of NMC Material Family be Detangled?

Raman spectroscopy is an advanced tool for investigating the structural and chemical properties of Li-ion battery materials. With the ability to probe the vibrational modes of crystals, it can provide valuable insights into the structural evolution and chemical reactions that occur during battery cycling. This technique has been used extensively to study electrode materials, solid electrolytes, and interfaces in Li-ion batteries, providing a deeper understanding of the mechanisms governing their performance and degradation. [1]Raman spectroscopy plays a crucial role in the characterization of LiNi1-x-yMnxCoyO2 (NMC) materials, which are widely used as positive electrodes. It can provide information on the phase transitions, crystal symmetry, and degradation that occur during battery cycling. [2] The Raman spectrum of LiMO2 is composed of peaks that correspond to the vibrational modes of the crystal lattice. The most prominent line in Raman spectrum of the R-3m space group symmetry should correspond to the A1g mode, which in case of LiMO2 crystal arises from the symmetric stretching vibration of the metal-oxygen (M-O) bonds in the octahedral coordination. The second predicted peak in the spectrum is Eg which involves the movement of oxygens in opposite directions across adjacent O-layers. [2] The interpretation of the NMC Raman spectra can be challenging due to several factors. One of the main difficulties is the complexity of its crystal structure, giving rise to a large number of vibrational modes in the spectrum. The presence of multiple metal-oxygen (M-O) bond types in the octahedral coordination can lead to overlapping Raman peaks, making it difficult to distinguish between the different modes. Another challenge is the presence of defects and disorder, which can lead to changes in the crystal symmetry and vibrational modes of the material, resulting in additional peaks or shifts in the Raman spectrum. Factors such as particle size, morphology, and orientation might also affect the Raman spectrum, as might the excitation wavelength and polarization of the incident light. To overcome these challenges, a combination of experimental and theoretical techniques, such as X-ray diffraction and density functional theory calculations, is typically used to assist in the interpretation of the Raman spectra. [3] Despite the efforts, the full interpretation of NMC Raman spectra, particularly with respect to its charged states, remains undone.In our investigation, we found noticeable changes in the Raman spectra across samples with similar, but non-identical, compositions. We also see that partially and fully charged NMC samples have significantly more than two or three Raman modes varied or shifted, likewise suggesting more complex spectrum. The systematic comparison of a larger number of spectra allowed us to identify these variations and correlate them with specific material compositions. We developed a novel approach for interpreting Raman spectra of NMC materials that involves an extensive collection of spectral data. This method requires us to gather Raman spectra from diverse NMC samples with varying compositions, particle sizes, and morphologies. We use advanced analysis to identify correlations and trends between the spectral features and the material properties. This demanding approach gives a more comprehensive understanding of the relationship between the Raman spectra and the composition of NMC samples, which can facilitate better interpretation and design of these materials for use in Li-ion batteries. In this work, we will highlight the potential of this method to enable us to more accurately interpret Raman spectra of charge and discharge states that might further help in developing easy monitoring of NMC electrodes during their operation. A detailed data analysis will be presented at the conference. Funding for this work was provided by the National Science Center in Poland under the Sonata BIS 11 program (No. UMO-2021/42/E/ST5/00390).[1] P.P.R.M.L. Harks et al. J. Power Sources 288 (2015) 92-105[2] E. Flores et al. Front. Energy Res., 6 (2018) 82[3] E. Flores et al. Chem. Mater. 2020, 32, 1, 186–194

Research on focusing of a triangle-exponential function modulation spiral polarization cosh-Gaussian vortex beam

The focus pattern of a triangle-exponential function modulation spiral polarized hyperbolic-cosine-Gaussian (cosh-Gaussian) vortex beam is examined according to the vector diffraction theory and the focus intensity with different parameters is disputed. By adjusting the polarization parameter C, the number of the focusing peaks can be changed: Specifically, as the absolute value of the polarization parameter C augments, so does the number of the focus peaks. When the beam parameter β is modified, the focus pattern is compressed and stretched in both the axial and radial directions, respectively, which helps to precisely adjust the shape of the focus pattern in the focus region. Meanwhile, the trigonometric modulation parameter l can change the axial component of the focus region. With a change in the trigonometric modulation parameter l, the focus pattern finally evolves into the light-like chain structure and the position of the focus peak in the axial direction also can be controlled. This shows that the correlation properties enrich our understanding of the cosh-Gaussian vortex beam. Therefore, cutting-edge optical applications including optical transmission, optical shaping, and multiple optical sensing could benefit from these results.

Design of an optical linear-discriminant filter: optimization for enhancement of filter transmittance and discrimination accuracy.

To discriminate fine concave and convex defects on a dielectric substrate, an optical machine learning system is proposed. This system comprises an optical linear-discriminant filter (OLDF) that performs linear discriminant analysis (LDA) of the scattered-wave distribution from target samples. However, the filter output from the OLDF is considerably weak and cannot be measured experimentally. Therefore, an algorithm is also proposed to improve the discrimination accuracy and filter transmittance. The designed filter is validated using a rigorous optical simulator based on vector diffraction theory. We also analyze and discuss a mechanism that provides high transmittance with high discrimination accuracy.

A boundary integration method for calculating diffraction intensity of crystalline materials with planar deformation

Defects and strain states in crystals can be investigated using X-ray and neutron diffraction, two types of penetrating, non-destructive detection techniques. Various approximations are frequently employed to minimize the amount of computation in the practical calculations because the present Fourier transform approach, established by Warren, Averbach et al. based on the Kinematic diffraction theory, has a huge computational cost. This paper develops a numerical method to precisely calculate diffraction intensity by integrating kinematic diffraction amplitude over the boundary, which is applicable to crystals with planar deformation. The precision of this method is assessed by contrasting it with Wilson's analytical equations for the X-ray diffraction results of a single screw dislocation. As an example, the difference in diffraction spots on a single edge dislocation irradiated by different incident X-ray widths are calculated and analyzed. When compared to the X-ray diffraction spots of an ideal material with a dislocation core dug out, the results indicate that if lattice information close to the dislocation core is to be retrieved by X-ray diffraction, the X-ray irradiation area should be restricted.

Effect of cavity's geometry and pellet shape on the electric field distribution and penetration depth of microwave in processing electric arc furnace dust

Microwave heating has a great potential application in pyrometallurgy because the usual steelmaking materials can interact with microwaves and generate heat. Thus, the penetrating ability and distribution of microwaves inside the materials affect the stability and efficiency of the overall heating process. This paper focuses on electric arc furnace dust (EAFD) as the raw material, the effects of the cavity's geometry and pellet shape on microwave penetration depth and distribution at a frequency of 2.45 GHz have been studied. The results are as follows: (1) Combining the Bruggeman practical medium theory (Br-EMT) and semi-qualities analysis of X-ray diffraction (XRD), the dielectric properties of EAFD can be determined; (2) Cavity has a geometry of regular hexahedral prism can improve the microwave penetration and uniform of distribution; (3) Ellipsoidal pellets (polar radius = 1/2 equatorial radius) make the stock column more easily penetrated by microwaves and keep a uniformed microwave distribution internal.

Distortions in focusing laser pulses due to spatio-temporal couplings: an analytic description

Abstract In ultra-short laser pulses, small changes in dispersion properties before the final focusing mirror can lead to severe pulse distortions around the focus and therefore to very different pulse properties at the point of laser–matter interaction, yielding unexpected interaction results. The mapping between far- and near-field laser properties intricately depends on the spatial and angular dispersion properties as well as the focal geometry. For a focused Gaussian laser pulse under the influence of angular, spatial and group-delay dispersion, we derive analytical expressions for its pulse-front tilt, duration and width from a fully analytic expression for its electric field in the time–space domain obtained with scalar diffraction theory. This expression is not only valid in and near the focus but also along the entire propagation distance from the focusing mirror to the focus. Expressions relating angular, spatial and group-delay dispersion before focusing at an off-axis parabola, where they are well measurable, to the respective values in the pulse’s focus are obtained by a ray tracing approach. Together, these formulas are used to show in example setups that the pulse-front tilts of lasers with small initial dispersion can become several tens of degrees larger in the vicinity of the focus while being small directly in the focus. The formulas derived here provide the analytical foundation for observations previously made in numerical experiments. By numerically simulating Gaussian pulse propagation and measuring properties of the pulse at distances several Rayleigh lengths off the focus, we verify the analytic expressions.

Revealing the mechanism of manganese doping in sulphoaluminate cement clinker

The production of cement clinker from solid waste generated by industrial development is a valid way to reduce the exploitation of natural resources and protect the environment. This paper reports the doping behavior of manganese (Mn) ions in sulphoaluminate cement (SAC) clinker. Results from energy dispersive spectrometer (EDS), X-ray diffraction (XRD), and density functional theory (DFT) simulations indicate that Mn ions enter C4AF by replacing Fe ions, and rarely incorporate into the other two minerals, C4A3S‾ and C2S. Further analysis of the partial density of states (PDOS) and electron density difference (EDD) indicates that the Mn doping mechanism can be ascribed to the comparable electronic contributions of the host and guest ions. These insights into the doping behavior of Mn ions will provide meaningful information to guide the utilization of Mn-containing solid waste as an alternative raw material for the synthesis of SAC clinker.

High-pressure structural behavior and elastic properties of Ce2In and Ce3In: A combined in situ synchrotron X-ray diffraction and density functional theory study

Across the cerium (Ce)-indium (In) binary phase diagram, there are five line compounds including Ce3In, Ce2In, Ce3In5, CeIn2 and CeIn3. So far, CeIn3 is the only compound whose high-pressure structural behavior and elastic properties have been studied in detail. In this work, we investigated the compression behavior of Ce3In and Ce2In at pressures up to 26.2 GPa using in situ high-pressure angle dispersive synchrotron powder X-ray diffraction (XRD). Our results indicate that Ce3In retains its Cu3Au-type structure in the pressure range investigated, whereas Ce2In undergoes a phase transformation from the Ni2In-type structure to an unidentified phase at ∼4.6 GPa. Unit-cell parameters as a function of pressure were obtained by Rietveld analysis of XRD data. Unit cell volumes were fitted to a second order Birch-Murnaghan equation of state (EOS). The experimentally determined bulk moduli (K0) of the two cerium indides are 50 ± 3 GPa for Ce3In and 39.2 ± 1.6 GPa for Ce2In. The zero-pressure compressibilites of the a-axis (βa,0) for Ce3In is 6.67 (±0.36) × 10–3 GPa–1 and of the a- and c-axis for Ce2In are βa,0 = 8.85 (±0.39) × 10−3 GPa−1 and βc,0 = 9.26 (±0.51) × 10−3 GPa−1, respectively. These results are in general agreement with those calculated by density functional theory (DFT + U) and open-source machine learning algorithms.

Super-oscillatory spots with different inhomogeneous linear polarized states

We present the formation of super-oscillatory (SO) spots by tightly focusing the inhomogeneous linear polarized beam of different polarization states. At the entrance pupil of the focusing lens, a suitable phase manipulation in the incident beam results in a small super-oscillatory spot. Our numerical study based on the vectorial diffraction theory shows that SO spots of controllable size and various polarization combinations are possible. We also discuss the effect of the different polarization patterns of the incident beam on the size and energy distribution of the generated SO spots, which are potentially valuable for the orientation determination of single molecules and polarization-resolved imaging. This study reveals more influence of polarization states on the different components of the focused beam under the utilization of the proposed method rather than the usual tight focusing conditions.

Fraunhofer diffraction at the two-dimensional quadratically distorted (QD) grating.

A two-dimensional (2D) mathematical model of quadratically distorted (QD) grating is established with the principles of Fraunhofer diffraction and Fourier optics. A discrete sampling method is applied for finding a numerical solution of the diffraction pattern of QD grating. An optimized working phase term, which determines the balanced energies and high efficiency of multi-plane images, can be obtained by the bisection algorithm. To confirm the analytical approach described above, the results have been compared with those obtained using a classical numerical model based on Fraunhofer diffraction theory and a fast Fourier transform (FFT) algorithm. The results show that our analytical approach allows the precise design of QD grating and improves the optical performance of simultaneous multi-plane imaging system. An optical setup based on our well-designed QD grating has been appended to the camera port of a commercial microscope, and some preliminary microscopy images have been successfully obtained. Further upgrade of our analytical model is in progress to improve the image quality and promote the applications.

Prediction of effective size of a propagated laser beam with a known phase profile and its experimental validation

In this paper we demonstrate that the size of a laser beam, which increases with propagation due to diffraction induced divergence, carrying a given phase profile, can be predicted and the same can be validated experimentally. Since an arbitrary phase profile is also a linear combination of a set of Zernike polynomials hence the divergence corresponding to each Zernike mode can be utilized to estimate the effective size of the beam carrying the arbitrary phase profile. Numerical simulation using the scalar diffraction theory shows how a laser beam with a certain Zernike mode describing its phase profile diverges. Observations from numerical simulations lead to construction of a functional form that can predict the effective size of a laser beam carrying a specific Zernike mode in its phase profile, at different propagation distances. In this paper we develop an experimental arrangement to holographically incorporate a specific phase profile into an incident laser beam. We utilize the programmable control of the beam size for a given propagation distance to achieve different Fresnel numbers. We further develop a detector assembly which can be used to measure the effective size of the beam in the observation plane. We then show experimentally that the effective size of a laser beam propagating distances corresponding to different Fresnel numbers and carrying a known phase profile, described either by a single Zernike mode or a random combination of several Zernike modes, can be very well predicted by the functional form even in a realistic scenario.

Multi-exposure diffraction pattern fusion applied to enable wider-angle transmission Kikuchi diffraction with direct electron detectors

Diffraction pattern analysis can be used to reveal the crystalline structure of materials, and this information is used to nano- and micro-structure of advanced engineering materials that enable modern life. For nano-structured materials typically diffraction pattern analysis is performed in the transmission electron microscope (TEM) and TEM diffraction patterns typically have a limited angular range (less than a few degrees) due to the long camera length, and this requires analysis of multiple patterns to probe a unit cell. As a different approach, wide angle Kikuchi patterns can be captured using an on-axis detector in the scanning electron microscope (SEM) with a shorter camera length. These ‘transmission Kikuchi diffraction’ (TKD) patterns present a direct projection of the unit cell and can be routinely analysed using EBSD-based methods and dynamical diffraction theory. In the present work, we enhance this analysis significantly and present a multi-exposure diffraction pattern fusion method that increases the dynamic range of the detected patterns captured with a Timepix3-based direct electron detector (DED). This method uses an easy-to-apply exposure fusion routine to collect data and extend the dynamic range, as well as normalise the intensity distribution within these very wide (>95°) angle patterns. The potential of this method is demonstrated with full diffraction sphere reprojection and highlight potential of the approach to rapidly probe the structure of nano-structured materials in the scanning electron microscope.

Two calcium-based metal organic frameworks with long afterglow as anticounterfeiting materials

Calcium-based metal–organic frameworks (Ca-MOFs) with room-temperature phosphorescence (RTP) properties are promising for applications. Herein, two 3D Ca-MOFs with robust RTP have been successfully synthesized with scaled-up production. The afterglows of these two Ca-MOFs are visible to the naked eye in darkness that lasts for approximately 13 s once they are excited with 365 nm UV light. It is mainly attributed to the rigid and dense structures of 3D Ca-MOFs via 4,5-Imidazole dicarboxylic acid tugging Ca2+ elucidated by means of single-crystal X-ray diffraction and density functional theory (DFT). Furthermore, a program was designed for dynamic anti-counterfeiting based on the long afterglow properties of Ca-MOFs, which can be extended for all kinds of material with long afterglow.

City-Train noise reduction in urban area by using acoustic mini-screens made of metamaterials

Noise and vibration from trains and tramlines pass-by's within urban context are always cause of complaints by citizens, due to the high level of annoyance especially when the vehicle activity involves night-time periods. This paper deals with the acoustic design of mini screens composed of metamaterials to be placed at the edge of railways for shielding the noise from trains crossing urban areas. Acoustic measurements have been undertaken by using the beamforming approach along with linear array microphones in order to identify whether the noise is the most originated. It has been identified that the friction between wheels and railways is the source of noise other than the weight of carriage that moderately impact the results. The measured results show that the noise source is located in the trolley area, precisely at a level higher than the rolling rails. This conclusion has been investigated by a reverse engineering method on microphones array data and based on diffraction theory. Moreover, it has been considered the variability of noise emission from convoys in transit by applying normalisation of the energy contents through time-frequency analysis (wavelet). Further studies have been focused on the location and geometry of the mini screens based on the best acoustic performance, which can achieve a reduction of 6-8 dB for distance of 10 m and 100 m across the horizontal plane, and up to 9 dB for distance of 40 m on vertical plane.

Investigation of dynamical X-ray back diffraction at grazing incidence

We report a theoretical investigation of X-ray back diffraction at grazing incidence. Based on the framework of the dynamical theory of X-ray diffraction, the grazing incidence for Si (12 4 0) back diffraction is taken as an example to resolve the eigenvalue problem inside the crystal. The dispersion surface and the resulting diffraction intensities are strongly affected by the miscut angle as well as the diffraction geometry of grazing incidence. The kinematical relationship between the incident angle and the miscut angle is well explained by Snell’s law. While only the two-beam diffraction is considered, our treatment can be further extended to include the cases for multiple diffractions as well.

Controlled Synthesis of a High‐Mobility Bi3O2.5Se2 Semiconductor by Oxidation of Bi2Se3 for Fast and Highly Sensitive Photodetectors

AbstractThe search of new high‐mobility two‐dimensional (2D) semiconductors is crucial for the development of next‐generation photodetectors, since current photodetectors based on single 2D semiconductors usually cannot simultaneously own ultrafast response rate and ultrahigh sensitivity. Here, using a facial method of sequentially oxidizing Bi2Se3 at optimal O content, a series of bismuth oxyselenide semiconductors (Bi3O2.5Se2, Bi2O2Se, Bi2SeO5) with appealing electronic applications are successfully synthesized. The crystal and band structures of a superlattice‐free Bi3O2.5Se2 phase are resolved by 3D electron diffraction and density functional theory calculations, showing a unique non‐neutral layered structure, moderate band gap, and small effective mass. More importantly, the concept of Bi2Se3 + O2 can be extended to synthesize the superlattice‐free Bi3O2.5Se2 ultrathin films by chemical vapor deposition, whose room‐temperature mobility can be as high as ≈150 cm2 V−1 s−1 based on Hall measurements. The ultrathin Bi3O2.5Se2 photodetectors with a simple device configuration simultaneously own ultrafast response time (≈31 µs), ultrahigh responsivity (≈8 × 104 A/W), and large detectivity (≈8 × 1013 Jones). This work not only introduces a facile way to regulate the phase in the bismuth oxyselenide family, but also provides an alternative candidate for ultrafast and ultrasensitive photodetectors.

Focusing field energy flow simulation of an azimuthally polarized Lorentz–Gaussian beam modulated by a concentric vortex phase mask

Based on the vector diffraction theory, this paper investigated the energy flow evolution of focusing an azimuthally polarized Lorentz–Gaussian beam modulated by concentric vortex phase mask. Three concentric zones make up the concentric vortex phase mask: the center zone, middle circular zone, and outer circular zone. Each zone has an adjusted phase. The findings demonstrate that flexible transverse energy flow rings can be obtained in the focal plane and that transverse energy flows with various polygonal forms can be produced by varying the middle circular radius or phase distribution. By adjusting the phase of the center zone and outer circular zone, the normalized transverse energy flow distribution can be rotated or changed. Findings demonstrate that this technique offers a potent means of controlling the distribution and orientation of Poynting vectors and electromagnetic fields. Moreover, a series of energy flow rings are generated to facilitate the transportation of absorptive particles to predetermined positions. These phenomena may provide a new approach for particle capture and optical particle manipulation.

Diffraction efficiency analysis of dual-layer diffractive elements with oblique incident angles.

This paper proposes a method that combines the effective area method and the oblique factors to analyze and design dual-layer diffractive optical elements at large incident angles. The method considers the effects of shadow and shield on the diffraction efficiency, as well as the correction of phase delay due to oblique incidence. The relationships among the diffraction efficiency, incident wavelengths, incident angles and period widths were analyzed with our method. A detailed comparison of the proposed method with the scalar diffraction theory is presented. The method was validated by numerical simulations of vector diffraction theory and showed similar diffraction efficiency distributions at different wavelengths and incident angles. The method provides a simple and efficient way to design and apply DLDOEs.

Dark field imaging of high aspect ratio structures - a simple model.

A simplified model for dark-field optical imaging of three-dimensional high aspect ratio micro- and nano- structures is proposed, to reduce the time taken to simulate object fields with in-plane scattering between different parts of the object. Primary scattering is found by assuming that illumination of Manhattan geometries generates a set of spherical edge waves, following the incremental theory of diffraction. Secondary scattering is found by assuming that primary scattering is re-scattered from nearby features. Diffraction coefficients are simplified, and the number of illuminating beams is limited to those generating waves that enter the objective lens. Images obtained using TE and TM polarizations are compared, and results are benchmarked against a vectorial finite element model. Applications lie in simulating optical inspection of structures containing vertically etched features including MEMS and NEMS.

Equivalence of knife‐edge diffraction model and uniform geometrical theory of diffraction applying Fresnel approximation for an absorbing screen

AbstractThe knife‐edge diffraction model (KED) and the uniform geometrical theory of diffraction (UTD) have been widely used to predict the shadowing effect at millimetre‐wave (mmWave) bands. This letter proposes a mathematical derivation to rigorously prove that, for an absorbing screen, UTD applying the narrow‐angle Fresnel approximation is equivalent to KED. The simulation scenarios are designed to validate the proposal by comparing KED with UTD in the narrow‐angle (less than 20°) and wide‐angle (over 20°) regions at mmWave bands (20100 GHz). Simulated results agree with the proposal that KED is identical to UTD with a low error of less than 0.1 dB in the narrow‐angle region, while they have a difference with an error of over 1 dB in the wide‐angle region. In addition, the average computational time is measured and results in both UTD and KED taking approximately 8.0 ms for one test. From the proposal, it can be theoretically explained the differences and similarities between KED and UTD for an absorbing screen.