Simulated Electron Diffraction Patterns Research Articles

Twisting two-dimensional iron sulfide layers into coincident site superlattices via intercalation chemistry.

Layered van der Waals (vdW) materials are susceptible not only to various stacking polymorphs through translations but also twisted structures due to rotations between layers. Here, we study the influence of such layer-to-layer twisting through the intercalation of ethylenediamine (EDA) molecules into tetragonal iron sulfide (Mackinawite FeS). Selected area electron diffraction patterns of intercalated FeS display reflections corresponding to multiple square lattices with a fixed angle between them, contrary to a single square lattice seen in the unintercalated phase. The observed twist angles of 49.13° and 22.98° result from a superstructure formation well described by the coincident site lattice (CSL) theory. According to the CSL theory, these measured twist angles lead to the formation of larger coincident site supercells. We build these CSL models for FeS using crystallographic group-subgroup transformations and find simulated electron diffraction patterns from the model to agree with the experimentally measured data.

An approach to investigate the crystallographic unit cell of human tooth enamel.

Human tooth enamel (HTE) is the hardest tissue in the human body and its structural organization shows a hierarchical composite material. At the nanometric level, HTE is composed of approximately 97% hydroxyapatite [HAP, Ca10(PO4)6(OH)2] as inorganic phase, and of 3% as organic phase and water. However, it is still controversial whether the hexagonal HAP phase crystallizes in P63/m or another space group. The observance in HTE of Ca2+, Mg2+ and Na+ ions using X-ray characteristic energy-dispersive spectroscopy in the scanning electron microscope has been explained by substitutions in the HAP unit cell. Thus, Ca2+ can be replaced by Na+ and Mg2+ ions; the PO43- group can be replaced by CO32- ions; and the OH- ions can also be replaced by CO32-. A unit-cell model of the hexagonal structure of HTE is not fully defined yet. In this work, density functional theory calculations are performed to study the hexagonal HAP unit cell when substitution by OH-, CO32-, Mg2+ and Na+ ions are carried out. An approach is presented to study the crystallographic unit cell of HTE by examining the changes resulting from the inclusion of these different ions in the unit cell of HAP. Enthalpies of formation and crystallographic characteristics of the electron diffraction patterns are analysed in each case. The results show an enhancement in structural stability of HAP with OH defects, atomic substitution of Mg2+, carbonate and interstitial Na+. Simulated electron diffraction patterns of the generated structures show similar characteristics to those of human tooth enamel. Hence, the results explain the indiscernible structural changes shown in experimental X-ray diffractograms and electron diffraction patterns.

Dynamic tilting in perovskites.

A new computational analysis of tilt behaviour in perovskites is presented. This includes the development of a computational program - PALAMEDES - to extract tilt angles and the tilt phase from molecular dynamics simulations. The results are used to generate simulated selected-area electron and neutron diffraction patterns which are compared with experimental patterns for CaTiO3. The simulations not only reproduced all symmetrically allowed superlattice reflections associated with tilt but also showed local correlations that give rise to symmetrically forbidden reflections and the kinematic origin of diffuse scattering.

Improved high-resolution EBSD analyses by correcting radial distortion of electron diffraction patterns

• An integrated DIC method is proposed to measure the radial optical distortion of electron diffraction cameras. • The method has a comparable accuracy with previous studies using chessboard samples. • Various high-resolution EBSD analyses benefit from the radial distortion corrections. Registering experimental and simulated electron diffraction patterns is increasingly used for advanced electron backscatter diffraction indexation (EBSD) analysis, yet the accuracy of registration is limited by several effects not accounted for in pattern simulation, such as the Kikuchi band (K-band) asymmetry, gray level reversal and (mainly radial) optical distortion. Radial distortion parameters have previously been measured with chessboard-type standard samples. Simulated patterns have been adopted to demonstrate the necessity of optical distortion removal in EBSD analyses. However there still lacks an efficient and precise radial distortion assessment and correction method. Here a simple radial distortion model, including barrel and pincushion distortions, is proposed to rectify the diffraction patterns during EBSD analyses. The correlation between experimental pattern and the simulated master pattern permits to index the diffraction pattern and assess the radial distortion simultaneously. The method is applied to three high-definition experimental electron diffraction datasets acquired with different cameras. The radial distortion parameter is identified with a relative uncertainty below 4%. The consideration of radial distortion improves the correlation between experimental and simulated patterns. Gray level profiles of the K-bands are analyzed to verify the correctness of image registration. The current method provides a fast, economic yet precise correction of the radial distortion for advanced EBSD analyses.

Improved EBSD indexation accuracy by considering energy distribution of diffraction patterns

Registering experimental and simulated electron diffraction patterns is increasingly used for advanced electron backscatter diffraction indexation (EBSD) analysis, yet the accuracy of registration is limited by several effects not accounted for in pattern simulation, such as the Kikuchi band asymmetry, gray level reversal, optical distortion and non-uniform electron energy. Though some of these phenomena can be simulated by Monte Carlo method and dynamical simulation, the computation is highly demanding and their effects on EBSD calibration are seldom analyzed. Here a simple weighting of energy for simulated diffraction pattern is proposed based on several master patterns calculated before-hand, to effectively account for the electron energy distribution. Integrated digital image correlation is alternatively applied to quantify the electron energy field and calibrate geometry parameters. A metric of the accuracy of indexed crystal orientation is proposed based on a large-area high-definition experimental EBSD acquisition on a (100)-face single crystal Si wafer. The consideration of inhomogeneous energy distribution reduces the crystal orientation discrepancy by 0.128° for the Si dataset.

Implications of gnomonic distortion on electron backscatter diffraction and transmission Kikuchi diffraction.

The effect of gnomonic distortion on orientation indexing of electron backscatter diffraction patterns is explored through simulation of electron diffraction patterns for sample-to-detector geometries associated with transmission Kikuchi diffraction (TKD) and electron backscatter diffraction (EBSD). Simulated data were analysed by computing a similarity index for both Hough transformed data and simulated patterns to determine the sensitivity of each method for detecting subtle differences in the effect of gnomonic distortions on electron diffraction patterns. These results indicate that the increased gnomonic distortions in electron diffraction patterns for a TKD geometry enhance the sensitivity for detecting subtle differences in interband angles. Additionally, the utilisation of a Hough transform-based indexing approach further enhances the sensitivity.

Simulation of electron diffraction patterns of organic crystals under continuous rotation

Simulation of electron diffraction patterns of organic crystals under continuous rotation

Calibration of crystal orientation and pattern center of EBSD using integrated digital image correlation

The accuracy of electron backscatter diffraction indexation has long been limited by pattern center determination, and numerous hardware and software methods have been proposed to improve the calibration. Here, an Integrated Digital Image Correlation (IDIC) procedure is proposed to determine simultaneously crystal orientation and pattern center by registering experimental and simulated electron diffraction patterns. To assess the performance and robustness of the procedure, numerous case studies are reported. Noise sensitivity is first explored on virtual data to assess convergence conditions and result uncertainty up to high noise level and small detector size. Two experimental data sets are further exploited. First, a high-definition detector shows that crystal orientation uncertainty as low as 3×10−2 degrees can be achieved, that is at least 80% less than commercial Hough-transformation based indexation method. Different sample tilt angles are tested, IDIC indexation proves much more tolerant with imprecise tilt angles than common EBSD indexation methods. Second, fast EBSD acquisitions with a coarse definition performed during an in-situ tensile test are analysed. A quantification of the residual noise allows one to formulate an optimized IDIC functional with a proper pixel-wise weight. With the latter refinement a two-pass procedure leads to a much enhanced precision of the determination of crystal orientation, giving access to more precise evaluation of maps of geometrically necessary dislocation densities.

Training artificial neural networks for precision orientation and strain mapping using 4D electron diffraction datasets

Techniques for training artificial neural networks (ANNs) and convolutional neural networks (CNNs) using simulated dynamical electron diffraction patterns are described. The premise is based on the following facts. First, given a suitable crystal structure model and scattering potential, electron diffraction patterns can be simulated accurately using dynamical diffraction theory. Secondly, using simulated diffraction patterns as input, ANNs can be trained for the determination of crystal structural properties, such as crystal orientation and local strain. Further, by applying the trained ANNs to four-dimensional diffraction datasets (4D-DD) collected using the scanning electron nanodiffraction (SEND) or 4D scanning transmission electron microscopy (4D-STEM) techniques, the crystal structural properties can be mapped at high spatial resolution. Here, we demonstrate the ANN-enabled possibilities for the analysis of crystal orientation and strain at high precision and benchmark the performance of ANNs and CNNs by comparing with previous methods. A factor of thirty improvement in angular resolution at 0.009˚ (0.16 mrad) for orientation mapping, sensitivity at 0.04% or less for strain mapping, and improvements in computational performance are demonstrated.

CloudEMAPS: A Cloud Computing Environment for Electron Microscopy Application Simulations

Abstract

High-precision orientation mapping from spherical harmonic transform indexing of electron backscatter diffraction patterns

The angular precision of crystal orientation determination by cross-correlating dynamically simulated electron diffraction patterns with experimental patterns via spherical harmonic analysis is investigated. The best precision found in this study is 0.016°, which approaches the level reported in the literature for other high-precision electron backscatter diffraction implementations. At this angular precision, the noise floor for geometrically necessary dislocation density calculations is found to be approximately 5×1013 m−2 at a 200 nm step size. Conventional Hough-transform indexing of the same raw patterns gave an angular precision of 0.156° and a dislocation noise floor of 6×1014 m−2, an order of magnitude larger for both parameters, albeit better than is typical for Hough indexing due to the high-quality patterns used. Experimental trade-off curves of precision versus exposure time, pattern resolution (i.e. camera binning), and analysis bandwidth are also presented, allowing for optimization of data collection and analysis rates once the desired level of precision has been determined.

CloudEMAPS: A Cloud Computing Environment for Electron Microscopy Application Simulations

The rapid progress in the performance of today's sophisticated transmission electron microscopes also demands computational and educational tools capable of simulating the intricacy of electron image formation. The tools ideally should be widely accessible to the microscopy community and capable of covering both the breadth and depth demanded by modern materials science. Here, a cloud-based microscopy simulation platform, called cloudEMAPS and powered by cloud computing and modern server-client web programming architecture, is described. Compared to the current desktop solutions for electron microscopy simulations, cloud computing offers the unique advantages of on-demand, data sharing, high-performance computation and internet easy access using the state-of-the-art web infrastructure. This article will demonstrate these advantages using examples of interactive simulations of electron diffraction patterns and aberration-corrected electron optics.

Predicting three-dimensional icosahedron-based boron B60

The icosahedron-based bulk boron structures have extremely chemical and structural complexity, and are usually semiconductors at ambient conditions. Here we predict bulk boron phases with a 60-atom orthorhombic unit cell from an ab initio evolutionary structure search, termed as ${\mathrm{B}}_{60}$. The metastable structures can be either a conductor or a semimetal depending on their interstitial atomic positions. In particular, an orthorhombic structure with $Pnma$ symmetry ($Pnma\ensuremath{-}{\mathrm{B}}_{60}$), consisting of ${\mathrm{B}}_{12}$ icosahedra and twisted interstitial two-atom wide boron ribbons, is identified to be a topological node-line semimetal with potential superior electronic transport. The band structure and simulated electron-diffraction pattern of $Pnma\ensuremath{-}{\mathrm{B}}_{60}$ are in satisfactory agreement with the experimental data, suggesting that it may exist in the form of nanomaterials.

Synthesis of rod-shaped Au-Cu intermetallic nanoparticles and SERS detection

Intermetallic phases in Au-Cu nanoparticles has been synthesized chemically in liquid phase. The heat-treatment of these nanoparticles at 180 °C for 1 h in solution phase led to the formation of Au-Cu alloy nanoparticles with nearly spherical shapes and monodispersed size of ∼10 nm. Subsequent heat-treatment at 300 °C for 30 min of these Au-Cu alloy nanoparticles not only revealed structural transformation to intermetallic phases (tetragonal AuCu (tP4) and cubic Cu3Au (cP4)) but also shape change occurs from spherical to rods having average aspect ratio ∼3.0. The structural determination at the particle has been carried out through nano-beam electron diffraction coupled with simulation of electron diffraction patterns and high resolution phase contrast images. These Au–Cu intermetallic nanoparticles exhibit an excellent surface enhanced Raman spectroscopic activity with methylene blue compared to that of Au-Cu alloy nanoparticles.

Simulated electron diffraction patterns of ω-Fe in Fe-C martensite

A metastable hexagonal ω-Fe phase with its particle size of about 1-2 nm coexists at the {112}<111>-type twinning boundaries in Fe-C martensite. The ω-Fe lattice parameters are dependent on their corresponding body centered cubic (BCC) phase (aω=2abcc,cω=3/2abcc). The above dependence and the unique distribution of the ω-Fe particles at the BCC {112}<111>-type twinning boundaries inevitably cause the overlapping of electron diffraction spots of fine ω-Fe with those of BCC and its twin during transmission electron microscope (TEM) observations. Thus, in order to understand the nature of the ultrafine ω-Fe phase in carbon steels, we have simulated its electron diffraction patterns by means of the commercial CrystalMaker software. In most of the zone axes, which show the electron diffraction pattern with three sets of diffraction spots [(1) the BCC matrix crystal, (2) the corresponding twin crystal, and (3) the possible twinning double diffraction spots] together, the simulated results have shown that the diffraction spots from the ω-Fe phase are all overlapped with those three sets of spots. However, in some specific zone axes, for example, in BCC [112] directions, the diffraction spots from the ω-Fe phase can be uniquely recognized since the BCC {112}<111>-type twinning boundary plane is perpendicular to the observation direction, and thus, no twinning double diffraction spots should be observed theoretically.

An average structure model of the intermediate phase between sodalite and cancrinite

Abstract Powder samples of the intermediate phase between sodalite and cancrinite (INT) have been synthesized hydrothermally. The formation of the INT phase was proved by both PXRD and TGA analysis and its stoichiometric composition was found to be |Na6.95(1)(CO3)0.48(2) (H2O)6.18(6)|[AlSiO4]6. The comparison of the intensity ratios of PXRD data with a SCXRD measurement indicates the formation of a comparable phase with the typical strong stacking disorder. The hexagonal lattice parameters with a=1266.3(2) pm and c=1586(1) pm and the unit cell setting were determined by Pawley fits. The average lattice and the stacking disorder along c axis could be confirmed by the reconstruction of three-dimensional ADT data. The average structure of INT was modeled considering only the combination of naturally existing (zeolitic) cages, restricted by the actual number of layers per unit cell. The possible combinations were further reduced by considering the amount of incorporated species. Through the comparison of simulated electron diffraction pattern to measured data the modeled framework could be confirmed. Using relative positions of the incorporated species in the natural cages as well as electron densities calculated by using only the framework of INT the positions of these species could be described.

Basic and charge density wave modulated structures of NbS3 -II

The basic and the charge density wave (CDW) structures of the monoclinic $NbS_3-II$ polymorph were studied by synchrotron x-ray diffraction, ab-initio calculation, simulation of electron diffraction patterns and by atomic-resolution transmission electron and low-temperature scanning tunneling microscopies. It is shown that the basic structure belongs to the space group $P2_1/m$ and is described with a unit cell, formed of four pairs of symmetry-related trigonal prismatic (TP) columns ($a_0$ = 0.96509(8) nm, $b_0$ = 0.33459(2) nm, $c_0$ = 1.9850(1) nm, $\beta_0$ = 110.695(4) deg), with all Nb and S atoms in $2e$ special positions. The two CDWs, with $\vec{q_1}$ = (0, 0.298,0) and $\vec{q_2}$ = (0, 0.352, 0), form their own modulation unit cells ($a_m$ = $2a_0$, $b_m$ = $b_0/q_{jb}$, $c_m$ = $c_0$, $\beta_m$ = $\beta_0$) and are ordered pairwise along adjacent isosceles TP columns. The symmetries of both $\vec{q_j}$ modes belong to the space group $Cm$ and are related according to the $2a$ special positions. If considered as long-period commensurate, the entire modulated structure with both CDWs included is best described with an enlarged unit cell ($a$ = $2a_0$, $b$ = $37b_0$, $c$ = $c_0$, $\beta$ = $\beta_0$), with all Nb and S atoms in $1a$ positions of the space group $P1$.

Efficient first principles simulation of electron scattering factors for transmission electron microscopy

Electron microscopy is a powerful tool for studying the properties of materials down to their atomic structure. In many cases, the quantitative interpretation of images requires simulations based on atomistic structure models. These typically use the independent atom approximation that neglects bonding effects, which may, however, be measurable and of physical interest. Since all electrons and the nuclear cores contribute to the scattering potential, simulations that go beyond this approximation have relied on computationally highly demanding all-electron calculations. Here, we describe a new method to generate ab initio electrostatic potentials when describing the core electrons by projector functions. Combined with an interface to quantitative image simulations, this implementation enables an easy and fast means to model electron scattering. We compare simulated transmission electron microscopy images and diffraction patterns to experimental data, showing an accuracy equivalent to earlier all-electron calculations at a much lower computational cost.

Reduction of Defects on Microstructure Aluminium Nitride Using High Temperature Annealing Heat Treatment

Aluminium Nitride (AlN) is a ceramic 111-nitride material that is used widely as components in functional devices. Besides good thermal conductivity, it also has a high band gap in emitting light which is 6 eV. AlN thin film is grown on the sapphire substrate (0001). However, lattice mismatch between both materials has caused defects to exist along the microstructure of AlN thin films. The defects have affected the properties of Aluminium Nitride. Annealing heat treatment has been proved by the previous researcher to be the best method to improve the microstructure of Aluminium Nitride thin films. Hence, this method is applied at four different temperatures for two hour. The changes of Aluminium Nitride microstructures before and after annealing is observed using Transmission Electron Microscope. It is observed that inversion domains start to occur at temperature of 1500 °C. Convergent Beam Electron Diffraction pattern simulation has confirmed the defects as inversion domain. Therefore, this paper is about to extract the matters occurred during the process of producing high quality Aluminium Nitride thin films and the ways to overcome this problem.

TEM study of the martensitic phases in the ductile DyCu and YCu intermetallic compounds

DyCu and YCu are representatives of the family of CsCl-type B2 rare earth intermetallic compounds that exhibit high room temperature ductility. Structure, orientation relationship, and morphology of the martensites in the equiatomic compounds DyCu and YCu are examined using transmission electron microscopy (TEM). TEM studies show that the martensite structures in DyCu and YCu alloys are virtually identical. The martensite is of orthorhombic CrB-type B33 structure with lattice parameters a = 0.38 nm, b = 1.22 nm, and c = 0.40 nm. (021¯) twins were observed in the B33 DyCu and YCu martensites. The orientation relationship of B33 and B2 phases is (111¯)[112]B33 || (110)[001]B2. The simulated electron diffraction patterns of the B33 phase are consistent with those of experimental observations. TEM investigations also reveal that a dominant orthorhombic FeB-type B27 martensite with lattice parameters a = 0.71 nm, b = 0.45 nm, and c = 0.54 nm exists in YCu alloy. (11¯ 1) twins were observed in the B27 YCu martensite. The formation mechanism of B2 to B33 and B2 to B27 phase transformation is discussed.