Indexing Of Diffraction Patterns Research Articles

Nanoscale Phase and Orientation Mapping in Multiphase Polycrystalline Hafnium Zirconium Oxide Thin Films Using 4D-STEM and Automated Diffraction Indexing.

Ferroelectric hafnium zirconium oxide (HZO) holds promise for nextgeneration memory and transistors due to its superior scalability and seamless integration with complementary metal-oxide-semiconductor processing. A major challenge in developing this emerging ferroelectric material is the metastable nature of the non-centrosymmetric polar phase responsible for ferroelectricity, resulting in a coexistence of both polar and non-polar phases with uneven grain sizes and random orientations. Due to the structural similarity between the multiple phases and the nanoscale dimensions of the thin film devices, accurate measurement of phase-specific information remains challenging. Here, the application of 4D scanning transmission electron microscopy is demonstrated with automated electron diffraction pattern indexing to analyze multiphase polycrystalline HZO thin films, enabling the characterization of crystallographic phase and orientation across large working areas on the order of hundreds of nanometers. This approach offers a powerful characterization framework to produce a quantitative and statistically robust analysis of the intricate structure of HZO films by uncovering phase composition, polarization axis alignment, and unique phase distribution within the HZO film. This study introduces a novel approach for analyzing ferroelectric HZO, facilitating reliable characterization of process-structure-property relationships imperative to accelerating the growth optimization, performance, and successful implementation of ferroelectric HZO in devices.

The characterisation of dental enamel using transmission Kikuchi diffraction in the scanning electron microscope combined with dynamic template matching

The remarkable physical properties of dental enamel can be largely attributed to the structure of the hydroxyapatite (HAp) crystallites on the sub-micrometre scale. Characterising the HAp microstructure is challenging, due to the nanoscale of individual crystallites and practical challenges associated with HAp examination using electron microscopy techniques. Conventional methods for enamel characterisation include imaging using transmission electron microscopy (TEM) or specialised beamline techniques, such as polarisation-dependent imaging contrast (PIC). These provide useful information at the necessary spatial resolution but are not able to measure the full crystallographic orientation of the HAp crystallites. Here we demonstrate the effectiveness of enamel analyses using transmission Kikuchi diffraction (TKD) in the scanning electron microscope, coupled with newly-developed pattern matching methods. The pattern matching approach, using dynamic template matching coupled with subsequent orientation refinement, enables robust indexing of even poor-quality TKD patterns, resulting in significantly improved data quality compared to conventional diffraction pattern indexing methods. The potential of this method for the analysis of nanocrystalline enamel structures is demonstrated by the characterisation of a human enamel TEM sample and the subsequent comparison of the results to high resolution TEM imaging. The TKD – pattern matching approach measures the full HAp crystallographic orientation enabling a quantitative measurement of not just the c-axis orientations, but also the extent of any rotation of the crystal lattice about the c-axis, between and within grains. Results presented here show how this additional information highlights potentially significant aspects of the HAp crystallite structure, including intra-crystallite distortion and the presence of multiple high angle boundaries between adjacent crystallites with rotations about the c-axis. These and other observations enable a more rigorous understanding of the relationship between HAp structures and the physical properties of dental enamel.

Indexing high-noise electron backscatter diffraction patterns using convolutional neural network and transfer learning

The crystal orientation indexing method based on Hough transform has many “zero solution” points when indexing the crystal orientation of materials, especially those with large strains. We propose an efficient and migratable indexing method for fast and autonomous crystal orientations indexing of experimental electron backscatter diffraction (EBSD) patterns of various crystal structures by transfer learning. To better evaluate the performance of the model, the performance of the model was assessed both quantitatively based on the numerical metrics and qualitatively through the Inverse Pole Figure (IPF). The results of indexing high-noise nickel EBSD patterns show that the CNN-based indexing method could not only obtain an acceptable indexing accuracy (a mean disorientation error of 1.77° for retraining and 2.31° for transfer learning), but also reasonably index the “zero solution” points remained in the Hough transform-based indexing method. And the results of indexing other materials by transfer learning show that the CNN has strong knowledge migration capability. In addition, the interpretability of the CNN was investigated by visualizing feature maps of each convolutional layer, and the sensitivity analysis of the CNN was realized by testing masked images.

A Denoising Autoencoder for Improved Kikuchi Pattern Quality and Indexing in Electron Backscatter Diffraction

The rapid collection and indexing of electron diffraction patterns as produced via electron backscatter diffraction (EBSD) has enabled crystallographic orientation and structural determination, as well as additional property-determining strain and dislocation density information with increasing speed, resolution, and efficiency. Pattern indexing quality is reliant on the noise of the collected electron diffraction patterns, which is often convoluted by sample preparation and data collection parameters. EBSD acquisition is sensitive to many factors and thus can result in low confidence index (CI), poor image quality (IQ), and improper minimization of fit, which can result in noisy datasets and misrepresent the microstructure. In an attempt to enable both higher speed EBSD data collection and enable greater orientation fit accuracy with noisy datasets, an image denoising autoencoder was implemented to improve pattern quality. We show that EBSD data processed through the autoencoder results in a higher CI, IQ, and a more accurate degree of fit. In addition, using denoised datasets in HR-EBSD cross correlative strain analysis can result in reduced phantom strain from erroneous calculations due to the increased indexing accuracy and improved correspondence between collected and simulated patterns.

Crystal growth, crystal structure determination, and computational studies of a new mixed (NH4)2Mn1–xZnx(SO4)2(H2O)6 Tutton salt

Tutton salts have been extensively explored in recent decades due to their attractive physical and chemical properties, which make them potential candidates for thermochemical heat storage systems and optical technologies. In this paper, a series of new mixed Tutton salts with the chemical formula (NH4)2Mn1–xZnx(SO4)2(H2O)6 is reported. Crystals are successfully grown by the solvent slow evaporation method and characterized by powder X-ray diffraction (PXRD) with Rietveld refinement. In particular, the crystal structure of the mixed (NH4)2Mn0.5Zn0.5(SO4)2(H2O)6 crystal is solved through PRXD data using the DICVOL06 algorithm for diffraction pattern indexing and the Le Bail method for lattice parameter and spatial group determination. The structure is refined using the Rietveld method implemented in TOPAS® and reported in the Cambridge Structural Database file number 2104098. Moreover, a computational study using Hirshfeld surface and crystal void analyses is conducted to identify and quantify the intermolecular interactions in the crystal structure as well as to determine the amount of free space in the unit cell. Furthermore, 2D-fingerprint plots are generated to evaluate the main intermolecular contacts that stabilize the crystal lattice. Density functional theory is employed to calculate the structural, thermodynamic, and electronic properties of the coordination [Zn(H2O)6]2+ and [Mn(H2O)6]2+ complexes present in the salts. Molecular orbitals, bond lengths, and the Jahn–Teller effect are also discussed. The findings suggest that in Mn-Zn salts several properties dependent on the electronic structure can be tuned up by modifying the chemical composition.

Processing of Multicrystal Diffraction Patterns in Macromolecular Crystallography Using Serial Crystallography Programs

Cryocrystallography is a widely used method for determining the crystal structure of macromolecules. This technique uses a cryoenvironment, which significantly reduces the radiation damage to the crystals and has the advantage of requiring only one crystal for structural determination. In standard cryocrystallography, a single crystal is used for collecting diffraction data, which include single-crystal diffraction patterns. However, the X-ray data recorded often may contain diffraction patterns from several crystals. The indexing of multicrystal diffraction patterns in cryocrystallography requires more precise data processing techniques and is therefore time consuming. Here, an approach for processing multicrystal diffraction data using a serial crystallography program is introduced that allows for the integration of multicrystal diffraction patterns from a single image. Multicrystal diffraction data were collected from lysozyme crystals and processed using the serial crystallography program CrystFEL. From 360 images containing multicrystal diffraction patterns, 1138 and 691 crystal lattices could be obtained using the XGANDALF and MOSFLM indexing algorithms, respectively. Using this indexed multi-lattice information, the crystal structure of the lysozyme could be determined successfully at a resolution of 1.9 Å. Therefore, the proposed approach, which is based on serial crystallography, is suitable for processing multicrystal diffraction data in cryocrystallography.

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.

Mechanical, microstructural and tribological behavior of stir cast Al8011/TiB2/SiC hybrid metal matrix composites

Modern technology requires enriched mechanical and thermal characteristics. In the present scenario, the decent mechanical and thermal properties of hybrid Metal matrix composites (MMCs) make them more demanding in various fields such as automotive, aviation, and structural applications. In this paper, an attempt has been made to fabricate the composite Al8011 + TiB2 + SiC with 9 different weight fractions follows as reinforcement 1(TiB2) by 2%,4%, and 6% with varying reinforcement 2(SiC) percentage by 1%,3%, and 5%. Fabrication is made through the stir casting technique by considering ideal process parameters such as stirring temperature, stirring speed, stirring time, preheating temperature, grain size, and wt.% of particulate reinforcements. With the help of Electron discharge machining (EDM), the specimens for the tests performed were cut according to the ASTM standards. The test results in the present investigation revealed that an increase in mechanical properties has been detected with the addition of reinforcements when compared with individual matrix and reinforcement materials. Wear test analysis illustrates that increase in resistance to wear of composite with the increase in TiB2 percentage of reinforcement. According to the microstructural analysis, an increase in stirring speed and stirring time reduces porosity. X-ray diffraction was used to identify crystalline phases of various MMCs. A unit cell dimensions can also be calculated based on the diffraction peak positions obtained from the X-ray diffractometer (XRD) test. The process of determining the unit cell dimensions from peak positions is known as indexing. Miller indices, hkl, must be assigned to each peak in a powder diffraction pattern to index it. The process of indexing electron diffraction patterns of a single crystal is to label the individual diffraction spots with their proper values and sign (+or -) of h, k, and l. When x-rays are scattered from a crystal lattice, peaks of scattered intensity are observed which correspond to the condition, the Angle of incidence = Angle of scattering and the path length integer is equal to an integer number of wavelengths. The condition for maximum intensity contained in Bragg's law above allows us to calculate details about the crystal structure, or if the crystal structure is known, to determine the wavelength of the x-rays incident upon the crystal. Indexing of diffraction patterns was done for all the metal matrix composites and in which the miller indices and interplanar d- spacing were calculated.

Indexation of electron diffraction patterns at grain boundaries

Grain boundaries play a vital role in materials science, and they are extensively studied through experimental and numerical methods. Electron backscatter diffraction (EBSD) is commonly used to characterize crystalline materials, yet its performance is often compromised at grain boundaries. The key difficulty is to index the overlapped electron backscatter patterns, where Kikuchi bands from multiple crystal orientations coexist. Hough-indexation often fails in treating overlapped EBSP, while the recently proposed dictionary indexation and sphere indexation give only one triplet of Euler angles from overlapped patterns. For all these methods, the orientation indexing precision drops for overlapped EBSP. Here we propose an integrated Digital Image Correlation (DIC) procedure to determine simultaneously and precisely multiple crystal orientations by registering the overlapped EBSP and the master pattern. The contribution ratio of each crystal orientation to the overlapped pattern is also available. Through an experimental EBSD dataset around a triple point, multiple benefits of the rich results from the method are demonstrated, such as refining grain boundaries, revealing EBSD scan errors and quantifying spatial resolution of EBSD. At the grain boundaries, the crystal orientation measurement uncertainty is 0.03∘ for both indexed crystal orientations, the same order for grain interiors, while their contribution ratios of uncertainty around 0.02 are obtained.

A remark on ab initio indexing of electron backscatter diffraction patterns

There is a growing interest in ab initio indexing of electron backscatter diffraction (EBSD) patterns. The methods of solving the problem are presented as innovative. The purpose of this note is to point out that ab initio EBSD indexing belongs to the field of indexing single-crystal diffraction data, and it is solved on the same principles as indexing of patterns of other types. It is shown that reasonably accurate EBSD-based data can be indexed by programs designed for X-ray data.

New Features in Crystal Orientation and Phase Mapping for Transmission Electron Microscopy

ACOM/TEM is an automated electron diffraction pattern indexing tool that enables the structure, phase and crystallographic orientation of materials to be routinely determined. The software package, which is part of ACOM/TEM, has substantially evolved over the last fifteen years and has pioneered numerous additional functions with the constant objective of improving its capabilities to make the tremendous amount of information contained in the diffraction patterns easily available to the user. Initially devoted to the analysis of local crystallographic texture, and as an alternative to both X-ray pole figure measurement and EBSD accessories for scanning electron microscopes, it has rapidly proven itself effective to distinguish multiple different phases contained within a given sample, including amorphous phases. Different strategies were developed to bypass the inherent limitations of transmission electron diffraction patterns, such as 180° ambiguities or the complexity of patterns produced from overlapping grains. Post processing algorithms have also been developed to improve the angular resolution and to increase the computing rate. The present paper aims to review some of these facilities. On-going works on 3D reconstruction are also introduced.

FCC and 4H structure coexistence in Ag nanoparticles determined through TEM imaging and a diffraction pattern indexing program (DPIP)

FCC and 4H structure coexistence in Ag nanoparticles determined through TEM imaging and a diffraction pattern indexing program (DPIP)

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.

Indexing of diffraction patterns for determination of crystal orientations.

The task of determining the orientations of crystals is usually performed by indexing reflections detected on diffraction patterns. The well known underlying principle of indexing methods is universal: they are based on matching experimental scattering vectors to some vectors of the reciprocal lattice. Despite this, the standard attitude has been to devise algorithms applicable to patterns of a particular type. This paper provides a broader perspective. A general approach to indexing of diffraction patterns of various types is presented. References are made to formally similar problems in other research fields, e.g. in computational geometry, computer science, computer vision or star identification. Besides a general description of available methods, concrete algorithms are presented in detail and their applicability to patterns of various types is demonstrated; a program based on these algorithms is shown to index Kikuchi patterns, Kossel patterns and Laue patterns, among others.

Indexing of electron back-scatter diffraction patterns using a convolutional neural network

Accurate indexing of EBSD patterns presents a challenging problem. We propose a new convolutional neural network (EBSD-CNN) to realize real-time indexing of EBSD patterns; we implement a disorientation loss function to adapt a standard CNN model for crystallographic orientation indexing. The indexing accuracy, rate, and robustness against noise are evaluated using both simulated and experimental data, and compared with other indexing methods (Hough-based indexing, dictionary indexing, and spherical indexing). The results suggest that a CNN can provide an alternative to commercial Hough-transform-based indexing with comparative accuracy and rate. We obtain insight into the network functionality by visualization of selected filters.

A dictionary indexing approach for EBSD

Dictionary indexing is a new approach to the indexing of electron backscatter diffraction (EBSD) patterns. In this contribution, we will describe the underlying forward model as well as the indexing approach that uses a similarity metric between experimental and simulated patterns instead of feature extraction. Then we provide a number of example applications drawn from the materials and geological communities.

Prediction of potential pseudo-symmetry issues in the indexing of electron backscatter diffraction patterns

A new methodology to predict potential pseudo-symmetric or systematically mis-indexed orientations for an arbitrary crystal structure is presented. The method leverages the recently proposed spherical indexing algorithm to index electron backscatter diffraction patterns. Potential pseudo-symmetric orientations are interpreted as secondary peaks in the autocorrelation of the Kikuchi sphere. The generality of the method is illustrated using a number of crystal systems, ranging from nickel, where no significant pseudo-symmetric issues are expected, to SrTiO3, with mild occurrence of such issues, to the olivine series, γ-TiAl and U-6%Nb systems, where the traditional Hough method systematically mis-indexes the pseudo-symmetric variants. Furthermore, the method predicts the severity of potential pseudo-symmetric matches and ranks all variants using a normalized autocorrelation coefficient.

A spherical harmonic transform approach to the indexing of electron back-scattered diffraction patterns

A new approach is proposed for the indexing of electron back-scattered diffraction (EBSD) patterns. The algorithm employs a spherical master EBSD pattern and computes its cross-correlation with a back-projected experimental pattern using the spherical harmonic transform (SHT). This approach is significantly faster than the recent dictionary indexing algorithm, but shares the latter’s robustness against noise. The underlying theory is presented, followed by example applications, one on a series of Ni EBSD data sets recorded with decreasing signal-to-noise ratio, the other on a large shot-peened Al data set. The dependence of indexing speed and memory usage on the SHT bandwidth is explored. The speed gains of the new algorithm are achieved by executing real-valued Fast Fourier Transforms, explicitly incorporating crystallographic symmetry in the cross-correlation computation, and using efficient loop ordering to improve the caching behavior. The algorithm produces a cross-correlation array in the zyz Euler space; an orientation refinement procedure is proposed based on analytical derivatives of the Wigner d functions. The new approach can be applied to any diffraction modality for which the scattered intensity can be represented on a spherical surface.

XGANDALF - extended gradient descent algorithm for lattice finding.

Serial crystallography records still diffraction patterns from single, randomly oriented crystals, then merges data from hundreds or thousands of them to form a complete data set. To process the data, the diffraction patterns must first be indexed, equivalent to determining the orientation of each crystal. A novel automatic indexing algorithm is presented, which in tests usually gives significantly higher indexing rates than alternative programs currently available for this task. The algorithm does not require prior knowledge of the lattice parameters but can make use of that information if provided, and also allows indexing of diffraction patterns generated by several crystals in the beam. Cases with a small number of Bragg spots per pattern appear to particularly benefit from the new approach. The algorithm has been implemented and optimized for fast execution, making it suitable for real-time feedback during serial crystallography experiments. It is implemented in an open-source C++ library and distributed under the LGPLv3 licence. An interface to it has been added to the CrystFEL software suite.

Reflector Selection for the Indexing of Electron Backscatter Diffraction Patterns.

We propose a new methodology for ranking the reflectors used in traditional Hough-based indexing of electron backscatter diffraction (EBSD) patterns. Instead of kinematic X-ray or electron structure factors (Fhkl) currently utilized, we propose the integrated Kikuchi band intensity parameter (βhkl) based on integrated dynamical electron backscatter intensities. The proposed parameter is compared with the traditional kinematical intensity, , as well as the average Hough transform peak intensity, and used to index EBSD patterns for a number of different material systems of varying unit cell complexities including nickel, silicon, rutile, and forsterite. For elemental structures, βhkl closely follows the kinematical ranking. However, significant ranking differences arise for more complex unit cells, with the βhkl parameter showing a better correlation with the integrated Hough intensities. Finally, Hough-based indexing of a simulated forsterite data set showed an appreciable improvement in the median confidence index (0.15 to 0.35) when βhkl is used instead of for ranking the reflectors.