Unsupervised machine learning applied to scanning precession electron diffraction data

Scanning precession electron diffraction (SPED) enables the local crystallography of materials to be probed on the nanoscale by recording a two-dimensional precession electron diffraction (PED) pattern at every probe position as a dynamically rocking electron beam is scanned across the specimen. SPED data from nanocrystalline materials commonly contain some PED patterns in which diffraction is measured from multiple crystals. To analyse such data, it is important to perform nanocrystal segmentation to isolate both the location of each crystal and a corresponding representative diffraction signal. This also reduces data dimensionality significantly. Here, two approaches to nanocrystal segmentation are presented, the first based on virtual dark-field imaging and the second on non-negative matrix factorization. Relative merits and limitations are compared in application to SPED data obtained from partly overlapping nanoparticles, and particular challenges are highlighted associated with crystals exciting the same diffraction conditions. It is demonstrated that both strategies can be used for nanocrystal segmentation without prior knowledge of the crystal structures present, but also that segmentation artefacts can arise and must be considered carefully. The analysis workflows associated with this work are provided open-source. LAY DESCRIPTION: Scanning precession electron diffraction is an electron microscopy technique that enables studies of the local crystallography of a broad selection of materials on the nanoscale. The technique involves the acquisition of a two-dimensional diffraction pattern for every probe position in an area of the sample. The four-dimensional dataset collected by this technique can typically comprise up to 500 000 diffraction patterns. For nanocrystalline materials, it is common that single diffraction patterns contain signals from overlapping crystals. To process such data, we use nanocrystal segmentation, where a representative diffraction pattern is constructed for each individual crystal, together with a real space image showing its morphology and location in the data. This reduces the dimensionality of the data and allows unmixing of signals from overlapping crystals. In this work, we demonstrate two methods for nanocrystal segmentation, one based on creating virtual dark-field images, and one based on unsupervised machine learning. A model system of partly overlapping nanoparticles is used to demonstrate the segmentation, and a demanding case for segmentation is highlighted, where some crystals are not discernible based on their diffraction patterns. To obtain a more complete nanocrystal segmentation, we add an image segmentation routine to both methods, and we discuss benefits and limitations of the two methods. The demonstration data and the used code are provided open-source, so that it can be used by everyone for analysis of nanocrystalline materials or as a starting point for further development of nanocrystal segmentation in scanning precession electron diffractiondata.

Mapping the spatial distribution of crystal phases with nm-scale spatial resolution is an important characterisation task in studies of multi-phase materials. One popular approach is to use scanning precession electron diffraction which enables semi-automatic phase mapping at the nanoscale by collecting a single precession electron diffraction pattern at every probe position over regions spanning up to a few micrometers. For a successful phase mapping each diffraction pattern must be correctly identified. In this work four different approaches for phase mapping of embedded precipitates in an Al-Cu-Li alloy are compared on a sample containing three distinct crystal phases. These approaches are based on: non-negative matrix factorisation, vector matching, template matching and artificial neural networks. To evaluate the success of each approach a ground truth phase map was manually created from virtual images based on characteristic phase morphologies and compared with the deduced phase maps. The percentage accuracy of all methods when compared to the ground truth was satisfactory, with all approaches obtaining scores above 98%. The optimal method depends on the specific task at hand. Non-negative matrix factorisation is suitable with limited prior data knowledge but performs best with few unique diffraction patterns and requires substantial post-processing. It has the advantage of reducing the dimensionality of the dataset and handles weak diffracted intensities well given that they occur repeatedly. The current vector matching implementation is fast, simple, based only on the Bragg spot geometry and requires few parameters. It does however demand that each Bragg spot is accurately detected in each pattern and the current implementation is limited to zone axis patterns. Template matching handles a large range of orientations, including off-axis patterns. However, achieving successful and reliable results often require thorough data pre-processing and do require adequate diffraction simulations. For artificial neural networks a substantial setup effort is demanded but once trained it excels for routine tasks, offering fast predictions. The implemented codes and the data used are available open-source. These resources and the detailed assessment of the methods will allow others to make informed decisions when selecting a data analysis approach for 4D-STEM phase mapping tasks on other material systems.

2xxx‐series Al alloys are Cu containing age‐hardenable alloys, which are strengthened by numerous metastable precipitates formed during heat treatment. Many different precipitates exist, some of which are not well defined crystallographically. However, phases known to contribute particularly to strengthening and that exist in the over‐aged condition are: θ' and T1 in Al‐Cu‐Li alloys [1], and Ω and S in Al‐Mg‐Cu‐Ag alloys [1]. These precipitates have various morphologies, ranging from long needles to thin plates, and coexist with inclusion particles as well as with dispersoids. The resulting microstructure is complex both in terms of coexistence and by precipitates deviating from simply defined phases. This makes complete characterization a demanding task for which techniques are required to enable statistical treatment of precipitate distributions in terms of their atomic structure. Here, we apply scanning precession electron diffraction (SPED) to heat‐treated Al‐Cu‐Li and Al‐Mg‐Cu‐Ag alloys, shedding light on the distribution of phases present and the complex interplay between these microstructural features. SPED involves scanning the electron beam across the specimen and recording a PED pattern at each point by rocking a focused probe in a hollow cone above the specimen, and de‐rocking it below. In this way, integrated diffraction intensities are recorded in the geometry of a conventional electron diffraction pattern [2]. A 4D dataset is obtained comprising a 2D PED pattern at each position in the 2D scan region. Combined with subsequent data processing, this constitutes a powerful method for extracting valuable crystallographic information and orientation relationships in complex multiphase materials [3]. In this work, SPED was performed using a NanoMEGAS DigiSTAR scan generator fitted to a JEOL 2100F FEG‐(S)TEM operated at 200 kV, with a precession angle of 1º and a step size of 4.5 nm. Typical datasets comprised 90 000 diffraction patterns (DPs), which were analysed using the open source platform HyperSpy [4] as described below. Obtained results from an Al‐Cu‐Li alloy are shown here as an example. All DPs in the SPED dataset were first summed (Fig. 1) and compared to a simulated DP, including the Al‐matrix in the [001] orientation and the aforementioned θ'‐ and T1 precipitates (Fig. 2). This allowed identification of reflections associated with these particular phases. These phases are then visualised in ‘virtual dark‐field’ (VDF) images, formed by plotting the intensity in pixels around selected reflections as a function of probe position (Fig. 3 and 4). For example, the thin T1‐precipitate plates are seen on {111} Al planes inclined relative to [001] Al , and it is noted that even overlapping plates can still be discerned and visualized. The obtained VDF images exhibit a sharper, more consistent contrast between precipitate phases and the Al matrix as compared conventional imaging techniques, such as dark‐field TEM. More sophisticated analysis applies machine learning in order to identify the main component patterns in the data, as well as their spatial localisation referred to as ‘loading maps’. These ‘loading maps’ look similar to VDF images but are obtained by an automated and objective approach, requiring little or no prior knowledge. This opens the possibility of identifying features with unexpected crystallographic structures. The analysis approaches demonstrated in this work offer important insight into the complex microstructures of these Al alloys.

Crystallographic, compositional and morphological complexity in modern engineering alloys necessitates the use of sophisticated tools for multi‐scale materials characterisation. Here, we develop scanning precession electron diffraction (SPED) for mapping crystalline phases in engineering alloys. SPED involves scanning the electron beam across the specimen and recording a PED pattern at each point by rocking a focused probe in a hollow cone above the specimen and de‐rocking the beam back to the optic axis below. In this way, integrated diffraction intensities are recorded in the geometry of a conventional electron diffraction pattern [1]. A 4D dataset is obtained comprising a 2D PED pattern at each position in the 2D scan region, which can be analysed in a number of ways. Most simply, ‘virtual diffraction images’ can be formed by plotting the intensity of a sub‐set of pixels in each PED pattern as a function of probe position to elucidate variations in the diffraction condition in a versatile post‐acquisition scheme. Phase and orientation maps can also be formed by matching each PED pattern to a library of simulated patterns [2]. Here, we use this approach to determine the phases of precipitates in a nickel base superalloy and to identify orientation relationships existing between these phases. To do this we explore the orientation data in disorientation space where the rotation axis and angle between the two crystallographic bases is plotted (Figure 1). This automated analysis enabled treatment of multiple precipitates yielding a more representative view of the microstructure compared to conventional SAED methods. New methods for strain mapping and phase characterisation based on machine learning were developed as part of this work to extract further insight into microstructural features. Strain maps were obtained by comparing each pattern to an unstrained reference and used to explore the strain distribution between precipitates in aluminium alloys (Figure 2). These SPED based strain maps offer a greater field of view as compared to methods based on atomic resolution imaging whilst retaining nm‐scale spatial resolution. This yields unique insights such as the ability to map the interaction of strain fields associated with multiple precipitates, which can be seen in Figure 2. Phase characterisation, on the other hand, addresses the challenge of determining the chemistry and crystallography of phases in the microstructure that are often embedded and overlap in projection. We apply machine learning algorithms to SPED [3] and STEM‐EDX [4] data acquired from the same region to achieve a correlated crystallographic and chemical characterisation of a Ti‐Fe‐Mo alloy with a nanometre scale lamellar microstructure (Figure 3). This approach learns component signals (spectra or patterns), which make up the particular dataset, together with their associated loading at each real space pixel. An efficient representation of the data is therefore found with minimal prior knowledge and signals from overlapping crystals are separated to achieve phase specific characterisation. Combined, the analysis approaches developed in this work provide comprehensive 'crystal cartography' of engineering alloys paving the way to better understanding of relationships between processing, structure and properties.

Transmission electron microscopes (TEM) are widely used in nanotechnology research. However, it is still challenging to characterize nanoscale objects; their small size coupled with dynamical diffraction makes interpreting real- or reciprocal-space data difficult. Scanning precession electron diffraction ((S)PED) represents an invaluable contribution, reducing the dynamical contributions to the diffraction pattern at high spatial resolution. Here a detailed analysis of wurtzite InP nanowires (30–40 nm in diameter) containing a screw dislocation and an associated wire lattice torsion is presented. It has been possible to characterize the dislocation with great detail (Burgers and line vector, handedness). Through careful measurement of the strain field and comparison with dynamical electron diffraction simulations, this was found to be compatible with a Burgers vector modulus equal to one hexagonal lattice cell parameter despite the observed crystal rotation rate being larger (ca. 20%) than that predicted by classical elastic theory for the nominal wire diameter. These findings corroborate the importance of the (S)PED technique for characterizing nanoscale materials.

High precision orientation mapping from 4D-STEM precession electron diffraction data through quantitative analysis of diffracted intensities

Reconstructing dual-phase nanometer scale grains within a pearlitic steel tip in 3D through 4D-scanning precession electron diffraction tomography and automated crystal orientation mapping

X-ray powder diffraction / HRTEM / SAED / PED structure solution Abstract. Electron microscopy techniques yield informa- tion for crystal structure analysis that is remarkably com- plementary to that obtained from X-ray powder diffraction data. Structures of polycrystalline materials that resist so- lution by either method alone can sometimes be solved by combining the two. For example, the intensities extracted from an X-ray powder diffraction pattern are kinematical and can be interpreted easily, while those obtained from a typical selected area electron diffraction (SAED) or preces- sion electron diffraction (PED) pattern are at least partially dynamical and therefore more difficult to use directly. On the other hand, many reflections in a powder diffraction pattern overlap and only the sum of their intensities can be measured, while those in an electron diffraction pattern are from a single crystal and therefore well separated in space. Although the intensities obtained from either SAED or PED data are less reliable than those obtained with X- rays, they can be used to advantage to improve the initial partitioning of the intensities of overlapping reflections. However, it is the partial crystallographic phase informa- tion that can be extracted either from high-resolution trans- mission electron microscopy (HRTEM) images or from PED data that has proven to be particularly useful in com- bination with high-resolution X-ray powder diffraction data. The dual-space (reciprocal and real space) structure determination programs Focus and Superflip have been shown to be especially useful for combining the two dif- ferent types of data.

Two-dimensional kinematic diffraction patterns from simulations of epitaxial growth

En el presente trabajo se describen de forma didáctica los alcances de la Microscopia Electrónica de Transmisión (TEM) para el estudio de nanosistemas. Para ilustrar el uso de las técnicas TEM, se utilizaron nanopartículas de Au y películas de Si adelgazadas con iones.Se describen técnicas de estudio convencional en TEM, como campo claro (BF), camp obscuro (DF), HAADF, SAED y EELS; además se mencionan las ventajas que ofrece el empleo de técnicas menos convencionales como CBED, LACBED y PED. También se brindan algunas sugerencias prácticas que permitirán describir y diferenciar de forma sencilla el contraste observado en las distintas técnicas disponibles en el TEM con el objetivo de ofrecer una visión, llamativa, clara y didáctica de los alcances actuales de la microscopia electrónica en México.

A systematic method to identify the space group from PED and CBED patterns part I - theory

Ultrathin metallic films are important functional materials for optical and microelectronic devices. Dedicated characterization with high spatial resolution and sufficient field of view is key to the understanding of the relation between microstructure and optical and electrical properties of such thin films. Here, we have applied on-axis transmission Kikuchi diffraction (TKD) and scanning precession electron diffraction (SPED) to study the microstructure of 10 nm thick polycrystalline gold films. The study compares the results obtained from the same specimen region by the two techniques and provides insights on the limits of each diffraction technique. We compare the physical spatial resolution of on-axis TKD and SPED and discuss challenges due to the larger probe size in scanning electron microscopy (SEM). Moreover, we present an improvement for the physical spatial resolution (PSR) of on-axis TKD through acquisition in immersion mode. We show how this method extends the capabilities of SEM-based microstructure characterization of ultrathin films and achieve PSR comparable to semi-automated SPED. • State of the art on-axis TKD SEM system comparison with SPED TEM system. • High resolution orientation mapping of ultrathin nano-crystalline metal films. • Improving TKD physical spatial resolution maps by immersion mode.

High-resolution scanning precession electron diffraction: Alignment and spatial resolution

The strong Coulombic interaction between a high energy electron and a thin crystal film gives rise to electron diffraction patterns encoded with information that is remarkably sensitive to the crystal potential. That exquisite sensitivity can be advantageous, for example in the determination of local symmetry and bonding, but can also be problematic in that in general the dynamical scattering inherent in electron diffraction prohibits the use of conventional crystallographic methods to recover structure factor phase information and solve unknown structures. One way to reduce this problem is to use precession electron diffraction (PED), introduced 20 years ago [1] as the electron analogue of Buerger's X-ray technique, in which the electron beam is first rocked in a hollow cone above the sample and then de-rocked below, the net effect of which is equivalent to precessing the sample about a stationary electron beam. PED is now used almost routinely as a starting point to solve crystal structures that cannot be solved for a variety of reasons using x-ray or neutron methods. In this keynote lecture we explore why the PED technique has been successful for structure determination, focussing on the PED geometry, the variation of intensities with precession angle and specimen thickness, and how this `mimics' kinematic behaviour, and the use of unconventional structure solution and refinement approaches [2]. New acquisition geometries will be discussed that rely on tilt series of PED patterns to yield a more complete 3D data set. The lecture will focus on how PED has been used also as a method for nanoscale orientation mapping [3], providing more information than conventional electron diffraction and a robust method with which to determine local crystallographic orientation. By scanning the beam, accurate orientation images can be derived from series of PED patterns and, by combining with tomographic methods, sub-volume orientation information is also available.

Thin film processing methods used to fabricate ferroelectric hafnium zirconium oxide typically result in small-grained films with a mixture of ferroelectric and nonferroelectric crystal phases with various crystallographic orientations. Although reliable, rapid determination of grain phase and orientation from four-dimensional scanning transmission electron microscopy maps is critical for measuring increased ferroelectric response, an assessment of automated analysis methods is not available. Here, a comparison of results between commercially available software (NanoMEGAS ASTAR) and an open-source code (py4DSTEM) is presented. Typically, the lamella used for STEM characterization are thicker than the average hafnium zirconium oxide (HZO) grain size, resulting in 4D maps where dynamical diffraction from more than one grain occurs in a significant number of pixels. Thus, precession electron diffraction (PED) data was required for reliable automated template matching analysis. Reliably distinguishing between the different crystal phases of HZO is challenging due to the small difference in lattice constant between phases and the possible presence of multiple orthorhombic phases. The HZO films in this study were characterized using PED, and precession diffraction simulation capability was added to py4DSTEM. Correlation of automated phase mapping with electrical verification of the ferroelectric effect confirmed the identification of the noncentrosymmetric space group 29 orthorhombic phase of HZO.