Smart Align—a new tool for robust non-rigid registration of scanning microscope data

Structural and compositional study of precipitates in under-aged Cu-added Al-Mg-Si alloy

Atomic scale characterization of fine precipitates in an under-aged Cu added Al-Mg-Si alloy was carried out by combination of atomically-resolved annular dark-field scanning transmission electron microscopy and energy dispersive X-ray spectroscopy. Two types of precipitates were observed in the alloy. In the case of ordered β” precipitates, β” was proposed as Mg_5-xAl_2+xSi₄ (x ≈ 1) with solute Cu atoms replacing Al site of β” precipitate. In the case of disordered precipitates, the precipitates were found to consist of β” sub-unit cells, three-fold symmetric structure without Cu atoms, Cu containing structures termed as “Cu sub-unit cluster”, and Q’ sub-unit cells. Among these structures, the morphologies of three-fold symmetric structure without Cu atoms, Cu sub-unit cluster, and Q’ sub-unit cell were almost the same, so that these structures should be the clusters of Q’ phase. Since the areal density, length and diameter of precipitates were almost equal between Cu free Al-Mg-Si alloy and Cu added Al-Mg-Si alloy, the increase of hardness by Cu addition should be due to the precipitation of Cu related precipitates, such as Cu sub-unit clusters and Q’ sub-unit cells.

Universal geometric frustration in pyrochlores

Materials with the pyrochlore/fluorite structure have diverse technological applications, from magnetism to nuclear waste disposal. Here we report the observation of structural instability present in the pyrochlores A₂Zr₂O₆Oʹ (A = Pr, La) and Yb₂Ti₂O₆Oʹ, that exists despite ideal stoichiometry, ideal cation-ordering, the absence of lone pair effects, and a lack of magnetic order. Though these materials appear to have good long-range order, local structure probes find displacements, of the order of 0.01 nm, within the pyrochlore framework. The pattern of displacements of the A₂Oʹ sublattice mimics the entropically-driven fluxional motions characteristic of and well-known in the silica mineral β-cristobalite. The universality of such displacements within the pyrochlore structure adds to the known structural diversity and explains the extreme sensitivity to composition found in quantum spin ices and the lack of ferroelectric behavior in pyrochlores.

The family of pyrochlore complex oxides includes many materials of fundamental or practical interest, such as spin ices and dielectrics. Trump et al. show that flexibility of the pyrochlores’ structure leads to local displacements that explain some of their unusual physical properties.

Maximising the resolving power of the scanning tunneling microscope

The usual way to present images from a scanning tunneling microscope (STM) is to take multiple images of the same area, to then manually select the one that appears to be of the highest quality, and then to discard the other almost identical images. This is in contrast to most other disciplines where the signal to noise ratio (SNR) of a data set is improved by taking repeated measurements and averaging them. Data averaging can be routinely performed for 1D spectra, where their alignment is straightforward. However, for serial-acquired 2D STM images the nature and variety of image distortions can severely complicate accurate registration. Here, we demonstrate how a significant improvement in the resolving power of the STM can be achieved through automated distortion correction and multi-frame averaging (MFA) and we demonstrate the broad utility of this approach with three examples. First, we show a sixfold enhancement of the SNR of the Si(111)-(7 × 7) reconstruction. Next, we demonstrate that images with sub-picometre height precision can be routinely obtained and show this for a monolayer of Ti₂O₃ on Au(111). Last, we demonstrate the automated classification of the two chiral variants of the surface unit cells of the (4 × 4) reconstructed SrTiO₃(111) surface. Our new approach to STM imaging will allow a wealth of structural and electronic information from surfaces to be extracted that was previously buried in noise.

Managing dose-, damage- and data-rates in multi-frame spectrum-imaging

As an instrument, the scanning transmission electron microscope is unique in being able to simultaneously explore both local structural and chemical variations in materials at the atomic scale. This is made possible as both types of data are acquired serially, originating simultaneously from sample interactions with a sharply focused electron probe. Unfortunately, such scanned data can be distorted by environmental factors, though recently fast-scanned multi-frame imaging approaches have been shown to mitigate these effects. Here, we demonstrate the same approach but optimized for spectroscopic data; we offer some perspectives on the new potential of multi-frame spectrum-imaging (MFSI) and show how dose-sharing approaches can reduce sample damage, improve crystallographic fidelity, increase data signal-to-noise, or maximize usable field of view. Further, we discuss the potential issue of excessive data-rates in MFSI, and demonstrate a file-compression approach to significantly reduce data storage and transmission burdens.

Periodic Giant Polarization Gradients in Doped BiFeO3 Thin Films

The ultimate challenge for the development of new multiferroics with enhanced properties lies in achieving nanoscale control of the coupling between different ordering parameters. In oxide-based multiferroics, substitutional cation dopants offer the unparalleled possibility to modify both the electric and magnetic properties at a local scale. Herein it is demonstrated the formation of a dopant-controlled polar pattern in BiFeO₃ leading to the spontaneous instauration of periodic polarization waves. In particular, nonpolar Ca-doped rich regions act as spacers between consecutive dopant-depleted regions displaying coupled ferroelectric states. This alternation of layers with different ferroelectric state creates a novel vertical polar structure exhibiting giant polarization gradients as large as 70 μC cm^-2 across 30 Å thick domains. The drastic change in the polar state of the film is visualized using high-resolution differential phase-contrast imaging able to map changes in ferroelectric polarization at atomic scale. Furthermore, a periodic distortion in the Fe-O-Fe bonding angle suggests a local variation in the magnetic ordering. The findings provide a new insight into the role of doping and reveal hitherto unexplored means to tailor the functional properties of multiferroics by doping engineering.

Prospects for Engineering Thermoelectric Properties in La1/3NbO3 Ceramics Revealed via Atomic-Level Characterization and Modeling

A combination of experimental and computational techniques has been employed to explore the crystal structure and thermoelectric properties of A-site-deficient perovskite La_1/3NbO₃ ceramics. Crystallographic data from X-ray and electron diffraction confirmed that the room temperature structure is orthorhombic with Cmmm as a space group. Atomically resolved imaging and analysis showed that there are two distinct A sites: one is occupied with La and vacancies, and the second site is fully unoccupied. The diffuse superstructure reflections observed through diffraction techniques are shown to originate from La vacancy ordering. La_1/3NbO₃ ceramics sintered in air showed promising high-temperature thermoelectric properties with a high Seebeck coefficient of S₁ = -650 to -700 μV/K and a low and temperature-stable thermal conductivity of k = 2-2.2 W/m·K in the temperature range of 300-1000 K. First-principles electronic structure calculations are used to link the temperature dependence of the Seebeck coefficient measured experimentally to the evolution of the density of states with temperature and indicate possible avenues for further optimization through electron doping and control of the A-site occupancies. Moreover, lattice thermal conductivity calculations give insights into the dependence of the thermal conductivity on specific crystallographic directions of the material, which could be exploited via nanostructuring to create high-efficiency compound thermoelectrics.

Stability of Schottky and Ohmic Au Nanocatalysts to ZnO Nanowires

Manufacturable nanodevices must now be the predominant goal of nanotechnological research to ensure the enhanced properties of nanomaterials can be fully exploited and fulfill the promise that fundamental science has exposed. Here, we test the electrical stability of Au nanocatalyst-ZnO nanowire contacts to determine the limits of the electrical transport properties and the metal-semiconductor interfaces. While the transport properties of as-grown Au nanocatalyst contacts to ZnO nanowires have been well-defined, the stability of the interfaces over lengthy time periods and the electrical limits of the ohmic or Schottky function have not been studied. In this work, we use a recently developed iterative analytical process that directly correlates multiprobe transport measurements with subsequent aberration-corrected scanning transmission electron microscopy to study the electrical, structural, and chemical properties when the nanowires are pushed to their electrical limits and show structural changes occur at the metal-nanowire interface or at the nanowire midshaft. The ohmic contacts exhibit enhanced quantum-mechanical edge-tunneling transport behavior because of additional native semiconductor material at the contact edge due to a strong metal-support interaction. The low-resistance nature of the ohmic contacts leads to catastrophic breakdown at the middle of the nanowire span where the maximum heating effect occurs. Schottky-type Au-nanowire contacts are observed when the nanowires are in the as-grown pristine state and display entirely different breakdown characteristics. The higher-resistance rectifying I-V behavior degrades as the current is increased which leads to a permanent weakening of the rectifying effect and atomic-scale structural changes at the edge of the Au interface where the tunneling current is concentrated. Furthermore, to study modified nanowires such as might be used in devices the nanoscale tunneling path at the interface edge of the ohmic nanowire contacts is removed with a simple etch treatment and the nanowires show similar I-V characteristics during breakdown as the Schottky pristine contacts. Breakdown is shown to occur either at the nanowire midshaft or at the Au contact depending on the initial conductivity of the Au contact interface. These results demonstrate the Au-nanowire structures are capable of withstanding long periods of electrical stress and are stable at high current densities ensuring they are ideal components for nanowire-device designs while providing the flexibility of choosing the electrical transport properties which other Au-nanowire systems cannot presently deliver.

Observation of metal nanoparticles at atomic resolution in Pt-based cancer chemotherapeutics

The chemotherapeutics cisplatin and oxaliplatin are important tools in the fight against cancer. Both compounds are platinum complexes. Aberration-corrected scanning transmission electron microscopy using the annular dark-field imaging mode now routinely provides single-atom sensitivity with atomic number contrast. Here, this imaging mode is used to directly image the platinum within the two drugs in their dried form on an amorphous carbon support film. The oxaliplatin is found to have wetted the supporting amorphous carbon, forming disordered clusters suggesting that the platinum has remained within the complex. Conversely, the cisplatin sample reveals 1.8-nm-diameter metallic platinum clusters. The size and shape of the clusters do not appear to be dependent on drying rate nor formed by beam damage, which may suggest that they were present in the original drug solution.

Evaluation of high-quality image reconstruction techniques applied to high-resolution Z-contrast imaging

High-quality image reconstruction techniques allow the generation of high pixel density images from a set of low-resolution micrographs. In general, these techniques consist of two main steps, namely, accurate registration, and formulation of an appropriate forward image model via some restoration method. There exist a wide variety of algorithms to cope with both stages and depending on their practical applications, some methods can outperform others, since they can be sensitive to the assumed data model, noise, drift, etc. When dealing with images generated by Z-contrast scanning transmission electron microscopes, a current trend is based on non-rigid approximations in the registration stage. In our work we aimed at reaching similar accuracy but addressing the most complex calculations in the reconstruction stage, instead of in the registration stage (as the non-rigid approaches do), but using a much smaller number of images. We review some of the most significant methods and address their shortcomings when they are applied to the field of microscopy. Simulated images with known targets will be used to evaluate and compare the main approaches in terms of quality enhancement and computing time. In addition, a procedure to determine the reference image will be proposed to minimise the global drift on the series. The best registration and restoration strategies will be applied to experimental images in order to point up the enhanced capability of this high quality image reconstruction methodology in this field.

Three-dimensional atomic models from a single projection using Z-contrast imaging: verification by electron tomography and opportunities

In order to fully exploit structure-property relations of nanomaterials, three-dimensional (3D) characterization at the atomic scale is often required. In recent years, the resolution of electron tomography has reached the atomic scale. However, such tomography typically requires several projection images demanding substantial electron dose. A newly developed alternative circumvents this by counting the number of atoms across a single projection. These atom counts can be used to create an initial atomic model with which an energy minimization can be applied to obtain a relaxed 3D reconstruction of the nanoparticle. Here, we compare, at the atomic scale, this single projection reconstruction approach with tomography and find an excellent agreement. This new approach allows for the characterization of beam-sensitive materials or where the acquisition of a tilt series is impossible. As an example, the utility is illustrated by the 3D atomic scale characterization of a nanodumbbell on an in situ heating holder of limited tilt range.

STEM moiré analysis for 2D strain measurements

A moiré pattern is created in a scanning transmission electron microscope (STEM) when the scan step is close to a crystalline periodicity. Usually, fringes are visible in only one direction, corresponding to a single set of lattice planes, but fringes can be formed in two directions or more. Using an accurate independent calibration, the strains in silicon devices have been determined from the spacing and orientation of one-directional STEM moiré fringes. In this report, we first discuss the origin of the STEM moiré, and then we show how an accurate calibration of the scan step can be obtained from the STEM moiré pattern itself, providing that we know initially only an approximate scan step and the planar spacing. The new calibration scheme also makes the STEM moiré experiments easier, since it can be applied for the moiré where the scan direction is not precisely aligned with the crystalline lattice. Finally, we show how the two-dimensional strain information will be readily extracted from two one-directional moiré patterns using the concept of geometric phase.

Atom size electron vortex beams with selectable orbital angular momentum

The decreasing size of modern functional magnetic materials and devices cause a steadily increasing demand for high resolution quantitative magnetic characterization. Transmission electron microscopy (TEM) based measurements of the electron energy-loss magnetic chiral dichroism (EMCD) may serve as the needed experimental tool. To this end, we present a reliable and robust electron-optical setup that generates and controls user-selectable single state electron vortex beams with defined orbital angular momenta. Our set-up is based on a standard high-resolution scanning TEM with probe aberration corrector, to which we added a vortex generating fork aperture and a miniaturized aperture for vortex selection. We demonstrate that atom size probes can be formed from these electron vortices and that they can be used for atomic resolution structural and spectroscopic imaging - both of which are prerequisites for future atomic EMCD investigations.

Precision controlled atomic resolution scanning transmission electron microscopy using spiral scan pathways

Atomic-resolution imaging in an aberration-corrected scanning transmission electron microscope (STEM) can enable direct correlation between atomic structure and materials functionality. The fast and precise control of the STEM probe is, however, challenging because the true beam location deviates from the assigned location depending on the properties of the deflectors. To reduce these deviations, i.e. image distortions, we use spiral scanning paths, allowing precise control of a sub-Å sized electron probe within an aberration-corrected STEM. Although spiral scanning avoids the sudden changes in the beam location (fly-back distortion) present in conventional raster scans, it is not distortion-free. “Archimedean” spirals, with a constant angular frequency within each scan, are used to determine the characteristic response at different frequencies. We then show that such characteristic functions can be used to correct image distortions present in more complicated constant linear velocity spirals, where the frequency varies within each scan. Through the combined application of constant linear velocity scanning and beam path corrections, spiral scan images are shown to exhibit less scan distortion than conventional raster scan images. The methodology presented here will be useful for in situ STEM imaging at higher temporal resolution and for imaging beam sensitive materials.

Atomap: a new software tool for the automated analysis of atomic resolution images using two-dimensional Gaussian fitting

Scanning transmission electron microscopy (STEM) data with atomic resolution can contain a large amount of information about the structure of a crystalline material. Often, this information is hard to extract, due to the large number of atomic columns and large differences in intensity from sublattices consisting of different elements. In this work, we present a free and open source software tool for analysing both the position and shapes of atomic columns in STEM-images, using 2-D elliptical Gaussian distributions. The software is tested on variants of the perovskite oxide structure. By first fitting the most intense atomic columns and then subtracting them, information on all the projected sublattices can be obtained. From this, we can extract changes in the lattice parameters and shape of A-cation columns from annular dark field images of perovskite oxide heterostructures. Using annular bright field images, shifts in oxygen column positions are also quantified in the same heterostructure. The precision of determining the position of atomic columns is compared between STEM data acquired using standard acquisition, and STEM-images obtained as an image stack averaged after using non-rigid registration.

Ultra-high resolution electron microscopy

The last two decades have seen dramatic advances in the resolution of the electron microscope brought about by the successful correction of lens aberrations that previously limited resolution for most of its history. We briefly review these advances, the achievement of sub-Ångstrom resolution and the ability to identify individual atoms, their bonding configurations and even their dynamics and diffusion pathways. We then present a review of the basic physics of electron scattering, lens aberrations and their correction, and an approximate imaging theory for thin crystals which provides physical insight into the various different imaging modes. Then we proceed to describe a more exact imaging theory starting from Yoshioka's formulation and covering full image simulation methods using Bloch waves, the multislice formulation and the frozen phonon/quantum excitation of phonons models. Delocalization of inelastic scattering has become an important limiting factor at atomic resolution. We therefore discuss this issue extensively, showing how the full-width-half-maximum is the appropriate measure for predicting image contrast, but the diameter containing 50% of the excitation is an important measure of the range of the interaction. These two measures can differ by a factor of 5, are not a simple function of binding energy, and full image simulations are required to match to experiment. The Z-dependence of annular dark field images is also discussed extensively, both for single atoms and for crystals, and we show that temporal incoherence must be included accurately if atomic species are to be identified through matching experimental intensities to simulations. Finally we mention a few promising directions for future investigation.

Peak separation method for sub-lattice strain analysis at atomic resolution: Application to InAs/GaSb superlattice

We report on a direct measurement of cation and anion sub-lattice strain in an InAs/GaSb type-II strained layer superlattice (T2SLs) using atomic resolution imaging and advanced image processing. Atomic column positions in InAs and GaSb are determined by separating the cation and anion peak intensities. Analysis of the InAs/GaSb T2SLs reveals the compressive strain in the nominal GaSb layer and tensile strain at interfaces between constituent layers, which indicate In incorporation into the nominal GaSb layer and the formation of GaAs like interfaces, respectively. The results are compared with the model-dependent X-ray diffraction measurements in terms of interfacial chemical intermixing and strain. Together, these techniques provide a robust measurement of atomic-scale strain which is vital to determine T2SL properties.

Non-rigid registration and non-local principle component analysis to improve electron microscopy spectrum images

Image registration and non-local Poisson principal component analysis (PCA) denoising improve the quality of characteristic x-ray (EDS) spectrum imaging of Ca-stabilized Nd2/3TiO3 acquired at atomic resolution in a scanning transmission electron microscope. Image registration based on the simultaneously acquired high angle annular dark field image significantly outperforms acquisition with a long pixel dwell time or drift correction using a reference image. Non-local Poisson PCA denoising reduces noise more strongly than conventional weighted PCA while preserving atomic structure more faithfully. The reliability of and optimal internal parameters for non-local Poisson PCA denoising of EDS spectrum images is assessed using tests on phantom data.

Directing Matter: Toward Atomic-Scale 3D Nanofabrication

Enabling memristive, neuromorphic, and quantum-based computing as well as efficient mainstream energy storage and conversion technologies requires the next generation of materials customized at the atomic scale. This requires full control of atomic arrangement and bonding in three dimensions. The last two decades witnessed substantial industrial, academic, and government research efforts directed toward this goal through various lithographies and scanning-probe-based methods. These technologies emphasize 2D surface structures, with some limited 3D capability. Recently, a range of focused electron- and ion-based methods have demonstrated compelling alternative pathways to achieving atomically precise manufacturing of 3D structures in solids, liquids, and at interfaces. Electron and ion microscopies offer a platform that can simultaneously observe dynamic and static structures at the nano- and atomic scales and also induce structural rearrangements and chemical transformation. The addition of predictive modeling or rapid image analytics and feedback enables guiding these in a controlled manner. Here, we review the recent results that used focused electron and ion beams to create free-standing nanoscale 3D structures, radiolysis, and the fabrication potential with liquid precursors, epitaxial crystallization of amorphous oxides with atomic layer precision, as well as visualization and control of individual dopant motion within a 3D crystal lattice. These works lay the foundation for approaches to directing nanoscale level architectures and offer a potential roadmap to full 3D atomic control in materials. In this paper, we lay out the gaps that currently constrain the processing range of these platforms, reflect on indirect requirements, such as the integration of large-scale data analysis with theory, and discuss future prospects of these technologies.

Extraction of structural and chemical information from high angle annular dark-field image by an improved peaks finding method

With the development of spherical aberration (Cs) corrected scanning transmission electron microscopy (STEM), high angle annular dark filed (HAADF) imaging technique has been widely applied in the microstructure characterization of various advanced materials with atomic resolution. However, current qualitative interpretation of the HAADF image is not enough to extract all the useful information. Here a modified peaks finding method was proposed to quantify the HAADF-STEM image to extract structural and chemical information. Firstly, an automatic segmentation technique including numerical filters and watershed algorithm was used to define the sub-areas for each atomic column. Then a 2D Gaussian fitting was carried out to determine the atomic column positions precisely, which provides the geometric information at the unit-cell scale. Furthermore, a self-adaptive integration based on the column position and the covariance of statistical Gaussian distribution were performed. The integrated intensities show very high sensitivity on the mean atomic number with improved signal-to-noise (S/N) ratio. Consequently, the polarization map and strain distributions were rebuilt from a HAADF-STEM image of the rhombohedral and tetragonal BiFeO3 interface and a MnO2 monolayer in LaAlO3 /SrMnO3 /SrTiO3 heterostructure was discerned from its neighbor TiO2 layers. Microsc. Res. Tech. 79:820-826, 2016. © 2016 Wiley Periodicals, Inc.

Influence of spatial and temporal coherences on atomic resolution high angle annular dark field imaging

Aberration-corrected (scanning) transmission electron microscopy ((S)TEM) has become a widely used technique when information on the chemical composition is sought on an atomic scale. To extract the desired information, complementary simulations of the scattering process are inevitable. Often the partial spatial and temporal coherences are neglected in the simulations, although they can have a huge influence on the high resolution images. With the example of binary gallium phosphide (GaP) we elucidate the influence of the source size and shape as well as the chromatic aberration on the high angle annular dark field (HAADF) intensity. We achieve a very good quantitative agreement between the frozen phonon simulation and experiment for different sample thicknesses when a Lorentzian source distribution is assumed and the effect of the chromatic aberration is considered. Additionally the influence of amorphous layers introduced by the preparation of the TEM samples is discussed. Taking into account these parameters, the intensity in the whole unit cell of GaP, i.e. at the positions of the different atomic columns and in the region between them, is described correctly. With the knowledge of the decisive parameters, the determination of the chemical composition of more complex, multinary materials becomes feasible.

Dynamic scan control in STEM: spiral scans

Scanning transmission electron microscopy (STEM) has emerged as one of the foremost techniques to analyze materials at atomic resolution. However, two practical difficulties inherent to STEM imaging are: radiation damage imparted by the electron beam, which can potentially damage or otherwise modify the specimen and slow-scan image acquisition, which limits the ability to capture dynamic changes at high temporal resolution. Furthermore, due in part to scan flyback corrections, typical raster scan methods result in an uneven distribution of dose across the scanned area. A method to allow extremely fast scanning with a uniform residence time would enable imaging at low electron doses, ameliorating radiation damage and at the same time permitting image acquisition at higher frame-rates while maintaining atomic resolution. The practical complication is that rastering the STEM probe at higher speeds causes significant image distortions. Non-square scan patterns provide a solution to this dilemma and can be tailored for low dose imaging conditions. Here, we develop a method for imaging with alternative scan patterns and investigate their performance at very high scan speeds. A general analysis for spiral scanning is presented here for the following spiral scan functions: Archimedean, Fermat, and constant linear velocity spirals, which were tested for STEM imaging. The quality of spiral scan STEM images is generally comparable with STEM images from conventional raster scans, and the dose uniformity can be improved.

Non-rigid alignment in electron tomography in materials science

Electron tomography is a key technique that enables the visualization of an object in three dimensions with a resolution of about a nanometre. High-quality 3D reconstruction is possible thanks to the latest compressed sensing algorithms and/or better alignment and preprocessing of the 2D projections. Rigid alignment of 2D projections is routine in electron tomography. However, it cannot correct misalignments induced by (i) deformations of the sample due to radiation damage or (ii) drifting of the sample during the acquisition of an image in scanning transmission electron microscope mode. In both cases, those misalignments can give rise to artefacts in the reconstruction. We propose a simple-to-implement non-rigid alignment technique to correct those artefacts. This technique is particularly suited for needle-shaped samples in materials science. It is initiated by a rigid alignment of the projections and it is then followed by several rigid alignments of different parts of the projections. Piecewise linear deformations are applied to each projection to force them to simultaneously satisfy the rigid alignments of the different parts. The efficiency of this technique is demonstrated on three samples, an intermetallic sample with deformation misalignments due to a high electron dose typical to spectroscopic electron tomography, a porous silicon sample with an extremely thin end particularly sensitive to electron beam and another porous silicon sample that was drifting during image acquisitions.

Quantitative STEM normalisation: The importance of the electron flux

Annular dark-field (ADF) scanning transmission electron microscopy (STEM) has become widely used in quantitative studies based on the opportunity to directly compare experimental and simulated images. This comparison merely requires the experimental data to be normalised and expressed in units of 'fractional beam-current'. However, inhomogeneities in the response of electron detectors can complicate this normalisation. The quantification procedure becomes both experiment and instrument specific, requiring new simulations for the particular response of each instrument's detector, and for every camera-length used. This not only impedes the comparison between different instruments and research groups, but can also be computationally very time consuming. Furthermore, not all image simulation methods allow for the inclusion of an inhomogeneous detector response. In this work, we propose an alternative method for normalising experimental data in order to compare these with simulations that consider a homogeneous detector response. To achieve this, we determine the electron flux distribution reaching the detector by means of a camera-length series or a so-called atomic column cross-section averaged convergent beam electron diffraction (XSACBED) pattern. The result is then used to determine the relative weighting of the detector response. Here we show that the results obtained by this new electron flux weighted (EFW) method are comparable to the currently used method, while considerably simplifying the needed simulation libraries. The proposed method also allows one to obtain a metric that describes the quality of the detector response in comparison with the 'ideal' detector response.