arXiv subjects

Benjamin Berkels

Publications and source records attributed to Benjamin Berkels.

At least 19 recordsLinked to original sources

arXiv2026

EBSD and Subtle Crystallographic Differences - A Study of Resolving Interlayer Spacings in Nb-Ni and Nb-Co mu-phases

In ordered intermetallics, slight variations in lattice site occupancy and specific interlayer spacings have been identified as the sources of significant changes in critical resolved shear stress and therefore how a given phase may affect alloy properties. So far, atom positions and lattice site occupancies have traditionally been characterised by high-resolution transmission electron microscopy (HR-TEM) and X-ray diffraction (XRD), which are methods that offer either local detail or high statistical significance but not both. Electron backscatter diffraction (EBSD), by contrast, provides high spatial resolution across large sample areas and therefore, has the potential to enable the local investigation of interlayer spacing and site lattice occupancy with improved statistical reliability. The objectives of the study are to benchmark EBSDs capability for resolving these subtle features and to correlate them with compositional and mechanical properties. In this case study, we therefore show that EBSD can resolve key crystallographic features of mu-phase intermetallics, specifically interlayer spacings. We combine pattern matching with large-scale dynamical simulations of template libraries guided by XRD based information on lattice parameters. For this, we generate structures that vary in the spacing between triple-layer and Kagome layer and in the site lattice occupancy of the 3a site. This approach successfully predicts the change of interlayer spacing between Kagome and triple layers in Nb-Co and Nb-Ni mu-phases, in good agreement with XRD and HR-TEM.

cond-mat.mtrl-sci↗

arXiv2025

A generalization bound for exit wave reconstruction via deep unfolding

Transmission Electron Microscopy enables high-resolution imaging of materials, but the resulting images are difficult to interpret directly. One way to address this is exit wave reconstruction, i.e., the recovery of the complex-valued electron wave at the specimen's exit plane from intensity-only measurements. This is an inverse problem with a nonlinear forward model. We consider a simplified forward model, making the problem equivalent to phase retrieval, and propose a discretized regularized variational formulation. To solve the resulting non-convex problem, we employ the proximal gradient algorithm (PGA) and unfold its iterations into a neural network, where each layer corresponds to one PGA step with learnable parameters. This unrolling approach, inspired by LISTA, enables improved reconstruction quality, interpretability, and implicit dictionary learning from data. We analyze the effect of parameter perturbations and show that they can accumulate exponentially with the number of layers $L$. Building on proof techniques of Behboodi et al., originally developed for LISTA, i.e., for a linear forward model, we extend the analysis to our nonlinear setting and establish generalization error bounds of order $\mathcal{O}(\sqrt{L})$. Numerical experiments support the exponential growth of parameter perturbations.

math.NA↗

arXiv2025

Chemically tailored planar defect phases in the Ta-Fe {\mu}-phase

Intermetallics often exhibit complex crystal structures, which give rise to intricate defect structures that critically influence their mechanical and functional properties. Despite studies on individual defect types, a comprehensive understanding of the defect landscape in {\mu}-phases, a class of topologically close-packed phases, remains elusive. In this study, we investigated the planar defect structures in the Ta-Fe {\mu}-phase across a compositional range of 46 to 58 at.% Ta using electron microscopy and density functional theory calculations. Electron backscatter diffraction and high-resolution scanning transmission electron microscopy reveal a transition from basal twin boundaries and planar faults containing C14 TaFe2 Laves phase layers at a low Ta content to pyramidal {1\bar{1}02} twins at a higher Ta content. Density functional theory calculations of defect formation energies confirm a chemical potential-driven stabilisation of Laves phase lamellae. The prevalence of pyramidal twins in Ta-rich {\mu}-phase samples is attributed to the competitive nature of different planar defects during solidification. A defect landscape for {\mu}-phases is proposed, illustrating the interplay between site occupancy, dislocation types and planar faults across the chemical potential space. These findings provide fundamental insights into defect engineering in structurally complex intermetallics and open pathways for optimising material properties through chemical tuning.

cond-mat.mtrl-sci↗

arXiv2024

On the importance of the $\varepsilon$-regularization of the distribution-dependent Mumford-Shah model for hyperspectral image segmentation

Recently, the distribution-dependent Mumford-Shah model for hyperspectral image segmentation was introduced. It approximates an image based on first and second order statistics using a data term, that is built of a Mahalanobis distance plus a covariance regularization, and the total variation as spatial regularization. Moreover, to achieve feasibility, the appearing matrices are restricted to symmetric positive definite ones with eigenvalues exceeding a certain threshold. This threshold is chosen in advance as a data-independent parameter. In this article, we study theoretical properties of the model. In particular, we prove the existence of minimizers of the functional and show its $\Gamma$-convergence when the threshold regularizing the eigenvalues of the matrices tends to zero. It turns out that in the $\Gamma$-limit we lose the guaranteed existence of minimizers; and we give an example of an image where the $\Gamma$-limit indeed has no minimizer. Finally, we derive a formula for the minimum eigenvalues of the covariance matrices appearing in the functional that hints under which conditions the functional is able to handle the data without regularizing the eigenvalues. The results of this article demonstrate the significance and importance of the eigenvalue regularization to the model and that it cannot be dropped without substantial modifications.

math.NA↗

arXiv2024

Joint denoising and line distortion correction for raster-scanned image series

The problem of noise in a general data acquisition procedure can be resolved more accurately if it is based on a model that describes well the distortions of the data including both spatial and intensity changes. The focus of this article is the modeling of the position distortions during sequential data acquisitions. A guiding example is the data obtained by Scanning Transmission Electron Microscopy (STEM) and High Angular Annular Dark Field (HAADF) data, in particular. The article discusses different models of the position noise and their numerical implementations comparing some computational results.

math.NA↗

arXiv2024

A Generalization Bound for a Family of Implicit Networks

Implicit networks are a class of neural networks whose outputs are defined by the fixed point of a parameterized operator. They have enjoyed success in many applications including natural language processing, image processing, and numerous other applications. While they have found abundant empirical success, theoretical work on its generalization is still under-explored. In this work, we consider a large family of implicit networks defined parameterized contractive fixed point operators. We show a generalization bound for this class based on a covering number argument for the Rademacher complexity of these architectures.

cs.LG↗

arXiv2023

A machine learning framework for quantifying chemical segregation and microstructural features in atom probe tomography data

Atom probe tomography (APT) is ideally suited to characterize and understand the interplay of chemical segregation and microstructure in modern multicomponent materials. Yet, the quantitative analysis typically relies on human expertise to define regions of interest. We introduce a computationally efficient, multistage machine learning strategy to identify chemically distinct domains in a semi automated way, and subsequently quantify their geometric and compositional characteristics. In our algorithmic pipeline, we first coarse grain the APT data into voxels, collect the composition statistics, and decompose it via clustering in composition space. The composition classification then enables the real space segmentation via a density based clustering algorithm, thus revealing the microstructure at voxel resolution. Our approach is demonstrated for a Sm(Co,Fe)ZrCu alloy. The alloy exhibits two precipitate phases with a plate-like, but intertwined morphology. The primary segmentation is further refined to disentangle these geometrically complex precipitates into individual plate like parts by an unsupervised approach based on principle component analysis, or a U-Net based semantic segmentation trained on the former. Following the chemical and geometric analysis, detailed chemical distribution and segregation effects relative to the predominant plate-like geometry can be readily mapped without resorting to the initial voxelization.

physics.chem-ph↗

arXiv2023

Constructing phase diagrams for defects by correlated atomic-scale characterization

Phase transformations and crystallographic defects are two essential tools to drive innovations in materials. Bulk materials design via tuning chemical compositions has been systematized using phase diagrams. We show here that the same thermodynamic concept can be applied to understand the chemistry at defects. We present a combined experimental and modelling approach to scope and build phase diagrams for defects. The discovery was enabled by triggering phase transformations of individual defects through local alloying, and sequentially imaging the structural and chemical changes using atomic-resolution scanning transmission electron microscopy. By observing atomic-scale phase transformations of a Mg grain boundary through Ga alloying, we exemplified the method to construct a grain boundary phase diagram using ab initio simulations and thermodynamic principles. The methodology enables a systematic development of defect phase diagrams to propel a new paradigm for materials design utilizing chemical complexity and phase transformations at defects.

cond-mat.mtrl-sci↗

arXiv2023

Direct Motif Extraction from High Resolution Crystalline STEM Images

During the last decade, automatic data analysis methods concerning different aspects of crystal analysis have been developed, e.g., unsupervised primitive unit cell extraction and automated crystal distortion and defects detection. However, an automatic, unsupervised motif extraction method is still not widely available yet. Here, we propose and demonstrate a novel method for the automatic motif extraction in real space from crystalline images based on a variational approach involving the unit cell projection operator. Due to the non-convex nature of the resulting minimization problem, a multi-stage algorithm is used. First, we determine the primitive unit cell in form of two lattice vectors. Second, a motif image is estimated using the unit cell information. Finally, the motif is determined in terms of atom positions inside the unit cell. The method was tested on various synthetic and experimental HAADF STEM images. The results are a representation of the motif in form of an image, atomic positions, primitive unit cell vectors, and a denoised and a modeled reconstruction of the input image. The method was applied to extract the primitive cells of complex $\mu$-phase structures Nb$_\text{6.4}$Co$_\text{6.6}$ and Nb$_\text{7}$Co$_\text{6}$, where subtle differences between their interplanar spacings were determined.

eess.IV↗

arXiv2023

Tailoring the plasticity of topologically close-packed phases via the crystals' fundamental building blocks

Brittle topologically close-packed precipitates form in many advanced alloys. Due to their complex structures little is known about their plasticity. Here, we present a strategy to understand and tailor the deformability of these complex phases by considering the Nb-Co {\mu}-phase as an archetypal material. The plasticity of the Nb-Co {\mu}-phase is controlled by the Laves phase building block that forms parts of its unit cell. We find that between the bulk C15-NbCo$_2$ Laves and Nb-Co {\mu}-phase, the interplanar spacing and local elastic modulus of the Laves phase building block change, leading to a strong reduction in hardness and elastic modulus, as well as a transition from synchroshear to crystallographic slip. Furthermore, as the composition changes from Nb$_6$Co$_7$ to Nb$_7$Co$_6$, the Co atoms in the triple layer are substituted such that the triple layer of the Laves phase building block becomes a slab of pure Nb, resulting in inhomogeneous changes in elasticity and a transition from crystallographic slip to a glide-and-shuffle mechanism. These findings open opportunities to purposefully tailor the plasticity of these topologically close-packed phases in bulk, but at the atomic scale of interplanar spacing and local shear modulus of the fundamental crystal building blocks in their large unit cells.

cond-mat.mtrl-sci↗

arXiv2023

Three-Dimensional Damage Characterisation in Dual Phase Steel using Deep Learning

High performance sheet metals with a multi-phase microstructure suffer from deformation induced damage formation during forming in the constituent phases but importantly also where these intersect. To capture damage in terms of the physical processes in three dimensions (3D) and its stochastic nature during deformation, two challenges remain to be tackled: First, bridging high resolution analysis towards large scales to consider statistical data and, second, characterising in 3D with a resolution appropriate for sub-micron sized voids at a large scale. Here, we present how this can be achieved using panoramic scanning electron microscopy (SEM), metallographic serial sectioning, and deep-learning assisted automatic image analysis. This brings together the 3D evolution of active damage mechanisms with volumetric and environmental information for thousands of individual damage sites. We also assess potential surface preparation artefacts in 2D analyses. Overall, we find that for the material considered here, a dual phase (DP800) steel, martensite cracking is the dominant but not sole origin of deformation induced damage and that for a quantitative comparison of damage density, metallographic preparation can induce additional surface damage density far exceeding what is commonly induced between uniaxial straining steps.

cond-mat.mtrl-sci↗

arXiv2022

Cell tracking for live-cell microscopy using an activity-prioritized assignment strategy

Cell tracking is an essential tool in live-cell imaging to determine single-cell features, such as division patterns or elongation rates. Unlike in common multiple object tracking, in microbial live-cell experiments cells are growing, moving, and dividing over time, to form cell colonies that are densely packed in mono-layer structures. With increasing cell numbers, following the precise cell-cell associations correctly over many generations becomes more and more challenging, due to the massively increasing number of possible associations. To tackle this challenge, we propose a fast parameter-free cell tracking approach, which consists of activity-prioritized nearest neighbor assignment of growing cells and a combinatorial solver that assigns splitting mother cells to their daughters. As input for the tracking, Omnipose is utilized for instance segmentation. Unlike conventional nearest-neighbor-based tracking approaches, the assignment steps of our proposed method are based on a Gaussian activity-based metric, predicting the cell-specific migration probability, thereby limiting the number of erroneous assignments. In addition to being a building block for cell tracking, the proposed activity map is a standalone tracking-free metric for indicating cell activity. Finally, we perform a quantitative analysis of the tracking accuracy for different frame rates, to inform life scientists about a suitable (in terms of tracking performance) choice of the frame rate for their cultivation experiments, when cell tracks are the desired key outcome.

cs.CV↗

arXiv2022

Automated Characterization of Catalytically Active Inclusion Body Production in Biotechnological Screening Systems

We here propose an automated pipeline for the microscopy image-based characterization of catalytically active inclusion bodies (CatIBs), which includes a fully automatic experimental high-throughput workflow combined with a hybrid approach for multi-object microbial cell segmentation. For automated microscopy, a CatIB producer strain was cultivated in a microbioreactor from which samples were injected into a flow chamber. The flow chamber was fixed under a microscope and an integrated camera took a series of images per sample. To explore heterogeneity of CatIB development during the cultivation and track the size and quantity of CatIBs over time, a hybrid image processing pipeline approach was developed, which combines an ML-based detection of in-focus cells with model-based segmentation. The experimental setup in combination with an automated image analysis unlocks high-throughput screening of CatIB production, saving time and resources. Biotechnological relevance - CatIBs have wide application in synthetic chemistry and biocatalysis, but also could have future biomedical applications such as therapeutics. The proposed hybrid automatic image processing pipeline can be adjusted to treat comparable biological microorganisms, where fully data-driven ML-based segmentation approaches are not feasible due to the lack of training data. Our work is the first step towards image-based bioprocess control.

q-bio.QM↗

arXiv2022

A hybrid multi-object segmentation framework with model-based B-splines for microbial single cell analysis

In this paper, we propose a hybrid approach for multi-object microbial cell segmentation. The approach combines an ML-based detection with a geometry-aware variational-based segmentation using B-splines that are parametrized based on a geometric model of the cell shape. The detection is done first using YOLOv5. In a second step, each detected cell is segmented individually. Thus, the segmentation only needs to be done on a per-cell basis, which makes it amenable to a variational approach that incorporates prior knowledge on the geometry. Here, the contour of the segmentation is modelled as closed uniform cubic B-spline, whose control points are parametrized using the known cell geometry. Compared to purely ML-based segmentation approaches, which need accurate segmentation maps as training data that are very laborious to produce, our method just needs bounding boxes as training data. Still, the proposed method performs on par with ML-based segmentation approaches usually used in this context. We study the performance of the proposed method on time-lapse microscopy data of Corynebacterium glutamicum.

cs.CV↗

arXiv2022

A distribution-dependent Mumford-Shah model for unsupervised hyperspectral image segmentation

Hyperspectral images provide a rich representation of the underlying spectrum for each pixel, allowing for a pixel-wise classification/segmentation into different classes. As the acquisition of labeled training data is very time-consuming, unsupervised methods become crucial in hyperspectral image analysis. The spectral variability and noise in hyperspectral data make this task very challenging and define special requirements for such methods. Here, we present a novel unsupervised hyperspectral segmentation framework. It starts with a denoising and dimensionality reduction step by the well-established Minimum Noise Fraction (MNF) transform. Then, the Mumford-Shah (MS) segmentation functional is applied to segment the data. We equipped the MS functional with a novel robust distribution-dependent indicator function designed to handle the characteristic challenges of hyperspectral data. To optimize our objective function with respect to the parameters for which no closed form solution is available, we propose an efficient fixed point iteration scheme. Numerical experiments on four public benchmark datasets show that our method produces competitive results, which outperform three state-of-the-art methods substantially on three of these datasets.

cs.CV↗

arXiv2022

Dynamic doping and Cottrell atmosphere optimize the thermoelectric performance of n-type PbTe

High thermoelectric energy conversion efficiency requires a large figure-of-merit, zT, over a broad temperature range. To achieve this, we optimize the carrier concentrations of n-type PbTe from room up to hot-end temperatures by co-doping Bi and Ag. Bi is an efficient n-type dopant in PbTe, often leading to excessive carrier concentration at room temperature. As revealed by density functional theory calculations, the formation of Bi and Ag defect complexes is exploited to optimize the room temperature carrier concentration. At elevated temperatures, we demonstrate the dynamic dissolution of Ag2Te precipitates in PbTe in situ by heating in a scanning transmission electron microscope. The release of n-type Ag interstitials with increasing temperature fulfills the requirement of higher carrier concentrations at the hot end. Moreover, as characterized by atom probe tomography, Ag atoms aggregate along parallel dislocation arrays to form Cottrell atmospheres. This results in enhanced phonon scattering and leads to a low lattice thermal conductivity. As a result of the synergy of dynamic doping and phonon scattering at decorated dislocations, an average zT of 1.0 is achieved in n-type Bi/Ag-codoped PbTe between 400 and 825 K. Introducing dopants with temperature-dependent solubility and strong interaction with dislocation cores enables simultaneous optimization of the average power factor and thermal conductivity, providing a new concept to exploit in the field of thermoelectrics.

cond-mat.mtrl-sci↗

arXiv2020

Work-stealing prefix scan: Addressing load imbalance in large-scale image registration

Parallelism patterns (e.g., map or reduce) have proven to be effective tools for parallelizing high-performance applications. In this paper, we study the recursive registration of a series of electron microscopy images - a time consuming and imbalanced computation necessary for nano-scale microscopy analysis. We show that by translating the image registration into a specific instance of the prefix scan, we can convert this seemingly sequential problem into a parallel computation that scales to over thousand of cores. We analyze a variety of scan algorithms that behave similarly for common low-compute operators and propose a novel work-stealing procedure for a hierarchical prefix scan. Our evaluation shows that by identifying a suitable and well-optimized prefix scan algorithm, we reduce time-to-solution on a series of 4,096 images spanning ten seconds of microscopy acquisition from over 10 hours to less than 3 minutes (using 1024 Intel Haswell cores), enabling derivation of material properties at nanoscale for long microscopy image series.

cs.DC↗

arXiv2020

Automation of Hemocompatibility Analysis Using Image Segmentation and a Random Forest

The hemocompatibility of blood-contacting medical devices remains one of the major challenges in biomedical engineering and makes research in the field of new and improved materials inevitable. However, current in-vitro test and analysis methods are still lacking standardization and comparability, which impedes advances in material design. For example, the optical platelet analysis of material in-vitro hemocompatibility tests is carried out manually or semi-manually by each research group individually. As a step towards standardization, this paper proposes an automation approach for the optical platelet count and analysis. To this end, fluorescence images are segmented using Zach's convexification of the multiphase-phase piecewise constant Mumford--Shah model. The resulting connected components of the non-background segments then need to be classified as platelet or no platelet. Therefore, a supervised random forest is applied to feature vectors derived from the components using features like area, perimeter and circularity. With an overall high accuracy and low error rates, the random forest achieves reliable results. This is supported by high areas under the receiver-operator and the prediction-recall curve, respectively. We developed a new method for a fast, user-independent and reproducible analysis of material hemocompatibility tests, which is therefore a unique and powerful tool for advances in biomaterial research.

q-bio.QM↗