Calcium silicate perovskite (CaPv) is the host for many trace elements in the lower mantle. Whether, when, and where it forms during the solidification of the magma ocean is fundamental to understanding the geochemical and geodynamical evolution of the early Earth. We performed first-principles molecular dynamics simulations to investigate the partitioning of Ca (alongside Sr and Ba) between bridgmanite and molten pyrolite and laser-heated diamond anvil cell experiments to replicate the crystallization of pyrolitic melt. Results show that Ca is incompatible in bridgmanite at all relevant crystallization conditions in the lower mantle, indicating a progressive enrichment of Ca in the magma ocean as it solidifies. This leads to the crystallization of CaPv during the final stages of solidification in the deep mantle. Coupled with the low bridgmanite-melt partition coefficients for Sr and Ba, our findings infer that both large ion lithophile elements and their host, CaPv, will be concentrated in the deep mantle at the end of magma ocean solidification.

Limited-angle electron tomography (ET) aims to reconstruct 3D shapes from 2D projections of transmission electron microscopy (TEM) within a restricted range and number of tilting angles, but it suffers from the missing-edge problem that causes severe reconstruction artefacts. Deep learning approaches have shown promising results in alleviating these artefacts, yet they typically require large high-quality training datasets with known 3D ground truth, which are difficult to obtain in electron microscopy. To address these challenges, we propose TEMDiff, a novel 3D diffusion-based iterative reconstruction framework. Our method is trained on readily available volumetric FIB-SEM data using a simulator that maps them to TEM tilt series, enabling the model to learn realistic structural priors without requiring clean TEM ground truth. By operating directly on 3D volumes, TEMDiff implicitly enforces consistency across slices without the need for additional regularization. In simulated ET datasets with limited angular coverage, TEMDiff outperforms the most advanced methods in reconstruction quality. We further demonstrate that a trained model TEMDiff generalizes well to real-world TEM tilts obtained under different conditions and can recover accurate structures from tilt ranges as narrow as 8 degrees, with 2 degrees increments, without any retraining or fine-tuning.

Constraining the complex dynamics of the inner Earth unites research efforts across several scientific disciplines, including geochemistry, geophysics and geodynamics. Seismological and geodynamic studies offer insights into the present state of the mantle structure, whereas geochemical approaches characterize its chemical and isotopic heterogeneities1, shedding light on the complexity of its evolution. One key challenge is determining the age and origin of its chemical heterogeneities. Here we present new high-precision Nd isotopic measurements in present-day volcanism that identify heterogeneities dating back to the Earth's earliest history. We report significantly positive 142Nd anomalies in lavas from the submarine Fani Maoré volcano in the Comoros archipelago. These anomalies require the preservation, in the mantle, of material depleted in light rare-earth elements (REE) and formed within the first 100 million years (Myr) of Earth's history. We suggest that this material is mainly composed of bridgmanite that crystallized from an early Earth magma ocean. This Hadean bridgmanite may be more widespread in the present-day mantle than previously expected, raising new questions about its survival over billions of years of plate tectonics and vigorous mantle convection.

Nanoscale phase separation via spinodal decomposition can govern the macroscopic behaviour of alloys, yet quantitatively characterizing its 3D morphology remains a challenge. Although atom probe tomography (APT) can recover the full 3D morphology, it presents challenges of specimen preparation and outcome success. In comparison, analytical transmission electron microscopy approaches offer both convenience and excellent spatial resolution, with electron energy-loss spectroscopy (EELS) further combining chemical sensitivity and insights into oxidation and valence states. However, EELS analysis typically suffers from low signal-to-noise ratios, potential to introduce biases through manual selection of fitting parameters, and the fact that it projects the 3D nature of the sample in 2D, producing superimposed features.,Here we address these issues with a physics-guided non-negative matrix factorization framework that embeds EELS-specific physical constraints directly into the optimization objective. Our machine learning approach replaces the traditional multi-stage denoise- fit-quantify pipeline, where each step is subject to human bias, with a single-step decomposition directly into a denoised, chemically quantified spectral basis. By enforcing a physically meaningful solution space, our method guarantees the recovery of energy-loss near-edge structures for individual chemical phases, and displays higher resilience to noise than conventional approaches. We demonstrate the capability of our method by characterizing the complex, nanometric morphology of a spinodally decomposed Fe-Cr alloy. From 2D EELS datasets, our algorithm extracts characteristic 3D structural parameters that show good agreement with reference to APT measurements. Our framework offers a general approach to retrieving the spatial and chemical characteristics of overlapping nanoscale phases from EELS datasets.

Uranium oxides occur in a variety of phases that differ in their crystal structure and uranium oxidation states. Electron energy loss spectroscopy (EELS) is one of the few techniques that has sufficient spatial resolution and sensitivity to electronic structure to distinguish among phases at the nanoscale. However, beam-sensitive materials, such as uranium oxides, are subject to spectral modification due to interactions with the electron beam. Therefore, theory support is essential to reliably exclude the impact of beam damage and generate true reference data sets. Here, we use a comparison of theoretical and experimental spectra to probe the impact of beam damage on the O K-edge and U N-edge (N 6,7 and N 4,5) EELS spectra of various single-valent and mixed-valence uranium oxide bulk phases. Using a low-dose experimental setup, we show that the K-edge theoretical spectra are in excellent agreement with experiment for both peak positions and relative intensities of respective peaks. In contrast, U N-edge features are less distinguishing due to the partially localized nature of the U 5f orbitals and overlapping multiplet and spin-orbit coupling effects. This work demonstrates that O K-edge EELS is sufficiently diagnostic to distinguish a wide range of uranium oxides and that the experimental approach used here minimizes beam damage and allows valence state discrimination across the U(IV), U(V), and U(VI) series. When combined with imaging modes available in electron microscopy, this work enables a detailed investigation and characterization of uranium redox transformations at the nanoscale.

Energy dispersive X-ray (EDX) spectrum imaging yields compositional information with a spatial resolution down to the atomic level. However, experimental limitations often produce extremely sparse and noisy EDX spectra. Under such conditions, every detected X-ray must be leveraged to obtain the maximum possible amount of information about the sample. To this end, we introduce a robust multiscale Bayesian approach that accounts for the Poisson statistics in the EDX data and leverages their underlying spatial correlations. This is combined with EDX spectral simulation (elemental contributions and Bremsstrahlung background) into a Bayesian estimation strategy. When tested using simulated datasets, the chemical maps obtained with this approach are more accurate and preserve a higher spatial resolution than those obtained by standard methods. These properties translate to experimental datasets, where the method enhances the atomic resolution chemical maps of a canonical tetragonal ferroelectric PbTiO3 sample, such that ferroelectric domains are mapped with unit-cell resolution.

We consider the problem of regularized Poisson Non-negative Matrix Factorization (NMF) problem, encompassing various regularization terms such as Lipschitz and relatively smooth functions, alongside linear constraints. This problem holds significant relevance in numerous Machine Learning applications, particularly within the domain of physical linear unmixing problems. A notable challenge arises from the main loss term in the Poisson NMF problem being a KL divergence, which is non-Lipschitz, rendering traditional gradient descent-based approaches inefficient. In this contribution, we explore the utilization of Block Successive Upper Minimization (BSUM) to overcome this challenge. We build approriate majorizing function for Lipschitz and relatively smooth functions, and show how to introduce linear constraints into the problem. This results in the development of two novel algorithms for regularized Poisson NMF. We conduct numerical simulations to showcase the effectiveness of our approach.

Energy dispersive X-ray (EDX) spectroscopy in the transmission electron microscope is a key tool for nanomaterials analysis, providing a direct link between spatial and chemical information. However, using it for precisely determining chemical compositions presents challenges of noisy data from low X-ray yields and mixed signals from phases that overlap along the electron beam trajectory. Here, we introduce a novel method, non-negative matrix factorization based pan-sharpening (PSNMF), to address these limitations. Leveraging the Poisson nature of EDX spectral noise and binning operations, PSNMF retrieves high-quality phase spectral and spatial signatures via consecutive factorizations. After validating PSNMF with synthetic data sets of different noise levels, we illustrate its effectiveness on two distinct experimental cases: a nanomineralogical lamella, and supported catalytic nanoparticles. Not only does PSNMF obtain accurate phase signatures, but data sets reconstructed from the outputs have demonstrably lower noise and better fidelity than from the benchmark denoising method of principle component analysis.

Energy-dispersive X-ray spectroscopy (EDXS) mapping with a scanning transmission electron microscope (STEM) is commonly used for chemical characterization of materials. However, STEM-EDXS quantification becomes challenging when the phases constituting the sample under investigation share common elements and overlap spatially. In this paper, we present a methodology to identify, segment, and unmix phases with a substantial spectral and spatial overlap in a semi-automated fashion through combining non-negative matrix factorization with a priori knowledge of the sample. We illustrate the methodology using a sample taken from an electron beam-sensitive mineral assemblage representing Earth's deep mantle. With it, we retrieve the true EDX spectra of the constituent phases and their corresponding phase abundance maps. It further enables us to achieve a reliable quantification for trace elements having concentration levels of ∼100 ppm. Our approach can be adapted to aid the analysis of many materials systems that produce STEM-EDXS datasets having phase overlap and/or limited signal-to-noise ratio (SNR) in spatially-integrated spectra.

We present the development of a new algorithm which combines state-of-the-art energy-dispersive X-ray (EDX) spectroscopy theory and a suitable machine learning formulation for the hyperspectral unmixing of scanning transmission electron microscope EDX spectrum images. The algorithm is based on non-negative matrix factorization (NMF) incorporating a physics-guided factorization model. It optimizes a Poisson likelihood, under additional simplex constraint together with user-chosen sparsity-inducing and smoothing regularizations, and is based on iterative multiplicative updates. The fluorescence of X-rays is fully modeled thanks to state-of-the-art theoretical work. It is shown that the output of the algorithm can be used for a direct chemical quantification. With this approach, it is straightforward to include a priori knowledge on the specimen such as the presence or absence of certain chemical elements in some of its phases. This work is implemented within two open-source Python packages, espm and emtables, which are used here for data simulation, data analysis and quantification. Using simulated data, we demonstrate that incorporating physical modeling in the decomposition helps retrieve meaningful components from spatially and spectrally mixed phases, even when the data are very noisy. For synthetic data with a higher signal, the regularizations yield a tenfold increase in the quality of the reconstructed abundance maps compared to standard NMF. Our approach is further validated on experimental data with a known ground truth, where state-of-the art results are achieved by using prior knowledge about the sample. Our model can be generalized to any other scanning spectroscopy techniques where underlying physical modeling can be linearized.

We present two open-source Python packages: "electron spectro-microscopy" (espm) and "electron microscopy tables" (emtables). The espm software enables the simulation of scanning transmission electron microscopy energy-dispersive X-ray spectroscopy datacubes, based on user-defined chemical compositions and spatial abundance maps of constituent phases. The simulation process uses X-ray emission cross-sections generated via state-of-the-art calculations made with emtables. These tables are designed to be easily modifiable, either manually or using espm. The simulation framework is designed to test the application of decomposition algorithms for the analysis of STEM-EDX spectrum images with access to a known ground truth. We validate our approach using the case of a complex geology-related sample, comparing raw simulated and experimental datasets and the outputs of their non-negative matrix factorization. In addition to testing machine learning algorithms, our packages will also help experimental design, for instance, predicting dataset characteristics or establishing minimum counts needed to measure nanoscale features.

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Journal Article Physics-Guided Machine Learning for the Analysis of Low SNR STEM-EDXS Data Get access Adrien Teurtrie, Adrien Teurtrie Electron Spectrometry and Microscopy Laboratory, Institute of Physics, EPFL, LausanneCurrent address : Unité Matériaux et Transformations, UMET, UMR-CNRS 8207, Université de Lille, France Search for other works by this author on: Oxford Academic Google Scholar Nathanaël Perraudin, Nathanaël Perraudin Swiss Data Science Center, EPFL and ETH Zürich, Lausanne and Zürich Search for other works by this author on: Oxford Academic Google Scholar Thomas Holvoet, Thomas Holvoet Swiss Data Science Center, EPFL and ETH Zürich, Lausanne and ZürichGhent University, Ghent Search for other works by this author on: Oxford Academic Google Scholar Hui Chen, Hui Chen Electron Spectrometry and Microscopy Laboratory, Institute of Physics, EPFL, Lausanne Search for other works by this author on: Oxford Academic Google Scholar Duncan T L Alexander, Duncan T L Alexander Electron Spectrometry and Microscopy Laboratory, Institute of Physics, EPFL, Lausanne Search for other works by this author on: Oxford Academic Google Scholar Guillaume Obozinski, Guillaume Obozinski Swiss Data Science Center, EPFL and ETH Zürich, Lausanne and Zürich Search for other works by this author on: Oxford Academic Google Scholar Cécile Hébert Cécile Hébert Electron Spectrometry and Microscopy Laboratory, Institute of Physics, EPFL, Lausanne Corresponding author: cecile.hebert@epfl.ch Search for other works by this author on: Oxford Academic Google Scholar Microscopy and Microanalysis, Volume 28, Issue S1, 1 August 2022, Pages 2978–2979, https://doi.org/10.1017/S1431927622011163 Published: 01 August 2022

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While lean Mg-Zn-Ca alloys are promising materials for temporary implants, questions remain on the impact of Zn and Ca on the microstructure. In this context, the precipitation of Zn and Ca in Mg-1.5Zn-0.25Ca (in wt.%), initially extruded at 330 & DEG;C, towards Mg-Ca binary precipitates or Ca-Mg-Zn ternary precipitates was probed in a multiscale correlative approach using atom probe tomography (APT) and an-alytical transmission electron microscopy (TEM). Particular focus was set on the ternary precipitate phase whose structure is debated. In the as-extruded material, the binary precipitates are made of hexagonal C14 Mg2Ca containing up to about 3 at.% of Zn. The ternary ones are based on the hexagonal Ca2Mg5Zn5 prototype structure with a composition close to Ca3Mg11Zn4, as deduced from atomically resolved EDS mapping and scanning TEM imaging, supported by simulations. The precipitation sequence was scru-tinized upon linear heating from room temperature to 375 ?, starting from the solutionized material. Three exothermic differential scanning calorimetry (DSC) peaks were observed, at respectively 125, 250 and 320 & DEG;C. Samples were taken after the peak decays, at respectively 205, 260 and 375? for structural analysis. At 205 & DEG;C, APT analysis revealed Ca-rich, Zn-rich and Zn-Ca-rich clusters of about 3 nm in size and with a number density of 5.7 x 10 23 m -3. At 260 ?, APT and TEM showed mono-layered Zn-Ca-rich Guinier-Preston (GP) zones of about 8 nm in size and with a number density of 1.3 x 10 23 m -3. At 375 ?, larger and highly coherent elongated precipitates were found, with a size of about 50 nm. They occur as binary Mg-Ca precipitates or ternary Ca2Mg6Zn3 precipitates, as deduced from scanning TEM-based energy dispersive X-ray spectroscopy (EDS) and nanodiffraction in TEM. Here, the binary precipitates outnumber the ternary ones, while in the as-extruded material the ternary precipitates outnumber the binary ones, which corresponds well to the calculated phase diagram. We correlated the microstruc-ture to hardness probed by Vickers testing. The largest hardening relates to the end of the 125 ? DSC peak and thus to GP zones, which outperform the hardening induced by the nanometer-sized clusters and the larger intermetallic particles. The complexity of the precipitation sequence in lean Mg-Zn-Ca alloys is discussed.(c) 2022 The Authors. Published by Elsevier Ltd on behalf of Acta Materialia Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Curvilinear structures frequently appear in microscopy imaging as the object of interest. Crystallographic defects, i.e dislocations, are one of the curvilinear structures that have been repeatedly investigated under transmission electron microscopy (TEM) and their 3D structural information is of great importance for understanding the properties of materials. 3D information of dislocations is often obtained by tomography which is a cumbersome process since it is required to acquire many images with different tilt angles and similar imaging conditions. Although, alternative stereoscopy methods lower the number of required images to two, they still require human intervention and shape priors for accurate 3D estimation. We propose a fully automated pipeline for both detection and matching of curvilinear structures in stereo pairs by utilizing deep convolutional neural networks (CNNs) without making any prior assumption on 3D shapes. In this work, we mainly focus on 3D reconstruction of dislocations from stereo pairs of TEM images.

Helium is one of the most inert elements in nature and its solubility in most materials is very low. When introduced by implantation, the energetic helium atoms induce the displacement of a large number of atoms from their lattice position creating excess defects (self-interstitials and vacancies) that may agglomerate to form larger clusters and/or may interact with the implanted atoms as well. In particular, the interaction of vacancies with helium leads to the formation of bubbles that may modify the mechanical and physical properties of materials. This leads to a very active research field in the nuclear domain, where bubbles are responsible for the embrittlement of materials. In covalent materials, helium bubbles can be formed following high fluence implantation as well and the idea to transform bubbles from a liability into an asset has emerged twenty years ago. The most known application is probably the formation of helium and hydrogen disc-like bubbles, the platelets, used to produce silicon-on-insulator wafers. But other potential applications have been demonstrated as well such as proximity gettering of metallic impurities for instance. For all these applications, the control of the bubble formation and evolution is essential. This requires an in-depth understanding of the underlying physical mechanisms. In this work, a multiscale picture of the formation mechanisms of helium bubbles in silicon and their evolution under annealing is derived from the combination of numerical simulations and Electron Energy Loss Spectroscopy (EELS) in the Transmission Electron Microscope (TEM). Using molecular dynamics (MD) and rate equation dynamics calculations, we have identified the atomic scale mechanisms involved in the nucleation and early growth steps of the bubbles and followed their dynamics during experimental timescale. For the smallest length scale, the optimal helium filling in small vacancy clusters was determined (Fig. 1a) [1]. Regarding bubble growth, MD simulations (Fig. 1b) suggest that both Ostwald ripening and migration-coalescence mechanisms are jointly activated during bubble growth. We also discover that an original mechanism, based on the splitting of bubbles, could have a significant contribution. Overall, helium atoms are found to delay growth, proportionally to their concentration. This can be clearly observed at the nanosecond timescale. However, for longer timescales, cluster dynamics calculations also reveal periods of accelerated growth for specific helium concentrations [2]. At larger length scales, the physical properties of the bubbles (helium density, pressure, morphology and size) were investigated experimentally using an original approach based on spatially resolved EELS that we have developed [3]. These experiments allow for an accurate determination of size, aspect ratio and helium density for a large number of single bubbles. These bubbles, 6 to 20 nm in diameter, were synthesized by high fluence helium implantation in silicon, followed by annealing. Very high helium densities, from 60 to 180 He/nm3, were measured in the bubbles depending on the conditions, in stark contrast with previous investigations of helium bubbles in metal with similar sizes. These results were confirmed by atomistic calculations performed for helium bubbles in the diameter range 1 to 13 nm [4]. The structural modifications and, simultaneously, the helium emission from individual bubbles were investigated by spectrum imaging during in situ annealing in the transmission electron microscope (Fig. 1c). We show that helium emission surprisingly takes place at temperatures where bubble migration had hardly started. At higher temperatures, the migration (and coalescence) of voids is clearly revealed. For helium density lower than 150 He.nm-3, the Cerofolini's model taking into account the thermodynamical properties of an ultradense fluid reproduces well the helium emission from the bubbles, leading to an activation energy of 1.8 eV. When bubbles exhibit a higher initial helium density, the Cerofolini's model fails to reproduce the helium emission kinetics. We ascribe this to the fact that helium may be in the solid phase and we propose a model to take into account the properties of the solid [5]. [1] L. Pizzagalli, M.-L. David, J. Dérès, Phys. Stat. Solidi A, 1700263 (2017) [2] L. Pizzagalli, J. Dérès, M.-L. David, T. Jourdan, J. Phys. D : Appl. Phys. 52, P. 455106 (2019) [3] K. Alix, M.-L. David, G. Lucas, D.T.L. Alexander, F. Pailloux, C. Hébert, L. Pizzagalli, Micron 77, p.57 (2015) [4] J. Dérès, M.-L. David, K. Alix, D.T.L. Alexander, C. Hébert, L. Pizzagalli, Phys. Rev. B 96, p. 014110 (2017) [5] K. Alix, M.-L. David, J. Dérès, C. Hébert, L. Pizzagalli, Phys. Rev. B 97, p. 104012 (2018) Figure 1