X-ray Linear Dichroic Tomography of Crystallographic and Topological Defects

The functionality of materials is determined by their composition and microstructure, that is, the distribution and orientation of crystalline grains, grain boundaries and the defects within them. The characterisation of the material's microstructure is therefore critical for materials applications such as catalysis, energy storage and buildings. Until now, characterization techniques that map the distribution of grains, their orientation, and the presence of defects have either been limited to surface investigations, to spatial resolutions of a few hundred nanometres, or to systems of thickness around one hundred nanometres, thus requiring destructive sample preparation for measurements and preventing the study of system-representative volumes or the investigation of materials under operational conditions. Here, we present X-ray linear dichroic orientation tomography, a quantitative, non-invasive technique that allows for an intra- and inter-granular characterisation of extended polycrystalline and amorphous materials in three dimensions (3D). We present the detailed characterisation of a polycrystalline sample of vanadium pentoxide (V2O5), a key catalyst in the production of sulfuric acid. In addition to determining the nanoscale composition, we map the crystal orientation throughout the polycrystalline sample with 73 nm spatial resolution. We identify grains, as well as twist, tilt, and twin grain boundaries. We further observe the creation and annihilation of topological defects promoted by the presence of volume crystallographic defects in 3D. Our method's non-destructive and spectroscopic nature opens the door to in-operando combined chemical and microstructural investigations of functional materials, including energy and mechanical materials in existing industries, as well as quantum materials for future technologies

Bayesian data analysis for Gaussian process tomography

Bayesian inference is used in many scientific areas as a conceptually well-founded data analysis framework. In this paper, we give a brief introduction to Bayesian probability theory and its application to the tomography problem in fusion research by means of a Gaussian process prior. This Gaussian process tomography (GPT) method is used for reconstruction of the local soft X-ray (SXR) emissivity in WEST and EAST based on line-integrated data. By modeling the SXR emissivity field in a poloidal cross-section as a Gaussian process, Bayesian SXR tomography can be carried out in a robust and extremely fast way. Owing to the short execution time of the algorithm, GPT is an important candidate for providing real-time feedback information on impurity transport and for fast MHD control. In addition, the Bayesian formulism allows for uncertainty analysis of the inferred emissivity

Deep Learning for Inverse Problems (hybrid meeting)

Machine learning and in particular deep learning offer several data-driven methods to amend the typical shortcomings of purely analytical approaches. The mathematical research on these combined models is presently exploding on the experimental side but still lacking on the theoretical point of view. This workshop addresses the challenge of developing a solid mathematical theory for analyzing deep neural networks for inverse problems

An Extended Field-Based Method for Noise Removal From Electron Tomographic Reconstructions

Molecular structure determination is important for understanding functionalities and dynamics of macromolecules, such as proteins and nucleic acids. Cryo-electron tomography (ET) is a technique that can be used to determine the structures of individual macromolecules, thus providing the snapshots of their native conformations. Such 3-D reconstructions encounter several types of imperfections due to missing, corrupted, and low-contrast data. In this paper, we demonstrate that extending the reconstruction space, which increases the dimensionality of the linear system being solved during reconstruction, facilitates the separation of signal and noise. A considerable amount of the noise associated with collected projection data arises independently from the geometric constraint of image formation, whereas the solution to the reconstruction problem must satisfy such geometric constraints. Increasing the dimensionality thereby allows for a redistribution of such noise within the extended reconstruction space, while the geometrically constrained approximate solution stays in an effectively lower dimensional subspace. Employing various tomographic reconstruction methods with a regularization capability we performed extensive simulation and testing and observed that enhanced dimensionality significantly improves the accuracy of the reconstruction. Our results were validated with reconstructions of colloidal silica nanoparticles as well as P. falciparum erythrocyte membrane protein 1. Although the proposed method is used in the context of Cryo-ET, the method is general and can be extended to a variety of other tomographic modalities