Advanced computational tools for EELS data reduction and clustering, quantitative analysis and 3D reconstructions

Abstract

This thesis has been primarily dedicated to the exploration and implementation of new computational analysis tools and techniques for the characterisation of nanomaterials and devices via transmission electron microscopy (TEM). In particular, the focus is set on the fields of electron energy loss spectroscopy (EELS) and electron tomography (ET). In the context of this PhD, EELS is used for the quantitative and qualitative analysis of elemental distributions at the nanoscale for several different materials, mainly transition metal and rare earth oxides. It is also used for the investigation of the distribution of elemental oxidation states at the nanoscale through the analysis of the so-called energy-loss near-edge structures (ELNES) of core-loss edges. The ever-growing size and complexity of the acquired spectral datasets, as well as a paradigmatic change towards the acquisition of larger but noisier spectral datasets, is the driving force behind the continuous push by the TEM community towards the implementation of new analysis techniques from the field of machine learning into the standard EELS characterization pipelines. The linear matrix factorization algorithms of principal component analysis (PCA) and non-negative matrix factorization (NMF) are among the first algorithms implemented for EELS analysis. Recently, several clustering analysis algorithms, such as K-means and hierarchical agglomerative clustering, have been used for the spectral segmentation of EELS spectrum images (SI) as well. In this thesis the combined use of a non-linear dimensionality reduction algorithm called uniform manifold approximation and projection (UMAP) for dimension reduction, and a clustering algorithm called hierarchical density-based spatial clustering of applications with noise (HDBSCAN), was explored as a viable solution towards a fully-data driven methodology for the spectral segmentation of EELS SI. Furthermore, a systematic revision of these new DRM and clustering methods (UMAP and HDBSCAN), the already stablished ones (PCA, NMF, K-means, etc.), and some of the possible combinations between them, was conducted. This revision includes several qualitative and quantitative performance analysis experiments, which are carried out for a series of specially designed synthetic datasets. The

acquired experience with these techniques is later applied to characterize a wide variety of materials. Also, the combination of clustering and non-linear least-squares (NLLS) fitting has also been proven as a promising solution to improve the stability of the latter. This methodology was addressed as part of work done during this PhD to provide a ready-to-go software solution for all these machine learning methodologies applied to EELS and ELNES analysis, leading to the development of a complete and independent software solution called WhatEELS. This modular tool provides the resources required to quantitatively resolve complex problems involving ELNES analysis. A clear example of its powerful capabilities is showcased through the characterization of a set of Pr-Gd doped CeO2 mesoporous materials. In this series of experiments, the local changes in the Ce oxidation state and the localized dopant segregation were successfully resolved. The field of ET provides the materials scientist with one of the most versatile toolsets for the characterization of materials at the nanoscale, as it allows the reconstruction of 3D volumes from a limited set of 2D projections acquired. In this PhD thesis, the work is mainly focused on the implementation of advanced algorithms for the ET reconstruction of nanomaterials in Python programming language. The attention is centred on the TVAL3 algorithm, a solver for the total variation minimization (TVM) problem with its theoretical foundations in the mathematical field of compressed sensing. This methodology based on the TVAL3 algorithm is used for the experimental characterisation of the 3D morphology and chemical composition of a wide variety of different nanomaterials, such as the 3D resolution of the dopant segregation in the CeO2 mesoporous material.

Esta tesis se centra, principalmente, en la exploración e implementación de nuevas herramientas y técnicas de análisis computacional para la caracterización de nanomateriales mediante espectroscopía de pérdida de energía de los electrones (EELS) y tomografía electrónica (TE). En el contexto de este doctorado, el EELS se utiliza para el análisis cuantitativo y cualitativo de distribuciones elementales a la nanoescala, principalmente para óxidos de metales de transición y de tierras raras. También se utiliza para la investigación de la distribución de estados de oxidación mediante el análisis de la estructura fina (ELNES). Para hacer dichos análisis, en esta tesis se demuestra que el uso combinado de un algoritmo de reducción de dimensionalidad (DRM) no lineal, UMAP, y un algoritmo jerárquico de agrupamiento (‘clustering’), HDBSCAN, es una solución viable hacia una metodología totalmente basada en los datos para la segmentación de imágenes de espectros de EELS. Además, se realizó una revisión sistemática de estos nuevos métodos de DRM y ‘clustering’ (UMAP y HDBSCAN), de los ya establecidos (PCA, NMF, K-means, etc.), y de algunas de sus posibles combinaciones. El uso combinado de ‘clustering’ y del ajuste de mínimos cuadrados no lineales (NLLS) se muestra también como una solución prometedora para el análisis de ELNES. Dicha metodología fue implementada como parte de una nueva herramienta de software llamada WhatEELS. Esta herramienta modular y de acceso gratuito proporciona los recursos necesarios para resolver cuantitativamente problemas complejos que involucran el análisis ELNES. Su potencial fue demostrado mediante el análisis de la segregación de dopantes y del cambio localizado del estado de oxidación catiónico para una serie de muestras de Ceria mesoporosa. Finalmente, parte de esta tesis también está dedicada a la implementación de algoritmos para el muestreo disperso en TE. En concreto, el algoritmo TVAL3 fue traducido al lenguaje de programación Python y utilizado para varios experimentos, incluida la resolución de la segregación de dopantes en 3D para los materiales mesoporosos de ceria ya mencionados.