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In the European Union, nanomaterials are regulated through different pieces of sectoral legislation. This legislation often requires risk assessments and thus reliable characterization data, for which regulatory guidance generally recommend electron microscopy. The guidance provides best practices for measurements but lacks requirements on how many particles to measure. Using transmission electron microscopy data of nanomaterials, a strategy based on repeated subsampling is proposed to establish, for different particle size and shape measurands, mathematical relationships between particle count and precision, and subsequently to determine the minimum particle count. Our results confirm that the minimum particle count generally depends on the width of the size and shape distributions and that the median of the distribution can be determined with the highest precision compared to other percentiles. Upon combining the precision uncertainty related to particle number with uncertainties from other sources, such as sample preparation, calibration and trueness, we reach an optimal particle count above which additional particle measurements only yield negligible improvements to the combined measurement uncertainty. Our findings offer an experimental approach for determining the minimum particle count to measure particle size and shape by electron microscopy. It enables efficient analyses and facilitates compliance with legislation addressing nanomaterials across various application domains.

In this work, we study the impact of order and disorder on the phase formation in (InxGa1−x )2O3 by means of transmission electron microscopy (TEM) and in-situ TEM. The studied thin film samples are grown epitaxially on crystalline substrates by pulsed laser deposition, molecular beam epitaxy and metalorganic vapor phase epitaxy, or deposited amorphously to be crystallized in-situ. Based on the experimental findings and ground-state energies of the various phases from cluster expansion, a phase diagram is developed. The last part of the thesis focuses on a computational study of high-angle annular dark field scanning TEM (HAADF-STEM) contrast in ordered materials. We find strong ordering on the cation sublattices of (InxGa1−x )2O3 in the case of epitaxial growth, which is energetically driven by the tendency of In and Ga to each assume their preferred coordination environment. The energetic stability of the ordered multi-coordinated monoclinic (β) and hexagonal (h) lattices requires a modification of the general assumption of ideal mixing in solid solutions to realistically estimate the configurational entropy. Based on these considerations, we construct the temperature dependent phase diagram, which was up to now not available in literature. While very narrow thermodynamically stable ranges exist for each phase, wide composition ranges of metastable compounds are predicted, which can be achieved at temperatures that are typical for epitaxy: the monoclinic phase is metastable in the composition range x ≤ 0.5, the hexagonal phase for 0.55 ≤ x ≤ 0.7, and the cubic bixbyite phase for x ≥ 0.91. The predictions of the model are in excellent agreement with other experimental findings in literature. When crystallizing (InxGa1−x )2O3 from the amorphous phase, the solubility of Ga in the bixbyite phase extends to x ≥ 0.33 and the miscibility gap between 0.7 < x < 0.91 for thermodynamic equilibrium is closed. This is explained by the fact that a high configurational entropy thermodynamically favors the bixbyite lattice, in which the cations are all octahedrally coordinated compared to the phases with multiple coordination. The high amount of configurational entropy frozen in the amorphous phase is kinetically stabilized below a critical temperature. In the compositional range x ≤ 0.22, we find in addition the formation of spinel γ-(InxGa1−x )2O3. A model is developed that describes the γ-phase as a disordered β-phase and the detailed atomic mechanisms that mediate the γ → β phase transition observed at higher annealing temperatures, are described. The last chapter shows that sublattice ordering in two-compound structures with relatively high and low Z components, such as β- and h-(InxGa1−x )2O3, strongly affects compositional quantification by Z-contrast. Ordering reduces the HAADF-STEM intensity compared to that found for disordered lattices of the same composition. This is a consequence of the 2s Bloch state excitation for an electron probe traveling on an atom column with high atomic number Z. Similar to the 1s channeling oscillation, the 2s excitation creates an oscillation in the electron wave function due to beating with the unbound Bloch states, which influences the scattering to the HAADF detector. This effect on the other hand can be used to measure the order parameter in solid solutions with known composition.

In this work, we emphasize the important contribution of the 2s Bloch wave state to the properties of a STEM electron probe propagating on an atomic column. For a strong enough column potential, the confinement of the 2s state leads to a long-period oscillation of the electron wave function, which is reflected in the resulting STEM-HAADF intensity. We show how this influences STEM composition quantification even at large thicknesses. We found additionally that the excitation of the 2s state affects the intensity of alloys where long-range order phenomena are present, which in turn provides a way to probe the degree of order in alloys.

In this work, we show the heteroepitaxial growth of single-crystalline bixbyite (In\\(_{1-x}\\)Ga\\(_x\\))\\(_2\\)O\\(_3\\) films on (111)-oriented yttria-stabilized zirconia substrates using plasma-assisted molecular beam epitaxy under various growth conditions. A pure In\\(_2\\)O\\(_3\\) buffer layer between the substrate and (In\\(_{1-x}\\)Ga\\(_x\\))\\(_2\\)O\\(_3\\) alloy is shown to result in smoother film surfaces and significantly improved crystallinity. Symmetric out-of-plane 2\\(\\theta - \\omega\\) x-ray diffraction scans show a single (111) crystal orientation and transmission electron microscopy confirms the single-crystallinity up to \\(x = 0.18\\) and only slight film quality deterioration with increasing Ga content. Partially relaxed layers are demonstrated via reciprocal space mapping with lattice parameters fitting well to Vegard's law. However, the Ga cations are not evenly distributed within the films containing nominally \\(x > 0.11\\): inclusions with high Ga density up to \\(x = 0.50\\) are observed within a \"matrix\" with \\(x \\approx 0.08\\). The cubic bixbyite phase is preserved, in both the \"matrix\" and the inclusions. Moreover, for \\(x \\geq 0.11\\), both the Raman phonon lines as well as the optical absorption onset remain nearly constant. Hard x-ray photoelectron spectroscopy measurements also indicate a widening of the band gap and exhibit similar saturation of the Ga 2p core level position for high Ga contents. This saturation behavior of the spectroscopic properties further supports the limited Ga incorporation into the \"matrix\" of the film.

Ga\\(_2\\)O\\(_3\\) and its polymorphs are attracting increasing attention. The rich structural space of polymorphic oxide systems such as Ga\\(_2\\)O\\(_3\\) offers potential for electronic structure engineering, which is of particular interest for a range of applications, such as power electronics. \\(\\gamma\\)-Ga\\(_2\\)O\\(_3\\) presents a particular challenge across synthesis, characterisation, and theory due to its inherent disorder and resulting complex structure -- electronic structure relationship. Here, density functional theory is used in combination with a machine learning approach to screen nearly one million potential structures, thereby developing a robust atomistic model of the \\(\\gamma\\)-phase. Theoretical results are compared with surface and bulk sensitive soft and hard X-ray photoelectron spectroscopy, X-ray absorption spectroscopy, spectroscopic ellipsometry, and photoluminescence excitation spectroscopy experiments representative of the occupied and unoccupied states of \\(\\gamma\\)-Ga\\(_2\\)O\\(_3\\). The first onset of strong absorption at room temperature is found at 5.1 eV from spectroscopic ellipsometry, which agrees well with the excitation maximum at 5.17 eV obtained by PLE spectroscopy, where the latter shifts to 5.33 eV at 5 K. This work presents a leap forward in the treatment of complex, disordered oxides and is a crucial step towards exploring how their electronic structure can be understood in terms of local coordination and overall structure.

Neoadjuvant ipilimumab and nivolumab induces high pathologic response rates (pRRs) in clinical stage III nodal melanoma, and pathologic response is strongly associated with prolonged relapse-free survival (RFS). The PRADO extension cohort of the OpACIN-neo trial ( NCT02977052 ) addressed the feasibility and effect on clinical outcome of using pathologic response after neoadjuvant ipilimumab and nivolumab as a criterion for further treatment personalization. In total, 99 patients with clinical stage IIIb–d nodal melanoma were included and treated with 6 weeks of neoadjuvant ipilimumab 1 mg kg −1 and nivolumab 3 mg kg −1 . In patients achieving major pathologic response (MPR, ≤10% viable tumor) in their index lymph node (ILN, the largest lymph node metastasis at baseline), therapeutic lymph node dissection (TLND) and adjuvant therapy were omitted. Patients with pathologic partial response (pPR; >10 to ≤50% viable tumor) underwent TLND only, whereas patients with pathologic non-response (pNR; >50% viable tumor) underwent TLND and adjuvant systemic therapy ± synchronous radiotherapy. Primary objectives were confirmation of pRR (ILN, at week 6) of the winner neoadjuvant combination scheme identified in OpACIN-neo; to investigate whether TLND can be safely omitted in patients achieving MPR; and to investigate whether RFS at 24 months can be improved for patients achieving pNR. ILN resection and ILN-response-tailored treatment were feasible. The pRR was 72%, including 61% MPR. Grade 3–4 toxicity within the first 12 weeks was observed in 22 (22%) patients. TLND was omitted in 59 of 60 patients with MPR, resulting in significantly lower surgical morbidity and better quality of life. The 24-month relapse-free survival and distant metastasis-free survival rates were 93% and 98% in patients with MPR, 64% and 64% in patients with pPR, and 71% and 76% in patients with pNR, respectively. These findings provide a strong rationale for randomized clinical trials testing response-directed treatment personalization after neoadjuvant ipilimumab and nivolumab. Results from the PRADO extension cohort of the OpACIN-neo trial show that pathologic response rate to neoadjuvant ipilimumab and nivolumab can be used as a criterion for personalization of further treatment in stage III nodal melanoma, with the potential to reduce treatment morbidity and increase patient quality of life.