Theses

This page collects my Bachelor thesis and Master thesis. Both works are older and should be read mainly as documentation of my studies and early technical work, not as current scientific or engineering guidance.

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Master Thesis

Site Preference of Aluminium and Gallium in Mixed-Doped LLZO Garnet Solid-Solution Series

Original German title:
Die Gitterplatzpräferenz von Aluminium und Gallium in gemischt dotierten Li₇La₃Zr₂O₁₂ Granat-(LLZO) Mischkristallreihen

Degree programme: Materials Science
University: Paris Lodron University Salzburg
Date: December 2014

Short English abstract

This thesis investigated mixed aluminium- and gallium-doped cubic LLZO garnets with the nominal composition Li_7-3(x+y)Ga_xAl_yLa₃Zr₂O₁₂. The work focused on the question of where Al and Ga ions are located in the garnet structure and whether different site preferences could explain conductivity differences reported in the literature.

Mixed solid-solution series were synthesized and characterized using X-ray powder diffraction, scanning electron microscopy and solid-state MAS NMR. The thesis reports that cubic mixed-doped LLZO could be prepared for several Al/Ga ratios and that gallium showed higher solubility than aluminium in the investigated compositions.

A central result was obtained from high-field NMR measurements at 21 Tesla. Resonances that had previously appeared as a single signal in the literature could be separated into two distinct contributions. These signals were assigned to fourfold coordinated crystallographic positions, 24d and 96h. The relative areas of the resonances followed the occupation concentration and indicated that gallium behaves similarly to aluminium with respect to these positions.

Because Ga-containing LLZO samples had often been discussed in connection with higher ionic conductivity and different site preferences, this thesis questioned whether the site-preference explanation alone is sufficient. A later investigation using ⁷Li MAS NMR was suggested to clarify the relationship between site preference and lithium-ion diffusivity.

Methods

• Solid-state synthesis of mixed Al/Ga-doped LLZO compositions.
• X-ray powder diffraction for phase identification and lattice-parameter trends.
• Scanning electron microscopy for selected sample series.
• ²⁷Al, ⁷¹Ga and ⁶Li MAS NMR for selected compositions.

Important result in plain language

The work suggests that Al and Ga do not behave as fundamentally different as a simple explanation of conductivity differences would require. Both dopants show comparable occupation behavior in the investigated LLZO garnet structure. Therefore, the higher conductivity of Ga-containing samples is probably not explained by site preference alone.

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Bachelor Thesis

Automated Hardness Testing Using Image Processing and Computer Vision

Original German title:
Automatisierte Härteprüfung mit Methoden der Bildverarbeitung und der Computer Vision — Härteprüfung nach Brinell

University: Paris Lodron University Salzburg
Date: April / May 2011

Short English abstract

This Bachelor thesis developed and tested software methods for automatically detecting Brinell hardness-test impressions in digital microscope images. In Brinell testing, a hard spherical indenter is pressed into a material surface. The resulting circular or slightly elliptical impression is measured, and the hardness value is calculated from the applied force and the impression surface.

The practical goal was to find the position and radius of circular or nearly circular impressions in difficult images of metallic surfaces. The images could contain poor contrast, grinding marks, background structures, concentric rings, noise, uneven illumination or distorted impression shapes.

Methods

• MATLAB-based image-processing implementations.
• Image preprocessing with histogram equalization and CLAHE.
• Removal or reduction of grinding marks using Fourier-transform-based approaches.
• Canny edge detection and Sobel-gradient concepts.
• Circle search using template matching.
• Circle search using a Daugman-inspired integro-differential operator.
• Bresenham / midpoint-circle logic for efficient circular masks.

Result in plain language

Both main approaches were able to find Brinell impressions in many images. The largest practical problem was not the circle-search method itself, but robust preprocessing. Some preprocessing steps improved one image while making another image worse. In particular, there was no stable universal parameter choice for contrast enhancement and the Canny edge detector.

In the comparison of the two implemented approaches, the Daugman-inspired integro-differential operator performed better overall. Template matching often found the approximate impression region, but could produce larger radius and center-position errors. The Daugman-based method was more accurate in many cases, but when it failed, it tended to produce complete outliers. A suggested improvement was to test several strong circle candidates and then re-rank them using additional plausibility checks based on segmentation and edge information.

Old but still interesting idea

From today’s perspective, the topic would probably be solved very differently, for example with modern OpenCV methods, robust Hough-transform variants, classical machine vision pipelines or even learned segmentation models. Still, the thesis documents a useful early attempt to solve a real industrial measurement problem using deterministic image-processing algorithms.

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