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Item Open Access Extracting thermodynamic information from local composition fluctuations in solids : extended theory and its application to simulated and experimental atom probe data(2024) Zheng, Jianshu; Schmitz, Guido (Prof. Dr. Dr. h.c.)In case of liquids, thermodynamic fluctuation theory has been applied for decades to obtain direct thermodynamic information (e.g. miscibility gap, mixing/demixing tendencies, critical solution temperature) from local composition fluctuations. Recently, this theory has been extended to solids by introducing an additional elastic work term between the evaluated sub-system and the entire system, which does not arise in liquids. This extended theory has been verified via atomistic simulations in an exemplary Cu-Ni embedded-atom system using Monte Carlo simulations at a fixed temperature over the entire composition range. Composition fluctuations in the system that are represented by the relative variance of the composition histogram are tracked in various-sized subvolumes over time, revealing a systematic dependence on the size of the evaluation volume due to interface effects. Nonetheless, these surface effects can be excluded by extrapolation to an infinitely large subvolume, leading to perfect agreement with the prediction by the extended theory. Thus, the recovery of the Gibbs free energy of mixing from evaluation of the fluctuations is possible also in the case of solids. Atom Probe Tomography (APT) delivers combined high-resolution chemical and sub nanometric three-dimensional (3D) spatial information, and is therefore the perfect technique to determine local composition fluctuations by using spatial frequency distribution analysis in practical applications. In this work, the applicability of the extended theory is tested on the Cu-Ni alloy and ionic CuO systems via frequency distribution analysis on simulated and experimental atom probe data, and eventually compared to available phase diagram data, thereby proving the validity of extracting the Gibbs free energy from local composition fluctuations in solids. In the first part of this work, the spatial frequency distribution analysis is applied to simulated crystals of long-range ordered L12 and monoclinic structures numerically modeled disregarding thermodynamic interaction between atoms. The relative variance displays an evaluation size dependence, but goes to zero (i.e. no composition fluctuations) if extrapolated to sufficiently large evaluation size. This result meets the expectation as no composition fluctuations should be found in perfectly ordered materials. In the second part, this approach is applied to simulated alloys including thermodynamic interactions. Cu-Ni alloys of various compositions are firstly equilibrated using a Monte Carlo simulation with an embedded-atom potential. Afterwards, the alloys are numerically field-evaporated by the evaporation simulation package TAPSim and the 3D coordinates of the field-evaporated sample are recovered through the usual reconstruction algorithm. Throughout this process, two practical considerations related to the atom probe technique have been effectively addressed: i) The newly developed model tackles the challenges associated with the limited detection efficiency and allows the reconstruction of the relative variance for the bulk system from limited atom probe data scaled by detection efficiency; ii) An additional correction term which is proportional to the evaluation size and magnitude of composition inhomogeneity is introduced. It enables the separation of thermodynamic fluctuations from artificial composition variations inherent in the experimental method based on their different size dependence, so that the extrapolation still recovers the intrinsic thermodynamic composition fluctuations. In the third part, this approach is finally applied to experimental atom probe data. The Cu-Ni alloys are prepared by induction melting of pure Cu and Ni and CuO thin films are prepared via ion beam sputtering. After sufficient equilibration by heat treatment, Cu-Ni and CuO specimens for the APT measurement are fabricated via focused ion beam cutting. By experimentally conducting the same approach as developed theoretically, local composition fluctuations are obtained for both Cu-Ni and CuO systems. After the elastic work term correction, the CALPHAD-style parametrization of the Gibbs free energy is obtained by linking it to the measured local composition fluctuations. In this way, the Cu-Ni miscibility gap is successfully reconstructed from data measured at elevated temperature (800 K), and the resulting phase diagram is in agreement with the CALPHAD results in literature. The frequency distribution analysis of the reconstructed CuO tends to approach the binomial distribution (i.e. behavior of random alloys), since field evaporation of molecules (e.g. CuO, Cu2O) but not only single ions destroys the long-range order structure and deteriorates the resolution in the reconstruction. This effect indicates the partial limitation of this method on ionic compounds. In summary, the present work has systematically extended and proven the application of the composition fluctuation theory to metallic alloys, and makes it possible to directly access thermodynamic information from local composition fluctuations. APT is demonstrated as a new technique to extract direct thermodynamic information, and a general route from the APT measurement to the Gibbs free energy is presented. Given that the composition fluctuation is a local property and only a substantially short diffusion length for equilibration is required, this represents an efficient methodology especially for systems where slow diffusion hinders the establishment of large scale thermodynamic equilibrium. APT, as a sub-nanometric resolution technique, promises to extract more accurate thermodynamic information in a wider temperature composition range. Besides, this study advances our understanding of the size dependence in the traditional frequency distribution analysis. It is pointed out that potential misinterpretation could happen and is presented in literature, if a sample evaluation size in the frequency distribution analysis is arbitrarily chosen. Only the bulk relative variance obtained via extrapolation to infinitely large sub-system is thermodynamically meaningful.Item Open Access Atom probe study on CuNi thin films : miscibility gap and grain boundary segregation(2023) Duran, Rüya; Schmitz, Guido (Prof. Dr. Dr. h. c.)In dieser Arbeit wurde die Lage der Mischungslücke, und die Korngrenzsegregation im Legierungssystem, Kupfer-Nickel, per Atomsondentomographie (APT) analysiert. Zur Untersuchung der Mischungslücke eines binären Systems mit langsamer Diffusion wurde ein neues Verfahren verwendet. Multilagen aus Cu- und Ni- Dünnschichten wurden mittels Ionenstrahlbeschichtung (IBS) auf Wolframpfosten beschichtet und durch fokussierte Ionenstrahlung (FIB) geformt. Bei drei unterschiedlichen Temperaturen, zwischen 573 und 673 K, wurden isotherme Auslagerungssequenzen an einem Ultrahochvakuumofen (UHV) durchgeführt und der Mischungsprozess analysiert. Ein Modell des Diffusionsprozesses wurde mittels mathematischer Überlegungen erstellt. Durch das Fitten der experimentellen Kompositionsprofile mittels dieses Modells konnten die Gleichgewichtskonzentrationen der Schichten auch mit relativ kurzen Auslagerungszeiten ermittelt werden. Darüber hinaus konnten aus den diffusionskontrollierten Zeit- und Temperaturdaten physikalische Eigenschaften wie der effektive Diffusionskoeffizient (Gitterdiffusion einschließlich Defektdiffusion) bestimmt werden. Dieser betrug Deff = 1.86 ∙ 10-10 m2/s ∙ exp(-164 kJ mol-1/RT). Während dem Vermischen wurde die Änderung der multilagigen Mikrostruktur bis zur vollständigen Mischung bei 623 und 673 K beobachtet, wobei Korngrenzen als schneller Diffusionsweg eine wichtige Rolle spielen. Bei 573 K wurde Nichtmischbarkeit experimentell deutlich nachgewiesen, wobei die Phasengrenzen bei cNi=26 at.% und cNi=66 at.% liegen. Mit diesen Phasengrenzen wurde die Mischungslücke über eine Redlich-Kister-Parametrisierung der Gibbs‘schen freien Energie über den gesamten Konzentrationsbereich rekonstruiert. Hierin wurde für die kritische Temperatur, TC, 608 K bei einer Konzentration von 45 at% Ni gefunden. Im zweiten Teil wurde die Korngrenzsegregation durch die FIB/tEBSD- (Transmissions-Elektronen-Rückstreubeugung) Technik, in Korrelation zu APT-Messung charakterisiert. Vier Legierungen mit einem Ni-Anteil zwischen 25 und 85 at.% wurden auf Wolframpfosten per IBS beschichtet, und bei 700 K für 24 h wärmebehandelt. Die Segregation von Cu in die Korngrenzen wurde beobachtet. Durch die Verwendung eines theoretischen Models wurde die Exzess-Kurve über den gesamten Konzentrationsbereich, und die Korngrenz-Formationsenergie auf Basis der experimentellen Daten berechnet. Die tEBSD-Analyse während der FIB-Präparation erlaubt die Identifikation der Körner und deren Orientierung. Ein neues Verfahren wurde entwickelt, um mithilfe der Orientierung benachbarter Körner, Berechnungen zur Ermittlung der Korngrenzorientierung durchzuführen und somit die Orientierung natürlicher Korngrenzen zu bestimmen. Mit diesem Verfahren konnte der zeitliche Aufwand dieser anspruchsvollen Auswertung (verglichen zur herkömmlichen Methode mittels TEM-Untersuchung) stark reduziert werden, so dass eine quantitative Analyse vieler Korngrenzen möglich wurde. Aus den einzelnen Korngrenzorientierungen wurde die Korngrenzrotation, und die jeweiligen Anteile an Kippung und Drehung berechnet. Eine Abhängigkeit der Feststoffsegregation vom Kipp- und Drehanteil der Korngrenze wurde beobachtet, die am kleinsten für die reine Kipp- und Drehrotation war. Die ermittelten Segregationsweiten sind signifikant größer als die strukturellen Korngrenzweiten und bewegen sich zwischen 12 und 85 Å. Dieses Verhalten wurde durch eine künstliche Verbreiterung der Korngrenze erklärt, die durch eine Flugbahnabweichung der Korngrenzatome während der Verdampfung verursacht wurde. Eine Korngrenzweite von w0 = (10.1 ± 1.5) Å wurde für eine unverfälschte Korngrenze gefunden.Item Open Access Li-ion transport and optical modulation in thin-film battery electrodes(2021) Joshi, Yug; Schmitz, Guido (Prof. Dr.)The optical modulation of lithium manganese oxide (LiMn2O4, LMO) and lithium titanate (Li4Ti5O12, LTO) due to Li-ion insertion is quantitatively characterized. Ion beam sputtering is used to deposit the layers of respective materials on top of already sputtered platinum which acts as the current collector/reflector. The structure and morphology of the layers were probed using X-ray diffraction, scanning electron microscopy, and transmission electron microscopy. Well-defined intercalation states were prepared electrochemically and investigated by optical spectrometry in reflectance geometry. The obtained dispersion curves were then modeled using the Clausius-Mossotti dispersion equation to obtain the complex refractive index as a function of wavelength at various intercalation states. A continuous change in the effective resonant wavelength with lithium intercalation was observed. This was found to be consistent with the evolution of the band structure upon ion insertion. In LMO, two significant resonances were identified in the visible region of the spectrum, which shifts with the degree of intercalation. By associating this shift with the evolving band structure, the resonances were attributed to electronic transitions between the O-2p band and the split Mn-d band. In the case of LTO, the mechanism and effect of the phase transformation (from spinel structured Li4Ti5O12 to rock-salt type Li7Ti5O12 upon lithium insertion) on the optical response is studied. The same model (using Clausius-Mossotti dispersion) unveils the presence of one and two major resonant wavelengths/frequencies in the case of Li4Ti5O12 and Li7Ti5O12, respectively, in the UV/visible/NIR region of light. The single resonance in the case of Li4Ti5O12 is allocated to a transition from O-2p to Ti-t2g i.e., across the band-gap. Whereas for the Li7Ti5O12 phase, the two resonances were characterized for the electronic transitions from O-2p to empty Ti-t2g and from filled Ti t2g to empty Ti-eg. The concentration dependence of the derived dielectric constants indicates a fast lithium-ion transport through the grain boundaries. This helps in nucleating the grain boundaries with a conductive lithium-rich phase. This increases the electronic conductivity of the thin films in the initial stages of intercalation and explains the debated understanding of the fast dis-/charge capability of Li4Ti5O12 electrodes on a nanoscale. On a micrometer scale, the diffusion is controlled by the bulk diffusion. To investigate the kinetics of lithium migration at this length scale, an innovative technique is developed that employs optical microscopy in a constrained region of the sputtered thin-film sample. At this constrained region, lithium is blocked from entering the LTO structure directly from the electrolyte. Therefore, the technique enables the observation of the lateral transport of lithium through the electrode due to the optical contrast generated in this material during the ion insertion and subsequent phase transformation. The poor diffusivity of lithium in its end phases (or Li4Ti5O12 and Li7Ti5O12) is confirmed but, this poor diffusivity challenges the notion of high dis-/charging performance reported in this material. Surprisingly, the movement of the phase boundary is hindered which has been refuted in prior reports. However, this hindrance is confirmed here by the slow, linear growth kinetics of the Li-rich phase in the initial stages of the lithium transport. Interestingly, the partial solubility of lithium in the spinel structured Li4+δTi5O12 phase increases the diffusivity of lithium in this spinel phase drastically. This drastic increase in diffusivity along with the reduction in the size of the electrode seems to be compensating for the kinetic hindrance experienced by the phase boundary.Item Open Access Basics of process physics and joint formation in resistance projection welding processes(2020) Wehle, Michael; Schmitz, Guido (Prof. Dr. Dr. h.c.)Diese Arbeit leistet einen Beitrag zur Verbesserung des Prozessverständnisses von Widerstands-Buckelschweißverfahren. Es werden die bekannten grundlegenden physikalischen Prozessgrößen von Widerstandsschweißprozessen auf diese Verfahren übertragen und deren Relevanz für den Prozess mittels analytischer und numerischer Methoden an Hand eines Prozessbeispiels abgeschätzt. Die Arbeit liefert somit ein physikalisches Prozessmodell, welches zum einen das Prozessverständnis vertieft zum anderen auch eine Grundlage für die Verbesserung der numerischen Finite Elemente Simulation bildet. Einen weiteren Fortschritt bringt die vorgelegte Arbeit durch die Untersuchungen zur Verbindungsbildung von Metallen (in diesem Fall rostfreie Stähle) im semi- festen Zustand mit sich. Durch die systematische Untersuchung der Einflussgrößen Temperatur, Druck und Scherung in der Grenzfläche zwischen zwei Probekörpern wird ein Kriterium erarbeitet, welches eine Abschätzung des Schweißergebnisses ermöglicht. Somit wird einerseits ein vertieftes allgemeines Verständnis des Festkörperschweißens sowie ein spezifisch für das Buckelschweißen gültige Verständnis aufgebaut. Eine Kombination des Verbindungsbildungskriteriums mit einem numerischen Modell zur Simulation des Gesamtprozesses ermöglicht eine Vorbewertung von Fügeaufgaben. Hierzu werden erste Ansätze präsentiert, um die Anwendbarkeit der Vorarbeiten in der numerischen Simulation aufzuzeigen. Durch die Ergebnisse dieser Arbeit wird somit eine Reduktion des experimentellen Aufwandes bei der Prozessentwicklung des untersuchten Verfahrens erreicht und die Vorbewertung künftiger Fügeaufgaben erleichtert. Des Weiteren lassen sich, durch die Gestaltung der durchgeführten Versuche, allgemeingültige Schlüsse ziehen, welche auch für artverwandte Widerstandsschweißverfahren einen Mehrwert darstellen.Item Open Access Reactive wetting of tin-based miniaturised solder joints(2022) Griffiths, Samuel J.; Schmitz, Guido (Prof. Dr.)Item Open Access Analysis of nickel- and iron-based superalloys on smallest length scales(2021) Lawitzki, Robert; Schmitz, Guido (Prof. Dr. Dr. h.c.)In this work, new experimental methods and techniques for the analysis of the microscopic and the micromechanical material behavior of nickel- and iron-based superalloys are developed with the emphasis on the material characteristics and processes at smallest length scales.Item Open Access Growth of oxide materials with Ruddlesden-Popper- and garnet-type structures via the optical float zone method: investigations of scintillation, optical, and magnetic properties, and post-growth modifications of single crystals via topochemical routes(2025) Yilmaz, Hasan; Clemens, Oliver (Prof. Dr.)With the continuous progress in materials science, the global market demand for high-performance functional materials, especially those with customized optical and magnetic properties, has increased significantly due to their critical role in next-generation technologies such as photonic devices, data storage systems, quantum computing, and biomedical applications. With this motivation, this dissertation is focused on the growth of high-quality oxide single crystals with Ruddlesden-Popper (RP) and garnet-type structures using the optical floating zone (OFZ) method and the detailed investigation of their scintillation, optical and magnetic properties. Furthermore, the use of chemical doping and post-growth topochemical modifications as strategies to modify material properties and stabilise metastable structures is also covered. With these approaches, we can classify this study into two parts: optical and magnetic properties. In the first part of this work, RP-type n = 1 LaSrGaO4 (LSGO) and Garnet-type Gd3In2Ga3O12 (GIGG) single crystals doped with different Rare Earths (RE) including Eu, Sm, Ho, Nd have been grown via OFZ method to investigate their luminescence, decay time kinetics and scintillation properties. To compare the scintillation behaviour, a well-known commercial scintillator, Gd2.98Ce0.02Al2Ga3O12 (0.02Ce:GAGG) single crystal, was synthesised and characterised using the same methods. This limits deviations in scintillation properties caused by different synthesis methods. Powder X-ray diffraction (XRD) and Single Crystal X-ray diffraction (SC-XRD) measurements together with Rietveld analysis confirmed phase purity and crystallinity, while Scanning Electron Microscopy (SEM-EDX) and backscatter electron imaging (BSE) confirmed the homogeneous distribution of the dopants. In addition to these analytical methods, Photoluminescence Spectroscopy (PL) and luminescence decay measurements have demonstrated that these RE-doped single crystals have strong emission, which is related to the low phonon energy of their host lattices. However, scintillation measurements under 137Cs gamma-ray point source excitation resulted in a limited gamma ray response. This response was significantly weaker than observed for the well-known commercial scintillator 0.02Ce:GAGG. Inefficient absorption of high-energy excitation or inadequate energy transfer to the activator ions in these materials are responsible for this relatively low scintillation performance. The second part of the thesis is focused on bilayer Ruddlesden-Popper nickelates. Single crystals of Sr3Ni2-xAlxO7-δ (SNAO) and its Y-substituted modification YᵧSr3-yNi2-xAlxO7-δ (YSNAO) have been grown by using strategically chemical substitutions and high oxygen pressure conditions to stabilize the RP phase. XRD and SC-XRD analysis confirmed the existence of the n = 2 RP-type structure by doping with Al, while thermogravimetric analysis (TGA) and X-ray photoelectron spectroscopy (XPS) indicated successful oxygen incorporation and corresponding changes in the Ni oxidation state. Magnetic susceptibility measurements (SQUID magnetometry) have demonstrated the antiferromagnetic ordering transitions in these doped nickelate single crystals, and transport measurements have shown enhanced electrical conductivity compared to the undoped parent compound. In addition, a topochemical fluorination process has been investigated as a post-growth modification for n = 1 RP-type La2NiO4+δ single crystals. Fluorine has been introduced into the crystal lattice at moderate temperatures using polytetrafluoroethylene (PTFE), polyvinylidene fluoride (PVDF), and CuF2 as fluorination reagent. PTFE has been found to be the most effective fluorinating agent, resulting in partially fluorinated La2NiO4+δ with a diffusion-limited penetration pattern. EDX and EDX-mapping analyses have demonstrated an inhomogeneous F distribution, indicating that fluorine incorporation is limited by diffusion kinetics. This inhomogeneity should be carefully considered in future structural and functional analyses as it may affect the accurate characterisation of intrinsic properties in fluorinated crystals. In summary, the results of this thesis demonstrate the flexibility of the optical floating zone technique for the growth of high-quality functional oxides and show how structural stability, and functional properties can be modified using specific chemical doping approaches. To optimise scintillation performance in novel garnet-type hosts and to improve the magnetic and electronic behaviour of RP-type nickelates, the combined approach of crystal growth and post-growth modification could provide an additional parameter for material modification.Item Open Access Nano-analysis of surface reaction kinetics of automotive exhaust gas catalyst(2025) Lee, Yoonhee; Schmitz, Guido (Prof. Dr. Dr. h.c.)This study aims to advance our comprehension of the reaction kinetics occurring in nano-sized noble metal catalysts. Advanced microscopy techniques were employed to investigate the precise details of oxidation and diffusion behavior at different temperatures. In particular, atom probe tomography (APT), a highly sophisticated characterization technique, was utilized to obtain accurate and detailed information regarding these processes. By employing this microscopy technique, a comprehensive analysis of the reaction kinetics of nano-sized noble metal catalysts could be achieved, contributing to the development of more efficient catalysts for automotive applications. Noble metal nanoparticles such as Pt, Pd, and PtPd exhibit distinct oxidation behaviors during NO conversion. Understanding the alterations in the catalyst surface is crucial, as it has a direct effect on the performance of the catalytic converter. For this study, wires were utilized made of pure Pt, pure Pd, and PtPd alloy to create sharp tip samples through electrochemical polishing or FIB annular milling. The hemispherical shape of the tip apex serves as a model for the nanosized catalyst surface. The tips were oxidized in the reaction chamber and investigated by APT. The effective oxide thicknesses were determined and compared to the NO conversion rates measured using a Flat Bed Reactor (FBR). Additionally, experimental results of studying the interdiffusion behavior of the Pt-Pd binary system at various temperatures are presented and discussed. To achieve this purpose, the samples were prepared and examined with two different methods, depending on the heating temperatures. For the temperature range between 673 and 973 K, the samples made of nano-sized multiple layers were investigated using APT. For the temperature range between 1073 and 1243 K micro-sized Pt/Pd diffusion couples were annealed and analyzed using energy dispersive X-ray spectroscopy (EDX). The interdiffusion coefficients for both methods were determined by representing them as Fourier series and the Boltzmann-Matano method, respectively. The latter study was conducted in collaboration with the department of Materials design. Consequently, the interdiffusion coefficients were compared with the results of density functional theory (DFT) simulations.