Sintering, a process of forming dense solid bodies from powder compacts remains the most important route for processing of ceramics. The process of sintering involves formation and growth of necks during initial stage, coarsening, relative particle rotation, filling of connected pores in intermediate stage, filling of isolated pores during final stage sintering and rapid grain growth towards the end of densification. The processes involve a combi-nation of grain boundary diffusion, surface diffusion, grain boundary migration and grain boundary sliding. Studies of interfacial processes during sintering are still of interest since modifying interface structure offers a means to tailor low and high temperature mechanical properties of ceramics. Many of the studies in literature on single phase systems are based on geometric changes during sintering. Sintering has been modelled as 1D or 2D array of spheres. The simplest of these consist of a contacting pair of spherical particles. Early models studied changes in size and shape of the necks during initial stage sintering and associated mass transport mechanisms. There have been studies on coarsening that report shrinkage rates of smaller particles is a system of two particles with different radii. In both the cases of neck growth and coarsening, thermodynamic variables as given by dihedral angle (relative grain boundary to surface energy of the system) and kinetic parameters of grain boundary surface diffusivity have been found to influence the size and shape evolution with time. Also, there have been studies comparing self similar geometries at different absolute length scales such as a system of micro and nano sized particles, which show different sintering behaviour depending on the absolute particle size. There have been studies on multi particle arrays both linear and closed. Early studies on linear arrays observed rearrangement of particles and relative rotation due to non spherical shape and bond angle of an array of three particles. Also there was a study that predicted rearrangement due to differential shrinkage in an assembly containing a combi-nation of large and small particles. Similar observations were also made on closed arrays of four or more particles both in 2D and 3D. Formation of high energy local configurations such as six grain boundaries (GBs) meeting at a line were found, followed by the topological transitions such as formation of new GBs or elimination of existing ones, leading to specific features in sintering behaviour. Geometrical evolution during final stage sintering is critical for forming dense final products. While most studies related the shrinkage behaviour to shape of the pore (convex or concave) and the number of grains surrounding a pore, later the absolute size of the pore was observed to be an important parameter. In 2D simulations and experiments large convex pores were found to shrink due to mass transport from surrounding GBs. In 3D simulations, pores with large coordination number as high as 32, pore shrinkage was observed followed by gradual reduction in coordination number and final elimination. Also studied are evolution of pore -GB configuration in case of small pores as separation of these from GB and entrapment into grains will freeze further shrinkage. In addition to the geometry related changes are also crystallography related microstructural changes. Crystallographic arrangement at the atomic scale leads to anisotropy of interfacial energies and diffusivities, that effect microstructural evolution. The presence of positive and negative ions in ionic solids can result in additional features such as charged and neutral planes Crystallography can affect the rotation of powder particles in initial stage sintering to subtle differences in microstructure evolution during grain growth in final stage sintering. Conversely crystallography has to be related to diffusion at interfaces. The rotation of spheres is governed by energetics. The final configuration corresponds to local energy minima in misorientations between the spheres and the single crystal plate. This technique is useful in finding a number of crystallography related aspects such as low energy GBs and equilibrium shapes of metal droplets. Rotation of unconstrained crystal related to neighbouring crystal has also been observed in thin films. Surface energy anisotropy has often been studied using topography of annealed sur-faces studied using atomic force microscopy (AFM). While low energy stable surfaces show perfectly flat surfaces, planes close to a stable plane form terrace and ledge structures whereas unstable planes form hill and valley structures. A method of “inverse Wulff shape” of pores trapped in single crystals has been used to find relative stability of sur-face planes using a combination of electron back scattered diffraction (EBSD) and AFM. Crystallography is very much related to the phenomenon of abnormal grain growth that occurs during later stages of sintering. Similarly, polycrystal assemblies have shown varying GB migration velocities for different crystallographic planes. Most recently, 3D EBSD has been used to study crystallography of GBs in sintered polycrystalline materials. In the present study, we address two specific issues. The first is related to the effect of microstructure of polycrystalline powder particles on initial stage sintering, where we compare sintering between particles with same particle size but different grain sizes. The second is related to the crystallographic aspects of interfaces in sintered materials with specific reference to yttria stabilized cubic zirconia. The present study is mostly confined to pressure less (free) sintering where the only driving force is the reduction in interfacial energy of the system. The effect of polycrystalline nature on initial stage sintering is investigated and com-pared with the behaviour of single crystal particles. We extend the model by Coble on single crystals to polycrystalline particles containing space filling tetrakaidecahedral grains with an identical grain size. The grain boundaries within particles are considered to be additional sources for mass to be plated at the neck and the flux equations are suitably modified. A model was developed to characterize the variation with time in the growth rate (x/R), where x and R are radii of the neck and particle respectively. The model indicated that the neck growth rate for polycrystalline spheres was faster compared to single crystals towards end of initial stage sintering (large value of x/R). There is large scope for extending the model further for complex geometries, diffusion distances and grain size distributions. Sintering experiments were conducted with annealed 2D random arrays of spheres of zirconia with two different grain sizes and a particle size of 40 m. Two different forms of zirconia (8YCZ and 3YTZ) were used as model systems for a few and a large number of grains in a particle respectively. The experimental results were limited, but broadly consistent with the new model. However necks were found to grow to a value f x=R = 0:12 and they did not grow further. In the second part of our study, grain boundaries in yttria stabilized cubic zirconia were studied in the context of macroscopic crystallographic parameters of misorientations of grains on either side of the grain boundary and crystallographic coordinates of grain boundary planes. Our aim was to study the evolution of misorientations and grain bound-ary planes during sintering process, starting from formation of necks during the initial stage to grain boundary migration during later stages. Orientation imaging microscopy based on an EBSD technique in an SEM was carried out on fully dense samples and also on porous samples obtained by interrupting sintering before attaining full density. The fraction of CSL misorientations on nearly dense cubic zirconia with grain sizes varying from submicrocrystalline 0.61 to 10 m was close to a random distribution. The number fraction of necks with CSLs formed in porous cubic zirconia with microcrysatlline particles was slightly higher than a random distribution. However, the present study covers only nearly dense-microcrystalline, nearly dense- submicrocrystalline, porous - microcrystalline regime , but misorientation information could not be obtained experimentally in a low density - submi-crocrystalline regime that is critical for sintering process. We also studied the distribution of grain boundary planes in fully dense 8YCZ with a grain size of 2.8 m by a stereological method using 2D OIM data. The overall distribution of grain boundary planes showed very weak anisotropy with slight maxima with 1.1 multiples of random distribution (MRD) at {100} planes, which is consistent with observations in literature on larger grain sizes. Interestingly, the planes that were abundant were not low energy surface planes (also mentioned in literature), in clear contrast with other ceramics studied in literature. The distribution of grain boundary planes was also plotted for specific misorientations, including those around low index axes of [100], [110], [111] and low misorientations. The grain boundary character distribution (GBCD) shows a high frequency of occurrence in position of pure twists about [100] and symmetric tilts at certain low misorientations . The highest frequency of occurrence was observed for coherent twin 3 on {111} plane and symmetric tilt (higher order twin) 11 on {113} plane, both corresponding to low energy GBs reported in literature in bicrystal experiments. With pure twists on {100} for rotations about [100] axis and pure tilts with {11w} or {1ww} planes for rotations about [110], both the criteria for specialness based on surface planes forming GB or symmetric tilts are found to be valid for specific cases. Notable is the frequency of occurrence of coherent twin 3 on {111} and 11 on {113}, that was 4.8 MRD for microcrystalline 8YCZ and as high as 7.8 MRD for submicrocrystalline 8YCZ samples, which is much higher than frequency of occurrence of any GB plane in any oxide studied in literature.

Abstract The aim of this work was to formulate separation process models with both predictive capabilities and robust solution strategies. Although all separation process models should have predictive capabilities, the current literature still has multiple applications in which predictive models having the combination of a clear phenomenon base and robust solving strategy are not available. The separation process models investigated in this work were liquid-liquid phase separation and membrane separation models. The robust solving of a liquid-liquid phase separation model typically demands the solution of a phase stability analysis problem. In addition, predicting the liquid-liquid phase compositions reliably depends on robust phase stability analysis. A phase stability analysis problem has multiple feasible solutions, all of which have to be sought to ensure both the robust solving of the model and predictive process model. Finding all the solutions with a local solving method is difficult and generally inexact. Therefore, the modified bounded homotopy methods, a global solving method, were further developed to solve the problem robustly. Robust solving demanded the application of both variables and homotopy parameter bounding features and the usage of the trivial solution in the solving strategy. This was shown in multiple liquid-liquid equilibrium cases. In the context of membrane separation models, predictive capabilities are achieved with the application of a Maxwell-Stefan based model. With the Maxwell-Stefan approach, multicomponent separation can be predicted based on pure component permeation data alone. On the other hand, the solving of the model demands a robust solving strategy with application-dependent knowledge. These issues were illustrated in the separation of a H2/CO2 mixture with a high-silica MFI zeolite membrane at high pressure and low temperature. Similarly, the prediction of mixture adsorption based on pure component adsorption data alone was successfully demonstrated. In the context of membrane separation models, predictive capabilities are achieved with the application of a Maxwell-Stefan based model. With the Maxwell-Stefan approach, multicomponent separation can be predicted based on pure component permeation data alone. On the other hand, the solving of the model demands a robust solving strategy with application-dependent knowledge. These issues were illustrated in the separation of a H2/CO2 mixture with a high-silica MFI zeolite membrane at high pressure and low temperature. Similarly, the prediction of mixture adsorption based on pure component adsorption data alone was successfully demonstrated. / Tiivistelmä Työn tavoitteena oli muotoilla prosessin käyttäytymisen ennustamiseen kykeneviä erotusprosessimalleja ja niiden ratkaisuun käytettäviä luotettavia strategioita. Vaikka kaikkien erotusprosessimallien tulisi olla ennustavia, on tällä hetkellä useita kohteita, joissa prosessin käyttäytymistä ei voida ennustaa siten, että käytettävissä olisi sekä ilmiöpohjainen malli että ratkaisuun soveltuva luotettava strategia. Tässä työssä erotusprosessimalleista kohteina tarkasteltiin neste-neste-erotuksen ja membraanierotuksen kuvaukseen käytettäviä malleja. Neste-neste-erotusmallien luotettava ratkaisu vaatii yleensä faasistabiilisuusongelman ratkaisua. Lisäksi faasien koostumusten luotettava ennustaminen pohjautuu faasistabiilisuusanalyysiin. Faasistabiilisuusongelmalla on useita mahdollisia ratkaisuja, jotka kaikki tulee löytää, jotta voitaisiin varmistaa luotettava mallin ratkaisu sekä prosessimallin ennustuskyvyn säilyminen. Kaikkien ratkaisujen löytäminen on sekä vaikeaa että epätarkkaa paikallisesti konvergoituvilla ratkaisumenetelmillä. Tämän vuoksi globaaleihin ratkaisumenetelmiin kuuluvia modifioituja rajoitettuja homotopiamenetelmiä kehitettiin edelleen, jotta faasistabiilisuusongelma saataisiin ratkaistua luotettavasti. Ratkaisun luotettavuus vaati sekä muuttujien että homotopiaparametrin rajoittamista ja ongelman triviaalin ratkaisun käyttöä ratkaisustrategiassa. Tämä käyttäytyminen todennettiin useissa neste-nestetasa-painoa kuvaavissa esimerkeissä. Membraanierotusta tarkasteltaessa ennustava malli voidaan muotoilla käyttämällä Maxwell-Stefan pohjaista mallia. Maxwell-Stefan lähestymistavalla voidaan ennustaa monikomponenttiseosten erotusta perustuen puhtaiden komponenttien membraanin läpäisystä saatuun mittausaineistoon. Toisaalta mallin ratkaisu vaatii luotettavan ratkaisustrategian, jossa hyötykäytetään kohteesta riippuvaa tietoa. Näitä kysymyksiä havainnollistettiin H2/CO2 seoksen erotuksessa MFI-zeoliitti-membraanilla korkeassa paineessa. Samoin seosten adsorboitumiskäyttäytymistä ennustettiin onnistuneesti pelkästään puhtaiden komponenttien adsorptiodatan pohjalta. Kokonaisuutena voidaan todeta, että tarkasteltujen erotusprosessimallien ennustavuutta voidaan parantaa yhdistämällä malli, jolla on selkeä ilmiöpohja ja luotettava ratkaisustrategia. Lisäksi mallien käytettävyys erotusprosessien suunnittelussa on parantunut työn tulosten pohjalta.

This thesis deals with deposition of gallium nitride thin films on silicon substrates covered by negative HSQ rezist. Rezist was patterned via electron beam lithography to create masks, where the selective growth of crystals was achieved. Growth of GaN layers was carried out by MBE method. For achievement of desired selective growth, the various deposition conditions were studied.

Hybridstrukturen aus organischen und anorganischen Halbleitern (HIOS) vereinen die besten Eigenschaften beider Materialklassen zu Konjugaten mit großem Anwendungspotential. Ihre engen Struktur-Eigenschafts-Beziehungen, eröffnen viele interessante wissenschaftliche Herausforderungen. Um z.B. ihre optoelektronischen Eigenschaften vorherzusagen, müssen die früher Stadien des Dünnschichtwachstums erforscht werden. Das erste Ziel dieser Arbeit ist es, den Einfluss der Entropie auf die Oberflächendiffusion von kurzen Polyphenyl Molekülen auf amorphem Siliziumdioxid, a-SiO2 zu untersuchen. Das zweite Ziel ist es, den Einfluss partieller Fluorierung auf para-Sexiphenyls (p-6P) zu untersuchen. Des Weiteren untersuchen wir Selbstdiffusion von p-6P auf einer Zinkoxid (ZnO) Oberfläche und Selbstorganisation bzw. Schichtwachstum auf a-SiO2. Hierfür verwenden wir klassische atomistische Molekular- und Langevin-Dynamik-Simulationen, kombiniert mit klassischer Diffusionstheorie. In Bezug auf das erste Ziel quantifizieren wir die entropischen Beiträge zu den Freie-Energie-Barrieren für die Oberflächendiffusion von Polyphenylen unterschiedlicher Länge und zeigen, dass die Entropie zum dominierenden Teil der freien Energie für längere Moleküle wird. Zweitens demonstrieren wir, dass die Erhöhung der Anzahl fluorierter Gruppen im p-6P die Diffusion in der apolaren Richtung der ZnO-Oberfläche verringert, aber die Diffusion in der polaren Richtung erhöht. Drittens untersuchen wir den Einfluss der Fluorierung auf die Nukleation und das Wachstum von p-6P auf a-SiO2 mit einem Simulationsmodell, das experimentelle Gasphasenepitaxie nachahmt. Wir reproduzieren korrekte Einheitszellen bei Raumtemperatur und zeigen, dass die Erhöhung der Anzahl fluorierter Gruppen zu einem Schicht-für-Schicht-Wachstum auf der Oberfläche führt. Diese Arbeit ebnet den Weg für zukünftige Simulationen von Dünnschichtwachstum kleiner organischer Moleküle auf anorganischen Oberflächen. / Hybrid structures of organic molecules and inorganic semiconductors (HIOS) combine favorable properties of each material into conjugates with great application potential. The optoelectronic properties of hybrid materials depend on the structure of individual molecules and their alignment relative to the inorganic surface. It is an interesting scientific challenge to predict the optoelectronic properties of HIOS based on studying the early stages of thin film growth and interface formation. The aim of this thesis is to investigate the effect of entropy in surface diffusion of short polyphenyl molecules on an amorphous silicon dioxide, a-SiO2. Second objective is to study the influence of partial fluorination of the organic para-sexiphenyl molecule (p-6P) on self-diffusion on an inorganic zinc oxide (ZnO) surface and on self-assembly and growth on the a-SiO2. For this we employ all-atom molecular dynamics and Langevin dynamics simulations, combined with classical diffusion theory. In respect to the first aim, we quantify entropic contributions to the free energy barrier of surface diffusion for short oligophenyls of varying length and demonstrate that entropy becomes even the dominant part of the free energy for longer molecules. For the second aim, we demonstrate that the increase in the number of fluorinated groups inside of the p-6P decreases the diffusivity in the apolar direction of the ZnO surface but increases the diffusivity in the polar direction. Thirdly, we study the influence of fluorination on nucleation and growth on a-SiO2 with a simulation model that mimics experimental deposition from the vapor. We reproduce the structures with correct room-temperature unit-cell parameters and demonstrate that the increase in the number of fluorinated groups leads to a layer-by-layer growth on the surface. This work can stimulate ideas for future simulations of nucleation and growth of small organic molecules with high tuning potential, on inorganic surfaces.

No description available.

<p dir="ltr">In Chapter 1, we introduce geometric motions from the general perspective of gradient flows. Here we develop the basic framework in which to pose the two main results of this thesis.</p><p dir="ltr">In Chapter 2, we examine the pinch-off phenomenon for a tubular surface moving by surface diffusion. We prove the existence of a one parameter family of pinching profiles obeying a long wavelength approximation of the dynamics.</p><p dir="ltr">In Chapter 3, we study a diffusion-based numerical scheme for curve shortening flow. We prove that the scheme is one time-step consistent.</p>

Dans le cadre général de la simulation du procédé de frittage en phase solide, ce travail propose une approche numérique, à l'échelle des particules, de la consolidation d'un compact pulvérulent céramique. Le frittage est un procédé mettant en jeu plusieurs chemins de diffusion activés thermiquement. Parmi ces chemins de diffusion, les plus importants sont : la diffusion surfacique, la diffusion aux joints des grains et la diffusion volumique. La mise en place de cette physique dans un cadre de calcul intensif doit permettre de mieux comprendre ces mécanismes de diffusion ainsi que leur influence sur l'évolution de la microstructure. Le but de ce travail consiste à développer un modèle ainsi qu'une stratégie numérique capable d'intégrer les différents mécanismes de diffusion dans un cadre de calcul intensif. Le flux de matière est calculé en fonction du Laplacien de la courbure dans les cas de la diffusion surfacique, tandis que pour la diffusion volumique ce flux est proportionnel au gradient de la pression hydrostatique. Le modèle physique est tout d'abord présenté dans le cadre de la mécanique des milieux continus. Ensuite, la stratégie numérique développée pour la simulation du frittage d'un empilement granulaire est détaillée. Cette stratégie est basée sur une discrétisation du problème par des éléments finis stabilisés couplée avec une méthode Level-set pour décrire la surface libre des particules. Cette stratégie nous permet de faire des simulations avec un "grand" nombre de particules. Plusieurs simulations en 3D, menées dans un cadre de calcul parallèle, montrent l'évolution qui a lieu sur un empilement granulaire réaliste. / Within the general context of solid-state sintering process, this work presents a numerical modeling approach, at the particle scale, of ceramic particle packing consolidation. Typically, the sintering process triggers several mass transport paths that are thermally activated. Among those diffusion paths, the most important ones are: surface diffusion, grain boundary diffusion and volume diffusion. Including this physics into a high-performance computing framework would permit to gain precious insights about the driving mechanisms. The aim of the present work is to develop a model and a numerical strategy able to integrate the different diffusion mechanisms into continuum mechanics framework. In the cases of surface diffusion and volume diffusion, the mass flux is calculated as a function of the surface curvature Laplacian and the hydrostatic pressure gradient, respectively. The physical model describing these two transport mechanisms is first presented within the framework of continuum mechanics. Then the numerical strategy developed for the simulation of the sintering of many particles is detailed. This strategy is based on a discretization of the problem by using a finite element approach coupled with a Level-Set method used to describe the particles free surface. This versatile strategy allows us to perform simulations involving a relatively large number of particles. Furthermore, a mesh adaptation technique allows the particles surface description to be improved, while the number of mesh elements is kept reasonable. Several 3D simulations, performed in a parallel computing framework, show the changes occurring in the structure of 3D granular stacks.

Aufgrund des großen Verhältnisses von Oberfläche zu Volumen zeigen Nanopartikel interessante, größenabhängige Eigenschaften, die man im ausgedehnten Festkörper nicht beobachtet. Sie sind daher von großem wissenschaftlichem und technologischem Interesse. Die Herstellung kleinster Partikel ist aus diesem Grund überaus wünschenswert. Dieses Ziel kann mit Hilfe von Mikroemulsionen als Templatphasen bei der Herstellung von Nanopartikeln erreicht werden. Mikroemulsionen sind thermodynamisch stabile, transparente und isotrope Mischungen von Wasser und Öl, die durch einen Emulgator stabilisiert sind. Sie können eine Vielzahl verschiedener Mikrostrukturen bilden. Die Kenntnis der einer Mikroemulsion zugrunde liegenden Struktur und Dynamik ist daher von außerordentlicher Bedeutung, um ein gewähltes System potentiell als Templatphase zur Nanopartikelherstellung einsetzen zu können.<br><br> In der vorliegenden Arbeit wurden komplexe Mehrkomponentensysteme auf der Basis einer natürlich vorkommenden Sojabohnenlecithin-Mischung, eines gereinigten Lecithins und eines Sulfobetains als Emulgatoren mit Hilfe der diffusionsgewichteten 1H-NMR-Spektroskopie unter Verwendung gepulster Feldgradienten (PFG) in Abhängigkeit des Zusatzes des Polykations Poly-(diallyl-dimethyl-ammoniumchlorid) (PDADMAC) untersucht. Der zentrale Gegenstand dieser Untersuchungen war die strukturelle und dynamische Charakterisierung der verwendeten Mikroemulsionen hinsichtlich ihrer potentiellen Anwendbarkeit als Templatphasen für die Herstellung möglichst kleiner Nanopartikel.<br><br> Die konzentrations- und zeit-abhängige NMR-Diffusionsmessung stellte sich dabei als hervorragend geeignete und genaue Methode zur Untersuchung der Mikrostruktur und Dynamik in den vorliegenden Systemen heraus. Die beobachtete geschlossene Wasser-in-Öl- (W/O-) Mikrostruktur der Mikroemulsionen zeigt deutlich deren potentielle Anwendbarkeit in der Nanopartikelsynthese. Das Gesamtdiffusionsverhalten des Tensides wird durch variierende Anteile aus der Verschiebung gesamter Aggregate, der Monomerdiffusion im Medium bzw. der medium-vermittelten Oberflächendiffusion bestimmt. Dies resultierte in einigen Fällen in einer anormalen Diffusionscharakteristik. In allen Systemen liegen hydrodynamische und direkte Wechselwirkungen zwischen den Tensidaggregaten vor.<br><br> Der Zusatz von PDADMAC zu den Mikroemulsionen resultiert in einer Stabilisierung der flüssigen Grenzfläche der Tensidaggregate aufgrund der Adsorption des Polykations auf den entgegengesetzt geladenen Tensidfilm und kann potentiell zu Nanopartikeln mit kleineren Dimensionen und schmaleren Größenverteilungen führen. / Owing to their large surface-to-volume ratio nanoparticles show interesting size-dependent properties that are not observable in bulk materials. Thus, they are of great scientific and technological interest. Thereby, the highly desirable preparation of as small particles as possible might be easily achieved using microemulsions as template phases. Microemulsions are thermodynamically stable, transparent and isotropic mixtures of water and oil stabilized by an emulsifying agent. However, microemulsions may form a great variety of different microstructures. Thus, it is of utmost importance to know the underlying microstructure and microdynamics of a chosen microemulsion system in order to use it as a template phase for nanoparticle formation.<br><br> In the present study complex multi-component microemulsion systems based on a naturally occurring soybean lecithin mixture, purified lecithin and sulfobetaine as emulsifiers were investigated by diffusion-weighted pulsed field gradient (PFG) 1H NMR spectroscopy in the presence and absence of the polycation poly-(diallyldimethylammonium chloride) (PDADMAC). The central topic of this study was to structurally and dynamically characterize the present microemulsions with respect to their potential use in nanoparticle formation.<br><br> The concentration- and time-dependent NMR diffusion measurements turned out to be a suitable and accurate tool to investigate the microstructure and microdynamics of the systems under investigation. They reveal closed water-in-oil (W/O) microemulsion microstructures which prove the potential suitability of the respective systems as template phases for the preparation of nano-sized particles. The overall diffusion behavior of surfactants were found to be governed by varying contributions from displacements of entire aggregates, monomer diffusion in the medium and bulk-mediated surface diffusion, respectively. In some cases this led to a marked anomalous diffusion characteristics. In all systems interactions between aggregates are dominated by hydrodynamic and direct forces.<br><br> The addition of PDADMAC to the microemulsion systems results in a stabilization of the liquid interface of surfactant aggregates due to the adsorption of the polycation at the oppositely charged surfactant film and may potentially lead to nanoparticles of smaller dimensions and narrower size distributions.

In this dissertation we study free boundary problems that model the evolution of interfaces in the presence of elasticity, such as thin film profiles and material void boundaries. These problems are characterized by the competition between the elastic bulk energy and the anisotropic surface energy. First, we consider the evolution equation with curvature regularization that models the motion of a two-dimensional thin film by evaporation-condensation on a rigid substrate. The film is strained due to the mismatch between the crystalline lattices of the two materials and anisotropy is taken into account. We present the results contained in [62] where the author establishes short time existence, uniqueness and regularity of the solution using De Giorgi’s minimizing movements to exploit the L2 -gradient flow structure of the equation. This seems to be the first analytical result for the evaporation-condensation case in the presence of elasticity. Second, we consider the relaxed energy introduced in [20] that depends on admissible pairs (E, u) of sets E and functions u defined only outside of E. For dimension three this energy appears in the study of the material voids in solids, where the pairs (E, u) are interpreted as the admissible configurations that consist of void regions E in the space and of displacements u of the atoms of the crystal. We provide the precise mathematical framework that guarantees the existence of minimal energy pairs (E, u). Then, we establish that for every minimal configuration (E, u), the function u is C 1,γ loc -regular outside an essentially closed subset of E. No hypothesis of starshapedness is assumed on the voids and all the results that are contained in [18] hold true for every dimension d ≥ 2.

Τα προηγμένα (δομικά ή λειτουργικά) κεραμικά θεωρούνται ως τα πλέον κατάλληλα υλικά για εφαρμογές όπου απαιτούνται υψηλές θερμοκρασίες. Διαθέτουν μία σειρά από πλεονεκτήματα όπως π.χ. αντοχή σε θερμικούς αιφνιδιασμούς, υψηλή σκληρότητα, αντοχή σε φθορά και διάβρωση και μεγάλο εύρος στις τιμές των ηλεκτρικών τους ιδιοτήτων. Από τεχνολογική άποψη ενδιαφέρον παρουσιάζει ο συνδυασμός τους με μεταλλικές φάσεις με στόχο την συνένωση υλικών ή την παρασκευή σύνθετων κεραμομεταλλικών υλικών. Κεραμικές ενώσεις οξειδίων μπορεί να χρησιμοποιηθούν στην τεχνολογία των κελιών καυσίμου στερεού ηλεκτρολύτη (SOFC) ως μονωτικά ή στεγανωτικά υλικά. Ιδιαίτερο ενδιαφέρον παρουσιάζει η αλληλεπίδραση τους στην διεπιφάνεια σε επαφή με άργυρο και κράματα με βάση τον άργυρο για χρήση ως εναλλακτικών, σε αντικατάσταση των υαλοκεραμικών, συγκολλητικών μεταξύ των στρώσεων των μεμονωμένων στοιβάδων των SOFC. Σημαντικό ρόλο στη μικροδομή και τις ιδιότητες των υλικών αυτών παίζουν τα φαινόμενα διαβροχής και η ισχύς του δεσμού που αναπτύσσεται στη διεπιφάνεια κεραμικού / μετάλλου, καθώς και οι επιφανειακές και διεπιφανειακές ενέργειες των υλικών ή των συστημάτων των υλικών που βρίσκονται σε επαφή. Για το λόγο αυτό η γνώση των επιφανειακών και διεπιφανειακών μεγεθών είναι απαραίτητη για την πρόβλεψη των ιδιοτήτων των συστημάτων σε επαφή. Σκοπός της παρούσας εργασίας είναι η μελέτη της συνάφειας και των διεπιφανειακών ιδιοτήτων σε συστήματα κεραμικών οξειδίων σε επαφή με ρευστές μεταλλικές φάσεις και ιδιαίτερα σε συστήματα του κεραμικών οξειδίων σε επαφή με ρευστές μεταλλικές φάσεις αργύρου, με τελικό σκοπό την εφαρμογή των συστημάτων αυτών στην τεχνολογία των SOFC. Στο πρώτο μέρος της εργασίας, εξετάσθηκε η επίδραση του διαλυτοποιημένου οξυγόνου στην επιφανειακή ενέργεια του ρευστού άργυρου και του ρευστού χαλκού. Από τις εξισώσεις που εξήχθησαν είναι δυνατός ο προσδιορισμός της επιφανειακής ενέργειας τους για δεδομένη θερμοκρασία και μερική πίεση οξυγόνου. Υπολογίσθηκε η ελεύθερη ενέργεια προσρόφησης του οξυγόνου στην επιφάνεια του ρευστού χαλκού, μέχρι τον κορεσμό. Διατυπώθηκε επίσης μία σχέση για τον υπολογισμό της διαλυτότητας ενός οξειδίου στα ρευστά μέταλλα σε εξάρτηση με την θερμοκρασία και την μερική πίεση του οξυγόνου στην ατμόσφαιρα του πειράματος. Στη συνέχεια, με χρήση ενός συνδυασμού βιβλιογραφικών και πειραματικών δεδομένων σχετικά με τις τιμές της επιφανειακής ενέργειας και τις γωνίας επαφής σε συστήματα κεραμικών οξειδίων σε επαφή με διάφορα ρευστά μέταλλα βελτιστοποιήθηκε μια εμπειρική σχέση η οποία, σε δεδομένη θερμοκρασία, συνδέει άμεσα την επιφανειακή ενέργεια των στερεών οξειδίων με την επιφανειακή ενέργεια των ρευστών μετάλλων και τη γωνία επαφής. Μέσω αυτής της σχέσης είναι δυνατή η εκτίμηση της επιφανειακής ενέργειας ενός στερεού οξειδίου ή της γωνίας επαφής σε μη διαβρέχοντα και μη αντιδρώντα συστήματα κεραμικών οξειδίων / ρευστών μετάλλων, με την προϋπόθεση ότι η μερική διαλυτοποίηση οξυγόνου του κεραμικού μέσα στο ρευστό μέταλλο δεν επηρεάζει τις διεπιφανειακές ιδιότητες του συστήματος. Η σχέση αυτή επαληθεύθηκε για διάφορα συστήματα κεραμικών οξειδίων / ρευστών μετάλλων και επιπλέον εφαρμόσθηκε για τον προσδιορισμό της επιφανειακής ενέργειας του πολυκρυσταλλικού οξειδίου Y2O3 μετά από πειράματα διαβροχής από ρευστό άργυρο, του πολυκρυσταλλικού οξειδίου 3YTZ (3mol% Yttria partial stabilized zirconia) και του μικτού πολυκρυσταλλικού οξειδίου 85wt% MgO + 15 wt% MgAl2O4, μετά από πειράματα διαβροχής με ρευστό άργυρο. Στο δεύτερο μέρος της εργασίας πραγματοποιήθηκαν πειράματα διαβροχής κεραμικών οξειδίων από τήγμα αργύρου σε οξειδωτικές συνθήκες (αέρας) για να εξετασθεί η επίδραση του οξυγόνου στις διεπιφανειακές ιδιότητες του συστήματος, καθώς η τεχνολογία των SOFC απαιτεί οι διεργασίες αυτές να πραγματοποιούνται σε συνθήκες περιβάλλοντος. Διαπιστώθηκε ότι η παρουσία οξυγόνου βελτιώνει τη διαβρεξιμότητα στα συστήματα κεραμικών / μετάλλου αυξάνοντας την ισχύ του δεσμού στην διεπιφάνεια, όμως η γωνία θ παραμένει θ > 90◦ (κακή διαβροχή). Σημαντική ελάττωση της γωνίας επαφής επιτυγχάνεται με προσθήκη διεπιφανειακά ενεργών συστατικών στο τήγμα του συγκολλητικού μετάλλου αυξάνοντας σημαντικά το έργο συνάφειας και ως εκ τούτου την ισχύ του δεσμού στην διεπιφάνεια κεραμικού/μετάλλου. Για τον ίδιο λόγο πραγματοποιήθηκαν πειράματα διαβροχής κεραμικών οξειδίων από οξείδια με βάση το βόριο και το λίθιο, στον αέρα, με σκοπό να εξετασθεί η συνοχή μεταξύ των φάσεων σε επαφή. Τέλος εξετάσθηκε η διαβροχή του χάλυβα Crofer 22 APU, ο οποίος χρησιμοποιείται στην τεχνολογία των SOFC, από τις ίδιες ρευστές φάσεις, με στόχο να εξετασθεί η δυνατότητα χρήσης τους ως συγκολλητικές φάσεις σε κελιά καυσίμου στερεού ηλεκτρολύτη. / Advanced ceramics (structural or functional) are considered to be the most suitable for use in high temperature applications. They have a number of advantages, such as resistance to thermal shocks, high hardness, wear and corrosion resistance and a wide range in the values of their electrical properties. Special interest is being manifested in the compounds of ceramics with metals and metal alloys, in the field of materials joining and the production of composite materials. Ceramic compounds are used in the field of solid oxide fuel cells (SOFC) as insulators and sealing materials. Particular interest has been stimulated in the interaction in the interface of ceramics in contact with liquid silver and silver based alloys, as alternatives to the glass-ceramics sealing materials in SOFC stacks. In all of these cases the surface and interfacial energies of the materials or the materials systems used, as well as the wetting and bonding phenomena at the interface, play a key role in obtaining materials with the desired properties and microstructure. The aim of the present work is the study of adhesion and interfacial properties in ceramic oxide / liquid metal systems, particularly in systems of ceramic oxides in contact with liquid silver and silver-based alloys, with the ultimate aim of implementing such systems in the SOFC technology. In the first part of this work, the effect of the dissoluted oxygen on the surface energy of liquid copper and liquid silver was examined. The equations that were deriverd can be used to calculate their surface energy as a function of the temperature and the partial pressure of the oxygen. The free energy of the oxygen adsorption in the surface of the liquid copper was calculated, until saturation. Also, an equation that allows to calculate the solubility of an oxide in a liquid metal was deriverd, as a function of the temperature and the oxygen partial pressure. Moreover, from the combination of literature and experimental data of interfacial energies and contact angles in non-wetting and non-reactive ceramic oxide/liquid metal systems where the limited solubility of oxygen of the ceramic oxides into the liquid metalls has no effect on the interfacial properties, has led to an empirical relationship which correlates at a given temperature the surface energy of the oxides with the contact angle and the surface energy of the liquid metal. This relationship allows either the calculation of the surface energy of an oxide from known values of the surface energy of a liquid metal and the contact angle, or conversely, the estimation of the contact angle value, as well as the work of adhesion, for known surface energy of the oxide. The formulated empirical relationship has been applied to additional non-wetting and non-reactive systems of oxides in contact with liquid metals and the results showed good agreement with literature data. In addition, the empirical formula was used to calculate the surface energies of the polycrystalline oxides Y2O3 and 3YTZ (3mol% Yttria partial stabilized zirconia) as well as the 85wt% MgO + 15 wt% MgAl2O4 mixed oxide, after wetting experiments with liquid copper and/or liquid silver in an Ar- 4%H2 atmosphere. In the second part of this work, the effect of the oxygen on the the interfacial properties of the ceramics / liquid silver systems was examined by wetting experiments, in order to achieve conditions similar to the SOFC operating conditions. The results showed that the presence of the oxygen improves the wetability in the ceramic / liquid metal systems, increasing the bond in the interface but the angle remains θ > 90◦ (non wetting systems). The addition of interfacial active compounds in the liquid metal led to a significant decrease in the contact angle value, with the simultaneous increase in the work of adhesion, and so to the increase in the strength of the bond. For this purpose and in order to examine the adhesion between the two phases, wetting experiments with lithium and borium based oxides took place. Finally, the above liquid phases were used in wetting experiments on steel substrate (Crofer 22 APU) in order to investigate the potential usage of them as sealing and insulators in SOFC technology.