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Die Durchdringung von Kuben ist in den vergangenen Jahren eines meiner Themen. Ausgehend von platonischen Körpern bildet der Tetraeder die “Stella Octangula“ aus zwei Tetraedern. Den doppelten Kubus habe ich bei der Zirkelkonstruktion der Blume des Lebens entdeckt. Durch abwechselnde Faltung des Zeichenblattes durch den Mittelpunkt, entlang der Linien zu den Ecken des Sechsecks, entfaltet sich ein Stern. Zwei Sterne fügen sich zu zwei Würfeln. Aus einer “BdL“ lassen sich die Pyramide, Ikosaeder, Tetraeder und ein Fünfeck ablesen. Die Verbindung von zwei BdL-Konstruktionen lässt einen Doppelwürfel entstehen. Zwei Würfel beinhalten eine regelmäßige hexagonale Fäche. Die Außenmaße sind in einem Würfel enthalten.

In 1992 Du and Hwang published a paper confirming the correctness of a well known 1968 conjecture of Gilbert and Pollak suggesting that the Euclidean Steiner ratio for the plane is 2/3. The original objective of this thesis was to adapt the technique used in this proof to obtain results for other Minkowski spaces. In an attempt to create a rigorous and complete version of the proof, some known results were given new proofs (results for hexagonal trees and for the rectilinear Steiner ratio) and some new results were obtained (on approximation of Steiner ratios and on transforming Steiner trees). The most surprising result, however, was the discovery of a fundamental gap in the proof of Du and Hwang. We give counter examples demonstrating that a statement made about inner spanning trees, which plays an important role in the proof, is not correct. There seems to be no simple way out of this dilemma, and whether the Gilbert-Pollak conjecture is true or not for any number of points seems once again to be an open question. Finally we consider the question of whether Du and Hwang's strategy can be used for cases where the number of points is restricted. After introducing some extra lemmas, we are able to show that the Gilbert-Pollak conjecture is true for 7 or fewer points. This is an improvement on the 1991 proof for 6 points of Rubinstein and Thomas. / Mathematical Sciences / Ph. D. (Mathematics)

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La déformation visco-plastique de la glace est fortement anisotrope, le plan de glissement préferé étant la plan de base. Le fait que dans un polycristal chaque grain possède sa propre direction de déformation produit des incompatibilités et un champ de contrainte complexe. La déformation à été étudiée expérimentellement en mésurant la dis- tortion des plans cristallins de mono- et polycristaux de glace artificielle. Les expériences ont été réalisées à l'aide d'un faisceau synchrotron. Une nouvelle procédure éxperimental, basée sur les méthodes de l'imagerie en diffraction de Bragg, comme lumière blanche, im- agerie sur la courbe de diffraction et topographie laminaire et ponctuelle, a été dévéloppée. Les désorientations angulaires, les largeurs à mi-hauteur et les intensités intégrées ont été mésurées dans les trois dimensions spatiales de l'échantillon et avec une résolution de 50× 50 × 50µm3. Les algorithmes d'analyse de données ont été écrits pour extraire des données des résultats quantitatifs, et pour calculer les neuf composantes du tenseur de courbure ainsi que la distortion entière des plans cristallins. Les résultats ont permis d'observer les premières étappes de la déformation de la glace. Par example la polygonisation d'un grain à été observée. / The viscoplastic deformation of ice is strongly anisotropic. The preferred glide system is on the basal plane. In a polycrystal each grain exhibits its own deformation direction. As a result the deformation of polycrystalline ice is associated with strain in- compatibilities, especially at the grain boundaries and the triple junction. The deforma- tion process was experimentally investigated by measuring crystal lattice distortions of single- and polycrystalline, artificially grown ice crystals. The experiments were benefic- ing from a synchrotron X-ray beam. A new experimental method, based on Bragg diffrac- tion imaging (X-ray topography) methods, as white beam X-ray diffraction topography, rocking curve imaging, section- and pinhole X-ray topography was used. Angular mis- orientations, full-width-half-maxima and integrated Bragg diffracted intensities have been measured along the three spatial dimensions of the sample and with a spatial resolution of around 50µm × 50µm × 50µm. Data analysis algorithms were written in order to extract quantitative results from the data and to calculate all nine components of the curvature ten- sor, as well as the entire lattice distortion in the sample. The results give an insight into the early stages of plastic deformation of ice, i.e. the polygonisation of a grain was observed.

Les propriétés (catalytiques, électriques, optiques ou magnétiques) des métaux ultra-divisés sont différentes du métal massif et sont influencées par la forme et la morphologie des nanomatériaux. Parmi les techniques de synthèses des nanomatériaux, la radiolyse est une méthode de choix pour réduire de façon contrôlée des ions métalliques et pour induire la polymérisation de monomères. Une matrice souple auto-assemblée, à partir de molécules de surfactants, a été employée comme nanoréacteur pour synthétiser des nanostructures (bi-)métalliques ou polymères de morphologie contrôlée. Les surfactants forment dans des conditions particulières des mésophases hexagonales quaternaires qui peuvent être gonflées, de façon continue, sur une large gamme. Le dopage des mésophases en sels métalliques ou en monomères peut être réalisé aussi bien en phase aqueuse qu’en phase organique, permettant d’obtenir des nanostructures de morphologie différentes. En phase aqueuse, la synthèse conduit à la formation de matériaux mésoporeux. Ceux-ci sont d’un intérêt tout particulier pour la catalyse en raison de leur très grande surface spécifique. Le contrôle du gonflement de la mésophase permet un ajustement fin de la porosité dans la structure métallique finale. Nous avons également mis en évidence que la composition de ces nanostructures métalliques Pd/Pt poreuses peut être contrôlée. Nous avons également synthétisé des nanostructures 1D dans la phase organique, comme des nanofils de palladium ou des nanofils de polymères. / The properties (catalytic, electrical, optical or magnetic) of ultra-divided metals are different from those from bulk and are influenced by the shape and morphology of the nanomaterials. Among the techniques of nanomaterials synthesis, radiolysis is a preferred method to reduce metal ions and to induce the polymerization of monomers. A soft template made of self-assembled surfactant molecules, has been used as nanoreactor to synthesize (bi-)metallic or polymer nanostructures of controlled morphology. Surfactants can form, under certain conditions, quaternary hexagonal mesophases, which can be inflated continuously over a wide range. Mesophases can be doped with metal salts or monomers, in aqueous phase or in organic phase, to obtain different nanostructures morphology. In aqueous phase, the synthesis leads to the formation of mesoporous materials. These are of particular interest for catalysis due to their large surface area. The control of the mesophase swelling allows a fine adjustment of the porosity in the final metal structure. We also demonstrated that the composition of porous bimetallic nanostructures Pd / Pt can be controlled. We also synthesized 1D nanostructures in the organic phase, such as metal (palladium) or polymer nanowires.

Submitted by Eunice Novais (enovais@uepg.br) on 2017-09-01T17:51:26Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Luiz Fernando K Unti.pdf: 6181881 bytes, checksum: b0280e86919fc3c265d97d1ffba8200e (MD5) / Made available in DSpace on 2017-09-01T17:51:26Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Luiz Fernando K Unti.pdf: 6181881 bytes, checksum: b0280e86919fc3c265d97d1ffba8200e (MD5) Previous issue date: 2017-01-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Dentre os materiais mais comuns utilizados para a construção de eletrólitos e eletrodos das células a combustível de óxido sólido (CaCOS) estão os óxidos com estrutura semelhante à perovisquita; estes apresentam características desejáveis para esta aplicação, como boa condutividade elétrica. Diversos são os estudos nesta área atualmente, onde um dos enfoques é o desenvolvimento de materiais com condutividade protônica para melhorar a performance destes condutores. O presente trabalho avaliou a viabilidade do composto Ba5Nb4O15 (BNO) como possível candidato na produção de elementos de CaCOS. Este composto possui uma estrutura de perovisquita hexagonal, e estudos recentes apontam que é largamente utilizado em ressoadores dielétricos e há indícios que este tipo de estrutura pode apresentar condutividade protônica. Nesse trabalho foi avaliada a síntese da fase BNO através de um método alternativo à reação no estado sólido, baseada no método Pechini modificado, usando para isto precursores no formato de óxido. Como há diversas rotas diferentes de processamento para esta fase, comparou-se a sinterabilidade dos pós obtidos nas sínteses através da densificação, após serem conformados e sinterizados em duas temperaturas: 1400 e 1450ºC. Também se estudou a influência da adição de dopantes de menor valência (titânio e zircônio) na estrutura e nas propriedades elétricas da fase pura. Foi possível obter a fase BNO em todas as sínteses, embora após a primeira calcinação houvesse diferentes fases na amostra obtida pelo método Pechini; estas fases secundárias desapareceram após a sinterização. Atingiu-se maior densificação ao submeter os pós sintetizados à moagem, previamente à conformação, onde se atingiu porosidades aparentes menores que 5%. As dopagens promoveram o refino do grão, mas não foram eficientes no aumento da condutividade do composto. Contudo, as amostras sinterizadas em 1450ºC apresentaram maior condutividade em atmosfera úmida (H2O) do que em água pesada (D2O), o que pode ser um indício da existência de condutividade protônica nesta estrutura. / Among the common materials used to produce solid oxide fuel cell’s (SOFC’s) electrolytes and electrodes areoxides with perovskite structures; they show desirable characteristics for this application, like good levels of ionic conduction. Nowadays, there are many different studies on this field, where developing new proton conduction materials to improve SOFC’s performance is one of them. Present work evaluated the viability of compound Ba5Nb4O15 (BNO) as a candidate to produce SOFC’s elements. This compound show a hexagonal perovskite structure and recent papers point this kind of structure is currently used can show some indications of proton conduction. At present study, it was evaluated BNO synthesis through an alternate method to solid-state reaction, based on Pechini method and using different oxides as precursors. Since there are many different processing routes to obtain this phase, it was compared sinterability of synthesized powders after pressing and sintering at two temperatures: 1400 and 1450ºC. The poisoning effect of titanium and zirconium on structure and electric properties was also studied. BNO phase was successful obtained in all synthesis, although non-stoichiometry phases were present on Pechini sample after first calcination; after sintering, these phases were no longer present though. A higher densification was obtained after milling synthesized powder previously to pressing: a bulk porosity smaller than 5% was achieved. Doping produce grain refinement, but it was not efficient improving electrical conductivity. However, sintered samples at 1450ºC had shown higher conductivity on humid atmosphere (H2O) than presented on heavy water atmosphere (D2O). This could be an indication of proton conductionin this structure. Keywords: proton conduction, hexagonal perovskites, Pechini method, solid oxide fuel cells.

This thesis explores the application of two-dimensional (2D) materials such as graphene and single layer hexagonal boron nitride (h-BN) which are produced by liquid phase exfoliation for use in printed electronics and energy composite applications. In Chapter 2 I give a broad overview of the electrical, mechanical and optical properties of 2D materials among other nanomaterials that were used in the thesis such as carbon nanotubes and conductive polymers. Additionally I review the techniques and theory behind the exfoliation and dispersion of functional layered materials. In Chapter 3 I present the coating and printing techniques which were used in this thesis along with the experimental techniques and methods which I use to characterise my inks, films and devices. Chapter 4 is the first experimental chapter of the thesis and demonstrates the printing of 2D material heterostructures to create fully printed dieletrically gated field effect transistors with 2D materials on textile and polymer substrates. In this chapter I also demonstrate reprogrammable volatile memory, p and n type inverters, complementary inverters, and logic gates which pave the way to fully printed integrated circuits, operational at room temperature and pressure with 2D materials processed in liquid. In Chapter 5, I review spray coating (a highly industrial scalable printing technique), in terms of the optimisation of its parameters to achieve thin films of nanomaterials on three-dimensional (3D) surfaces. I then demonstrate that it is possible to create large area (∼750 cm2) transparent conducting films around curved surfaces with spray coating enabling a semi-transparent (around 360°) spherical touch sensor for interactive devices. Chapter 6 explores printed photonics for applications in terahertz (THz) frequencies. Here I demonstrate the feasibility of liquid phase exfoliated graphene to create THz saturable absorbers (SAs) which could enable many applications in THz frequencies such as tomography or time-resolved spectroscopy that require mode-locked (i.e. enabling a train of short pulses to be derived from continuous-wave operation) THz pulses. I also demonstrate that these SAs can be inkjet printed on demand providing unprecedented compactness in a quantum cascade laser system. Finally in Chapter 7, I look at the application of graphene in microbial fuel cells (MFC). I demonstrate that enhanced MFC output arises from the interplay of the improved surface area, enhanced conductivity, and catalytic surface groups of a graphene based electrode. As a final step graphene based anodes and cathodes which were entirely platinum free were combined to create an environmentally sustainable energy source.

Boron nitride (BN) materials have unique properties, which has led to interest in them in the last few years. The deformation of boron nitride materials including hexagonal boron nitride, boron nitride nanosheets (BNNSs) and boron nitride nanotubes have been studied by Raman spectroscopy. Both mechanical and liquid exfoliations were employed to obtain boron nitride nanostructures. Boron nitride glass composites were synthesised and prepared in thin films to be deformed by bending test in-situ Raman spectroscopy. Hexagonal boron nitride in the form of an individual flake and as flakes dispersed in glass matrices has been deformed and Raman measurement shows its response to strain. The shift rates were, -4.2 cm-1/%, -6.5 cm-1/% for exfoliated h-BN flake with thick and thin regions and -7.0 cm-1/%, -2.8 cm-1/% for the h-BN flakes in the h-BN/ glass (I) and glass (II) composites. Boron nitride nanosheets (BNNSs) shows a G band Raman peak at 1367.5 cm-1, and the deformation process of BNNSs/ glass composites gives a shift rate of -7.65 cm-1/% for G band. Boron nitride nanotubes (BNNTs) have a Raman peak with position at 1368 cm-1, and their deformation individually and in composites gives Raman band shift rates of -25.7 cm-1/% and -23.6 cm-1/%. Glass matrices shows compressive stresses on boron nitride fillers and this was found as an upshift in the frequencies of G band peak of boron nitride materials. Grüneisen parameters of boron nitride (BN) were used to calculate the residual strains in glass matrices of BNNSs nanocomposites as well as to estimate the band shift rates which found to be in agreement with the experimental shift rate of bulk BN and BNNTs.

This thesis, submitted to the University of Manchester, covers a range of topics related to current research in two-dimensional materials under the title: 'Investigations into the interfacial interaction of graphene with hexagonal boron nitride.'In the last decade, two-dimensional materials have become a rich source of original research and potential applications. The main advantage lies in the ability to produce novel composite structures, so-called 'layered heterostructures', which are only a few atomic layers thick. One can utilise the unique properties of several species of crystal separately, or how they interact to realise a diverse range of uses. Two such crystals are graphene and hexagonal boron nitride. Hexagonal boron nitride has, so far, been used primarily as a substrate for graphene, allowing researchers to get the most out of graphene's impressive individual properties. However, in this thesis, the non-trivial van der Waals interaction between graphene and hexagonal boron nitride is examined. The interface potential reveals itself as a relatively large-scale, orientation-dependant superlattice, which is described in chapters 1 and 2.I In Chapter 4, the effect of this superlattice is examined by measurement of its effect upon the electrons in graphene, where its modulation leads to the creation of second and third generation Dirac points, revealing Hofstadter's Butterfly. As well as an excellent example of the physics possible with graphene, it also presents a new tool with which to create novel devices possessing tailored electronic properties. II In chapter 5, the consequential effect of the superlattice potential on the structure of graphene is studied. Results are discussed within the framework of the Frenkel-Kontorova model for a chain of atoms on a static background potential. Results are consistent with relaxation of the graphene structure leading to the formation of a commensurate ground state. This has exciting consequences for the production of heterostructures by demonstrating that alignment angle can have large effects upon the physical properties of the crystals. III In chapter 6, the van der Waals potential is shown to be responsible for the self-alignment of the two crystals. This effect is important for the fabrication of perfectly aligned devices and may lead to new applications based on nanoscale motion.