a função espectral mostra uma estrutura bem definida com superfícies de Fermi exibindo uma simetria rotacional de ordem 8 ao redor desse preenchimento, apesar de sua nova estrutura eletrônica, e descobrimos que esses estados são estendidos para a maioria dos preenchimentos, e mostram que, estudamos as propriedades eletrônicas dos mosaicos de Ammann-Beenker, exceto no pseudogap, exceto próximo ao pseudogap. Para estudar a supercondutividade, executamos o escalonamento de tamanho finito do parâmetro de ordem supercondutor e mostramos que ele permanece essencialmente constante, Motivados por uma recente observação experimental de supercondutividade nos quase cristais, onde diminui com o tamanho do aproximante e para valores pequenos da atração U. Isso está de acordo com as observações experimentais, os quasecristais exibem supercondutividade convencional do tipo BCS., ou octogonal, que diz que a energia de Fermi de um quase cristal provavelmente cai sobre um pseudogap. Notavelmente, resolvemos as equações de Bogoliubov-de Gennes e o modelo de pareamento de autovalores exatos para aproximantes de diferentes tamanhos. Em seguida, um exemplo de um quase cristal bidimensional para diferentes tamanhos de aproximantes. O modelo tight-binding resultante mostra uma densidade d / Motivated by a recent experimental observation of superconductivity in the quasicrystals, we study the electronic properties of the Ammann-Beenker, or octagonal tiling, an example of a two-dimensional quasicrystal for different approximant sizes. The resulting tightbinding model shows a very spike density of states and a pseudogap at a filling corresponding to the inverse of the square of the silver ratio. This is a relevant filing due to the Hume-Rothery mechanism, which says that the Fermi energy of a quasicrystal is likely to lie in a pseudogap. Remarkably, the spectral function shows a well-defined structure with Fermi-like pockets displaying an 8-fold rotational symmetry around this filling. We use the Kohn\' localization tensor and the inverse participation ratio to describe the nature of the single-particle eigenstates, and we find that these states are extended for most fillings, except close to the pseudogap. To study the superconductivity, we then solve the Bogoliubov-de Gennes equations and paring of exacts eigenstates for approximants of different sizes. We then perform the finite size scaling of the superconducting order parameter and show that it remains constant, except at pseudogap, where it diminishes with the approximant size for small values of the attraction U. This is line with the experimental observations and show that, despite their novel electronic structure, quasicrystals are prone to display conventional BCS-like superconductivity.

In 2005, Park et al. demonstrated that the 2-fold surface of a d-AlNiCo quasicrystal exhibits an 8-fold frictional anisotropy, as measured by atomic-force microscopy, between the periodic and aperiodic directions [40, 41]. It has been well known that quasicrystals exhibit lower friction than their crystalline counterparts [38, 18, 51, 30, 12, 54]; however, the discovery of the frictional anisotropy allows for a unique opportunity to study the effect of periodicity on friction when chemical composition, oxidation, and wear are no longer variables. The work presented herein is focused on obtaining an understanding of the mechanisms of friction and the dependence of friction on the periodicity of a structure at the atomic level, focusing on the d-AlNiCo quasicrystal studied by Park et al. Using the LAMMPS [44] package to simulate the compression and sliding of an 'adamant' tip, see section 3.3, on a d-AlNiCo quasicrystalline approximant substrate, we have demonstrated, in preliminary results, an 8-fold frictional anisotropy, but in more careful studies the anisotropy is found to be much smaller. The simulations were accomplished using Widom-Moriarty pair potentials to define the interactions between the atoms [36, 56, 55, 9]. The studies presented in this work have shown a clear velocity dependence on the measured frictional response of the quasicrystalline approximant's surface. The final results show between a 1.026-fold and 1.127-fold anisotropy between sliding in the periodic and 'aperiodic' directions, depending on the sliding velocity.

In a 2005 article in Science [45], Park et al. measured in vacuum the friction between a coated atomic-force-microscope tip and the clean two-fold surface of an AlNiCo quasicrystal. Because the two-fold surface is periodic in one direction and aperiodic (with a quasiperiodicity related to the Fibonacci sequence) in the perpendicular direction, frictional anisotropy is not unexpected; however, the magnitude of that anisotropy in the Park experiment, a factor of eight, is unprecedented. By eliminating chemistry as a variable, the experiment also demonstrated that the low friction of quasicrystals must be tied in some way to their quasiperiodicity. Through various models, we investigate generic geometric mechanisms that might give rise to this anisotropy.

We examine various models of soft matter, and one model of quasicrystals, focusing on abrupt changes as density is varied. We consider in detail two models, one of granular matter and another of confined wires, showing that the models become ordered as density is increased, with crystalline order observed in the former and nematic order observed in the latter. We associate the phenomenon of random close packing with the onset of crystalline order in our granular model, and we conjecture that crumpled wires should exhibit a nematic transition with increasing compaction. We also consider two other models of granular matter: one which describes dilatancy onset as a second order phase transition, and one which describes random loose packing as a precise, well- defined density. Finally, we examine an equilibrium model of quasicrystals with a first order phase transition to a solid phase without any crystalline order. / text

In this Dissertation thesis the spectral theory of Schrödinger operators modeling quasicrystals in dimension one ist investigated. We allow for a large class of measures as potentials covering also point interactions. The main results can be stated as follows: If the potential can be very well approximated by periodic potentials, then the correspondig Schrödinger operator does not have any eigenvalues. If the potential is aperiodic and satisfies a certain finite local complexity condition, the absolutely continuous spectrum is absent. We also prove Cantor spectra of zero Lebesgue measure for a large class of (a randomized version of) the operator.

Thesis (Ph. D.)--Duke University, 2008. / Includes bibliographical references.

Made available in DSpace on 2015-05-08T14:59:46Z (GMT). No. of bitstreams: 1 parte1.pdf: 1839351 bytes, checksum: 34e86046fc8cf8f52125675d2e7267f6 (MD5) Previous issue date: 2009-03-03 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Melt spinnng processing is one of the most common processes to obtaining quasicrystaline structures. This is because of the fast cooling rate it imposes on the system, favoring such type of structure. This work deals with the production of quasycristaline phases (Al60Cu27,5Fe12,5 e Al57Cu27,5Fe12,5B3) via melt-spinning. The alloys were initially cast via induction melting under atmospheric air, with the designed chemical composition of the quasicrystals. Hence, the ribbons were produce by melt-spinning were characterized by means of x-ray diffraction and scanning electron microscopy. The results indicate that the icosahedral ψ - Al65Cu20Fe15 phase formed in both types of starting compositions. It seams that the boron contributes to stabilize the icosahedral phase. / O processo melt-spinning por imprimir altas taxas de resfriamento, é um dos principais meios para a obtenção de ligas com estrutura quasicristalinas, sendo o primeiro método utilizado para produzir materiais quasicristalinos. Neste trabalho utilizou-se este processo para a elaboração das ligas quasicristalinas Al(60-x)Cu25Fe15Bx, Al(60-x)Cu27,5Fe12,5Bx e Al(65-x)Cu20Fe15Bx (x=0 e x=3%at de boro). As ligas foram previamente fabricadas, por fusão, em atmosfera de argônio, em forno à indução, para em seguida serem submetidas ao processo melt-spinning , onde se obteve o material na forma de fita. As amostras foram caracterizadas por difração de raios-x e microscopia eletrônica de varredura. Os resultados indicaram a formação da fase icosaedral ψ - Al65Cu20Fe15 nas composições estudadas e uma provável contribuição do boro na produção dessa fase icosaedral

The field of crystallography has recently been expanded to include the science of quasicrystals, crystalline structures lacking unit cells and conventional periodicity. This resulted in a paradigm shift in the field, opening up for a whole new branch on the subject of structural chemistry. Despite this, not much is known about the abilities of quasicrystalline and approximant materials. Quasicrystalline approximants in the RE-Au-SM system have previously shown promising results regarding magnetic properties. To explore and discover properties like this is key to further improve the understanding of quasicrystalline materials.   The scope of the project was to explore the Gd-Au-Si system with compositions theoretically calculated to yield possible quasicrystals. In three batches with varying composition ratios, crystals were synthesised, using an arc-melting self-flux method. These were then analysed with powder X-ray diffraction, single crystal X-ray diffraction and electron dispersive spectroscopy (EDS) to characterise the synthesised compounds using diffraction data and composition data respectively. The resulting crystals were determined to be of a ternary composition close to what was theoretically calculated. The phase synthesised is yet to be found in any previous work or database, possibly marking it out as a new phase, albeit the structure not being quasicrystalline in nature. Thus, the exploratory study yielded a so for unobserved composition in the Gd-Au-Si system.

The quasicrystals are characterized by unusual rotational symmetries that are not observed in the crystalline materials, which is the cause of their interesting material properties. Because of that a particular attention was paid to quasicrystalline structures in the literature research. The research also contains a description of electron beam technology, spark plasma sintering method and introduction to the problematics of wear. As the default materials for the experimental part were selected Titanium Grade 2 powder and Cristome A5 powder which was partially composed of quasicrystalline phase. The first series of samples was sintered only from powder Cristome A5. The second series was sintered from the mixture of 80 % Titanium Grade 2 powder and 20 % Cristome A5 powder. For the compaction of samples spark plasma sintering technology was selected. Samples were then systematically modified by electron beam and subjected to pin on disc tests. Samples modified at 750 °C had the best wear resistance. Samples modified at 1150 °C contained increased amount of quasicrystalline phase.

Název práce: Studium defekt· v kvazikrystalech Autor: Marián Vlček Katedra: Katedra fyziky nízkých teplot Vedoucí disertační práce: doc. Mgr. Jakub ížek, Ph.D., Katedra fyziky nízkých teplot Abstrakt: V predloženej práci boli pomocou spektroskopie doby života poz- itrónov a koincidenčnej spektroskopie Dopplerovského rozšírenia anihilačného píku študované zliatiny WE43 s prídavkom zinku a ternárne zliatiny Mg-Zn-Y. V týchto zliatinách bola nedávno zistená prítomnos' ikosahedrálnej fázy Mg3Zn6Y1 s kvázikryštalickou štruktúrou, čo pritiahlo pozornos' výskumníkov. Spektroskopia doby života pozitrónov preukázala prítomnos' unikátnych vakanciám podobných defektov na rozhraní ikosahedrálnej fázy a horčíkovej matrice, ktoré sú charakter- istické pre horčíkové zliatiny obsahujúce ikosahedrálnu fázu. Tepelné spracovanie skúmaných zliatin vedie k významným zmenám morfológie hraničných fáz. Ke¤že vakanciám podobné defekty spojené s ikosahedrálnou fázou sa vyskytujú na jej rozhraní s horčíkovou matricou, zmeny v morfológii ikosahedrálnej fázy vedú k výrazným zmenám koncentrácie týchto defektov. "alej boli skúmané vzorky pripravené uhlovým pretláčaním kanálom rovnakého prierezu. Typy defektov prítomné v týchto zliatinách a ich teplotná stabilita bola určená pomocou spektroskopie doby života pozitrónov a merania tvrdosti...