Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 119-133). Also available in electronic version.

No description available.

Thesis (Ph. D.)--Boston University, 2003. / In this thesis, studies which concern two different subjects related to phase transitions in fluids and crystalline solids are presented. Condensed matter formation, structure, and phase transitions are modeled using molecular dynamics simulations of simple discontinuous potentials with attractive and repulsive interactions. Novel phase diagrams are proposed for quasicrystals, crystals, and liquids. In the first part of the thesis, the formation of a quasicrystal in a two dimensional monodisperse system is investigated using molecular dynamics simulations of hard sphere particles interacting via a two-dimensional square-well potential. It is found that for certain values of the square-well parameters more than one stable crystalline phase can form. By quenching the liquid phase at a very low temperature, an amorphous phase is obtained. When this the amorphous phase is heated, a quasicrystalline structure with five-fold symmetry forms. From estimations of the Helmholtz potentials of the stable crystalline phases and of the quasicrystal, it is concluded that within a specific temperature range, the observed quasicrystal phase can be the stable phase. The second part of the thesis concerns a study of the liquid-liquid phase transition for a single-component system in three dimensions, interacting via an isotropic potential with a repulsive soft-core shoulder at short distance and an attractive well at an intermediate distance. The potential is similar to potentials used to describe [TRUNCATED}

In this study, new compositions of Tsai-type 1/1 quasicrystal approximants Gd(14)Au(70)Si(16), Gd(14)Au(67)Ge(19), Tb(14)Au(70)Si(16) and Yb(16)Au(65)Ge(19)are synthesized using both self-flux and arc-melting-annealing techniques. Both syntheses routes resulted single phase samples. The crystal structures of the compounds are determined by collecting single crystal X-ray and/or powder X-ray and powder neutron diffraction intensities.  The atomic structure refinements indicated that the compounds are essentially iso-structural with the prototype Tsai-type 1/1 approximant crystal, YbCd6. However, there are subtle structural variations at their cluster centers and in the so-called cubic interstices which affects some of their physical properties. Thermoelectric and magnetic properties of the compounds are investigated. Significant differences are observed in the thermoelectric properties of Gd(14)Au(70)Si(16), Gd(14)Au(67)Ge(19) and Yb(16)Au(65)Ge(19) compounds which are explained on the bases of their crystal structures and chemical compositions. Magnetic susceptibility and specific heat measurements revealed ferromagnetic transitions at low temperatures, Tc ≈ 22.5 K for Gd(14)Au(70)Si(16) and Tc ≈ 13.1 K for Gd(14)Au(67)Ge(19), whereas, for the Tb(14)Au(70)Si(16) compound a ferrimagnetic-like transition is observed at Tc ≈ 9 K. Moreover, a re-entrant spin-glass transition is observed at TRSG ≈ 3.3 K for Gd(14)Au(67)Ge(19) compound. Finally, the magnetic structure of the Tb(14)Au(70)Si(16) compound was determined from powder neutron diffraction data which is to our knowledge the first magnetic structure refinement report in the family of quasicrystals and approximants.

Thesis (Ph.D.)--McMaster University (Canada), 1995. / Source: Dissertation Abstracts International, Volume: 56-12, Section: B, page: 6844. Adviser: D. Walton.

No description available.

Quasicrystals are long-range ordered and yet non-periodic. This interplay results in a wealth of intriguing physical phenomena, such as the inheritance of topological properties from higher dimensions, self-similarity, and the presence of non-trivial structure on all scales. The concept of aperiodic order has been extensively studied in mathematics and geometry, exemplified by the celebrated Penrose tiling. However, the understanding of physical quasicrystals (the vast majority of them are intermetallic compounds) is still incomplete owing to their complexity, regarding both growth processes and stability. Ultracold atoms in optical lattices offer an ideal, yet untested environment for investigating quasicrystals. Optical lattices, i.e. standing waves of light, allow the defect-free formation of a large variety of potential landscapes, including quasiperiodic geometries. In recent years, optical lattices have become one of the most successful tools in the large-scale quantum simulation of condensed-matter problems. This study presents the first experimental realisation of a two-dimensional quasicrystalline potential for ultracold atoms, based on an eightfold symmetric optical lattice. It is aimed at bringing together the fields of ultracold atoms and quasicrystals - and the more general concept of aperiodic order. The first part of this thesis introduces the theoretical aspects of aperiodic order and quasicrystalline structure. The second part comprises a detailed account of the newly designed apparatus that has been used to produce quantum-degenerate gases in quasicrystalline lattices. The third and final part summarises the matter-wave diffraction experiments that have been performed in various lattice geometries. These include one- and two-dimensional simple cubic lattices, one-dimensional quasiperiodic lattices, as well as two-dimensional quasicrystalline lattices. The striking self-similarity of this quasicrystalline structure has been directly observed, in close analogy to Shechtman's very first discovery of quasicrystals using electron diffraction. In addition, an in-depth study of the diffraction dynamics reveals the fundamental differences between periodic and quasicrystalline lattices, in excellent agreement with ab initio theory. The diffraction dynamics on short timescales constitutes a continuous-time quantum walk on a homogeneous four-dimensional tight-binding lattice. On the one hand, these measurements establish a novel experimental platform for investigating quasicrystals proper. On the other hand, ultracold atoms in quasicrystalline optical lattices are worth studying in their own right: Possible avenues include the observation many-body localisation and Bose glasses, as well as the creation of topologically non-trivial systems in higher dimensions.

Thesis (M.App.Sc.) - Carleton University, / Includes bibliographical references (p. 79-81). Also available in electronic format on the Internet.

This dissertation is a summary of the graduate study in the past few years. In first part, we develop efficient spectral methods for the spectral fractional Laplacian equation and parabolic PDEs with spectral fractional Laplacian on rectangular domains. The key idea is to construct eigenfunctions of discrete Laplacian (also referred to Fourier-like basis) by using the Fourierization method. Under this basis, the nonlocal fractional Laplacian operator can be trivially evaluated, leading to very efficient algorithms for PDEs involving spectral fractional Laplacian. We provide a rigorous error analysis for the proposed methods, as well as ample numerical results to show their effectiveness.<div><br>In second part, we propose a method suitable for the computation of quasiperiodic interface, and apply it to simulate the interface between ordered phases in Lifschitz-Petrich model, which can be quasiperiodic. The function space, initial and boundary conditions are carefully chosen such that it fix the relative orientation and displacement, and we follow a gradient flow to let the interface and its optimal structure. The gradient flow is discretized by the scalar auxiliary variable (SAV) approach in time, and spectral method in space using quasiperiodic Fourier series and generalized Jacobi<br>polynomials. We use the method to study interface between striped, hexagonal and dodecagonal phases, especially when the interface is quasiperiodic. The numerical examples show that our method is efficient and accurate to successfully capture the interfacial structure.</div>

Rapidly solidified nanoquasicrystalline Al₉₃Fe₃Cr₂Ti₂ at% alloy has previously shown outstanding mechanical performance and microstructural stability up to elevated temperatures. Despite this, no in-depth study had previously been performed assessing the active strengthening mechanisms, the long term microstructural stability and the effect of plastic deformation at elevated temperature to simulate the production methods utilised for engineering applications. The current project analysed eight bars consisting of a nanoquasicrystalline Al₉₃Fe₃Cr₂Ti₂ at% alloy matrix with varying amounts of pure Al fibres, produced through gas atomisation and warm extrusion. Microstructural characterisation and thermal analysis of the as-atomized powder was carried out to assess whether microstructural changed were likely to occur at the extrusion temperature. A microstructure made primarily of nanometre-sized icosahedral particles in an FCC-Al matrix was observed through a combination of SEM, TEM (and CBDP), EDX, XRD. Thermal analysis of the powders performed by DSC showed that no change was expected to occur at the extrusion temperature. Five bars were extruded during the course of this project: one bar of pure Al-Fe-Cr-Ti alloy, two composite bars with 10 vol% added pure Al and two bars with 20 vol% added Al. Three more bars were received from a previous project and analysed. Warm extrusion caused the powder particles to become well bonded and elongated in the extrusion direction introducing a preferred orientation in the FCC-Al grains. A bimodal distribution of grain size was observed after extrusion. Several low angle (5-15 &deg;) grain boundaries were also identified by EBSD along the extrusion direction. No obvious change in size or shape was observed by TEM in the icosahedral phase (a bimodal distribution of hard, incoherent precipitates was observed after extrusion), or any change in the amount of solutes in solid solution in the Al matrix. Mechanical properties at room temperature were tested by Vickers microhardness, quasi-static tensile tests, dynamic tensile tests and dynamic compression tests. A theoretical model correlating the microstructures observed with the various active strengthening mechanisms was applied in order to predict an estimate of the yield strength of the material produced. It was found that the strength of the Al₉₃Fe₃Cr₂Ti₂ alloy came primarily from a combination of the effect of the hard, incoherent nanoparticles, the small grain size and work hardening. The fibre addition to this alloy caused a linear decrease in mechanical strength with increasing vol% pure Al. This work represents the first quantitative estimate of which strengthening mechanisms are active and how much they influence the mechanical strength of Al₉₃Fe₃Cr₂Ti₂ alloy and composites. An understanding of the yield strength is essential as engineering components would only be safe to use within the elastic region. To investigate the thermal stability of the alloy and composites, thermal analyses involving DSC and long heat treatments (up to a maximum of 1000 hours) were performed at various temperatures along with microstructural characterisation by XRD, SEM and TEM and microhardness tests. No microstructural change was detected, however a 2-5% decrease in microhardness was observed. Compression tests were performed across a range of temperatures and strain rates to simulate the behaviour of these composites under typical conditions necessary to process them into useful engineering components. Phase changes occurring during plastic deformation at high temperature were investigated by XRD. The measured yield strength at 350 &deg;C was over 3x that of high strength 7075 T6 Al alloy showing outstanding thermal stability and mechanical performance. However, the microstructure was shown by XRD to undergo a phase transformation which resulted in the decomposition of the icosahedral phase at 500 &deg;C into more stable intermetallic phases. Serrated flow was also observed in some of the tests. The high temperature compressive data was then used for the first time in a semi-quantitative analysis to determine which species in solid solution (Fe, Cr or Ti) was likely to cause the serrations. A dynamic strain ageing model, which calculates the diffusion coefficients at the minimum in ductility and strain rate sensitivity, suggested that the Ti in solid solution in the matrix could be the most likely candidate.