# Browsing by Subject "quasicrystal"

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Item Open Access Computational Study of Low-friction Quasicrystalline Coatings via Simulations of Thin Film Growth of Hydrocarbons and Rare Gases(2008-04-25) Setyawan, WahyuQuasicrystalline compounds (QC) have been shown to have lower friction compared to other structures of the same constituents. The abscence of structural interlocking when two QC surfaces slide against one another yields the low friction. To use QC as low-friction coatings in combustion engines where hydrocarbon-based oil lubricant is commonly used, knowledge of how a film of lubricant forms on the coating is required. Any adsorbed films having non-quasicrystalline structure will reduce the self-lubricity of the coatings. In this manuscript, we report the results of simulations on thin films growth of selected hydrocarbons and rare gases on a decagonal Al$_{73}$Ni$_{10}$Co$_{17}$ quasicrystal (d-AlNiCo). Grand canonical Monte Carlo method is used to perform the simulations. We develop a set of classical interatomic many-body potentials which are based on the embedded-atom method to study the adsorption processes for hydrocarbons. Methane, propane, hexane, octane, and benzene are simulated and show complete wetting and layered films. Methane monolayer forms a pentagonal order commensurate with the d-AlNiCo. Propane forms disordered monolayer. Hexane and octane adsorb in a close-packed manner consistent with their bulk structure. The results of hexane and octane are expected to represent those of longer alkanes which constitute typical lubricants. Benzene monolayer has pentagonal order at low temperatures which transforms into triangular lattice at high temperatures. The effects of size mismatch and relative strength of the competing interactions (adsorbate-substrate and between adsorbates) on the film growth and structure are systematically studied using rare gases with Lennard-Jones pair potentials. It is found that the relative strength of the interactions determines the growth mode, while the structure of the film is affected mostly by the size mismatch between adsorbate and substrate's characteristic length. On d-AlNiCo, xenon monolayer undergoes a first-order structural transition from quasiperiodic pentagonal to periodic triangular. Smaller gases such as Ne, Ar, Kr do not show such transition. A simple rule is proposed to predict the existence of the transition which will be useful in the search of the appropriate quasicrystalline coatings for certain oil lubricants. Another part of this thesis is the calculation of phase diagram of Fe-Mo-C system under pressure for studying the effects of Mo on the thermodynamics of Fe:Mo nanoparticles as catalysts for growing single-walled carbon nanotubes (SWCNTs). Adding an appropriate amount of Mo to Fe particles avoids the formation of stable binary Fe$_3$C carbide that can terminate SWCNTs growth. Eventhough the formation of ternary carbides in Fe-Mo-C system might also reduce the activity of the catalyst, there are regions in the Fe:Mo which contain enough free Fe and excess carbon to yield nanotubes. Furthermore, the ternary carbides become stable at a smaller size of particle as compared to Fe$_3$C indicating that Fe:Mo particles can be used to grow smaller SWCNTs.Item Open Access Physics of Hexagonal Limit-Periodic Phases: Thermodynamics, Formation and Vibrational Modes(2016) Belley, Catherine Cronin MarcouxLimit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.

A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case.

In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state.

LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.