Quasicrystal

For a class of discrete quasi-periodic Schrödinger operators defined by covariant representations of the rotation algebra, a lower bound on phase-averaged transport in terms of the multifractal dimensions of the density of states is proven. This result is established under a Diophantine condition on the incommensuration parameter. The relevant class of operators is distinguished by invariance with respect to symmetry automorphisms of the rotation algebra. It includes the critical Harper (almost-Mathieu) operator. As a by-product, a new solution of the frame problem associated with Weyl-Heisenberg-Gabor lattices of coherent states is given.

ABSTRACT Mechanical alloying of Ti45Zr38–x Ni17+x and Ti45–x Zr38Ni17+x (0 ≤ x ≤ 8) elemental powders produced an amorphous phase, but subsequent annealing converted the amorphous phase into an icosahedral quasicrystal phase, along with a Ti2Ni-type phase. The discharge capacities, measured in a three-electrode cell at room temperature for both the amorphous and quasicrystal electrodes, increased with increasing Ni substitution for Zr or Ti. The highest discharge capacities, which were about 60 mAh/g for the amorphous electrode and 100 mAh/g for the quasicrystal electrode, were obtained from (Ti45Zr30Ni25) after substitution of Ni for Zr. For the Ti45Zr30Ni25 composition, the discharge performance of the quasicrystal electrode was stable over charge/discharge cycling, but that of the amorphous electrode gradually decreased with cycling. The structure of the quasicrystal phase in the electrodes was stable, even after 15 charge/discharge cycles, but the amorphous phase converted to a (Ti, Zr)H2 f.c.c. hydride.

Abstract. It is known that any two domino tilings of a polygon are flip-accessible, i.e., linked by a finite sequence of local transformations, called flips. This paper considers flip-accessibility for domino tilings of the whole plane, asking whether two of them are linked by a possibly infinite sequence of flips. The answer turning out to depend on tilings, we provide three equivalent characterizations of flip-accessibility. Résumé. Étant donnés deux pavages par dominos d’un mme polygone, on sait qu’on peut toujours passer de l’un l’autre en effectuant un nombre fini de transformations locales, appelées flips; ces pavages sont dits flip-accessibles. Dans ce papier, nous étendons cette notion de flip-accessibilité aux pavages par dominos du plan entier, en s’autorisant cette fois effectuer un nombre infini de flips. Dans ce cas, la flip-accessibilité dépend des pavages considérés et nous en donnons trois caractérisations équivalentes.

We perform numerical studies including Monte Carlo simulations of high rotational symmetry random tilings. For computational convenience, our tilings obey fixed boundary conditions in regular polygons. Such tilings are put in correspondence with algorithms for sorting lists in computer science. We obtain statistics on path counting and vertex coordination which compare well with predictions of mean-field theory and allow estimation of the configurational entropy, which tends to the value 0.568 per vertex in the limit of continuous symmetry. Tilings with phason strain appear to share the same entropy as unstrained tilings, as predicted by mean-field theory. We consider the thermodynamic limit and argue that the limiting fixed boundary entropy equals the limiting free boundary entropy, although these differ for finite rotational symmetry.

Abstract Al-Cu-Fe (Al 65 Cu 20 Fe 15 ) films were fabricated using an RF triode magnetron sputtering technique. The films were characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), selected area electron diffraction (SAED) and energy dispersive spectroscopy (EDS) techniques. The as-sputtered Al-Cu-Fe films had an amorphous structure. The Al-Cu-Fe film annealed at 750°C for 2 h had an icosahedral quasicrystalline structure, but annealing at temperatures from 200°C to 550°C produced a mixed structure of amorphous and quasicrystalline phases. Nanoindentation measurements showed that the hardness and elastic modulus of the as-sputtered Al-Cu-Fe films (9.44 GPa and 114.4 GPa, respectively) increased as the amount of the quasicrystalline phase increased on annealing. The Al-Cu-Fe film annealed at 550°C for one hour had a hardness of 13.49 GPa and a Young's modulus of 141.4 GPa. A systematic increase in wear resistance with increasing annealing temperature was observed, based on the scratch track width measurements. Both the as-sputtered (amorphous) and annealed (amorphous + quasicrystalline) Al-C-Fe films had low coefficients of friction (0.09–0.11) that were of the same order as for TiN films produced by reactive ion plating (RIP).

This paper is a first report of thermally sprayed Ti 60 Cr 32 Si 8 (at.%) alloy coating. It has been reported previously that such an alloy assumes quasicrystallinity in the presence of oxygen, when made to undergo rapid quenching. In these cases, either TiO or SiO 2 is used as an ...

Quasicrystalline materials have unique properties such as high hardness, excellent surface properties, good resistance to oxidation and corrosion and low electrical and thermal conductivities. These materials can be obtained by conventional methods of metallurgy. However, quasicrystals are quite weak and this characteristic complicates their use in the form of billets for the manufacture of mechanical components. For this reason, the evaluation of mechanical properties of quasicrystalline materials using conventional methods, such as tension, compression, fatigue, among others, is not feasible. One method to evaluate the mechanical properties of quasicrystals is through instrumented indentation, once it is a very efficient tool for the calculation of properties such as hardness, fracture toughness and modulus of elasticity. The latter was the property studied in this work and that it is an important design criterion for the manufacturing of quasicrystalline alloys for their use in i...