Quasicrystal Surfaces Research Articles

Hamiltonian Cycles on Ammann-Beenker Tilings

We provide a simple algorithm for constructing Hamiltonian graph cycles (visiting every vertex exactly once) on a set of arbitrarily large finite subgraphs of aperiodic two-dimensional Ammann-Beenker (AB) tilings. Using this result, and the discrete scale symmetry of AB tilings, we find exact solutions to a range of other problems which lie in the complexity class NP-complete for general graphs. These include the equal-weight traveling salesperson problem, providing, for example, the most efficient route a scanning tunneling microscope tip could take to image the atoms of physical quasicrystals with AB symmetries; the longest path problem, whose solution demonstrates that collections of flexible molecules of any length can adsorb onto AB quasicrystal surfaces at density one, with possible applications to catalysis; and the three-coloring problem, giving ground states for the q-state Potts model (q≥3) of magnetic interactions defined on the planar dual to AB, which may provide useful models for protein folding. Published by the American Physical Society 2024

Surface plasmon resonance methane sensor based on the D-type photonic quasi-crystal fiber with double-layer films

A high-sensitivity photonic quasi-crystal fiber surface plasmon resonance (PQF-SPR) methane sensor is designed and analyzed. The six-fold Penrose PQF has a D-type structure with two grooves on which TiO2 and Au films are deposited, and methane-sensitive film containing cryptophane-E is coated on the surface of the D-type structure. The characteristics of the sensor are analyzed by the finite element method and the influence of different coating materials (Au-TiO2, Au-MgF2, Au-ITO) on the sensitivity and FOM of the sensor is analyzed and compared. The results show that the PCF-SPR sensor with the dual Au-TiO2 film has better sensing properties. The maximum wavelength sensitivity and average wavelength sensitivity reach 40 nm/% and 34.74 nm/% in the methane concentration range of 0–3.5 % respectively. These properties are significantly better than those of similar sensors reported recently, and the sensor thus has large potential in the development of high-sensitivity and miniaturized methane sensors.

The local atomic and electronic structure of quasicrystal i-Al65Cu23Fe12 powder

This work presents an experimental and theoretical study of the atomic and electronic structures of the icosahedral Al65Cu23Fe12 quasicrystalline (QС) powder. The i-Al65Cu23Fe12 QС powder was investigated using X-ray diffraction, scanning electron microscopy, Mössbauer spectroscopy, X-ray absorption spectroscopy (XANES and EXAFS) and X-ray photoelectron spectroscopy. It was found that the i-Al65Cu23Fe12 quasicrystal surface consisted of an oxidized shell of Al2O3 and Cu2O, whereas the bulk fraction consisted of icosahedral Al65Cu23Fe12 quasicrystal and cubic β-Al(Cu0.5Fe0.5) phases. The proposed theoretical model of the structure of i-Al65Cu23Fe12 QC, based on the transformation of the crystalline analogue of Al7Cu2Fe, has good agreement with the experimental structural data obtained from EXAFS and XANES analysis. The electronic structure of the top of the valence band and the bottom of the conduction band of the i-Al65Cu23Fe12 QC was investigated using X-ray photoelectron spectroscopy, analysis of XANES, and ab initio calculations.

Impact of Tuned Oxidation on the Surface Energy of Sintered Samples Produced from Atomised B-Doped Al-Cu-Fe Quasicrystalline Powders

Super-hydrophobic surfaces and coatings have stimulated a great deal of research, with the aim being to achieve better wetting properties. Factors such as surface chemistry and roughness play an important role in changing the surface energy, which in turn leads to changes in the wettability. Here, we have analysed the time dependence of the oxide layer and possible surface adsorbates on the surface topography of an Al59Cu25Fe13B3 quasicrystalline material in relation to changes in the wettability. The quasicrystalline matrix phase was 94% of the sample volume, and it was covered by a very smooth, amorphous oxide layer. The AlB12 and AlFe2B2 boron-rich phases were embedded in the quasicrystalline material as a result of the 3 at.% boron addition, which made atomisation of the material a simpler process. Under ambient conditions, the sample was naturally covered by an oxide layer; therefore, it is referred to as “surfenergy” to distinguish it from the conventional surface energy of a bare quasicrystal surface. The growth of the oxide layer with atmospheric ageing and annealing at 500 °C in air for various times was investigated for both cases. The phase most prone to oxidation was the boron-rich AlFe2B2, which influenced the topography of the surface and accordingly the wetting behaviour of the specimen. We demonstrated that the surfenergy depends on the polar component, which is the most sensitive to the operating conditions. A correlation between the surfenergy components and the surface roughness was found. In addition, theoretical models to determine the wettability were included.

On the propagation of plane waves in cubic quasicrystal plates with surface effects

In this paper, an exact solution of propagation characteristics of plane waves in an infinite cubic quasicrystal plate with surface effects has been derived. Based on the energy density of quasicrystal elastic deformation, the continuum theory of surface elasticity and new boundary conditions for quasicrystal surface layers are derived, from which we obtain an explicit closed form for dispersion relations of quasicrystal plates with the advanced boundary-value problems. The numerical results indicate that the overall stiffness of the quasicrystal plates strengthens with increasing surface elastic parameters and surface residual stresses, resulting in a continuous decrease in the phase velocity.

Tunable bilayer photonic quasicrystal

The unique properties of incommensurate two-dimensional bilayer structures, a wide class of optical materials, are largely determined by the relative rotation angle between the layers. Here, we present a comprehensive theoretical analysis of the optical properties of a dodecagonal quasicrystal based on twisted bilayer material with hexagonal layers rotated by 30°. By assuming that the quasicrystal is tuned to the Bragg condition, we calculate its reflectance spectra and reveal the Wood anomalies therein, which are characteristics of structures with a long-range order. It is also shown that the reflectance spectra can be dynamically controlled by the external electric field applied perpendicular to the quasicrystal's surface. This feature can be used to create tunable photonic devices such as optical switches and sharp M-shape bandpass filters.

Two-dimensional metal structures revealed by evolutionary computations: Pb/Al13Co4(100) as a case study

We have combined extensive density functional theory calculations with an evolutionary algorithm to investigate possible structural models for two-dimensional (2D) Pb films supported on the Al13Co4(100) quasicrystal approximant surface. The minimization of the total energy while maximizing the atomic density in the layer leads to 2D atomic arrangement with pentagonal motifs, reflecting the symmetry of the substrate. Our findings show that the 2D structure can be interpreted as a stable structure with 16 Pb atoms per surface cell in the film, in line with the measured coverage. This conclusion is also supported by the reasonable agreement between the experimental scanning tunneling microscopy images and those simulated using this structural model. Alternatively, a metastable 2D film made of 15 Pb atoms fits with the experimental observations. This study opens a route toward the prediction of supported complex 2D films.

Growth of pentacene molecules on Tsai-type quasicrystals and related crystal surfaces

We present a study of the adsorption of pentacene (Pn) molecules on the high symmetry (fivefold, threefold, and twofold) surfaces of the icosahedral (i) Ag–In–Yb quasicrystal. We also compare the results with adsorption of Pn on a surface of a periodic crystal related to this quasicrystal, the (111) surface of the Au–Al–Tb 1/1 approximant. Scanning tunneling microscopy reveals that Pn molecules on the quasicrystal surfaces are aligned along the high symmetry directions of the substrates and selectively adsorb on Yb atoms and thus exhibit quasicrystalline order. Pn molecules on the Au–Al–Tb approximant surface also preferably adopt Tb sites. The behavior of selective adsorption can be understood in terms of the geometry and electronic properties of the adsorbate and substrate. The Yb–Yb (Tb–Tb) separations are comparable to the C–C or H–H distances in a Pn molecule. Pn is an electron donor, whereas the unoccupied electronic states of the substrate are dominated by the rare earth atoms, suggesting that there is an electronic transfer between the Pn molecules and Yb (Tb) atoms.

Topological reconstruction of a stretched transparent surface relief grating via an optical diffraction pattern.

The optical characterization of transparent and stretchable patterned surfaces replicated from the fabrication of quasicrystal structures on azopolymer thin films is presented. The complexity of the quasicrystal surface fabrication is obtained by superimposed multiple light exposures. Azopolymer surface patterns are used as a replica molding master. The microscopic elongation of nanocavities induced by macroscopic stretchings of the elastomeric quasicrystal replication is characterized via optical diffraction. An original numerical method is presented to reconstruct the structured surface deduced from the optical diffraction measurements. The measurements show that drastic topologic changes, e.g., going from cavities to a canal, happens on the surface. This could be ingeniously used for creating actionable structured surfaces or nanoparticles trapping surfaces.

Accuracy of Cluster Model Calculations for Quasicrystal Surface

Accuracy of the adsorption energy on a quasicrystal surface calculated with the density functional theory and cluster models were discussed. Two types of cluster models of various sizes were tested to represent a fivefold surface of the Ag–In–Yb quasicrystal. Some cylindrical clusters caused unnaturally rippled potential energy surfaces regardless of the cluster thickness. However, it was confirmed that the ripples are disappeared with a cluster radius of 1.4 nm or larger. A similar trend was observed even in the hemispherical clusters, and also confirmed in their root mean square errors. It was concluded that both cluster models with a certain size are expected to give relative adsorption energy within an error of 0.15 eV.

High symmetry nano-photonic quasi-crystals providing novel light management in silicon solar cells

Reduction of surface reflection loss is crucial for high efficiency next generation Si solar cells. Surface texturing provides a viable method to reduce loss over the full solar bandwidth. Previous studies have concentrated on simple moth-eye silicon pillar arrays protruding from the surface. Using FDTD simulation methods, we undertake a systematic investigation into performance benefits provided by complex semi-random photonic quasi-crystal surface patterning methodologies whereby arrays of air holes are etched deep into the solar cell surface. In contrast to other studies we carefully investigate the effect of lattice symmetry, systematically comparing performance of simple 6-fold symmetric triangular photonic crystal patterning to 12 fold symmetry photonic quasicrystal patterning and infinitely symmetric 2D Fibonacci patterning. We optimize key geometric parameters such as lattice pitch, hole size and etch depth to maximize optical performance for each lattice type. 12 fold photonic quasi crystal lattice is found to provide best overall anti-reflectance performance providing a solar-corrected average reflectance of 8.3% for a hole depth of 1.5 µm and 300 nm diameter, in comparison to 36.4% for a bare silicon solar cell surface. Practical feasibility of the optimal designs is demonstrated by fabrication of physical prototypes consisting of arrays of nm scale air-holes etched into the surface of a silicon slab fabricated Using e-beam lithography and ICP/RIE etching. FDTD Simulation methodology is validated by convergence studies as well as comparison to optical measurements on these fabricated devices. Furthermore, in contrast to previous studies we provide an in depth analysis of the physical mechanisms responsible for reduction in surface reflection, determining the parameter space where conventional Gaussian optical processes such as effective refractive index, refraction and Fresnel reflection dominate, vs parameter space where sub wavelength photonic crystal scattering effects play the main role. We finish up with an analysis of electrical performance for the optimal designs to further validate real world performance. Taking electrical performance into account we determine that infinite-symmetry 2D Fibonacci patterning far outperforms lower symmetry 12 fold and triangular arrangement. We believe that this is the first in depth investigation into 2D Fibonacci patterning in silicon solar cells.

An enhanced quasicrystalline Ti1.4V0.6Ni alloy electrode modified by uniformly covered RGO for nickel metal hydride battery

Herein, we provided a facile route to coat a flat and uniformly covered reduced graphene oxide (RGO) film on Ti1.4V0.6Ni quasicrystal alloy electrode surface by electrodeposition of graphene oxide and subsequent reduction with HI vapor. Raman spectrum showed HI has a better reduced effect than electrochemical reduction. The RGO coated alloy electrode exhibited a higher discharge capacity of 290.3 mA h g−1 and 23.8% higher capacity retention than the bare one after 50 cycles for the RGO layer effectively forbidding the direct contact of electrode and electrolyte. Moreover, Ti1.4V0.6Ni quasicrystal alloy with RGO coating exhibited faster hydrogen uptake kinetics by initial activation curve of gaseous hydrogen storage measurement and higher maximum hydrogen storage performance of 1.66 wt% than the bare Ti1.4V0.6Ni alloy. Thus, the enhanced properties of RGO as a multifunctional layer for Ti1.4V0.6Ni quasicrystal alloy were proved which could be achieved by a facile route.

Multi-scale pattern with surface quasi crystal for wettability tuning

Transparent and stretchable structures with multi-scale patterns on PDMS surfaces for a tunable superhydrophobicity are presented. The samples result in the transfer of photoinduced quasi-crystal structures of azopolymer-based thin films onto an elastomer. The quasi-crystal surface patterns have different complexities generated with superimposed multiple exposures. The obtained samples can be stretched or compressed. Periodic circular nanocavities as small as 500 nm could be obtained with their shapes changed by stretching. The surface stretching or compressing induced on the elastomer surface allows the size manipulation of nanocavities. An application of these surfaces is presented for a large control of the super-hydrophobicity. The wetting of these patterns is compared to the same surface pattern modified with metal nanoparticles obtained by a metal dewetting process where the roughness is increased. We show that in this case the hydrophobicity is higher, and the droplet is sticky on these surfaces leading to a rose-petal effect.

Deterministic Realization of Quasicrystal Surface Relief Gratings on Thin Azopolymer Films

AbstractSpatially structured UV–visible light fields generate topographic modulations on the surface of films of azobenzene‐containing polymers. The geometry of the surface reliefs depends on the spatiotemporal distribution of light over the sample. If multistep sequential irradiations are used, even illumination configurations as simple as the interference of two linearly polarized beams produce complex surface textures. This is the case of the quasicrystal geometries, obtainable as the superposition of multiple sinusoidal surface relief gratings oriented in different directions over the surface. The quantitative relief design would require a comprehensive theoretical description of the light‐induced relief formation mechanism, which is still elusive for azopolymers. Here, despite limiting the description at a phenomenological level, the deterministic design of the quasicrystal surface reliefs obtained in sequential light exposures of an azopolymer film is demonstrated. The model provides an excellent agreement between simulated and experimental relief textures, predicting also the dependence of relief structural features on illumination parameters as the number of exposure steps and the beam interference angle. The deterministic texture design allows the controlled tailoring of surface functionalities related to the relief geometry like light diffraction properties of the samples, which are here exploited to manipulate, split, and trap diffracted light.

Unique growth mode observed in a Pb thin film on the threefold surface of an i-Ag-In-Yb quasicrystal

Novel epitaxial quasicrystalline films can be grown using the surfaces of intermetallic quasicrystals as templates. Here, we present a study of Pb adsorption on the threefold i-Ag-In-Yb surface, where Pb grows in a manner contrasting with conventional thin-film growth modes. Pb atoms are found to adsorb at sites over a range of heights, which are explained by bulk atomic positions left vacant by surface truncation, producing three-dimensional, isolated quasicrystalline Pb structures. This finding is contrasted with the growth of Pb on the more commonly used fivefold surface of the same quasicrystal, where smooth epitaxial layers result. We suggest that this unique structure originates due to the lower atomic density of the threefold surface, compared to the fivefold surface. Similar atomic density can be found in lower symmetry planes of periodic systems, but these planes are often unstable and become facetted. This stable low-density quasicrystalline substrate provides a facile route to achieve this type of templated growth.

C60 on impurity phases of the 2–fold surface of the Al–Pd–Mn quasicrystal

Using STM, we show several off-stoichiometric impurity phases detected at the 2-fold Al–Pd–Mn quasicrystal surface. By comparing the observed surface structure to planes from similar bulk phases in the Al–Pd system, we identify these phases as β–Al–Pd and Pd5Mn3. C60 is adsorbed at these domains, forming simple hexagonal close packed (hcp) structures. We identify potential adsorption schemes, and compare the adsorption behaviour to C60 on the quasicrystalline phase.

Nature-Inspired Quasicrystal SRG Using Fibonacci Sequences in Photo-Reconfiguration on Azo Polymer Films

In this study, we present the fabrication route of quasicrystal surface relief grating (SRG) of azopolymer. Based on photo-reconfigurable azobenzene property, various morphologies of grating patterns were inscribed on azopolymer thin-films by two-beam coupling light interference lithography (LIL) process. Multiplexing the LIL with different rotation sequence on azopolymers resulted in unusual surface structures including quasicrystal-like SRGs with Fibonacci sequences in rotational LIL. We investigated the effect of rotation sequence on the grating patterns by atomic force microscope, revealing that rotation sequence is a critical parameter determining surface structures of azopolymer films.

Medium energy ion scattering (MEIS) study from the five-fold surface of icosahedral Ag-In-Yb quasicrystal

Medium energy ion scattering (MEIS) is employed to characterize the composition and structure of the five-fold surface of the icosahedral Ag42In42Yb16 quasicrystal. The composition of the surface after sputtering is dominated by Ag and In, and when the surface is annealed at temperatures approaching 430°C, Yb is restored at the surface. The composition is that expected from the bulk structure if the surface is formed at bulk planes involving the centre of rhombic triacontahedral clusters, the building blocks of the system. Structural analysis of MEIS results are also consistent with a surface after annealing that is in close agreement with bulk truncation intersecting the cluster centre.

Atomistic simulation of frictional anisotropy on quasicrystal approximant surfaces

Park {\it et al.} have reported eight times greater atomic-scale friction in the periodic than in the quasiperiodic direction on the two-fold face of a decagonal Al-Ni-Co quasicrystal. We present results of molecular-dynamics simulations intended to elucidate mechanisms behind this giant frictional anisotropy. Simulations of a bare atomic-force-microscope tip on several model substrates and under a variety of conditions failed to reproduce experimental results. On the other hand, including the experimental passivation of the tip with chains of hexadecane thiol, we reproduce qualitatively the experimental anisotropy in friction, finding evidence for entrainment of the organic chains in surface furrows parallel to the periodic direction.

Crystal to Quasicrystal Surface Phase Transition: An Unlocking Mechanism for Templated Growth

In this experimental work we have studied and characterized a surface phase transition on a decagonal Al72Ni11Co17 sample between a crystalline phase, which is induced by sputtering with energetic noble gas ions, and the bulklike decagonal phase. The surface transition to the stable, quasicrystalline phase was followed as a function of temperature by two complementary techniques: high-resolution X-ray photoelectron spectroscopy (HR-XPS) and low-energy electron diffraction (LEED). The observation of shifts in the core–electron binding energies of the constituent atoms and of other photoemission line shape parameters as the surface undergoes the phase transition and the comparison with the structural information obtained from the LEED data enabled us to determine the evolution of the surface from 5 twinned cubic crystalline domains to the decagonal phase. A quasicrystalline chemical environment with some degree of long-range order is observed for Al before the quasicrystalline surface is fully recovered, po...