Structure Of Quasicrystals Research Articles

Supramolecular self-assembly of naphthalene diimide bolaamphiphile with biologically important amines: Cyclam, spermine and melamine

A rigid bolaamphiphile molecule (NDI-1) was synthesized consisting of a naphthalenediimide unit with glutamic acid head groups. Co-assembly of NDI-1 with cyclam, spermine and melamine bearing amine functional groups is studied herein giving significantly different microstructures. NDI-1 was designed to induce geometrically favourable hydrogen bonding with its counterpart molecules in the co-assembly to trigger supramolecular micro- and nano-architectures formation. The interaction between the bolaamphiphile NDI-1 and biologically important amines such as cyclam, spermine and melamine was investigated by UV–vis and fluorescence emission spectroscopy and the nanostructure morphology was studied using scanning electron microscopy. It was found that the co-assembly of NDI-1 with cyclam resulted in fractal-like morphology. Co-assembly of NDI-1 with spermine yielded a crystalline microstructure based on an α-helix molecular arrangement changed into a quasicrystal structure. Self-assembly of NDI-1 in the presence of melamine resulted in a highly crystalline needle-like morphology. The nucleation and growth of the nanostructures were tuned by analytes into distinct classes. Such changes in morphology are significant to the fabrication of various nanomaterials via non-covalent interactions with distinct properties.

Structure of icosahedral quasicrystals within the multiple-cell approach

The multiple-cell approach is discussed as an alternative to the higher-dimensional crystallographic description of icosahedral quasicrystals. Four types of quasi-unit cells fill the space without gaps and overlappings. Every cell in the whole tiling is decorated by specific atoms in a particular way and is associated with a triad: type, position, and orientation. The key features of the proposed approach are the subgroup/coset decomposition of icosahedral symmetry groups in accordance with the orbit-stabilizer theorem, a strict mathematical formalization of the substitution rules for all types of quasi-unit cells in the Socolar-Steinhardt tiling, formalization of the recursive inflation/deflation rules, and the eigenvalue-eigenvector analysis of corresponding substitution matrices. The similar approach can be applied to almost all types of quasicrystals.

An atomic scale study of two-dimensional quasicrystal nucleation controlled by multiple length scale interactions.

Formation of quasicrystal structures has always been mysterious since the discovery of these magic structures. In this work, the nucleation of decagonal, dodecagonal, heptagonal, and octagonal quasicrystal structures controlled by the coupling among multiple length scales is investigated using a dynamic phase-field crystal model. We observe that the nucleation of quasicrystals proceeds through local rearrangement of length scales, i.e., the generation, merging and stacking of 3-atom building blocks constructed by the length scales, and accordingly, propose a geometric model to describe the cooperation of length scales during structural transformation in quasicrystal nucleation. Essentially, such cooperation is crucial to quasicrystal formation, and controlled by the match and balance between length scales. These findings clarify the scenario and microscopic mechanism of the structural evolution during quasicrystal nucleation, and help us to understand the common rule for the formation of periodic crystal and quasicrystal structures with various symmetries.

Dodecagonal bilayer graphene quasicrystal and its approximants

Dodecagonal bilayer graphene quasicrystal has 12-fold rotational order but lacks translational symmetry which prevents the application of band theory. In this paper, we study the electronic and optical properties of graphene quasicrystal with large-scale tight-binding calculations involving more than ten million atoms. We propose a series of periodic approximants which reproduce accurately the properties of quasicrystal within a finite unit cell. By utilizing the band-unfolding method on the smallest approximant with only 2702 atoms, the effective band structure of graphene quasicrystal is derived. The features, such as the emergence of new Dirac points (especially the mirrored ones), the band gap at M point and the Fermi velocity are all in agreement with recent experiments. The properties of quasicrystal states are identified in the Landau level spectrum and optical excitations. Importantly, our results show that the lattice mismatch is the dominant factor determining the accuracy of layered approximants. The proposed approximants can be used directly for other layered materials in honeycomb lattice, and the design principles can be applied for any quasi-periodic incommensurate structures.

Dielectric metamaterials with quasicrystal structure

Three types of quasicrystal lattices based on the Penrose tiling are considered. We analyze the maximum filling fraction of these structures and find a design with the filling fraction corresponding to the case of periodic lattices. By using simulations of a Gaussian beam propagation through the quasicrystal structure we obtain a homogeneous field distribution that is a hallmark of near-zero regimes in metamaterials.

Tunable On‐Chip Sources with Aperiodic Metasurface

AbstractSurface plasmons show tremendous capability in integrated communication, quantum computing and sensing. Excitations and manipulations of surface plasmons are essential in developing integrated photonic devices. Here, a systematic study of tunable emission of surface plasmons with an eightfold quasicrystal metasurface, which acts as an on‐chip source, is presented. It is shown that the quasicrystal structure can switch on or off the surface plasmons propagation channels in the desired direction. Meanwhile, such a quasicrystal structure can be polarization‐dependent or polarization‐independent based on different constituent slit pairs. The proposed quasicrystal design provides more freedom for steering surface plasmons in the launching process. Thus, it may significantly simplify the design and fabrication of integrated plasmonic devices.

Higher-dimensional quasicrystalline approach to the Hofstadter butterfly topological-phase band conductances: Symbolic sequences and self-similar rules at all magnetic fluxes

The topological properties of the quantum Hall effect in a crystalline lattice, described by Chern numbers of the Hofstadter butterfly quantum phase diagram, are deduced by using a geometrical method to generate the structure of quasicrystals: the cut and projection method. Based on this, we provide a geometric unified approach to the Hofstadter topological phase diagram at all fluxes. Then we show that for any flux, the bands conductance follow a two letter symbolic sequence . As a result, bands conductance at different fluxes obey inflation/deflation rules as the ones observed to build quasicrystals. The bands conductance symbolic sequences are given by the Sturmian coding of the flux and can be found by considering a circle map, a billiard or trajectories on a torus. Simple and fast techniques are thus provided to obtain Chern numbers at any magnetic flux. This approach rationalize the previously observed topological equivalences between the Fibonacci and Harper potentials (also known as the almost Mathieu operator problem) or with other trigonometric potential, as well as the relationship with Farey sequences and trees.

A surface-stacking structural model for icosahedral quasicrystals

An original structural model for the description of icosahedral quasicrystals is proposed. This novel theoretical approach is based on a surface-stacking image of icosahedral quasicrystals and is in concert with the step-terrace morphology observed in many experimental investigations of real icosahedral surfaces. According to this model, the infinite icosahedral structure is constructed by stacking two arrangements of quasi-periodic surfaces along each of the 5-fold axis of the icosahedral symmetry. In this stacking order, the spacings between the layered surfaces are governed by Fibonacci sequence. The proposed model operates within the real physical (Euclidean) space and provides a direct three-dimensional visual representation of the icosahedral superstructure, which can be instrumental for conducting different modes of experimentations, analyses, and fabrication strategies; eliminating a major roadblock for researchers especially outside the fields of crystallography and material science. More importantly, understanding the long-range surface-stacking logic of the icosahedral structure will hopefully provide a deeper understanding of the structure of quasicrystals at an atomic scale and help achieve improved control over material compositions and structure.

Al–Cu–Fe quasicrystals as the anode for lithium ion batteries

In this paper, Al–Cu–Fe quasicrystal alloy was used as the anode material for lithium-ion batteries. The first specific discharge capacity of quasicrystal was 204 mA h/g. Cyclic voltammetry showed that the oxidation peak of the Al–Cu–Fe quasicrystal was at about 1.4 V. The reduction peak was at 0.3 V. The Al–Cu–Fe quasicrystals had a higher Li-ion diffusion impedance and Warburg impedance in the first cycle. X-ray diffraction analysis demonstrated that Li atoms enter into the quasicrystal structure and can-not fully leave the quasicrystal during the first charge-discharge cycle, which induces an irreversible capacity.

Transition Kinetics of Self-Assembled Supramolecular Dodecagonal Quasicrystal and Frank-Kasper σ Phases in ABn Dendron-Like Giant Molecules.

A series of noncrystalline ABn dendron-like giant molecules DPOSS-MPOSSn (n = 2-6, DPOSS: hydrophilic polyhedral oligomeric silsesquioxane (POSS) cage; MPOSS: hydrophobic POSS cage) were synthesized. These samples present a thermodynamically stable phase formation sequence from the hexagonal cylinder phase (plane group of P6mm), to the Frank-Kasper (F-K) A15 phase (space group of Pm3̅n), and further to the F-K σ phase (space group of P42/mnm), with increasing the number of MPOSS in a single molecule (n, from 2 to 6). Moreover, for DPOSS-MPOSS5 and DPOSS-MPOSS6, an intriguing dodecagonal quasicrystal (DQC) structure has been identified and revealed as a kinetic favorable metastable phase at lower temperatures, while the thermodynamically stable phase is the σ phase. The detailed investigation of the transition kinetics between the DQC and σ phase in these samples makes it possible to identify how the self-assembly directs the phase transition in terms of molecular and supramolecular aspects.

Discrete time quasicrystals

Between space crystals and amorphous materials there exists a third class of aperiodic structures which lack translational symmetry but reveal long-range order. They are dubbed quasi-crystals and their formation, similarly as the formation of space crystals, is related to spontaneous breaking of translational symmetry of underlying Hamiltonians. Here, we investigate spontaneous emergence of quasi-crystals in periodically driven systems. We consider a quantum many-body system which is driven by a harmonically oscillating force and show that interactions between particles result in spontaneous self-reorganization of the motion of a quantum many-body system and in the formation of a quasi-crystal structure in time.

The research of colorimetric sensor based on one-dimensional Fibonacci quasicrystal structure

Based on the principle of photonic crystal structure color, a one-dimensional Fibonacci quasi-crystal structure colorimetric sensor is designed and optimized. The optical model of quasi-crystal structure was constructed by iterative method with the number of iterations being 5. Quasicrystal structure consists of alternating arrangement of chitin and ethanol. A structure with higher color sensitivity was designed by changing the chitin filling ratio in the quasicrystal structure. Based on this structure, a high-sensitivity colorimetric sensor was designed by changing the amount of ethanol volatilization to monitor the change of reflectance spectrum.

The Investigation of Photonic Band Gap of 2D Multi-fold Photonic Quasicrystals

Two dimensional photonic quasicrystals (PQCs) with different rotational symmetries are constructed based on holographic interference patterns. The photonic band gap (PBG) are obtained by calculating the transmission and reflection spectra based on the finite element method (FEM). The maximum PBG of different PQCs is obtained and investigated by considering the same dielectric constant and different fill factors. All the simulation settings are the same except for the structure itself in this process. The results show that 10-fold quasicrystal exhibit better band gap richness than the others. This may provide a reference to select appropriate quasicrystal structures for photonic devices.

Discovery of quasicrystals: The early days

Abstract This paper is a survey of the initial developments of the research on quasicrystals starting from their discovery by Daniel Shechtman (Nobel Prize in Chemistry in 2011) in 1982 at the National Bureau of Standards (now National Institute for Standard and Technology) in Gaithersburg (Maryland, USA) up to the beginning of the early 1990s, a time when the crystallographic methods were well developed and mastered enough to decipher the ultimate atomic structures of quasicrystals. These early works have enlarged our understanding of spatial order in solids through a strong multidisciplinary effort between mathematicians, physicists, chemists and material scientists.

Photonic bandgap properties of two dimensional photonic quasicrystals with multiple complex structures

Abstract Two dimensional photonic quasicrystals (PQCs) with different rotational symmetries are constructed based on holographic interference patterns. Their photonic bandgap (PBG) properties are obtained by using finite element method (FEM) to calculate the transmission and reflection spectra with different directions. The maximum gap-midgap ratio among different dielectric constant contrast and fill factor is given for all the PQCs to compare their abilities to produce bandgaps. The results show that 10-fold (five beams interference) and 12-fold quasicrystals are easier to form bandgaps than others. This may provide a reference to select appropriate quasicrystal structures for photonic devices and optimize device performance.

Исследование надмолекулярной структуры нефтяных асфальтенов

The article is devoted to the topical problem of studying the supramolecular structure of petroleum asphaltenes. They are the prospective materials for molecular electronics and nanotechnology. At present, the properties of asphaltenes at the supramolecular level are studied by various experimental methods and methods of mathematical modeling. As objects of a research the asphaltenes concentrated in residual fractions of vacuum distillation of the West Siberian oil with a temperature of boiling more than 500 °C were used. Asphaltenes of samples allocated with dissolution of fractions in toluene with the subsequent sedimentation by surplus of n-heptane by Golde's technique. Results of ASM-researches show existence of steady units from nanoclusters of oil asphaltenes in the form of structures of an ellipsoidal form about 4.5 nm high and with a lateral size up to 100 nm. The research of supramolecular structure of nanoclusters of oil asphaltenes in the GAUSSIAN software package is executed. Calculation was carried out by method of molecular mechanics of MM with full optimization of geometry. The structure of molecular fragments of a nanoparticle of asphaltenes is defined according to data of 1H, 13C NMR and IR of spectroscopy and the chemical analysis earlier. These data will be agreed with results of works on identification of molecules of asphaltenes by the ASM method of high resolution. Follows from calculations that the nanoclusters having an appearance of quasicrystal reniform structures with number of molecular fragments from 2 to 10 are steadiest, at the same time the distance between the planes of molecular fragments of a nanocluster is in the range from 3.53 up to 3.67 Å, and diameter of particles 11-40 Å. Data on height of nanoclusters will well be agreed with results of ASM-researches for small structures. Calculations of supramolecular structure of oil asphaltenes by method of molecular mechanics show considerable energy of intermolecular interaction of structural molecular fragments of 60-118 kJ/mol that testifies to a possibility of self-assembly of ordered structures from these nanoparticles visualized by means of ASM. The received results are confirmed by data of the X-ray diffraction analysis and electric measurements on energy of activation of hopping conductivity (129.58 kJ/mol) and also the carried-out earlier thermodynamic calculations. As appears from calculations, the increased stability of quasicrystal structure which arises, most likely, as a result of transfer of a charge between fragments as molecules have the low potential of ionization and high affinity to an electron is characteristic of nanoclusters.

Preparation of bulk metallic glasses by modifying local structure of icosahedral quasicrystals

An attempt is carried out to design metallic glasses by modifying the local structure of icosahedral quasicrystals. A series of metallic glasses are prepared by introducing beryllium to the quasicrystal former, Zr40Ti40Ni20, and the maximum diameter of the glasses reaches 20 mm. A phase transformation diagram is constructed for the alloys of (Zr40Ti40Ni20)100-xBex, revealing the transition from stable crystal to quasicrystal and then to metallic glasses with the increased Be content. This study shows a connection between the formation of metallic glasses and the specific thermodynamics of the initially precipitated quasicrystals. Interestingly, both improvements in the forming ability for glasses and quasicrystals are observed over a wide composition range. Ab initio molecular dynamic simulations show the evolution of the structural features of the metallic melts for the optimised glass forming region, which guarantee the primary precipitation of quasicrystal.

A high-birefringent photonic quasi-crystal fiber with two elliptical air holes

A photonic quasi-crystal fiber (PQF) with high birefringence based on ZrF4-BaF2-LaF3-AlF3-NaF (ZBLAN) is described. There are two elliptical air holes in the core to increase birefringence and the outer air hole array has a twelve-fold Stampfli-type quasi-crystal structure. ZBLAN reduces absorption loss in the infrared region resulting in higher birefringence. The birefringence and confinement loss of the PQF are analyzed numerically by the full-vector finite element method. Birefringence is higher than that of conventional polarization-maintaining fibers due to the two elliptical air holes in the center and reaches the maximum of 4.15×10−2 at a wavelength of 2 μm. The novel structure has great potential in high-performance optical devices.

Static response of functionally graded multilayered one-dimensional hexagonal piezoelectric quasicrystal plates using the state vector approach

The effect of the non-homogeneity of material properties has been considered the important variation mechanism in the static responses of quasicrystal structures, but the existing theoretical model for it is unable to simulate the material change format beyond the exponential function. In this paper, we create a new model of functionally graded multilayered 1D piezoelectric quasicrystal plates using the state vector approach, in which varying functionally graded electro-elastic properties can be extended from exponential to linear and higher order in the thickness direction. Based on the state equations, an analytical solution for a single plate has been derived, and the result for the corresponding multilayered case is obtained utilizing the propagator matrix method. The present study shows, in particular, that coefficient orders of two varying functions (the power function and the exponential function) of the material gradient provide the ability to tailor the mechanical behaviors in the system’s phonon, phason, and electric fields. Moreover, the insensitive points of phonon stress and electric potential under functionally graded effects in the quasicrystal layer are observed. In addition, the influences of stacking sequences and discontinuity of horizontal stress are explored in the simulation by the new model. The results are very useful for the design and understanding of the characterization of functionally graded piezoelectric quasicrystal materials in their applications to multilayered systems.

Aperiodic ordered surface structures investigated by scanning tunneling microscopy

In recent years, much progress has been made in aperiodic ordered surface structures such as fractal and quasicrystal that can be synthesized by molecular self-assembly. Here we review the research progress of Sierpinski triangle fractal structures and quasicrystal structures on metal surfaces investigated by scanning tunneling microscopy. Constructions of Sierpinski triangle fractals with halogen, hydrogen, coordination and covalent bonds were realized on different basal surfaces via changing the precursor types, and complete fifth-order fractals were successfully prepared by a combination of the templating and co-assembly methods overcoming the surface kinetic limitations. Surface molecular quasicrystals were fabricated by utilizing the hydrogen bond between carboxylic acid groups through molecular self-assembly for the first time, and metal-organic coordination quasicrystals were successfully prepared by the coordination between organic molecule and rare-earth atoms.