Quasicrystalline Structure Research Articles

Fluorescent Microscopy-Based Detection of Chitin in Intact Drosophila melanogaster.

Chitin is the major scaffolding component of the insect cuticle. Ultrastructural analyses revealed that chitin adopts a quasi-crystalline structure building sheets of parallel running microfibrils. These sheets called laminae are stacked either helicoidally or with a preferred orientation of the microfibrils. Precise control of chitin synthesis is mandatory to ensure the correct chitin assembly and in turn proper function of cuticular structures. Thus, evaluation of chitin-metabolism deficient phenotypes is a key to our understanding of the function of the proteins and enzymes involved in cuticle architecture and more generally in cuticle biology in insects. Usually, these phenotypes have been assessed using electron microscopy, which is time-consuming and labor intensive. This stresses the need for rapid and straightforward histological methods to visualize chitin at the whole tissue level. Here, we propose a simple method of chitin staining using the common polysaccharide marker Fluorescent brightener 28 (FB28) in whole-mount Drosophila melanogaster. To overcome the physical barrier of FB28 penetration into the cuticle, staining is performed at 65°C without affecting intactness. We quantify FB28 fluorescence in three functionally different cuticular structures namely wings, dorsal abdomens and forelegs by fluorescence microscopy. We find that, as expected, cuticle pigmentation may interfere with FB28 staining. Down-regulation of critical genes involved in chitin metabolism, including those coding for chitin synthase or chitinases, show that FB28 fluorescence reflects chitin content in these organs. We think that this simple method could be easily applied to a large variety of intact insects.

Из опыта преподавания. X. Правильные, полуправильные и неправильные разбиения плоскости

The article deals with regular, semi-regular and irregular plane partitions, among the latter are partitions into equal polygons and arbitrary partitions with simple knots. It continues the author's supplementary lectures to the university textbook «Crystallography» by G. M. Popov and I. I. Shafranovsky, which was recommended to the students of geology of the St. Petersburg Mining University. The new topic is interesting because the first problem is solved elementary in the form of a Diophantine equation, the second is solved by algorithmic enumeration of variants, the third is related to the 18th Gilbert problem and is not exhausted yet, and the fourth shows the transition to the geometry of quasi-crystalline and amorphous structures. It gives examples of easily formulated but difficult to solve problems and encourages students to be scientifically creative in geometric crystallography and related disciplines (petrography, materials science). The presentation of the theory is illustrated with examples of plane partitions in urban interiors of St. Petersburg.

The Largest Quasicrystalline Tiling with Dodecagonal Symmetry from a Single Pentablock Quarterpolymer of the AB1CB2D Type.

A quasicrystalline tiling pattern with tile size of ca. 60 nm has been discovered in the bulk state of a four-component pentablock polymer molecule of the AS1IS2P type, where A, S, I, and P denote poly(4-vinylbenzyldimethylamine), polystyrene, polyisoprene, and poly(2-vinylpyridine), respectively. The polymer samples used were prepared by anionic polymerizations and have narrow molecular weight distribution. The sample films were obtained by an extremely slow solvent-cast process from dilute solutions of tetrahydrofuran for 14 days. It has been found by TEM observation that the quarterpolymer, AS1IS2P-4 (Mn = 149 kg/mol, ϕA/ϕS1/ϕI/ϕS2/ϕP = 0.12/0.27/0.20/0.29/0.13), reveals two final stable structures, i.e., a 3.3.4.3.4 periodic tiling pattern as a minor component and a quasicrystalline (QC) tiling with dodecagonal symmetry as a major component, where the former includes a triangle/square number ratio of 2 and the latter has one of approximately 2.28, which is close enough to the ideal ratio, 4/ 2.31, for the triangle/square random tiling of the dodecagonal QC tiling (DDQC). Two structures were also clearly proved by SAXS diffraction patterns. Here, it should be noted this QC structure having a tile side length of ca. 60 nm was created with a single block polymer molecule.

Fano resonance line shapes in the Raman spectra of tubulin and microtubules reveal quantum effects

Microtubules are self-assembling biological nanotubes made of the protein tubulin that are essential for cell motility, cell architecture, cell division, and intracellular trafficking. They demonstrate unique mechanical properties of high resilience and stiffness due to their quasi-crystalline helical structure. It has been theorized that this hollow molecular nanostructure may function like a quantum wire where optical transitions can take place, and photoinduced changes in microtubule architecture may be mediated via changes in disulfide or peptide bonds or stimulated by photoexcitation of tryptophan, tyrosine, or phenylalanine groups, resulting in subtle protein structural changes owing to alterations in aromatic flexibility. Here, we measured the Raman spectra of a microtubule and its constituent protein tubulin both in dry powdered form and in aqueous solution to determine if molecular bond vibrations show potential Fano resonances, which are indicative of quantum coupling between discrete phonon vibrational states and continuous excitonic many-body spectra. The key findings of this work are that we observed the Raman spectra of tubulin and microtubules and found line shapes characteristic of Fano resonances attributed to aromatic amino acids and disulfide bonds.

Effective Debye temperature of ionic liquids and their binary mixtures

Assuming the quasicrystalline structure to ionic liquids the effective Debye temperature of seven pure ionic liquids (H2O, DEAA, DEAS, TEAA, TEAS, TMAA, and TMAS.) has been calculated. Further, the model has been extended to six binary mixtures of (DEAA + H2O, DEAS + H2O, TEAA + H2O, TEAS + H2O, TMAA + H2O, and TMAS + H2O.). This is our first attempt in the study of thermal properties of pure ionic liquids and their binary mixtures. The concept of excess Debye temperature (θDE) has been introduced and correlated with interactions in ionic liquid systems. The input data desired are density, sound speed, heat capacity and ratio of heat capacities (CP/CV).

Quantum Many-Body Topology of Quasicrystals

In this paper, we characterize quasicrystalline interacting topological phases of matter i.e., phases protected by some quasicrystalline structure. We show that the elasticity theory of quasicrystals, which accounts for both "phonon" and "phason" modes, admits non-trivial quantized topological terms with far richer structure than their crystalline counterparts. We show that these terms correspond to distinct phases of matter and also uncover intrinsically quasicrystalline phases, which have no crystalline analogues. For quasicrystals with internal $\mathrm{U}(1)$ symmetry, we discuss a number of interpretations and physical implications of the topological terms, including constraints on the mobility of dislocations in $d=2$ quasicrystals and a quasicrystalline generalization of the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem. We then extend these ideas much further and address the complete classification of quasicrystalline topological phases, including systems with point-group symmetry as well as non-invertible phases. We hence obtain the "Quasicrystalline Equivalence Principle," which generalizes the classification of crystalline topological phases to the quasicrystalline setting.

Microstructural features and mechanical properties of a novel Ti- and Zr-modified Al-Mn alloy processed by laser powder bed fusion

The expansion of the material library for the laser powder bed fusion (LPBF) process is essential for the further establishment of the process in areas such as the aerospace and automotive industries. In this study, we designed a high-strength and low-cost Al-Mn-Ti-Zr alloy specifically tailored to the unique conditions of the LPBF process. Gas-atomized pre-alloyed powder was prepared and used as feedstock to fabricate LPBF specimens for microstructural examination and mechanical testing. By taking advantage of the high solidification rate, unconventionally large amounts of Mn (3.7 ± 0.5 wt%) are metastably frozen within the α-Al matrix, contributing significantly to solid solution hardening (~104 MPa ≙ 37% share of yield strength). The as-built specimens exhibit a yield strength of 284 ± 3 MPa, an ultimate tensile strength of 320 ± 1 MPa, and an elongation at fracture of 16.9 ± 0.2%. This new alloy exhibits a bimodal microstructure consisting of alternately distributed fine equiaxed and coarse columnar grain regions. Further microstructural analyses reveal a high number of primary L12 cubic Al3(Tix Zr1 - x) nanoparticles within the equiaxed α-Al grains near the bottom of the melt pool. A highly coherent interface with the α-Al matrix confirms high efficiency for heterogeneous nucleation during solidification. In addition to the Al3(Tix Zr1 - x) nanoparticles, an AlxMn(Fe, Si) phase with a quasi-crystalline structure is observed along the grain boundaries and interdendritic areas.

Peculiarities in the Structure Formation and Corrosion of Quasicrystalline Al65Co20Cu15 Alloy in Neutral and Acidic Media

In the present study, the structure and corrosion properties of quasicrystalline conventionally solidified Al65Co20Cu15 alloy cooled at 5 К/s were investigated. Structure was characterized by metallography, X-Ray diffraction, scanning electron microscopy, and energy dispersive spectroscopy. Corrosion properties were determined by gravimetric and potentiodynamic methods at room temperature. The investigations performed confirm the peritectic formation of stable quasicrystalline decagonal D-phase that coexists with crystalline Al4(Co,Cu)3 and Al3(Cu,Co)2 phases in the structure of Al65Co20Cu15 alloy. According to energy dispersive spectroscopy, the stoichiometric composition of D-phase is Al63Co24Cu13. The susceptibility of the Al65Co20Cu15 alloy to corrosion significantly decreases with increasing pH from 1.0 (acidic media) to 7.0 (neutral medium). A corrosion rate of the Al65Co20Cu15 alloy in the aqueous acidic solutions (pH=1.0) increases in the order HNO3®HCl®H2SO4®H3PO4. The mass of the specimens decreases in the solutions of H2SO4 or H3PO4 and increases in the solutions of HNO3 or HCl which relates to different rate ratios of accumulation and dissolution of corrosion products. The Al65Co20Cu15 alloy exhibits the highest corrosion resistance in the NaCl solution (pH=7.0) in which it corrodes under electrochemical mechanism with oxygen depolarization. The better corrosion resistance in sodium chloride solution is achieved due to the formation of passive chemical compounds blocking the surface. Free corrosion potential of the Al65Co20Cu15 alloy has value –0.43 V, the electrochemical passivity region extends from –1.0 V to –0.4 V, and a corrosion current density amounts to 0.18 mА/сm2. Depending on media, two typical surface morphologies are revealed after corrosion of quasicrystalline specimens of the Al65Co20Cu15 alloy. In the H2SO4 and H3PO4 acidic solutions, clean specimens’ surface due to its homogeneous dissolution is observed except for the more defective areas, such as boundaries of crystalline Al3(Cu,Co)2 phase containing less Co, which dissolve at a higher rate. In the HNO3, HCl or NaCl solutions, a porous layer on the surface is formed which is visually revealed as surface darkening. After staying in the NaCl solution, on the surface of the Al65Co20Cu15 alloy, the pits are also found due to preferential dissolution of components where the boundaries of Al3(Cu,Co)2 phase and flaws are located.

Moiré, Euler and self-similarity - the lattice parameters of twisted hexagonal crystals.

A real-space approach for the calculation of the moiré lattice parameters for superstructures formed by a set of rotated hexagonal 2D crystals such as graphene or transition-metal dichalcogenides is presented. Apparent moiré lattices continuously form for all rotation angles, and their lattice parameter to a good approximation follows a hyperbolical angle dependence. Moiré crystals, i.e. moiré lattices decorated with a basis, require more crucial assessment of the commensurabilities and lead to discrete solutions and a non-continuous angle dependence of the moiré-crystal lattice parameter. In particular, this lattice parameter critically depends on the rotation angle, and continuous variation of the angle can lead to apparently erratic changes of the lattice parameter. The solutions form a highly complex pattern, which reflects number-theoretical relations between formation parameters of the moiré crystal. The analysis also provides insight into the special case of a 30° rotation of the constituting lattices, for which a dodecagonal quasicrystalline structure forms.

Topological states in quasicrystals

With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals, particularly focusing on one-dimensional (1D) and 2D systems. We first give a brief introduction to quasicrystalline structures. Then, we discuss topological phases in 1D quasicrystals where the topological nature is attributed to the synthetic dimensions associated with the quasiperiodic order of quasicrystals. We further present the generalization of various types of crystalline topological states to 2D quasicrystals, where real-space expressions of corresponding topological invariants are introduced due to the lack of translational symmetry in quasicrystals. Finally, since quasicrystals possess forbidden symmetries in crystals such as five-fold and eight-fold rotation, we provide an overview of unique quasicrystalline symmetry-protected topological states without crystalline counterpart.

Electronic instabilities in Penrose quasicrystals: Competition, coexistence, and collaboration of order

Quasicrystals lack translational symmetry, but can still exhibit long-range order, promoting them to candidates for unconventional physics beyond the paradigm of crystals. Here, we apply a real-space functional renormalization group approach to the prototypical quasicrystalline Penrose tiling Hubbard model treating competing electronic instabilities in an unbiased, beyond-mean-field fashion. Our work reveals a delicate interplay between charge and spin degrees of freedom in quasicrystals. Depending on the range of interactions and hopping amplitudes, we unveil a rich phase diagram including antiferromagnetic orderings, charge density waves, and subleading, superconducting pairing tendencies. For certain parameter regimes, we find a competition of phases, which is also common in crystals, but additionally encounter phases coexisting in a spatially separated fashion and ordering tendencies which mutually collaborate to enhance their strength. We therefore establish that quasicrystalline structures open up a route towards this rich ordering behavior uncommon to crystals and that an unbiased, beyond-mean-field approach is essential to describe this physics of quasicrystals correctly.6 MoreReceived 31 August 2020Revised 17 December 2020Accepted 12 May 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023180Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAntiferroelectricityCharge density wavesEdge statesElectrical propertiesMagnetic orderPhase transitionsQuasicrystalline structurePhysical Systems2-dimensional systemsQuasicrystalsTechniquesHubbard modelMean field theoryRenormalization groupSecond quantizationSymmetries in condensed matterTight-binding modelCondensed Matter, Materials & Applied Physics

On the nonmonotonous behavior of the thermal properties of fullerene C60 / o-xylene solutions

This paper presents the experimental data for the thermal properties of fullerene C60 / o-xylene solutions over a wide range of state parameters. The density was experimentally measured within a fullerene mass concentration range of 0–0.55% and a temperature range 273 K − 353 K. It was shown that the additives of fullerene C60 reduced the density of o-xylene in the concentration range from 0 to (0.05 ± 0.01) wt.%. The temperature and concentration dependences of the isothermal compressibility and density fluctuations were analyzed. It was demonstrated that the temperature dependences of the density fluctuations show up as practically equidistant lines. This fact can be explained due to thermodynamically similar behavior of fullerene C60 / o-xylene solutions and pure o-xylene. We found that the concentration dependences of the isothermal compressibility and density fluctuations in the concentration range of fullerene 0 ≤ wC6 ≤ 0.2% have zones of extremal changes. The zones coincide in the concentration range of fullerene with a zone of extreme decrease in the density. In our opinion, the reason of a nonmonotonous behavior of the thermal properties of fullerene C60 / o-xylene solutions is the effect of fullerene on the density fluctuations of the base liquid as well as a quasicrystalline structure of a liquid phase.

Homogenization of Quasi-Crystalline Functionals via Two-Scale-Cut-and-Project Convergence

We consider a homogenization problem associated with quasi-crystalline multiple integrals of the form $u_\varepsilon\in L^p(\Omega;\mathbbm{R}^d) \mapsto \int_\Omega f_R(x,\frac{x}{\varepsilon}, u_\varepsilon(x)), dx,$ where \(u_ǎrepsilon) is subject to constant-coefficient linear partial differential constraints. The quasi-crystalline structure of the underlying composite is encoded in the dependence on the second variable of the Lagrangian, (f_R), and is modeled via the cut-and-project scheme that interprets the heterogeneous microstructure to be homogenized as an irrational subspace of a higher-dimensional space. A key step in our analysis is the characterization of the quasi-crystalline two-scale limits of sequences of the vector fields (u_ǎrepsilon) that are in the kernel of a given constant-coefficient linear partial differential operator, (\mathcalA), that is, (\mathcalA u _ǎrepsilon =0). Our results provide a generalization of related ones in the literature concerning the (\mathcalA =curl ) case to more general differential operators (\mathcalA) with constant coefficients and without coercivity assumptions on the Lagrangian (f_R).

Propagation-dependent evolution of interfering multiple beams and kaleidoscopic vortex lattices

In this Letter, we experimentally explore the propagation-dependent evolution of generating the pseudo-nondiffracting quasi-crystalline (crystalline) beams based on the multibeam interference. We originally derived an analytical formula to exactly manifest the propagation evolution of interfering multiple beams. With the analytical formula, the formation of quasi-crystalline structures in the focal plane can be explicitly verified. Furthermore, the distance of the effective propagation-invariant region can be verified in terms of experimental parameters. More importantly, we employed the developed formula to confirm the formation of kaleidoscopic vortex lattices by means of numerically computing the propagation-dependent phase singularities.

Evolution of local motifs and topological proximity in self-assembled quasi-crystalline phases.

Using methods from the field of topological data analysis, we investigate the self-assembly and emergence of three-dimensional quasi-crystalline structures in a single-component colloidal system. Combining molecular dynamics and persistent homology, we analyse the time evolution of persistence diagrams and particular local structural motifs. Our analysis reveals the formation and dissipation of specific particle constellations in these trajectories, and shows that the persistence diagrams are sensitive to nucleation and convergence to a final structure. Identification of local motifs allows quantification of the similarities between the final structures in a topological sense. This analysis reveals a continuous variation with density between crystalline clathrate, quasi-crystalline, and disordered phases quantified by 'topological proximity', a visualization of the Wasserstein distances between persistence diagrams. From a topological perspective, there is a subtle, but direct connection between quasi-crystalline, crystalline and disordered states. Our results demonstrate that topological data analysis provides detailed insights into molecular self-assembly.

Generation of regular optical patterns and photonic structures by a single Gaussian beam in a photorefractive LiNbO3:Fe crystal

We report 2D micrometric scale regular optical patterns formation induced by a laser beam propagating through a Fe doped lithium niobate (LN:Fe) crystal. A single mode CW laser radiation at 632.8 nm wavelength and beam powers from 0.5 to 10 mW and LN:Fe samples with 0.03 wt% Fe concentration and thicknesses of 4 mm and 10 mm were used in the experiments. The observed phenomenon of optical patterns formation in photorefractive crystal is explained with the light-induced complex refractive index variation with a central minimum (negative lens) and symmetric maxima (positive lenses) on each side due to photovoltaic effect in the crystal. Light-induced complex lenses produce beam defocusing from the beam center and focusing on the periphery. Mutual interference of the beams leads to a regular optical pattern formation. Regular optical pattern, in its turn, leads to the formation of quasi-crystalline photonic structure in LN:Fe crystal. Experimental results are supported by numerical simulations.

Search for the boron quasicrystal by first-principle-calculation

Among quasicrystals, no semiconductor has been reported, and the existence of semiconducting quasicrystal is one of the major questions in the solid-state physics, and a semiconducting quasicrystal is expected to be a high performance thermoelectric material. First-principles calculations was performed on four real crystalline structures and hypothetical approximant crystalline and quasicrystalline structures, and total energies were calculated. The formation energy of the α-type 1/1-cubic approximant crystal was found to be very close to the estimated value based on the approximate equation using the formation energy and abundance ratio of α-prolate and α-oblate. From this, it is considered that the estimated value by the approximate equation is reliable, and it is estimated that the β-type 1/1-cubic approximant crystal and β-type quasicrystal have the almost the same formation energy as the α-tetragonal boron phase known as metastable phase. This suggests the possibility of formation of boron quasicrystal as a metastable phase. In addition, the electronic density of states was clarified in the α-type 1/1-cubic approximant crystal. As a result, it was shown that the α-type 1/1-cubic approximant crystal is a semiconductor having a band gap of about 0.25 eV, and it can be strongly expected that the boron quasicrystal is also a semiconductor.

Phason mechanism for diffusion in quasicrystalline structures

Specific properties of quasicrystals (QCs) with regards to their structures are discussed with emphasis on diffusion process. To fulfil this, regular mechanisms in the solids are introduced. The experimental results show that the predominant mechanism in quasicrystals is phason which is caused by the absence of proper matching in their structure and the vacancies in the lattice. Monolayers of Al were deposited on the surface of an i-Al-Pd-Mn quasicrystal at constant temperature and the diffusion of the elements into the surface measured by low energy ion scattering. According to our results the activation energy for Al diffusion in the i-Al-Pd-Mn quasicrystal is found to be smaller than that for Al diffusion in regular crystals. It was therefore concluded that a phason mechanism controlled the diffusion. The results of this work can be phason mechanism predominate which is agreement with the some theoretical scientists who believe to phason mechanism at least in low temperatures.

Phase transformations in commercial cold-rolled Al–Zn–Mg–Cu alloys with Sc and Zr addition

The influence of cold rolling on thermal and mechanical properties together with microstructure observation of cast AlZnMgCu(ScZr) alloys has been investigated. Differential scanning calorimetry measurements and microhardness were compared to microstructure that was observed by microscopy (scanning electron and transmission), electron backscatter and X-ray diffractions. Microstructure observation of all studied alloys proved eutectic phase at (sub)grain boundaries. The eutectic phase at grain boundary in the AlZnMgCuScZr has a disordered quasicrystalline structure (known as the T phase or Mg32(Al,Cu,Zn)49). In the AlZnMgCu alloy, the eutectic phase consists of two phases—predominant MgZn2 phase and minor quasicrystalline T phase. During casting and subsequent cooling, multilayer primary Al3(Sc,Zr) particles also precipitated in the alloy with Sc,Zr addition. Solute clusters and/or Guinier–Preston zones were dissolved during the annealing up to ~ 170 °C in the alloys. The highest hardening is caused by particle formation of metastable η′ and stable η phase in AlZnMgCu system observed at ~ 200 °C. Precipitation of the secondary Al3(Sc,Zr) particles is probably the reason of hardening after annealing above 300 °C in the Sc,Zr-containing alloys. Melting of eutectic phases was observed in DSC curves at temperatures ~ 481 and ~ 493 °C in the studied alloys. Activation energies of the Guinier–Preston zones dissolution and/or solute clusters were calculated using Kissinger and Starink method as QA ≈ 100 kJ mol−1 and the formation of the particles of Al–Zn–Mg–Cu system as QB ≈ 150 kJ mol−1. No significant effect on the calculation of activation energy values of thermal processes was observed in deformed alloys. Sc,Zr addition in the alloys stabilizes grains, and there is no recrystallization in the AlZnMgCuScZr alloy at temperature 450 °C/10 h.

Mini-Workshop: Mathematics of Crystallisation

Crystallisation, by which we mean the formation of solids precipitating from a solution, is the central theme of the present mini-workshop. Participants discussed different approaches towards a rigorous mathematical understanding of crystallisation as well as detecting, modelling and establishing properties of crystalline and quasicrystalline structures