Electrical discharge triggers quasicrystal formation in an eolian dune.

We report the discovery of a dodecagonal quasicrystal Mn72.3Si15.6Cr9.7Al1.8Ni0.6-composed of a periodic stacking of atomic planes with quasiperiodic translational order and 12-fold symmetry along the two directions perpendicular to the planes-accidentally formed by an electrical discharge event in an eolian dune in the Sand Hills near Hyannis, Nebraska, United States. The quasicrystal, coexisting with a cubic crystalline phase with composition Mn68.9Si19.9Ni7.6Cr2.2Al1.4, was found in a fulgurite consisting predominantly of fused and melted sand along with traces of melted conductor metal from a nearby downed power line. The fulgurite may have been created by a lightning strike that combined sand with material from downed power line or from electrical discharges from the downed power line alone. Extreme temperatures of at least 1,710 °C were reached, as indicated by the presence of SiO2 glass in the sample. The dodecagonal quasicrystal is an example of a quasicrystal of any kind formed by electrical discharge, suggesting other places to search for quasicrystals on Earth or in space and for synthesizing them in the laboratory.

Topological magnetic textures and long-range orders in terbium-based quasicrystal and approximant.

The quasicrystal (QC) possesses a unique lattice structure with rotational symmetry forbidden in periodic crystals. The electric property is far from complete understanding. It has been a long-standing issue whether magnetic long-range order is realized in the QC. Here, we report our theoretical discovery of the ferromagnetic long-range order in the Tb-based QC. The difficulty in past theoretical studies on the QC was lack of the microscopic theory of the crystalline electric field (CEF), which is crucially important in the rare earth systems. By analyzing the CEF in the Tb-based QC, we clarify that magnetic anisotropy plays a key role in realizing unique magnetic textures in the Tb-based QC and approximant crystal (AC). By constructing the minimal model, we show that various magnetic textures on the icosahedron, at whose vertices Tb atoms are located, are realized. We find that the hedgehog state is characterized by the topological charge of one and the whirling-moment state is characterized by an unusually large topological charge of three. The hedgehog and whirling-moment states are shown to be realized as antiferromagnetic orders transcribed as the emergent monopole and antimonopole in the 1/1 AC. We find that these states exhibit the topological Hall effect under applied magnetic field accompanied by the topological as well as metamagnetic transition. Our model and the determined phase diagram are expected to be relevant to the broad range of the rare earth-based QCs and ACs with strong magnetic anisotropy, which are useful not only to understand magnetism but also, to explore topological properties.

Entropic formation of a thermodynamically stable colloidal quasicrystal with negligible phason strain.

Quasicrystals have been discovered in a variety of materials ranging from metals to polymers. Yet, why and how they form is incompletely understood. In situ transmission electron microscopy of alloy quasicrystal formation in metals suggests an error-and-repair mechanism, whereby quasiperiodic crystals grow imperfectly with phason strain present, and only perfect themselves later into a high-quality quasicrystal with negligible phason strain. The growth mechanism has not been investigated for other types of quasicrystals, such as dendrimeric, polymeric, or colloidal quasicrystals. Soft-matter quasicrystals typically result from entropic, rather than energetic, interactions, and are not usually grown (either in laboratories or in silico) into large-volume quasicrystals. Consequently, it is unknown whether soft-matter quasicrystals form with the high degree of structural quality found in metal alloy quasicrystals. Here, we investigate the entropically driven growth of colloidal dodecagonal quasicrystals (DQCs) via computer simulation of systems of hard tetrahedra, which are simple models for anisotropic colloidal particles that form a quasicrystal. Using a pattern recognition algorithm applied to particle trajectories during DQC growth, we analyze phason strain to follow the evolution of quasiperiodic order. As in alloys, we observe high structural quality; DQCs with low phason strain crystallize directly from the melt and only require minimal further reduction of phason strain. We also observe transformation from a denser approximant to the DQC via continuous phason strain relaxation. Our results demonstrate that soft-matter quasicrystals dominated by entropy can be thermodynamically stable and grown with high structural quality--just like their alloy quasicrystal counterparts.

Understanding the Role of Trapezoids in Honeycomb Self-Assembly-Pathways between a Columnar Liquid Quasicrystal and its Liquid-Crystalline Approximants.

Quasiperiodic patterns and crystals-having long range order without translational symmetry-have fascinated researchers since their discovery. In this study, we report on new p-terphenyl-based T-shaped facial polyphiles with two alkyl end chains and a glycerol-based hydrogen-bonded side group that self-assemble into an aperiodic columnar liquid quasicrystal with 12-fold symmetry and its periodic liquid-crystalline approximants with complex superstructures. All represent honeycombs formed by the self-assembly of the p-terphenyls, dividing space into prismatic cells with polygonal cross-sections. In the perspective of tiling patterns, the presence of unique trapezoidal tiles, consisting of three rigid sides formed by the p-terphenyls and one shorter, incommensurate, and adjustable side by the alkyl end chains, plays a crucial role for these phases. A delicate temperature-dependent balance between conformational, entropic and space-filling effects determines the role of the alkyl chains, either as network nodes or trapezoid walls, thus resulting in the order-disorder transitions associated with emergence of quasiperiodicity. In-depth analysis suggests a change from a quasiperiodic tiling involving trapezoids to a modified one with a contribution of trapezoid pair fusion. This work paves the way for understanding quasiperiodicity emergence and develops fundamental concepts for its generation by chemical design of non-spherical molecules, aggregates, and frameworks based on dynamic reticular chemistry.

Rapid Phase Transitions of Thermotropic Glycolipid Quasicrystal and Frank-Kasper Mesophases: A Mechanistic Rosetta Stone.

Experimental results are presented that serve to lower the barrier for developing the science and technology of non-classical thermotropic glycolipid mesophases, which now include dodecagonal quasicrystal (DDQC) and Frank-Kasper (FK) A15 and σ mesophases that can be produced under mild conditions from a versatile class of sugar-polyolefin conjugates. By employing "alloys" comprised of mono- and disaccharide-polyolefin conjugates, and optionally with vitamin E as a small molecule phase modulator, we report the spontaneous formation of stable A15 mesophases at ambient temperature. We further document a rich thermotropic phase map that includes DDQC, A15, and σ mesophases of tunable periodicity that are connected through rapid thermotropic phase transitions as a function of increasing temperature in the order: liquid-like packing (LLP)→DDQC → A15→σ→ disorder. This first direct observation of a rapid thermotropic A15→σ phase transition provides support for a diffusionless martensitic process proceeding through strain-induced introduction of planar defects into the A15 lattice.

A Highly Versatile Porous Core Photonic Quasicrystal Fiber Based Refractive Index Terahertz Sensor.

Miniaturized real-time fiber optic sensing systems with high sensing performance are in extreme demand. In this work, we propose a novel photonic quasicrystal fiber sensor in the terahertz region and test its sensing characteristics using the finite element method. The proposed simulated sensor numerically investigates the cancer-infected cells from the normal cells in the human cervix, blood, adrenal glands, and breast based on the difference in their refractive index changes. The effective refractive index of core-guided mode is due to the interaction of light between the refractive index of the fiber material and infiltrated normal and cancer cells, respectively. The proposed sensor exhibits a high birefringence of 0.03, a low dispersion of 0.35 ps/THz/cm, along with a high numerical aperture of 0.99. Besides, the sensor holds a less-effective material loss of 2.53 × 10-9 (dB/cm), a maximum power fraction of 88.10, a maximum relative sensitivity of 82.67%, and an effective mode area of 3.16 mm2. The results envisage that the proposed sensor displays high sensing performances with a rapid cancer detection mechanism.

Generic Orbital Design of Higher-Order Topological Quasicrystalline Insulators with Odd Five-Fold Rotation Symmetry.

In addition to crystals, topological phases in quasicrystals and disorder systems have drawn increasing attention lately. Here, we propose a generic double band-inversion mechanism underlying the higher-order topological phase in quasicrystals, that is.,"higher-order topological quasicrystalline insulator" (HOTQI), which exploits local atomic orbital and lattice symmetries. It is generally applicable to both quasicrystals and crystals with either odd-rotational (OR) or even-rotational symmetry (ERS), different from previous HOTI mechanisms whose applicability is limited by symmetry types. The HOTQI is characterized by topological corner states at the nonordinary corners of pentagonal (octagonal) samples of five-fold (eight-fold) quasicrystals, which violate the translational invariance and ordinary crystalline symmetries. The role of quasicrystalline symmetry, the robustness against symmetry breaking, and possible experimental realizations are discussed. Our findings not only provide a concrete example of HOTQIs that is incompatible with classical crystallographic symmetry but also offer useful guidance to the search of higher-order topological materials and metamaterials.

Interaction instability of localization in quasiperiodic systems.

Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport properties discontinuously change from localization to diffusion upon switching on interaction. This demonstrates an inherent instability of a possible many-body localization in a quasiperiodic potential at small interactions. We also show how the transport properties can be strongly modified by engineering potential at only a few lattice sites.

Metastable quasicrystal-induced nucleation in a bulk glass-forming liquid.

This study presents a unique Mg-based alloy composition in the Mg-Zn-Yb system which exhibits bulk metallic glass, metastable icosahedral quasicrystals (iQCs), and crystalline approximant phases in the as-cast condition. Microscopy revealed a smooth gradual transition from glass to QC. We also report the complete melting of a metastable eutectic phase mixture (including a QC phase), generated via suppression of the metastable-to-stable phase transition at high heating rates using fast differential scanning calorimetry (FDSC). The melting temperature and enthalpy of fusion of this phase mixture could be measured directly, which unambiguously proves its metastability in any temperature range. The kinetic pathway from liquid state to stable solid state (an approximant phase) minimizes the free-energy barrier for nucleation through an intermediate state (metastable QC phase) because of its low solid-liquid interfacial energy. At high undercooling of the liquid, where diffusion is limited, another approximant phase with near-liquid composition forms just above the glass-transition temperature. These experimental results shed light on the competition between metastable and stable crystals, and on glass formation via system frustration associated with the presence of several free-energy minima.

Geometry induced sequence of nanoscale Frank-Kasper and quasicrystal mesophases in giant surfactants.

Frank-Kasper (F-K) and quasicrystal phases were originally identified in metal alloys and only sporadically reported in soft materials. These unconventional sphere-packing schemes open up possibilities to design materials with different properties. The challenge in soft materials is how to correlate complex phases built from spheres with the tunable parameters of chemical composition and molecular architecture. Here, we report a complete sequence of various highly ordered mesophases by the self-assembly of specifically designed and synthesized giant surfactants, which are conjugates of hydrophilic polyhedral oligomeric silsesquioxane cages tethered with hydrophobic polystyrene tails. We show that the occurrence of these mesophases results from nanophase separation between the heads and tails and thus is critically dependent on molecular geometry. Variations in molecular geometry achieved by changing the number of tails from one to four not only shift compositional phase boundaries but also stabilize F-K and quasicrystal phases in regions where simple phases of spheroidal micelles are typically observed. These complex self-assembled nanostructures have been identified by combining X-ray scattering techniques and real-space electron microscopy images. Brownian dynamics simulations based on a simplified molecular model confirm the architecture-induced sequence of phases. Our results demonstrate the critical role of molecular architecture in dictating the formation of supramolecular crystals with "soft" spheroidal motifs and provide guidelines to the design of unconventional self-assembled nanostructures.

Very large thermal rectification in bulk composites consisting partly of icosahedral quasicrystals.

The bulk thermal rectifiers usable at a high temperature above 300 K were developed by making full use of the unusual electron thermal conductivity of icosahedral quasicrystals. The unusual electron thermal conductivity was caused by a synergy effect of quasiperiodicity and by a narrow pseudogap at the Fermi level. The rectification ratio, defined by TRR = [Formula: see text], reached vary large values exceeding 2.0. This significant thermal rectification would lead to new practical applications for the heat management.

Tailoring microstructure of Mg-Zn-Y alloys with quasicrystal and related phases for high mechanical strength.

The occurrence of a stable icosahedral (i-) phase, which is quasicrystalline with an icosahedral (fivefold) symmetry, on the equilibrium phase diagram of Mg-Zn-RE (RE = Y, Gd, Tb, Dy, Ho or Er) alloys opened up an interesting possibility of developing a new series of magnesium alloys for structural applications. Alloys based on the i-phase have been studied for the past 14 years. Ultra-high strengths combined with good ductility have been shown. Here we show two strategies for tailoring microstructures for very high strengths in Mg-Zn-Y alloys. One of them involves strengthening by a fine distribution of rod-like [Formula: see text] precipitates, where the matrix grain size is not critical. The alloy is solutionized at a high temperature of 480 °C to dissolve a large part of the i-phase, followed by a high temperature extrusion (∼430 °C) and a low temperature ageing to reprecipitate phases with fine size distribution. At first, phase transformations involved in this procedure are described. The closeness of the structure of the [Formula: see text] precipitates to the i-phase is brought out. By this procedure, tensile yield strengths of over 370 MPa are obtained in grain sizes of 20 µm. In another strategy, the alloys are chill cast and then extruded at low temperatures of about 250 °C. Ultra-fine grains are produced by enhanced recrystallization due to presence of the i-phase. At the same time nano-sized precipitates are precipitated dynamically during extrusion from the supersaturated matrix. Ultra-high tensile strengths of up to 400 MPa are obtained in combination with ductility of 12 to 16%. Analysis of the microstructure shows that strengthening by the i-phase occurs by enhanced recrystallization during extrusion. It produces ultra-fine grain sizes to give very high strengths, and moderate texture for good ductility. Fine distribution of the i-phase and precipitates contribute to strengthening and provide microstructre stability. Ultra-high strength over a very wide range of grain sizes is thus demonstrated, by utilizing different strengthening effects.

Photonic crystals, amorphous materials, and quasicrystals.

Photonic crystals consist of artificial periodic structures of dielectrics, which have attracted much attention because of their wide range of potential applications in the field of optics. We may also fabricate artificial amorphous or quasicrystalline structures of dielectrics, i.e. photonic amorphous materials or photonic quasicrystals. So far, both theoretical and experimental studies have been conducted to reveal the characteristic features of their optical properties, as compared with those of conventional photonic crystals. In this article, we review these studies and discuss various aspects of photonic amorphous materials and photonic quasicrystals, including photonic band gap formation, light propagation properties, and characteristic photonic states.

Activation of Al-Cu-Fe quasicrystalline surface: fabrication of a fine nanocomposite layer with high catalytic performance.

A fine layered nanocomposite with a total thickness of about 200 nm was formed on the surface of an Al63Cu25Fe12 quasicrystal (QC). The nanocomposite was found to exhibit high catalytic performance for steam reforming of methanol. The nanocomposite was formed by a self-assembly process, by leaching the Al-Cu-Fe QC using a 5 wt% Na2CO3 aqueous solution followed by calcination in air at 873 K. The quasiperiodic nature of theQC played an important role in the formation of such a structure. Its high catalytic activity originated from the presence of highly dispersed copper and iron species, which also suppressed the sintering of nanoparticles.

Surfaces of Al-based complex metallic alloys: atomic structure, thin film growth and reactivity.

We present a review on recent work performed on periodic complex metallic alloy (CMA) surfaces. The electronic and crystallographic structures of clean pseudo-tenfold, pseudo-twofold, sixfold surfaces will be presented along with the recent findings on CMA of lower structural complexity, i.e. with a smaller unit cell. The use of CMA surfaces as templates for thin film growth and the formation of surface alloy will also be introduced. The reactivity of these complex surfaces and their impact in the field of heterogeneous catalysis will be discussed. Finally, common trends among these systems will be highlighted when possible and future challenges will be examined.

Metallic-covalent bonding conversion and thermoelectric properties of Al-based icosahedral quasicrystals and approximants.

In this article, we review the characteristic features of icosahedral cluster solids, metallic-covalent bonding conversion (MCBC), and the thermoelectric properties of Al-based icosahedral quasicrystals and approximants. MCBC is clearly distinguishable from and closely related to the well-known metal-insulator transition. This unique bonding conversion has been experimentally verified in 1/1-AlReSi and 1/0-Al12Re approximants by the maximum entropy method and Rietveld refinement for powder x-ray diffraction data, and is caused by a central atom inside the icosahedral clusters. This helps to understand pseudogap formation in the vicinity of the Fermi energy and establish a guiding principle for tuning the thermoelectric properties. From the electron density distribution analysis, rigid heavy clusters weakly bonded with glue atoms are observed in the 1/1-AlReSi approximant crystal, whose physical properties are close to icosahedral Al-Pd-TM (TM: Re, Mn) quasicrystals. They are considered to be an intermediate state among the three typical solids: metals, covalently bonded networks (semiconductor), and molecular solids. Using the above picture and detailed effective mass analysis, we propose a guiding principle of weakly bonded rigid heavy clusters to increase the thermoelectric figure of merit (ZT) by optimizing the bond strengths of intra- and inter-icosahedral clusters. Through element substitutions that mainly weaken the inter-cluster bonds, a dramatic increase of ZT from less than 0.01 to 0.26 was achieved. To further increase ZT, materials should form a real gap to obtain a higher Seebeck coefficient.

Heptatic liquid quasi-crystals by colloidal lithographic pre-assembly.

HYPOTHESIS: We hypothesize that pre-assembled lithographic Brownian seven-fold quasi-crystals (QCs) of colloidal tiles at high densities can exhibit a heptatic liquid quasi-crystal (LQC) phase upon release; such heptatic LQCs can undergo heterogeneous dynamics at different length scales, reflecting the underlying symmetry, corrugation, and hierarchy of local sets of tiles. EXPERIMENTS: We design, fabricate, and release a seven-fold QC composed of three differently shaped rhombic tiles using the method of lithographically pre-assembled monolayers (litho-PAMs). High resolution optical microscopy enables spatio-temporal particle tracking of Brownian fluctuations of many tiles in a large area over a long time. We develop an edge-proximity tessellation method for analyzing nearest neighboring particles that can be applied to assemblies and dense systems of complex shapes. FINDINGS: A fluctuating heptatic LQC phase is identified at high tile area fractions. Heterogenous dynamics and order at different length scales indicate diverse, hierarchical motif structures. We show that certain motifs can collectively rotate without any cage breaking, leading to alterations of the local tile-structure reminiscent of phason-flips in atomic QCs; this rotation causes a slow decline in the system's spatial order. We anticipate that edge-proximity tessellation will help elucidate phase transitions of other systems made of diverse building blocks having significant geometrical complexity at multiple length scales.

The physical space model of the Tsai-type quasicrystal.

The binary Cd5.7Yb phase representing the Tsai-type category of the icosahedral quasicrystals is solved by the assignment of a unique atomic decoration to rhombohedral units in the Ammann-Kramer-Neri tiling. The unique decoration is found for units with an edge length of 24.1 Šand 3m internal point symmetry. The structural refinement was carried out for two underlying tilings generated by the projection method for 6D space. The difference lies in the location of the origin point which for one tiling is in the vertex and for the second one in the center of the 6D unit cell. The two tilings exhibit mutual duality. The choice of the tiling has a minor effect on the final structural model as both converge to an R factor of ∼11.5%. The main difference is related to the treatment of the Cd4 tetrahedral motif which is either orientationally ordered and aligned with the threefold axis or disordered and modeled as a partially occupied icosahedron. Both models can be presented as a covering by rhombic triacontahedral clusters with identical positions of clusters within rhombohedral units. The shell structure is Tsai-type in the case of the first tiling and Bergman-type for the other.

Quasicrystal Nanosheet/α-Fe2O3 Heterostructure-Based Low Power NO2 Sensors: Experimental and DFT Studies.

Industrial emissions, environmental monitoring, and medical fields have put forward huge demands for high-performance and low power consumption sensors. Two-dimensional quasicrystal (2D QC) nanosheets of metallic multicomponent Al70Co10Fe5Ni10Cu5 have emerged as a promising material for gas sensors due to their excellent catalytic and electronic properties. Herein, we demonstrate highly sensitive and selective NO2 sensors developed by low-cost and scalable fabrication techniques using 2D QC nanosheets and α-Fe2O3 nanoparticles. The sensitivity (ΔR/R%) of the optimal amount of 2D QC nanosheet-loaded α-Fe2O3 sensor was 32%, which is significantly larger about 3.5 times than bare α-Fe2O3 sensors for 1 ppm of NO2 at 150 °C operating temperature. The sensors exhibited p-type conduction, and resistance was reduced when exposed to NO2, an oxidizing gas. The enhanced sensing characteristics are a result of the formation of nanoheterojunctions between 2D QC and α-Fe2O3, which improved the charge transport and provided a large sensing signal. In addition, the heterojunction sensor demonstrated excellent NO2 selectivity over other oxidizing and reducing gases. Furthermore, density functional theory calculation examines the adsorption energy and charge transfer between NO2 molecules on the α-Fe2O3(110) and QC/α-Fe2O3(110) heterostructure surfaces, which coincides well with the experimental results.

Low-temperature and elastic properties of the 1/1 Tsai-type quasicrystal approximant GdCd6investigated by ultrasonic measurements.

Low-temperature and elastic properties of the quasicrystal approximant GdCd6have been investigated by means of an ultrasonic measurement. Salient elastic anomalies were observed in the temperature and magnetic field dependence of the principal elastic constants, most probably being associated with the successive multiple magnetic phase transitions showing up at low temperatures. Based on the experimental data, a magnetic field vs temperature phase diagram was constructed. In a zero magnetic field, at least four phases appear to exist. However, the phase diagram both for the magnetic field applied forH//⟨100⟩andH//⟨110⟩is richer, and interestingly some phase boundaries correspond to the development of field-induced phases, leading to the intricate magnetic phase diagram possibly with multiple ordered phases. We discuss the elastic and electronic properties at low temperatures, and also the nature of the multiple magnetic phase transitions of GdCd6.