Quasicrystals Research Articles

Heptatic liquid quasi-crystals by colloidal lithographic pre-assembly

HypothesisWe 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. ExperimentsWe 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. FindingsA 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.

Creep behaviors of Mg–6Zn-0.4Mn-0.3Al-0.2Ca (wt.%) alloy enhanced by icosahedral quasicrystal

Magnesium (Mg) alloys are considered to be the lightest metal structural materials, however, their poor creep resistance considerably limits their applications. In this study, a novel Mg–6Zn-0.4Mn-0.3Al-0.2Ca (ZMAX6000) alloy with icosahedral quasicrystal phases (I-phases) distributed at almost all triangular grain boundaries was developed by hot extrusion and heat treatment. Tensile creep tests were systematically conducted on the alloy at temperatures of 398 K, 423 K, and 448 K under stresses of 50 MPa, 70 MPa, and 90 MPa, respectively. These I-phases could reduce the accumulation of creep damage at triangular grain boundaries, hinder grain boundary sliding, and delay the generation of cracks. As a result, the ZMAX6000 alloy exhibited far superior creep properties compared to ZK60 and AZ91 alloys. During the creep process, non-basal slip occurred and the texture intensity of the sample was weakened. Dislocation characterization results showed that the creep mechanisms of the alloy at 448 K under 90 MPa were cross-slip and pyramidal < c + a > slip.

Dispersion of stable quasicrystal phase by precipitation during extrusion in a Mg–Zn–Al alloy: Microstructure and mechanical properties

Precipitation of stable icosahedral quasicrystalline phase (i) has been recently reported in a Mg6Zn3Al (in wt%, ZA63) alloy on ageing after solutionizing treatment of cast alloy to dissolve dendritic i-phase. This offers an opportunity to disperse this phase in a ZA alloy through a solutionizing treatment followed by extrusion, thereby precipitating the i-phaseduring extrusion. By this process, the i-phasecan be dispersed in the alloy uniformly, instead of dispersion from the cast structure by extrusion. In this study, a cast ingot of ZA63 alloy was solutionized at 400 ∘C, followed by extrusions at 255 ∘C and 300 ∘C. Extrusion at 255 ∘C resulted in larger amount of i-phaseprecipitation (about 4.5 mass%), in which spherical precipitates of size about 100 nm or less were distributed in the matrix and boundaries of grains of average size 2.4 ± 1.0μm, exhibiting true yield strengths of 263.7±1.4MPa in tension and 255.4±5.0MPa in compression (with elongation to failure of about 18% in both cases). Extrusion at the higher temperature of 300 ∘C resulted in fewer precipitates (about 1.4 mass%) and larger average grain size of 12.9 ± 6.1μm and i-phaseprecipitates of size 500 nm which were mostly at the grain boundaries, and consequently lower true yield strengths of 214.4±1.3MPa in tension and 159.3±0.3MPa in compression. The strength after extrusion at 300 ∘C increased by 48 MPa in tension and 38 MPa in compression on ageing at 250 ∘C for 20 min. Ageing precipitate phases were identified to be i-phase, Mg4Zn7 and possibly ternary ϕ-phase. Phase equilibrium and change in morphology of phases during ageing has been discussed. The peculiar nature of work hardening during tensile deformation has also been discussed.

Alloy Quasicrystals: Perspectives and Some Open Questions at Forty Years

Four decades have elapsed since the first quasiperiodic crystal was discovered in the Al–Mn alloy system, and much progress has been made during this time on the science of quasicrystals (QCs). Notwithstanding this, a significant number of open questions still remain regarding both fundamental and technological aspects. For instance: What are QCs good for? How can we improve the current provisional QC definition? What is the role of the underlying quasiperiodic order and the characteristic inflation symmetry of these compounds in the emergence of their unusual physicochemical properties? What is the nature of chemical bonding in QCs formed in different sorts of materials such as alloys, oxides, or organic polymers? Herein these and other closely related issues are discussed from an interdisciplinary perspective as well as prospective future work in the field in the years to come.

Electrical resistivity of coatings of quasicrystalline and crystalline phases of the Ti—Zr—Ni system in the temperature range 4–300 K

The temperature dependence of the electrical resistivity in the temperature range from 4.4 to 300 K for Ti41Zr41Ni18 (at. %) thin coatings of different crystal perfection and phase composition was studied. The coatings were deposited by magnetron sputtering with subsequent vacuum annealing in various modes ensuring the formation of several heterophase combinations, which included 1/1 and 2/1 approximation phases, a quasicrystalline icosahedral phase, a Laves phase (Ti, Zr)2Ni, and an α-Ti (Zr) solid solution. The structure before and after annealing was studied by X-ray diffractometry. It was established that coatings with a predominant content of amorphous, quasicrystalline, or approximant 2/1 phases have a temperature coefficient of resistance less than zero, while samples with a predominance of crystalline phases demonstrate characteristic metallic conductivity. The temperature dependence of the electrical resistivity of the Ti41Zr41Ni18 quasicrystalline coating turned out to be similar to the dependence in bulk samples of the Ti40Zr40Ni20 composition. The electrical resistivity of the approximant 2/1 phase with a low content of the additional Laves phase in the film has an almost constant value in the entire investigated temperature range.

Analytical solutions for the plane thermoelastic problem of a nano-open crack in one-dimensional hexagonal quasicrystal non-periodic plane

As a stable material at high temperatures, the presence of cracks and other defects greatly reduces the performance of quasicrystals (QCs). The plane thermoelastic problem of one-dimensional hexagonal quasicrystals (1DHQ) non-periodic plane containing a nano-open crack is analyzed using surface elasticity theory. The closed form solutions are obtained to describe the thermoelastic field corresponding to the nano-crack by the Fourier integral transformation technique. The analytical solutions of the thermal stress intensity factors (TSIFs) and the strain energy density factor (SEDF) at the crack tip are derived explicitly. The influence of the applied loads, the surface effects and the multi-field coupling effects on the TSIFs and SEDF are discussed. The numerical results reveal that the surface effects have an obvious impact on TSIFs with small applied loads, and the surface effects will inhibit the propagation of nano-open cracks. The research results of this study provide some reliable theoretical references for the development of nano-QCs.

Effective elastic properties of one-dimensional hexagonal quasicrystal composites with spring-type imperfect interfaces

Considering the spring-type imperfect interfaces, the effective elastic properties of one-dimensional (1D) hexagonal quasicrystal (QC) are investigated systematically. The spring-type imperfect interface between QC matrix and inclusion is an ultra-thin, soft and weakly conductive interface. The Mori–Tanaka method is presented to determine the effective elastic constants of phonon, phason and phonon–phason coupling field. The numerical results are provided to show that the existence of imperfect interfaces reduces the effective elastic constants to some extent. It indicates that the interface plays an important role in the elastic properties of QC composites. Besides, the effective elastic constants are also subject to the aspect ratio and the volume fraction of inclusions.

Heterogeneous nucleation and orientation relationships of icosahedral phase with TiB2 inoculants

This study confirms that crystalline TiB2 particles can act as a potent site for the heterogeneous nucleation of the metastable icosahedral quasicrystalline phase (IQC) formed in cast Al-Mn-Si-Cu-Mg alloys. The results show that a primary metastable IQC phase nucleates on facets of TiB2 particles. Electron backscatter diffraction patterns and selected-area electron diffraction patterns confirmed that at least five orientation relationships (ORs) exist between the stable TiB2 and the metastable IQC phase. The IQC adopts different ORs with the crystallineTiB2 particles to form low energy interfaces by matching close-packed planes at the interfaces. In the IQC phase, the close-packed planes are the 5-fold and 2-fold. Microstructural analyses show that inoculation has a noticeable influence on the size and distribution of the primary IQC phase, which in turn has a noticeable influence on the compressive properties of the investigated alloys. Due to their exceptional mechanical properties, these alloys could become a prime candidate for lightweight applications, especially in the automotive and aerospace industries.

Magnetic dynamics and nonreciprocal excitation in uniform hedgehog order in icosahedral 1/1 approximant crystal

The hedgehog state in the icosahedral quasicrystal (QC) has attracted great interest as the theoretical discovery of topological magnetic texture in aperiodic systems. The revealed magnetic dynamics exhibits nonreciprocal excitation in the vast extent of the reciprocal lattice {varvec{q}}-energy omega space, whose emergence mechanism remains unresolved. Here, we analyze the dynamical as well as static structure of the hedgehog order in the 1/1 approximant crystal (AC) composed of the cubic lattice with spatial inversion symmetry. We find that the dispersion of the magnetic excitation energy exhibits nonreciprocal feature along the N-P-Gamma line in the {varvec{q}} space. The dynamical structure factor exhibits highly structured intensities where high intensities appear in the high-energy branches along the Gamma-H line and the P-Gamma-N line in the {varvec{q}} space. The nonreciprocity in the 1/1 AC and also in the QC is understood to be ascribed to inversion symmetry breaking by the hedgehog ordering. The sharp contrast on the emergence regime of nonreciprocal magnetic excitation between the QC and the 1/1 AC indicates that the emergence in the vast {varvec{q}}-omega regime in the QC is attributed to the QC lattice structure.

Structural Analysis of the Gd-Au-Al 1/1 Quasicrystal Approximant Phase across Its Composition-Driven Magnetic Property Changes.

Gd14AuxAl86-x Tsai-type 1/1 quasicrystal approximants (ACs) exhibit three magnetic orders that can be finely tuned by the valence electron concentration (e/a ratio). This parameter has been considered to be crucial for controlling the long-range magnetic order in quasicrystals (QCs) and ACs. However, the nonlinear trend of the lattice parameter as a function of Au concentration suggests that Gd14AuxAl86-x 1/1 ACs are not following a conventional solid solution behavior. We investigated Gd14AuxAl86-x samples with x values of 52, 53, 56, 61, 66, and 73 by single-crystal X-ray diffraction. Our analysis reveals that increasing Au/Al ordering with increasing x leads to distortions in the icosahedral shell built of the Gd atoms and that trends observed in the interatomic Gd-Gd distances closely correlate with the magnetic property changes across different x values. Our results demonstrate that the e/a ratio alone may be an oversimplified concept for investigating the long-range magnetic order in 1/1 ACs and QCs and that the mixing behavior of the nonmagnetic elements Au and Al plays a significant role in influencing the magnetic behavior of the Gd14AuxAl86-x 1/1 AC system. These findings will contribute to improved understanding towards tailoring magnetic properties in emerging materials.

Microstructural characterization of rapidly solidified Al-13.5 at.% Cr and Al-13.5 at.% V alloys for catalytic applications

Intermetallic compounds, due to their well-defined stoichiometry, arrangement of atoms and controlled crystal structure, are a promising alternative to expensive noble metal catalysts. In this paper, the catalytic properties of Al-13.5 at.% Cr and Al-13.5 at.% V alloys, corresponding to the quasicrystalline approximants Al45Cr7 and Al45V7, were investigated for the first time.The alloys in the form of fragmented brittle ribbons were produced by the melt-spinning. The microstructure of the ribbons, both in the as-spun state and after heat treatment (100 h at 600 °C), was characterized by X-ray diffraction, scanning electron microscopy and transmission electron microscopy. In the as-spun state, the ribbons showed a multiphase microstructure. In addition to the Al45Cr7 phase in the Al-Cr alloy and the Al3V phase in the Al-V alloy, they also contained α(Al) solid solution and icosahedral quasicrystalline phases. After heat treatment, the alloys became almost single phase, consisting mainly of stable monoclinic phases: Al45Cr7 or Al45V7. The catalytic performance of the phenylacetylene hydrogenation reaction was tested on as-spun and heat-treated alloys that had previously been pulverized and sieved to select a powder fraction of less than 32 µm. All the tested materials show high substrate conversion, above 80% after 1 h reaction, along with high activity rate. The homogenized powders demonstrated a slightly better properties in relation to as-spun materials. These results confirm the potential of intermetallic catalysts, including the tested alloys, in hydrogenation reactions and verify the possibility of using the metallurgical method to obtain catalytically active materials.Graphical abstract

Investigating the local structure of icosahedral phases by atomic resolution holography

Investigating the local structure of icosahedral phases by atomic resolution holography

Controlled Self-Assembly of Gold Nanotetrahedra into Quasicrystals and Complex Periodic Supracrystals.

The self-assembly of shape-anisotropic nanocrystals into large-scale structures is a versatile and scalable approach to creating multifunctional materials. The tetrahedral geometry is ubiquitous in natural and manmade materials, yet regular tetrahedra present a formidable challenge in understanding their self-assembly behavior as they do not tile space. Here, we report diverse supracrystals from gold nanotetrahedra including the quasicrystal (QC) and the dimer packing predicted more than a decade ago and hitherto unknown phases. We solve the complex three-dimensional (3D) structure of the QC by a combination of electron microscopy, tomography, and synchrotron X-ray scattering. Nanotetrahedron vertex sharpness, surface ligands, and assembly conditions work in concert to regulate supracrystal structure. We also discover that the surface curvature of supracrystals can induce structural changes of the QC tiling and eventually, for small supracrystals with high curvature, stabilize a hexagonal approximant. Our findings bridge the gap between computational design and experimental realization of soft matter assemblies and demonstrate the importance of accurate control over nanocrystal attributes and the assembly conditions to realize increasingly complex nanopolyhedron supracrystals.

Formation mechanism of the quasicrystal in Al-Cu-Mg-Zn aluminum alloy resistance spot weld

In this study, the formation mechanism of the quaternary quasicrystal phase (59.59Al-8.85Cu-16.85Mg-14.71Zn, at. %) in the Al-Cu-Mg-Zn alloy resistance spot welding nugget was revealed. Transmission electron microscopy shows the quasicrystal phase was located at the inner-dendrite zone of which selected area electron diffraction spot exhibits a typical pattern of an icosahedral quasicrystal (fivefold axes). During the cooling process, Cu-Mg-Zn solute enriched within the remnant liquid at the inter-dendrite zone with short-range-ordered clusters structure. Instead transforming to typical crystalline phases, this undercooled remnant liquid forms the icosahedral quasicrystal phase due to the rapid cooling rate of resistance spot welding. This study shows the feasibility of acquiring massive quasicrystal phase in commercially-used aluminum alloy under common processing condition.

A group of ductile metallic glasses prepared by modifying local structure of icosahedral quasicrystals

Inspired by research into the association between icosahedral local orders and the plasticity of metallic glasses (MGs), beryllium (Be) is added to the icosahedral quasi-crystal forming alloy Zr40Ti40Ni20. In this way, bulk metallic glasses (BMGs) with favorable compressive plasticity are fabricated. Therein, the icosahedral quasi-crystalline phase is the main competing phase of amorphous phases and icosahedral local orders are the main local atomic motifs in amorphous phases. The alloys of (Zr40Ti40Ni20)76Be24 and (Zr40Ti40Ni20)72Be28 with their greater plastic strain capacity show similar characteristics to highly plastic amorphous systems: The serrated flow of compression curves always follows a near-exponential distribution. The primary and secondary shear bands intersect each other, bifurcate, and bend. Typical vein patterns are densely distributed on the fracture surfaces. The relaxation enthalpy of four MGs is linearly correlated with the plastic strain, that is, the greater the relaxation enthalpy, the larger the plastic strain.

Structure and electrical conductivity of Ti-Zr-Ni films of quasicrystalline and related crystalline phases

The temperature dependence of electrical resistivity in the temperature range from 4.4 to 300 K for Ti41Zr41Ni18 (at.%) thin coatings of various crystal perfection and phase compositions has been investigated. The films were deposited by the magnetron sputtering method. The following vacuum annealing in various modes provided several combinations of the film phases such as 1/1 and 2/1 crystal-approximant phases, the quasicrystalline icosahedral phase, Laves (Ti,Zr)2Ni phase and α-Ti(Zr) solid solution phase. The structure and composition of the films before and after annealing were studied in detail by X-ray diffractometry and cross-sectional high-resolution transmission electron microscopy. Samples with predominant amorphous, quasi-crystalline, and approximant 2/1 phases have a temperature coefficient of resistance less than zero, while samples dominated by crystalline phases exhibit the characteristic metallic conductivity. For the quasicrystalline Ti41Zr41Ni18 film, the temperature dependence of the electrical resistance turned out to be similar to that of bulk samples with the composition Ti40Zr40Ni20. A significant effect of the presence of phases with metallic conduction on the overall conductivity of the coating is described. The electrical resistance of the 2/1 approximant phase with a low content of the additional Laves phase in the film has an almost constant value over the entire temperature range under study.

Mode-I Plane Elasticity Problem of Two Asymmetrical Edge Cracks Emanating from an Elliptical Hole in Two-Dimensional Decagonal Quasicrystals

We consider the plane elasticity problem of two asymmetrical edge cracks emanating from an elliptical hole in two-dimensional decagonal quasicrystals (QCs) under remotely uniform tensile stress. A complex variation method of two-dimensional QCs is developed to solve the plane elasticity problem of two-dimensional decagonal QCs containing complex defects. The analytical solutions for the stress field and the stress intensity factors near the crack tip are expressed by using a conformal mapping technique and complex potential theory. Some special cases of the results are also obtained, such as the T-type crack, cross crack, and Griffith crack. The effects of geometrical parameters of crack configuration on the stress intensity factors are presented graphically.

The relation between the glass forming ability and nucleation kinetics of metastable quasicrystals in Mg–Zn–Yb liquid

Bulk metallic glass (BMG), metastable quasicrystals (QCs) and two types of approximant phases concurrently form from the melt during cooling at different rates in a Mg–Zn–Yb model alloy. Such an enriched phase competition between various metastable and stable crystals has also been found during the heating of Mg–Zn–Yb metallic glass between the glass transition and liquidus temperatures. Metastable QC acts as a transient phase that nucleates first from the melt and subsequently transforms into an equilibrium approximant phase. During heating, a metastable approximant phase transforms into the Mg-QC phase mixture which then transforms into the Mg and equilibrium approximant eutectic microstructure. Nucleation kinetics of QCs is critical to analyze for further understanding the relation between QC formation and glass forming ability of the alloy. For this purpose, a metastable phase diagram for QCs has been determined using a novel experimental strategy via fast differential scanning calorimetry (FDSC). Along compositional line binding Mg to Zn17Yb3, one stable eutectic point, i.e. Mg68.6Zn26.7Yb4.7 at 390°C, and one metastable eutectic composition, i.e. Mg64.6Zn30.1Yb5.3 at 350°C, were determined during interrupted heating experiments. We have demonstrated that the glass forming ability of Mg–Zn–Yb alloys strongly depends on the metastable phase diagram of QCs and their nucleation kinetics. Nucleation of metastable QCs limits the metallic glass formation, therefore the bulk metallic glass forming compositional region was found to be below metastable hypoeutectic compositions.

Development and optimization of novel sulfur-containing Ti-based bulk metallic glasses and the correlation between primarily crystallizing phases, thermal stability and mechanical properties

The effect of sulfur on the glass forming ability, thermal stability and mechanical properties of the eutectic alloy Ti33.4Zr33.3Cu33.3 was investigated by conventional X-ray diffraction, differential scanning calorimetry and 3-point flexural experiments. A novel region of bulk glass formation with a critical casting diameter of up to 4 mm was found in the quaternary Ti-Zr-Cu-S system, however, brittle fracture behavior was predominant. Various alloying strategies were employed to improve mechanical properties and a compositional transition from brittle to ductile fracture has been identified (e.g. for Ti36Zr33.5Cu24.5S6). A change of the primary precipitating phases from a C14 Laves to an intermetallic (Ti,Zr)2Cu phase can be observed, as well as a stabilization of the supercooled liquid. The origin of the thermally unstable behavior in Ti-based bulk metallic glasses is traced back to the easy formation of the icosahedral phase upon heating, which is structurally close to the supposedly predominant icosahedral short-range order in the amorphous state. The systematic study carried out in this work indicates a strong correlation between primary crystallizing phase and thermal stability, both pointing to the frozen short-range order in the amorphous state which is predetermining the mechanical properties. The transition from the Laves to the intermetallic (Ti,Zr)2Cu phase as well as the enlarged supercooled liquid region appear to be directly related to a destabilization of the icosahedral short-range order and ultimately to the improved mechanical properties.

Enhanced Light Scattering Using a Two-Dimensional Quasicrystal-Decorated 3D-Printed Nature-Inspired Bio-photonic Architecture

A number of strategies have been exploited so far to trap photons inside living cells to obtain high-contrast imaging. Also, launching light inside biological materials is technically challenging. Using photon confinement in a three-dimensional (3D)-printed biomimetic architecture in the presence of a localized surface plasmon resonance (LSPR) promoter can overcome some of these issues. This work compares optical confinement in natural and 3D-printed photonic architectures, namely, fish scale, in the presence of atomically thin Al70Co10Fe5Ni10Cu5 quasicrystals (QCs). Due to their wideband LSPR response, the QCs work as photon scattering hotspots. The architecture acts as an additive source of excitation for the two-dimensional (2D) QCs via total internal reflection (TIR). The computational analysis describes the surface plasmon-based scattering property of 2D QCs. The 3D-printed fish scale’s image contrast with the 2D Al70Co10Fe5Ni10Cu5 QC has been compared with other 2D materials (graphene, h-BN, and MoS2) and outperforms them. The present study conceptually presents a new approach for obtaining high-quality imaging of biological imaging, even using high-energy photons.