We report the discovery of a dodecagonal quasicrystal Mn
Si
Cr
Al
Ni
-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 Mn
Si
Ni
Cr
Al
, 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 SiO
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.
•Free vibration of the PQC microbeams is investigated.•Various shear displacement beam models are considered.•Modified couple stress theory with two material length scale parameters is ...adopted.•Differential quadrature method is used to solve the equations of motion.
In this paper, the free vibration of one-dimensional (1D) piezoelectric quasicrystal (PQC) microbeam is investigated. Varies shear displacement models for the PQC microbeam are developed. The modified couple stress theory with two material length scale parameters for PQC microbeam is used to capture the size effect of the phonon and phason fields. The differential quadrature method (DQM) is adopted to solve the equations of motion for the PQC microbeam, which is derived by the Hamilton's principle. Numerical results for the vibration of the 1D PQC microbeam are calculated. The effects of the geometry, electric voltage, material length scale parameter and boundary conditions on natural frequency of the PQC microbeam are demonstrated.
Superconductivity is ubiquitous as evidenced by the observation in many crystals including carrier-doped oxides and diamond. Amorphous solids are no exception. However, it remains to be discovered in ...quasicrystals, in which atoms are ordered over long distances but not in a periodically repeating arrangement. Here we report electrical resistivity, magnetization, and specific-heat measurements of Al-Zn-Mg quasicrystal, presenting convincing evidence for the emergence of bulk superconductivity at a very low transition temperature of Formula: see text K. We also find superconductivity in its approximant crystals, structures that are periodic, but that are very similar to quasicrystals. These observations demonstrate that the effective interaction between electrons remains attractive under variation of the atomic arrangement from periodic to quasiperiodic one. The discovery of the superconducting quasicrystal, in which the fractal geometry interplays with superconductivity, opens the door to a new type of superconductivity, fractal superconductivity.
Quasicrystals are long-range ordered but not periodic, representing an interesting middle ground between order and disorder. We experimentally and numerically study the localization transition in the ...ground state of noninteracting and weakly interacting bosons in an eightfold symmetric quasicrystalline optical lattice. In contrast to typically used real space in situ techniques, we probe the system in momentum space by recording matter wave diffraction patterns. Shallow lattices lead to extended states whereas we observe a localization transition at a critical lattice depth of V0≈1.78(2)Erec for the noninteracting system. Our measurements and Gross-Pitaevskii simulations demonstrate that in interacting systems the transition is shifted to deeper lattices, as expected from superfluid order counteracting localization. Quasiperiodic potentials, lacking conventional rare regions, provide the ideal testing ground to realize many-body localization in 2D.
In the present investigation, attempts were made to study the effect of Al–Cu–Fe (40 vol%) quasicrystalline (QC) reinforcement on the structure, morphology and phase composition of 6082 Al matrix ...nanocomposites (AMCs) processed through mechanical milling (MM) and spark plasma sintering (SPS). The characterization of these MM and SPSed AMCs was done through X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM). The MM induces microstructural refinement of matrix and partial structural transformation of QC phase to Al13Fe4 approximant phase (a = 1.549 nm, b = 0.808 nm, c = 1.248 nm, α = β = 90°, γ = 107.72°; mC102; C2/m). The presence of (311111) diffraction peak of the QC phase in AMCs confirms the existence of face-centred QC phase even after 50 h of MM. The consolidation of Al-QC at 450 °C (723 K) and 550 °C (823 K) results in the fabrication of AMCs having a density of 2.921 and 3.319 g cm−3 respectively. The compressive yield strength and ultimate strength of these AMCs is ∼519 MPa and 639 MPa respectively. The enhancement in the mechanical properties may be attributed to strong interfacial bonding of the Al matrix and QC reinforcement due to interfacial reactions.
•Face-centred ordered IQC in Al-40IQC NC MM upto 50 h.•Homogenous distribution of IQC in Al-40IQC.•Partial structural transformation of IQC to Al13Fe4 phase in Al-40IQC NC during MM.•Evolution of approximant phases due to interfacial reaction in Al-40IQC NC during SPS.•Enhanced compressive strength due to both direct and indirect strengthening.
Moiré lattices consist of two superimposed identical periodic structures with a relative rotation angle. Moiré lattices have several applications in everyday life, including artistic design, the ...textile industry, architecture, image processing, metrology and interferometry. For scientific studies, they have been produced using coupled graphene-hexagonal boron nitride monolayers
, graphene-graphene layers
and graphene quasicrystals on a silicon carbide surface
. The recent surge of interest in moiré lattices arises from the possibility of exploring many salient physical phenomena in such systems; examples include commensurable-incommensurable transitions and topological defects
, the emergence of insulating states owing to band flattening
, unconventional superconductivity
controlled by the rotation angle
, the quantum Hall effect
, the realization of non-Abelian gauge potentials
and the appearance of quasicrystals at special rotation angles
. A fundamental question that remains unexplored concerns the evolution of waves in the potentials defined by moiré lattices. Here we experimentally create two-dimensional photonic moiré lattices, which-unlike their material counterparts-have readily controllable parameters and symmetry, allowing us to explore transitions between structures with fundamentally different geometries (periodic, general aperiodic and quasicrystal). We observe localization of light in deterministic linear lattices that is based on flat-band physics
, in contrast to previous schemes based on light diffusion in optical quasicrystals
, where disorder is required
for the onset of Anderson localization
(that is, wave localization in random media). Using commensurable and incommensurable moiré patterns, we experimentally demonstrate the two-dimensional localization-delocalization transition of light. Moiré lattices may feature an almost arbitrary geometry that is consistent with the crystallographic symmetry groups of the sublattices, and therefore afford a powerful tool for controlling the properties of light patterns and exploring the physics of periodic-aperiodic phase transitions and two-dimensional wavepacket phenomena relevant to several areas of science, including optics, acoustics, condensed matter and atomic physics.
Based on the nonlocal theory, three-dimensional (3D) buckling of composite nanoplates with coated one-dimensional (1D) quasicrystal (QC) is analyzed. The nanoplate is embedded in an elastic medium ...and is under uniaxial or biaxial compression. All edges of the QC nanoplate are simply supported and its interaction with the surrounding medium is simulated by the Pasternak-type model. In terms of the extended displacement and traction vectors, the eigensystem is first derived from the basic equations of nonlocal QC materials. Then 3D analytical solutions of the critical buckling load under compression are derived by using the propagator matrix method and the continuity condition on the interfaces of the nanoplate. The influence of the thickness and length-to-width ratio of the nanoplate, Winkler stiffness and shear modulus of the elastic medium, coating thickness and nonlocal parameter on the critical buckling load is analyzed. For a sandwich nanoplate made of QC and soft metallic aluminium, our numerical results indicate that QC coatings could offer an interesting alternative to surface reinforcement of soft metallic materials in industrial applications. The present 3D buckling model could further serve as a benchmark for various thin-nanoplate theories and for numerical methods in multilayered QC nanoplate modeling with nonlocal effect.
Colloids are rarely perfectly uniform but follow a distribution of sizes, shapes, and charges. This dispersity can be inherent (static) or develop and change over time (dynamic). Despite a long ...history of research, the conditions under which nonuniform particles crystallize and which crystal forms is still not well understood. Here, we demonstrate that hard spheres with Gaussian radius distribution and dispersity up to 19% always crystallize if compressed slowly enough, and they do so in surprisingly complex ways. This result is obtained by accelerating event-driven simulations with particle swap moves for static dispersity and particle resize moves for dynamic dispersity. Above 6% dispersity, AB_{2} Laves, AB_{13}, and a region of Frank-Kasper phases are found. The Frank-Kasper region includes a quasicrystal approximant with Pearson symbol oS276. Our findings are relevant for ordering phenomena in soft matter and alloys.
The three-dimensional fundamental equations of elasticity of quasicrystals with extension to quasi-static electric effect are expresses in both differential and variational invariant forms for a ...regular region of quasicrystal material. The principle of conservation of energy is stated for the regular region and the constitutive relations are obtained for the piezoelasticity of material. A theorem is proved for the uniqueness in solutions of the fundamental equations by means of the energy argument. The sufficient boundary and initial conditions are enumerated for the uniqueness. Hamilton’s principle is stated for the regular region and a three-field variational principle is obtained under some constraint conditions. The constraint conditions, which are generally undesirable in computation, are removed by applying an involutory transformation. Then, a unified variational principle is obtained for the regular region, with one or more fixed internal surface of discontinuity. The variational principle operating on all the field variables generates all the fundamental equations of piezoelasticity of quasicrystals under the symmetry conditions of the phonon stress tensor and the initial conditions. The resulting equations, which are expressible in any system of coordinates and may be used through simultaneous approximation upon all the field variables in a direct method of solutions, pave the way to the study of important dislocation, fracture and interface problems of both elasticity and piezoelasticity of quasicrystal materials.
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