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.
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•This work confirms for the first time that crystalline TiB2 inoculants can serve as an effective substrate for IQC phase nucleation.•EBSD and SAED patterns confirm that at least five orientation relationships exist between the close-packed planes of the phases.•The microstructural analyses show that inoculation has a noticeable effect on the size and distribution of the primary IQC phase.•The size and distribution of the primary IQC phase clearly affect the compressive properties.•As-cast, a compressive yield strength of 380 MPa, a compressive strength of 680 MPa, and a compressive fracture strain of 20 % were achieved.
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The phase behaviour of a free energy functional with two length scales is examined by comparing the free energy of different candidate phases including three-dimensional icosahedral quasicrystals. ...Accurate free energy of the quasicrystals has been obtained using the recently developed projection method. The results reveal that the icosahedral quasicrystal and body-centred-cubic spherical phase are the stable ordered phases of the model. Furthermore, the difference between the results obtained from the projection method and the one-mode approximation has been analyzed in detail. The present study extends previous results on two-dimensional systems, demonstrating that the interactions between density waves at two length scales can stabilize two- and three-dimensional quasicrystals.
Although the grain refinement of yellow gold alloys with Ir has been used in industry and known for nearly half a century, the basic mechanism is still unknown. The present contribution shows that ...the mechanism is the same as that evidenced recently in Al–Zn alloys, when small amounts of Cr (1000ppm) are added to the melt (Kurtuldu et al., 2013). The reduced face-centered cubic (fcc) crystal size, the abnormal fraction of twin, or near-twin, grain boundaries and the 5-fold symmetry crystallographic orientation of multiple nearest-neighbor grains reproduce the symmetry of icosahedral quasicrystals (iQCs) with the following heteroepitaxial relationships: {111}fcc/〈110〉fcc⊥ 3-fold/2-fold symmetry axes of iQCs. While iQCs and the approximant stable Al45Cr7 phase, which contains several 5-fold symmetry building blocks in its unit cell, are known to exist in Al–Cr alloys, no such phases have been reported for yellow gold +Ir. Nevertheless, when minute amounts of Ir (≲200ppm) are added to the gold alloy melt, it is shown that the grain refinement from 248 to 30μm is accompanied by a spectacular increase in the fraction of twinned grain boundaries, i.e. from less than 1% without Ir to 11% with 200ppm Ir. Furthermore, up to 9 grains have been shown to reproduce the six 5-fold symmetry axes of the icosahedron, while many other grain configurations exhibit this heteroepitaxial relationship with the icosahedron or interlocked icosahedron. This confirms that fcc crystals can form in a supercooled liquid by heteroepitaxial growth from an iQC template.
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One of the most intriguing problems of light transport in solids is the localization that has been observed in various disordered photonic structures. The light localization in defect‐free ...icosahedral quasicrystals has recently been predicted theoretically without experimental verification. Herein, the fabrication of submicron‐size dielectric icosahedral quasicrystals is reported and the results of detailed studies of the photonic properties of these structures are demonstrated. The first direct experimental observation of intrinsic light localization in defect‐free quasicrystals is presented. This result is obtained in time‐resolved measurements at different laser wavelengths in the visible. The localization is linked with the aperiodicity of the icosahedral structure, which leads to uncompensated scattering of light from an individual structural element over the entire sphere, providing multiple scattering inside the sample and, as a result, the intrinsic localization of light.
Light localization in defect‐free icosahedral quasicrystals has recently been predicted theoretically without experimental verification. Here, the fabrication of submicron‐size dielectric icosahedral quasicrystals is reported and the first direct experimental observation of intrinsic light localization in defect‐free quasicrystals is presented. This result is obtained in time‐resolved measurements at different laser wavelengths in the visible range.
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This paper presents a new, highly stable, periodic approximant to the Al‐based F‐type icosahedral quasicrystals, i‐Al–Pd–TM (TM = transition metals). The structure of this intermetallic Al–Pd–Cr–Fe ...compound is determined ab initio using single‐crystal X‐ray diffraction, where the space group is identified to be and the lattice constant 40.5 Å. The structure is well described as a dense packing of clusters of two kinds, which are called the pseudo‐Mackay‐type and the mini‐Bergman‐type clusters. Adjacent clusters can be markedly interpenetrated, while the structure requires no glue atoms to fill in the gaps between the clusters. It is shown that the clusters are centred at the vertices of a canonical cell tiling, which corresponds to a 2 × 2 × 2 superstructure of Henley's cubic 3/2 packing, and that the parity of each vertex determines the kind of associated cluster. The proper quasi‐lattice constant for describing the cluster packing is 1/τ (τ = golden mean) times the conventional one used to describe Al‐based P‐type icosahedral alloys. The superstructure ordering of the present approximant turns out to be of a different kind from the P‐type superstructure ordering previously reported in i‐Al–Pd–Mn. The present results will greatly improve the understanding of atomic structures of F‐type icosahedral quasicrystals and their approximants.
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In this paper we describe a group theoretical approach to the study of structural transitions of icosahedral quasicrystals and point arrays. We apply the concept of Schur rotations, originally ...proposed by Kramer, to the case of aperiodic structures with icosahedral symmetry; these rotations induce a rotation of the physical and orthogonal spaces invariant under the icosahedral group, and hence, via the cut-and-project method, a continuous transformation of the corresponding model sets. We prove that this approach allows for a characterisation of such transitions in a purely group theoretical framework, and provide explicit computations and specific examples. Moreover, we prove that this approach can be used in the case of finite point sets with icosahedral symmetry, which have a wide range of applications in carbon chemistry (fullerenes) and biology (viral capsids).
Dodecahedral structures with Mosseri–Sadoc tiles Ozdes Koca, Nazife; Koc, Ramazan; Koca, Mehmet ...
Acta crystallographica. Section A, Foundations and advances,
March 2021, Volume:
77, Issue:
2
Journal Article
Peer reviewed
Open access
The 3D facets of the Delone cells of the root lattice D6 which tile the 6D Euclidean space in an alternating order are projected into 3D space. They are classified into six Mosseri–Sadoc tetrahedral ...tiles of edge lengths 1 and golden ratio τ = (1 + 51/2)/2 with faces normal to the fivefold and threefold axes. The icosahedron, dodecahedron and icosidodecahedron whose vertices are obtained from the fundamental weights of the icosahedral group are dissected in terms of six tetrahedra. A set of four tiles are composed from six fundamental tiles, the faces of which are normal to the fivefold axes of the icosahedral group. It is shown that the 3D Euclidean space can be tiled face‐to‐face with maximal face coverage by the composite tiles with an inflation factor τ generated by an inflation matrix. It is noted that dodecahedra with edge lengths of 1 and τ naturally occur already in the second and third order of the inflations. The 3D patches displaying fivefold, threefold and twofold symmetries are obtained in the inflated dodecahedral structures with edge lengths τn with n ≥ 3. The planar tiling of the faces of the composite tiles follows the edge‐to‐edge matching of the Robinson triangles.
A generalization of Penrose tiling to 3D Euclidean space with icosahedral symmetry is proposed. The dodecahedral tiling system composed of four prototiles with faces of Robinson triangles determines the 3D quasicrystallographic structures.
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Magnetism of 3D quasicrystals is extensively researched, mainly for rare-earth or iron-based alloys. In this contribution, magnetic properties of the icosahedral Ti45Zr38Ni17 quasicrystal are ...reported. Namely, the results of magnetometric and neutron diffraction studies in the broad temperature ranges of 1.5–300K and 2–700K respectively are discussed. The magnetometric studies reveal that the alloy exhibits an extremely weak ferromagnetic signal, however it is associated with the traces of nickel clusters at the grains boundaries. The neutron scattering studies, including diffraction in external magnetic field, indicate no possibility of long-rage magnetic ordering in the icosahedral Ti45Zr38Ni17 alloy. According to our studies, the investigated material exhibits Pauli-like paramagnetic behaviour.
•Pauli-paramagnetic behaviour of the icosahedral Ti45Zr38Ni17 quasicrystal is shown.•No possibility of long-range magnetic ordering in the Ti45Zr38Ni17 alloy is proved.•Occurrence of magnetostriction effects is excluded in magnetic field up to 5T.•Magnetisation measurements become a key method of tracing magnetic impurities.
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The relative stability of three-dimensional icosahedral quasicrystals in multi-component systems has been investigated based on a phenomenological coupled-mode Swift-Hohenberg model with two-length ...scales. A recently developed projection method, which provides a unified numerical framework to study periodic crystals and quasicrystals, is used to compute free energy to high accuracy. Compared with traditional approaches, the advantage of the projection method has also been discussed in detail. A rigorous and systematic computation demonstrates that three-dimensional icosahedral quasicrystal and two-dimensional decagonal quasicrystal are both stable phases in such a simple multi-component coupled-mode Swift-Hohenberg model. The result extends the two-length scales interaction mechanism of stabilising quasicrystals from single-component to multi-component systems.
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