TOPOLOGICAL CONSTRAINTS FOR QUASICRYSTALS

1989 ◽  
Vol 03 (06) ◽  
pp. 877-896 ◽  
Author(s):  
P.A. KALUGIN ◽  
L.S. LEVITOV
Keyword(s):  
Physical Space ◽  
Icosahedral Symmetry ◽  
Topological Constraints ◽  
Icosahedral Quasicrystals ◽  
New Type ◽  
Quasiperiodic Structure

Topological constraints necessary for the existence of icosahedral quasicrystals having continuous phasons are found. As a result of application of these constraints a model of a new type for icosahedral quasicrystals is constructed. The “atomic surfaces” in R6 in this model are free of discontinuities, i.e. the displacements of atoms are continuous as functions of a phason shift. The positions of atoms in the physical space R3 from 60 interpenetrating rhombohedral lattices. The model exhibits diffraction properties of an ideal quasiperiodic structure and has perfect icosahedral symmetry.

The periodic average structure of particular quasicrystals

1999 ◽  
Vol 55 (1) ◽  
pp. 48-57 ◽  
Author(s):  
Walter Steurer ◽  
Torsten Haibach
Keyword(s):  
Physical Space ◽  
Maximum Distance ◽  
Oblique Projection ◽  
Bond Lengths ◽  
Average Structure ◽  
Lattice Periodicity ◽  
Crystallographic Symmetry ◽  
Quasiperiodic Structures ◽  
Quasiperiodic Structure ◽  
Average Structures

The non-crystallographic symmetry of d-dimensional (dD) quasiperiodic structures is incompatible with lattice periodicity in dD physical space. However, dD quasiperiodic structures can be described as irrational sections of nD (n > d) periodic hypercrystal structures. By appropriate oblique projection of particular hypercrystal structures onto physical space, discrete periodic average structures can be obtained. The boundaries of the projected atomic surfaces give the maximum distance of each atom in a quasiperiodic structure from the vertices of the reference lattice of its average structure. These maximum distances turn out to be smaller than even the shortest atomic bond lengths. The metrics of the average structure of a 3D Ammann tiling, for instance, with edge lengths of the unit tiles equal to the bond lengths in elemental aluminium, correspond almost exactly to the metrics of face-centred-cubic aluminium. This is remarkable since most stable quasicrystals contain aluminium as the main constitutent. The study of the average structure of quasicrystals can be a valuable aid to the elucidation of the geometry of quasicrystal-to-crystal transformations. It can also contribute to the derivation of the physically most relevant Brillouin (Jones) zone.

scholarly journals Space oddity: musical syntax is mapped onto visual space

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Neta B. Maimon ◽  
Dominique Lamy ◽  
Zohar Eitan
Keyword(s):  
Spatial Perception ◽  
Physical Space ◽  
Visual Space ◽  
Lateral Position ◽  
Vertical Position ◽  
Musical Structure ◽  
Spatial Metaphors ◽  
Musical Syntax ◽  
Musical Discourse ◽  
New Type

AbstractIncreasing evidence has uncovered associations between the cognition of abstract schemas and spatial perception. Here we examine such associations for Western musical syntax, tonality. Spatial metaphors are ubiquitous when describing tonality: stable, closural tones are considered to be spatially central and, as gravitational foci, spatially lower. We investigated whether listeners, musicians and nonmusicians, indeed associate tonal relationships with visuospatial dimensions, including spatial height, centrality, laterality, and size, implicitly or explicitly, and whether such mappings are consistent with established metaphors. In the explicit paradigm, participants heard a tonality-establishing prime followed by a probe tone and coupled each probe with a subjectively appropriate location (Exp.1) or size (Exp.4). The implicit paradigm used a version of the Implicit Association Test to examine associations of tonal stability with vertical position (Exp.2), lateral position (Exp3) and size (Exp.5). Tonal stability was indeed associated with perceived physical space: the spatial distances between the locations associated with different scale-degrees significantly correlated with the tonal stability differences between these scale-degrees. However, inconsistently with musical discourse, stable tones were associated with leftward (instead of central) and higher (instead of lower) spatial positions. We speculate that these mappings are influenced by emotion, embodying the “good is up” metaphor, and by the spatial structure of music keyboards. Taken together, the results demonstrate a new type of cross-modal correspondence and a hitherto under-researched connotative function of musical structure. Importantly, the results suggest that the spatial mappings of an abstract domain may be independent of the spatial metaphors used to describe that domain.

scholarly journals Long-range magnetic order in real icosahedral quasicrystals

2021 ◽  
Author(s):  
Ryuji Tamura ◽  
Asuka Ishikawa ◽  
Shintaro Suzuki ◽  
Akihiro Kotajima ◽  
Yujiro Tanaka ◽  
...  
Keyword(s):  
Specific Heat ◽  
Long Range ◽  
Magnetic Order ◽  
Global Symmetry ◽  
Icosahedral Symmetry ◽  
Ferromagnetic Transition ◽  
Range Magnetic Order ◽  
Magnetic Orders ◽  
Icosahedral Quasicrystals ◽  
Long Range Magnetic Order

Abstract Quasicrystals (QCs), first discovered in 1984, generally do not exhibit long-range magnetic order. Here, we report on long-range magnetic order in the real icosahedral quasicrystals (i QCs) Au–Ga–Gd and Au–Ga–Tb. The Au65Ga20Gd15 i QC exhibits a ferromagnetic transition at TC = 23 K, manifested as a sharp anomaly in both magnetic-susceptibility and specific-heat measurements. Quick magnetic saturation to almost the full moment (7μB/Gd3+) is observed under 100 Oe at 2 K. This is the first observation of long-range magnetic order in a real quasicrystal, in contrast to the spin-glass-like behaviours observed for the other magnetic quasicrystals found to date. Moreover, when Gd is replaced by Tb, i.e. for the Au65Ga20Tb15 i QC, a ferromagnetic behaviour is still retained with TC = 16 K. Although the sharp anomaly in the specific heat observed for the Au65Ga20Gd15 i QC is significantly broadened upon Tb substitution, neutron-diffraction experiments clearly show the marked development of magnetic Bragg peaks below TC, indicating long-range magnetic order for the Au65Ga20Tb15 i QC also. Our findings can contribute to the further investigation of exotic magnetic orders formed on real quasiperiodic lattices with unprecedented highest global symmetry, i.e. icosahedral symmetry.

scholarly journals Space Oddity: Musical Syntax is Mapped onto Visual Space

2021 ◽  
Author(s):  
Neta Batya Maimon ◽  
Dominique Lamy ◽  
Zohar Eitan
Keyword(s):  
Implicit Association Test ◽  
Physical Space ◽  
Visual Space ◽  
Lateral Position ◽  
Implicit Associations ◽  
Vertical Position ◽  
Musical Structure ◽  
Musical Discourse ◽  
New Type ◽  
The Stability

Abstract Musicians ubiquitously apply spatial metaphors when describing the stability hierarchy established by tonal syntax: stable tones are considered spatially central and, as gravitational foci, spatially lower. We investigated whether listeners, musicians and non-musicians, indeed associate tonal relationships with visuospatial dimensions, including spatial height, centrality, laterality, and size, and whether such mappings are consistent with tonal discourse. We examined explicit and implicit associations. In the explicit paradigm, participants heard a tonality-establishing prime followed by a probe tone and coupled each probe with a subjectively appropriate location on a two-dimensional grid (Exp. 1) or with one of 7 circles differing in size (Exp. 4). The implicit paradigm used a version of the Implicit Association Test to examine associations of tonal stability with vertical position (Exp. 2), lateral position (Exp. 3) and object size (Exp. 5). Tonal stability was indeed as- sociated with perceived physical space: the spatial distances between the locations associated with different scale-degrees significantly correlated with the tonal stability differences between these scale degrees. However, inconsistently with the hypotheses implied by musical discourse, stable tones were associated with leftward and higher spatial positions, relative to unstable tones, rather than with central and lower spatial positions. We speculate that these mappings are influenced by emotion, embodying the “good is up” metaphor, and by the spatial structure of music keyboards. Taken together, results suggest that abstract syntactical relationships may consistently map onto concrete perceptual dimensions across modalities, demonstrating a new type of cross-modal cor- respondence and a hitherto under-researched connotative function of musical structure.

α-AlMnSi phase to a bcc structure by XE+ ion-beam irradiation

1996 ◽  
Vol 54 ◽  
pp. 720-721
Author(s):  
Y.X. Guo ◽  
L.M. Wang ◽  
R.C. Ewing
Keyword(s):  
Ion Beam ◽  
Alloy System ◽  
Icosahedral Quasicrystal ◽  
Icosahedral Symmetry ◽  
Structure Unit ◽  
Α Phase ◽  
Bcc Structure ◽  
Icosahedral Quasicrystals ◽  
Mackay Icosahedron ◽  
Important Structure

AlMnSi alloy system has attracted great attentions since the first report on the icosahedral quasicrystal materials in 1984. The rapidly quenched AlMnSi alloy around the stoichiometry of the α-AIMnSi phase (α-phase below) may form icosahedral quasicrystals. And the structure unit of the α-phase is of near icosahedral symmetry. The α-phase has a cubic structure with space group Pm3 (a= 1.268 nm). In each unit cell there are 138 atoms. The most important structure unit in this phase is the so-called MacKay icosahedron. In such a structure unit, 12 Al atoms are decorating the vertices of an icosahedron. Surrounding this icosahedron is another same oriented icosahedron of 12 Mn atoms, which is about twice the diameter of the former. Furthermore, 30 Al atoms define a shell outside the two inner icosahedra with each atom sitting at the midpoint just out of the Mn icosahedron edges. In the structure of α-phase, the icosahedra are slightly distorted and are connected along those of their three fold axes that coincide with the <111> direction of the cubic lattice.

scholarly journals Computational prediction of an icosahedral quasicrystal

2014 ◽  
Vol 70 (a1) ◽  
pp. C890-C890
Author(s):  
Michael Engel ◽  
Pablo Damasceno ◽  
Carolyn Phillips ◽  
Sharon Glotzer
Keyword(s):  
Self Assembly ◽  
Computational Prediction ◽  
Real Space ◽  
Icosahedral Quasicrystal ◽  
Icosahedral Symmetry ◽  
Structure Model ◽  
Colloidal Systems ◽  
Naturally Occurring ◽  
Higher Dimensional ◽  
Icosahedral Quasicrystals

From the first quasicrystal discovered in the laboratory 30 years ago to the only known specimen of naturally occurring quasicrystals, quasicrystals with icosahedral symmetry have received great attention. There are more than one hundred stable icosahedral quasicrystals in metallic alloys; all are identified by their diffraction spectra. Despite this abundance, resolving the positions of the atoms within the solid has been possible only indirectly. Moreover, unlike dodecagonal and other axial quasicrystals, icosahedral quasicrystals have been observed neither in simulations nor in non-atomic (e.g. micellar or colloidal) systems, where real-space information would be available. Here we present an icosahedral quasicrystal discovered in computer simulation via self-assembly from the liquid phase. We provide a structure model by analyzing atomic surfaces and report the presence of phason flips. Our results constitute a direct microscopic confirmation of the higher-dimensional crystallographic description of icosahedral quasicrystals.

scholarly journals A cubic quasicrystal in a rapidly-solidified Mg-Al alloy

2014 ◽  
Vol 70 (a1) ◽  
pp. C91-C91
Author(s):  
Takeshi Kato ◽  
Takehito Seki ◽  
Eiji Abe
Keyword(s):  
Rotational Symmetry ◽  
Point Group ◽  
Physical Space ◽  
Al Alloy ◽  
Fold Axis ◽  
Cubic Symmetry ◽  
Quasiperiodic Structure ◽  
Diffraction Patterns ◽  
Analysis Of The Images ◽  
Rapidly Solidified

It is commonly accepted that the definition of quasicrystal should include a rotational symmetry forbidden in periodic crystals. On the other hand, the quasicrystal with a conventional point group is theoretically possible [1,2]. In a rapidly-solidified Mg-Al alloy, intriguing electron diffraction patterns (EDPs) were reported, which show a cubic symmetry with aperiodic arrays of Bragg reflections [2]. In the present work, we investigate the detailed structure of the rapidly-solidified Mg-Al phase based on direct structure observations using STEM. In a rapidly-solidified Mg-61 at.% Al alloy, 2-fold, 3-fold, and 4-fold EDPs are obtained (Fig. a), which shows that the structure has the cubic point group. However, the relevant diffraction spots are arranged aperiodically. Especially in the 2-fold EDP, a high density of the spots is observed, and the corresponding HADDF-STEM image shows several remarkable features (Fig. b). Two length scales, L and S, can be definitely observed, and they are arranged quasiperiodically along the 3-fold axis. Their arrangement can be well described by the hyperspace crystallography; a physical space tilted by the angle θ , where tanθ ∼ 1.4, successfully generates the observed quasiperiodic pattern. Simulated EDPs from a simple model without detailed atomic decoration reproduces fairly well the experimental patterns. Further analysis of the images reveals that the present quasiperiodic structure has similar local structure to the stable β-Mg2Al3phase; two lengths correspond to L and S may be reasonably defined. The quasicrystal with a cubic symmetry is unambiguously determined for the first time, based on a direct structural observation. The present results strongly suggest that the noncrystallographic rotational symmetry is not an essential factor to form the quasiperiodic structure, raising a very fundamental, universal question on the physical origin of a long-range order of condensed matters.

scholarly journals Concomitant singularities of Yb-valence and magnetism at a critical lattice parameter of icosahedral quasicrystals and approximants

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Keiichiro Imura ◽  
Hitoshi Yamaoka ◽  
Shinjirou Yokota ◽  
Kazushi Sakamoto ◽  
Yoshiya Yamamoto ◽  
...  
Keyword(s):  
Fermi Liquid ◽  
Lattice Parameter ◽  
Fluorescence Yield ◽  
Structure Property ◽  
Disorder Phase Transition ◽  
Icosahedral Quasicrystals ◽  
New Type ◽  
Critical Lattice ◽  
Long Range Ordering ◽  
Relationship Of

Abstract Non-Fermi-liquid (NFL), a significant deviation from Fermi-liquid theory, usually emerges near an order-disorder phase transition at absolute zero. Recently, a diverging susceptibility toward zero temperature was observed in a quasicrystal (QC). Since an electronic long-range ordering is normally absent in QCs, this anomalous behaviour should be a new type of NFL. Here we study high-resolution partial-fluorescence-yield x-ray absorption spectroscopy on Yb-based intermediate-valence icosahedral QCs and cubic approximant crystals (ACs), some of which are new materials, to unveil the mechanism of the NFL. We find that for both forms of QCs and ACs, there is a critical lattice parameter where Yb-valence and magnetism concomitantly exhibit singularities, suggesting a critical-valence-fluctuation-induced NFL. The present result provides an intriguing structure–property relationship of matter; size of a Tsai-type cluster (that is a common local structure to both forms) tunes the NFL whereas translational symmetry (that is present in ACs but absent in QCs) determines the nature of the NFL against the external/chemical pressure.

The Microstructure of Shock-Synthesized Diamond

1967 ◽  
Vol 25 ◽  
pp. 324-325
Author(s):  
Lucien F. Trueb
Keyword(s):  
Single Crystals ◽  
Preferred Orientation ◽  
High Magnification ◽  
Texture Pattern ◽  
Shock Process ◽  
New Type ◽  
Diffraction Diagram

A new type of synthetic industrial diamond formed by an explosive shock process has been recently developed by the Du Pont Company. This material consists of a mixture of two basically different forms, as shown in Figure 1: relatively flat and compact aggregates of acicular crystallites, and single crystals in the form of irregular polyhedra with straight edges.Figure 2 is a high magnification micrograph typical for the fibrous aggregates; it shows that they are composed of bundles of crystallites 0.05-0.3 μ long and 0.02 μ. wide. The selected area diffraction diagram (insert in Figure 2) consists of a weak polycrystalline ring pattern and a strong texture pattern with arc reflections. The latter results from crystals having preferred orientation, which shows that in a given particle most fibrils have a similar orientation.

New type electron gun with electrostatic and electromagnetic lenses

1978 ◽  
Vol 36 (1) ◽  
pp. 62-63
Author(s):  
T. Ichinokawa ◽  
H. Maeda
Keyword(s):  
Electron Microscopy ◽  
Electron Beam ◽  
Optimum Condition ◽  
Bias Voltage ◽  
Electron Gun ◽  
Charge Effect ◽  
Micro Fabrication ◽  
Maximum Brightness ◽  
New Type ◽  
The Ideal

I. IntroductionThermionic electron gun with the Wehnelt grid is popularly used in the electron microscopy and electron beam micro-fabrication. It is well known that this gun could get the ideal brightness caluculated from the Lengumier and Richardson equations under the optimum condition. However, the design and ajustment to the optimum condition is not so easy. The gun has following properties with respect to the Wehnelt bias; (1) The maximum brightness is got only in the optimum bias. (2) In the larger bias than the optimum, the brightness decreases with increasing the bias voltage on account of the space charge effect. (3) In the smaller bias than the optimum, the brightness decreases with bias voltage on account of spreading of the cross over spot due to the aberrations of the electrostatic immersion lens.In the present experiment, a new type electron gun with the electrostatic and electromagnetic lens is designed, and its properties are examined experimentally.

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