The generation of a dodecagonal columnar liquid quasicrystal is revealed by Carsten Tschierske, Feng Liu and co‐workers in their Research Article (e202314454). Constructed by the T‐shaped facial ...polyphiles, a special trapezoid tile with three aromatic walls and one flexible aliphatic wall becomes crucial for reaching the delicate balance between steric and entropic effects required by quasiperiodicity.
Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The underlying mathematics, known as the theory of aperiodic order, is the ...subject of this comprehensive multi-volume series. This first volume provides a graduate-level introduction to the many facets of this relatively new area of mathematics. Special attention is given to methods from algebra, discrete geometry and harmonic analysis, while the main focus is on topics motivated by physics and crystallography. In particular, the authors provide a systematic exposition of the mathematical theory of kinematic diffraction. Numerous illustrations and worked-out examples help the reader to bridge the gap between theory and application. The authors also point to more advanced topics to show how the theory interacts with other areas of pure and applied mathematics.
•Magnetocaloric effects of ferromagnetic approximants Au64Al22R14 (R = Gd, Tb, and Dy) investigated.•Magnetic entropy change is from unique spin configuration over second icosahedron shell.•Promising ...approximant and quasicrystal materials design to develop larger magnetocaloric effect.
We report the magnetocaloric effect of the Tsai-type 1/1 quasicrystal approximants Au64Al22R14 (R = Gd, Tb, and Dy) with the space group of Im3̅. These approximants with the electron-per-atom (e/a) ratio of 1.72 exhibit a ferromagnetic transition in bulk at the Curie temperatures of 27, 15, and 9.5 K for R = Gd, Tb, and Dy, respectively, as confirmed by both magnetic susceptibility and specific heat measurements. The magnetic entropy change (ΔSM) of the materials for a field change of 7 T are 6.3, 4.4, and 4.8 J/K mol-R for R = Gd, Tb, and Dy, respectively. Other parameters related to the magnetocaloric effect, the adiabatic temperature change (ΔTad) and the relative cooling power (RCP) are also evaluated. We also discuss the obtained magnetocaloric effect of the approximants with relation to the recently reported unique magnetic order formed on the icosahedral clusters, a building unit of the Tsai-type 1/1 quasicrystal approximants.
The generation of a dodecagonal columnar liquid quasicrystal is revealed by Carsten Tschierske, Feng Liu and co‐workers in their Research Article (e202314454). Constructed by the T‐shaped facial ...polyphiles, a special trapezoid tile with three aromatic walls and one flexible aliphatic wall becomes crucial for reaching the delicate balance between steric and entropic effects required by quasiperiodicity.
Quasicrystals and their Approximants in 2D Ternary Oxides Förster, Stefan; Schenk, Sebastian; Maria Zollner, Eva ...
Physica Status Solidi B-basic Solid State Physics,
July 2020, 2020-07-00, Volume:
257, Issue:
7
Journal Article
Peer reviewed
Open access
2D oxide quasicrystals (OQCs) are recently discovered aperiodic, but well‐ordered oxide interfaces. In this topical review, an introduction to these new thin‐film systems is given. The concept of ...quasicrystals and their approximants is explained for BaTiO3‐ and SrTiO3‐derived OQCs and related periodic structures in these 2D oxides. In situ microscopy unravels the high‐temperature formation process of OQCs on Pt(111). The dodecagonal structure is discussed regarding tiling statistics and tiling decoration based on the results of atomically resolved scanning tunneling microscopy and various diffraction techniques. In addition, angle‐resolved ultraviolet photoemission spectroscopy and X‐ray photoelectron spectroscopy results prove a metallic character of the 2D oxide.
The recently discovered 2D oxide quasicrystals represent aperiodic, but well‐ordered oxide interfaces. An introduction to these new thin‐film systems is given here. The presence of well‐defined quasicrystalline structures adds another degree of freedom to perovskite oxide interfaces beyond the formation of 2D electron gases, new forms of topology, and new ferroic coupling mechanisms.
The plane problem of two‐dimensional decagonal quasicrystals with a rigid circular arc inclusion was investigated under infinite tension and concentrated force. Based on complex representations of ...stresses and displacements of two‐dimensional decagonal quasicrystals, the above problem is transformed into Riemann boundary problem by using the analytic continuation principle of complex functions. The general solutions of two‐dimensional decagonal quasicrystals under the action of plane concentrated force and infinite uniform tension are derived. The closed solutions of complex potential functions in several typical cases are obtained, and the formula of singular stress field at the tip of rigid line inclusions is given. The results show that the stress field at the tip of circular arc rigid line inclusions has singularity of oscillation under plane load. Numerical examples are given to analyze the effects of inclusion radius, different inclusions, the coupling coefficient and phason field parameter on stress singularity coefficients.
The plane problem of two‐dimensional decagonal quasicrystals with a rigid circular arc inclusion was investigated under infinite tension and concentrated force. Based on complex representations of stresses and displacements of two‐dimensional decagonal quasicrystals, the above problem is transformed into Riemann boundary problem by using the analytic continuation principle of complex functions. The general solutions of two‐dimensional decagonal quasicrystals under the action of plane concentrated force and infinite uniform tension are derived.…
Photographic slides of an aperiodic dodecagonal tiling were used as two-dimensional diffraction gratings to describe and demonstrate the basic properties of dodecagonal quasicrystals. This paper ...complements our earlier publication on Penrose (decagonal) and Ammann (octagonal) quasicrystals, where we constructed and presented the corresponding diffraction gratings.
PDF
