Intrinsic photonic wave localization in a three-dimensional icosahedral quasicrystal

2017 ◽  
Vol 13 (4) ◽  
pp. 363-368 ◽  
Author(s):  
Seung-Yeol Jeon ◽  
Hyungho Kwon ◽  
Kahyun Hur
Keyword(s):  
Three Dimensional ◽  
Icosahedral Quasicrystal ◽  
Wave Localization

Other topics

2018 ◽  
Author(s):  
Ted Janssen ◽  
Gervais Chapuis ◽  
Marc de Boissieu
Keyword(s):  
Photonic Crystals ◽  
Crystal Morphology ◽  
Three Dimensional ◽  
Icosahedral Quasicrystal ◽  
Crystal Surfaces ◽  
Decagonal Quasicrystal ◽  
System A ◽  
Fundamental Law ◽  
Quasiperiodic Systems ◽  
Aperiodic Crystals

The law of rational indices to describe crystal faces was one of the most fundamental law of crystallography and is strongly linked to the three-dimensional periodicity of solids. This chapter describes how this fundamental law has to be revised and generalized in order to include the structures of aperiodic crystals. The generalization consists in using for each face a number of integers, with the number corresponding to the rank of the structure, that is, the number of integer indices necessary to characterize each of the diffracted intensities generated by the aperiodic system. A series of examples including incommensurate multiferroics, icosahedral crystals, and decagonal quaiscrystals illustrates this topic. Aperiodicity is also encountered in surfaces where the same generalization can be applied. The chapter discusses aperiodic crystal morphology, including icosahedral quasicrystal morphology, decagonal quasicrystal morphology, and aperiodic crystal surfaces; magnetic quasiperiodic systems; aperiodic photonic crystals; mesoscopic quasicrystals, and the mineral calaverite.

scholarly journals Gold’s Structural Versatility within Complex Intermetallics: From Hume-Rothery to Zintl and even Quasicrystals

2013 ◽  
Vol 1517 ◽  
Author(s):  
Gordon J. Miller ◽  
Srinivasa Thimmaiah ◽  
Volodymyr Smetana ◽  
Andriy Palasyuk ◽  
Qisheng Lin
Keyword(s):  
Complex Networks ◽  
Intermetallic Compounds ◽  
Chemical Bonding ◽  
Three Dimensional ◽  
The Other ◽  
Icosahedral Quasicrystal ◽  
Bulk Solids ◽  
Atomic Properties ◽  
Polar Intermetallics ◽  
Structural Versatility

ABSTRACTRecent exploratory syntheses of polar intermetallic compounds containing gold have established gold’s tremendous ability to stabilize new phases with diverse and fascinating structural motifs. In particular, Au-rich polar intermetallics contain Au atoms condensed into tetrahedra and diamond-like three-dimensional frameworks. In Au-poor intermetallics, on the other hand, Au atoms tend to segregate, which maximizes the number of Au-heteroatom contacts. Lastly, among polar intermetallics with intermediate Au content, complex networks of icosahedra have emerged, including discovery of the first sodium-containing, Bergman-type, icosahedral quasicrystal. Gold’s behavior in this metal-rich chemistry arises from its various atomic properties, which influence the chemical bonding features of gold with its environment in intermetallic compounds. Thus, the structural versatility of gold and the accessibility of various Au fragments within intermetallics are opening new insights toward elucidating relationships among metal-rich clusters and bulk solids.

scholarly journals On the indexing and reciprocal space of icosahedral quasicrystal

1999 ◽  
Vol 14 (11) ◽  
pp. 4182-4187 ◽  
Author(s):  
Alok Singh ◽  
S. Ranganathan
Keyword(s):  
Three Dimensional ◽  
Icosahedral Phase ◽  
Reciprocal Space ◽  
Fourth Generation ◽  
Icosahedral Quasicrystal ◽  
Sixth Generation

Important features of the icosahedral reciprocal space have been brought out. All reciprocal vectors up to sixth generation (by addition of icosahedral vectors) have been considered. Some more relationships for indexing the icosahedral phase are derived, and it is shown that the zone law using Cahn indices is also analogous to that valid for crystals. All important vectors, i.e., up to fourth generation and sixth generation, have been identified. Poles of all these vectors have been determined and shown to be one of the zone axes formed by these vectors. The types of indices that the planes and axes will have in three-dimensional and six-dimensional coordinates is discussed.

Terahertz wave localization at a three-dimensional ceramic fractal cavity in photonic crystals

2008 ◽  
Vol 103 (10) ◽  
pp. 103106 ◽  
Author(s):  
Yoshinari Miyamoto ◽  
Hideaki Kanaoka ◽  
Soshu Kirihara
Keyword(s):  
Photonic Crystals ◽  
Three Dimensional ◽  
Terahertz Wave ◽  
Wave Localization

Structure factor for an icosahedral quasicrystal within a statistical approach

2015 ◽  
Vol 71 (3) ◽  
pp. 279-290 ◽  
Author(s):  
Radoslaw Strzalka ◽  
Ireneusz Buganski ◽  
Janusz Wolny
Keyword(s):  
Structure Factor ◽  
Statistical Approach ◽  
Structural Model ◽  
Three Dimensional ◽  
Physical Space ◽  
Icosahedral Quasicrystal ◽  
Penrose Tiling ◽  
Higher Dimensional ◽  
Average Unit ◽  
Detailed Derivation

This paper describes a detailed derivation of a structural model for an icosahedral quasicrystal based on a primitive icosahedral tiling (three-dimensional Penrose tiling) within a statistical approach. The average unit cell concept, where all calculations are performed in three-dimensional physical space, is used as an alternative to higher-dimensional analysis. Comprehensive analytical derivation of the structure factor for a primitive icosahedral lattice with monoatomic decoration (atoms placed in the nodes of the lattice only) presents in detail the idea of the statistical approach to icosahedral quasicrystal structure modelling and confirms its full agreement with the higher-dimensional description. The arbitrary decoration scheme is also discussed. The complete structure-factor formula for arbitrarily decorated icosahedral tiling is derived and its correctness is proved. This paper shows in detail the concept of a statistical approach applied to the problem of icosahedral quasicrystal modelling.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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