Superquasicrystals: self-similar-ordered structures with non-crystallographic point symmetries

Niizeki, Komajiro; Fujita, Nobuhisa

doi:10.1088/0305-4470/38/13/l01

Cited by 5 publications

(22 citation statements)

References 20 publications

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“…According to this view, a more appropriate term for these solids would probably be hypercrystals [19][20][21]. By adopting the hyperspace perspective, the contribution by Farhad A. Namin and Douglas H. Werner exploits the unit cell in the higher dimensional space to obtain the atomic surfaces' Fourier series expansion in closed-form [22].…”

Section: Quasiperiodic Crystals Structurementioning

confidence: 99%

Quo Vadis Quasicrystals?

Barber

2017

Crystals

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This Special Issue aims at gaining a deeper understanding on the relationship between the underlying structural order and the resulting physical properties in aperiodic systems, including quasicrystalline and related complex metallic alloys, photonic quasicrystals, and other structures exhibiting long-range aperiodic order. This Special Issue contains 12 papers which highlight recent developments in quasiperiodic crystal structure, photonic quasicrystals and related optical devices, the intrinsic electrical, thermal, and mechanical properties of icosahedral and decagonal metallic alloys, and the nature of chemical bonding in intermetallic compounds, from a multidisciplinary perspective. In light of the results presented in the contributions collected in this Special Issue, we can confidently expect that new insights into the interdisciplinary science of quasicrystals will be gained in the years to come, providing a sharper picture of their structures and related physical properties, and spurring further progress in practical issues related to both materials engineering science and nanotechnology.

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Section: Quasiperiodic Crystals Structurementioning

confidence: 99%

Quo Vadis Quasicrystals?

Barber

2017

Crystals

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“…In fact, geometrically, a limit-quasiperiodic structure can be regarded as a section of a limit-periodic lattice in a higher dimension space, just as quasiperiodic structures can be obtained as sections of periodic lattices in high dimensions. [29] In the chart depicted in Fig. 1 bottom panel we properly zoom out the left column of Fig.…”

Section: Introductionmentioning

confidence: 99%

Spectral Classification of One‐Dimensional Binary Aperiodic Crystals: An Algebraic Approach

Maciá

2017

Annalen der Physik

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A spectral classi…cation of general one-dimensional binary aperiodic crystals (BACs) based on both their di¤raction patterns and energy spectrum measures is introduced along with a systematic comparison of the zeroth-order energy spectrum main features for BACs belonging to di¤erent spectral classes, including Fibonacci-class, precious means, metallic means, mixed means and period doubling based representatives. These systems are described by means of mixed-type Hamiltonians which include both diagonal and o¤-diagonal terms aperiodically distributed. An algebraic approach highlighting chemical correlation e¤ects present in the underlying lattice is introduced.Close analytical expressions are obtained by exploiting some algebraic properties of suitable blocking schemes preserving the atomic order of the original lattice. The existence of a resonance energy which de…nes the basic anatomy of the zeroth-order energy spectra structure for the standard Fibonacci, the precious means and the Fibonacci-class quasicrystals is disclosed. This eigenstate is also found in the energy spectra of BACs belonging to other spectral classes, but for speci…c particular choices of the corresponding model parameters only. The transmission coe¢ cient of these resonant states is always bounded below, although their related Landauer conductance values may range from highly conductive to highly resistive ones, depending on the relative strength of the chemical bonds.

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“…Recently, the above setup has been extended to limit-quasiperiodic structures with NCPG's [3]. Although such structures resemble the quasiperiodic counterparts in many ways, they exhibit markedly different characteristics.…”

Section: Introductionmentioning

confidence: 99%

“…Although such structures resemble the quasiperiodic counterparts in many ways, they exhibit markedly different characteristics. We call such structures superquasicrystals (SQC's) because of their inherent hierarchical superstructures [3]. So far only few concrete examples have been known for this type of structures.…”

Section: Introductionmentioning

confidence: 99%