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Symmetry
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Symmetry and Asymmetry in Quasicrystals or Amorphous Materials
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Symmetry and Asymmetry in Quasicrystals or Amorphous Materials

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Chemistry: Symmetry/Asymmetry".

Deadline for manuscript submissions: closed (31 December 2019) | Viewed by 17141

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Dr. Enrique Maciá Barber

E-Mail Website
Guest Editor
Departamento de Física de Materiales, Facultad CC. Físicas, Universidad Complutense de Madrid, E-28040 Madrid, Spain
Interests: quasicrystals, complex metallic alloys, quasiperiodic heterostructures; photonic and phononic quasicrystals, electronic and thermal transport in DNA molecules, thermoelectric materials

Special Issue Information

Dear Colleagues,

Quasicrystals (QCs) are long-range ordered materials with a symmetry incompatible with translation invariance. Accordingly, QCs exhibit high-quality diffraction patterns containing a collection of discrete Bragg reflections. Notwithstanding this, it is still common to read in the recent literature that these materials occupy an intermediate position between amorphous materials and periodic crystals. This misleading terminology can be understood as probably arising from the use of models and notions borrowed form the amorphous solids conceptual framework (such us tunneling states, weak interference effects, variable range hopping, or spin glass) in order to explain certain physical properties observed in QCs. On the other hand, the absence of a general, full-fledged theory of quasiperiodic systems certainly makes it difficult to clearly distinguish the features related to short-range order atomic arrangements from those stemming from long-range order correlations.

This Special Issue aims to share the latest knowledge and developments in both experimental and fundamental aspects in order to gain a deeper understanding of the relationship between the underlying structural order and the resulting physical properties in quasicrystals and their related approximant phases, focusing on the analogies and differences between these properties and those reported for amorphous materials of similar composition.

The Special Issue on “Symmetry and Asymmetry in Quasicrystals or Amorphous Materials” is intended to provide a unique international forum aimed at critically review past and current modeling frameworks used to interpret the physical properties of these two different classes of matter arrangements in order to gain a deeper understanding of the role of long-range quasiperiodic versus short-range local order in the physical and chemical properties of quasicrystals and related materials. Scientists working in a wide range of disciplines are invited to contribute to this goal.

Prof. Dr. Enrique Maciá Barber
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Local and global symmetry in condensed matter
  • Quasicrystals as cluster aggregates
  • Hierarchical order and fractal structures
  • Short-range order dominated physical properties
  • The role of defects in the physico-chemical properties of approximant phases
  • Transitions involving amorphous phases, periodic approximants, and quasicrystals
  • Phason dynamics in aperiodic crystals

Published Papers (6 papers)

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Editorial

Jump to: Research, Review

3 pages, 194 KiB  
Editorial
Symmetry and Asymmetry in Quasicrystals or Amorphous Materials
by Enrique Maciá Barber
Symmetry 2020, 12(8), 1326; https://doi.org/10.3390/sym12081326 - 9 Aug 2020
Viewed by 1877
Abstract
Quasicrystals (QCs) are long-range ordered materials with a symmetry incompatible with translation invariance. Accordingly, QCs exhibit high-quality diffraction patterns containing a collection of discrete Bragg reflections. Notwithstanding this, it is still common to read in the recent literature that these materials occupy an [...] Read more.
Quasicrystals (QCs) are long-range ordered materials with a symmetry incompatible with translation invariance. Accordingly, QCs exhibit high-quality diffraction patterns containing a collection of discrete Bragg reflections. Notwithstanding this, it is still common to read in the recent literature that these materials occupy an intermediate position between amorphous materials and periodic crystals. This misleading terminology can be understood as probably arising from the use of models and notions borrowed from the amorphous solid’s conceptual framework (such us tunneling states, weak interference effects, variable range hopping, or spin glass) in order to explain certain physical properties observed in QCs. On the other hand, the absence of a general, full-fledged theory of quasiperiodic systems certainly makes it difficult to clearly distinguish the features related to short-range order atomic arrangements from those stemming from long-range order correlations. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quasicrystals or Amorphous Materials)

Research

Jump to: Editorial, Review

10 pages, 12251 KiB  
Article
The Study of A New Symmetrical Rod Phase in Mg-Zn-Gd Alloys
by Jianhang Yue, Yun Feng, Hao Wu, Guorong Zhou, Min Zuo, Jinfeng Leng and Xinying Teng
Symmetry 2019, 11(8), 988; https://doi.org/10.3390/sym11080988 - 2 Aug 2019
Cited by 3 | Viewed by 2245
Abstract
Quasicrystal alloys have a wide application prospect because of excellent performances and characteristics; meanwhile, magnesium alloys are known as green engineering materials because of their high specific strength and light weight. Therefore, the study of Mg-Zn-Gd quasicrystal alloys is of great significance for [...] Read more.
Quasicrystal alloys have a wide application prospect because of excellent performances and characteristics; meanwhile, magnesium alloys are known as green engineering materials because of their high specific strength and light weight. Therefore, the study of Mg-Zn-Gd quasicrystal alloys is of great significance for the development of new materials. In this paper, Mg(70-x)Zn30Gdx(x=3,4,5) alloys were prepared by a conventional casting method and the morphologies and properties of these alloys were studied. There was a new symmetrical rod phase found in the Mg66Zn30Gd4 alloy and the symmetrical rod phase was identified as a ternary phase by mapping scanning and energy dispersive spectroscopy (EDS) analysis. The Zn/Gd ratio of the symmetrical rod phase was found to be 4.8 and the TEM images obtained were different from the typical diffraction spots patterns of quasicrystalline, which means it is unlikely to be quasicrystalline. With different melt holding time, the symmetrical rod phase evolved gradually over time from a lamellar eutectic structure; differential scanning calorimetry (DSC), heat treatment, and microhardness tests showed that the melting temperature of the rod phase was 453 °C and that its thermal stability and microhardness are better than quasicrystalline. Hence, the symmetrical rod phase is a new kind of complex metallic alloy phase whose composition and properties are close to those of quasicrystals but is not quasicrystalline. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quasicrystals or Amorphous Materials)
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Review

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21 pages, 1941 KiB  
Review
Real Space Theory for Electron and Phonon Transport in Aperiodic Lattices via Renormalization
by Vicenta Sánchez and Chumin Wang
Symmetry 2020, 12(3), 430; https://doi.org/10.3390/sym12030430 - 7 Mar 2020
Cited by 6 | Viewed by 3313
Abstract
Structural defects are inherent in solids at a finite temperature, because they diminish free energies by growing entropy. The arrangement of these defects may display long-range orders, as occurring in quasicrystals, whose hidden structural symmetry could greatly modify the transport of excitations. Moreover, [...] Read more.
Structural defects are inherent in solids at a finite temperature, because they diminish free energies by growing entropy. The arrangement of these defects may display long-range orders, as occurring in quasicrystals, whose hidden structural symmetry could greatly modify the transport of excitations. Moreover, the presence of such defects breaks the translational symmetry and collapses the reciprocal lattice, which has been a standard technique in solid-state physics. An alternative to address such a structural disorder is the real space theory. Nonetheless, solving 1023 coupled Schrödinger equations requires unavailable yottabytes (YB) of memory just for recording the atomic positions. In contrast, the real-space renormalization method (RSRM) uses an iterative procedure with a small number of effective sites in each step, and exponentially lessens the degrees of freedom, but keeps their participation in the final results. In this article, we review aperiodic atomic arrangements with hierarchical symmetry investigated by means of RSRM, as well as their consequences in measurable physical properties, such as electrical and thermal conductivities. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quasicrystals or Amorphous Materials)
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36 pages, 14969 KiB  
Review
Localization Properties of Non-Periodic Electrical Transmission Lines
by Edmundo Lazo
Symmetry 2019, 11(10), 1257; https://doi.org/10.3390/sym11101257 - 9 Oct 2019
Cited by 1 | Viewed by 2034
Abstract
The properties of localization of the I ω electric current function in non-periodic electrical transmission lines have been intensively studied in the last decade. The electric components have been distributed in several forms: (a) aperiodic, including self-similar sequences (Fibonacci and m-tuplingtupling Thue–Morse), [...] Read more.
The properties of localization of the I ω electric current function in non-periodic electrical transmission lines have been intensively studied in the last decade. The electric components have been distributed in several forms: (a) aperiodic, including self-similar sequences (Fibonacci and m-tuplingtupling Thue–Morse), (b) incommensurate sequences (Aubry–André and Soukoulis–Economou), and (c) long-range correlated sequences (binary discrete and continuous). The localization properties of the transmission lines were measured using typical diagnostic tools of quantum mechanics like normalized localization length, transmission coefficient, average overlap amplitude, etc. As a result, it has been shown that the localization properties of the classic electric transmission lines are similar to the one-dimensional tight-binding quantum model, but also features some differences. Hence, it is worthwhile to continue investigating disordered transmission lines. To explore new localization behaviors, we are now studying two different problems, namely the model of interacting hanging cells (consisting of a finite number of dual or direct cells hanging in random positions in the transmission line), and the parity-time symmetry problem ( PT -symmetry), where resistances R n are distributed according to gain-loss sequence ( R 2 n = + R , R 2 n − 1 = − R ). This review presents some of the most important results on the localization behavior of the I ω electric current function, in dual, direct, and mixed classic transmission lines, when the electrical components are distributed non-periodically. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quasicrystals or Amorphous Materials)
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Graphical abstract

12 pages, 4423 KiB  
Review
Aperiodic-Order-Induced Multimode Effects and Their Applications in Optoelectronic Devices
by Hao Jing, Jie He, Ru-Wen Peng and Mu Wang
Symmetry 2019, 11(9), 1120; https://doi.org/10.3390/sym11091120 - 4 Sep 2019
Cited by 3 | Viewed by 2437
Abstract
Unlike periodic and random structures, many aperiodic structures exhibit unique hierarchical natures. Aperiodic photonic micro/nanostructures usually support optical multimodes due to either the rich variety of unit cells or their hierarchical structure. Mainly based on our recent studies on this topic, here we [...] Read more.
Unlike periodic and random structures, many aperiodic structures exhibit unique hierarchical natures. Aperiodic photonic micro/nanostructures usually support optical multimodes due to either the rich variety of unit cells or their hierarchical structure. Mainly based on our recent studies on this topic, here we review some developments of aperiodic-order-induced multimode effects and their applications in optoelectronic devices. It is shown that self-similarity or mirror symmetry in aperiodic micro/nanostructures can lead to optical or plasmonic multimodes in a series of one-dimensional/two-dimensional (1D/2D) photonic or plasmonic systems. These multimode effects have been employed to achieve optical filters for the wavelength division multiplex, open cavities for light–matter strong coupling, multiband waveguides for trapping “rainbow”, high-efficiency plasmonic solar cells, and transmission-enhanced plasmonic arrays, etc. We expect that these investigations will be beneficial to the development of integrated photonic and plasmonic devices for optical communication, energy harvesting, nanoantennas, and photonic chips. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quasicrystals or Amorphous Materials)
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26 pages, 1096 KiB  
Review
Tight-Binding Modeling of Nucleic Acid Sequences: Interplay between Various Types of Order or Disorder and Charge Transport
by Konstantinos Lambropoulos and Constantinos Simserides
Symmetry 2019, 11(8), 968; https://doi.org/10.3390/sym11080968 - 1 Aug 2019
Cited by 15 | Viewed by 3944
Abstract
This review is devoted to tight-binding (TB) modeling of nucleic acid sequences like DNA and RNA. It addresses how various types of order (periodic, quasiperiodic, fractal) or disorder (diagonal, non-diagonal, random, methylation et cetera) affect charge transport. We include an introduction to TB [...] Read more.
This review is devoted to tight-binding (TB) modeling of nucleic acid sequences like DNA and RNA. It addresses how various types of order (periodic, quasiperiodic, fractal) or disorder (diagonal, non-diagonal, random, methylation et cetera) affect charge transport. We include an introduction to TB and a discussion of its various submodels [wire, ladder, extended ladder, fishbone (wire), fishbone ladder] and of the process of renormalization. We proceed to a discussion of aperiodicity, quasicrystals and the mathematics of aperiodic substitutional sequences: primitive substitutions, Perron–Frobenius eigenvalue, induced substitutions, and Pisot property. We discuss the energy structure of nucleic acid wires, the coupling to the leads, the transmission coefficients and the current–voltage curves. We also summarize efforts aiming to examine the potentiality to utilize the charge transport characteristics of nucleic acids as a tool to probe several diseases or disorders. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quasicrystals or Amorphous Materials)
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