Topical Collection "Structure and Properties of Quasicrystals"

Editor

Prof. Dr. Enrique Maciá Barber
Website
Collection Editor
Dept. Física de Materiales, Facultad Ciencias Fisicas, Universidad Complutense de Madrid, E-28040 Madrid, Spain
Interests: quasicrystals; complex metallic alloys; bulk thermoelectric materials; quasiperiodic heterostructures; photonic and phononic quasicrystals; electronic and thermal transport in DNA molecules
Special Issues and Collections in MDPI journals

Topical Collection Information

Dear Colleagues,

This Collection aims to promote international exchange and to share the latest knowledge and developments in both experimental and fundamental aspects in order to gain a deeper understanding on the relationship between the underlying structural order and the resulting physical properties in quasicrystals and their related approximant phases. The capability of exploiting aperiodic order in the design of novel devices based on dielectric multilayers or semiconductor heterostructures is also addressed. Interdisciplinary approaches encompassing the notion of quasiperiodic order in mineralogy, quantum chemistry and bio-inspired systems of current interest will be considered as well.

Prof. Dr. Enrique Maciá Barber

Collection 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 papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the collection 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. Crystals 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 1600 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

  • Quasicrystals
  • Complex metallic alloys
  • Chemical bonding in quasicrystals
  • Surface properties of quasicrystals and approximant phases
  • Electrical, thermal and thermoelectric transport properties of quasicrystals
  • Magnetic, mechanical properties of quasicrystals
  • Photonic and phononic quasicrystals

Related Special Issue

Published Papers (8 papers)

2019

Jump to: 2018, 2017

Open AccessArticle
Twisted Graphene Bilayers and Quasicrystals: A Cut and Projection Approach
Crystals 2019, 9(10), 519; https://doi.org/10.3390/cryst9100519 - 10 Oct 2019
Abstract
In this work, a modified version of the cut and projection approach is proposed to describe the structure of graphene bilayers with twist angles. With this method, the rotation between two graphene layers is viewed as a rotation of the projection space and [...] Read more.
In this work, a modified version of the cut and projection approach is proposed to describe the structure of graphene bilayers with twist angles. With this method, the rotation between two graphene layers is viewed as a rotation of the projection space and the resulting projected structure is interpreted as the set of points of best fit between the two rotated structures. Additionally, focus is given to the pertinence of the many algebraic and geometric tools used in grain boundaries and in quasicrystals to graphene bilayer system (or any other bilayer system, for that matter) case. Full article
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Open AccessArticle
Aperiodic Photonics of Elliptic Curves
Crystals 2019, 9(9), 482; https://doi.org/10.3390/cryst9090482 - 14 Sep 2019
Abstract
In this paper we propose a novel approach to aperiodic order in optical science and technology that leverages the intrinsic structural complexity of certain non-polynomial (hard) problems in number theory and cryptography for the engineering of optical media with novel transport and wave [...] Read more.
In this paper we propose a novel approach to aperiodic order in optical science and technology that leverages the intrinsic structural complexity of certain non-polynomial (hard) problems in number theory and cryptography for the engineering of optical media with novel transport and wave localization properties. In particular, we address structure-property relationships in a large number (900) of light scattering systems that physically manifest the distinctive aperiodic order of elliptic curves and the associated discrete logarithm problem over finite fields. Besides defining an extremely rich subject with profound connections to diverse mathematical areas, elliptic curves offer unprecedented opportunities to engineer light scattering phenomena in aperiodic environments beyond the limitations of traditional random media. Our theoretical analysis combines the interdisciplinary methods of point patterns spatial statistics with the rigorous Green’s matrix solution of the multiple wave scattering problem for electric and magnetic dipoles and provides access to the spectral and light scattering properties of novel deterministic aperiodic structures with enhanced light-matter coupling for nanophotonics and metamaterials applications to imaging and spectroscopy. Full article
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Open AccessArticle
Analytic Solutions to Two-Dimensional Decagonal Quasicrystals with Defects Using Complex Potential Theory
Crystals 2019, 9(4), 209; https://doi.org/10.3390/cryst9040209 - 17 Apr 2019
Cited by 1
Abstract
An analytical treatment for two-dimensional point group 10 mm decagonal quasicrystals with defects was suggested based on the complex potential method. On the basis of the assumption of linear elasticity, two new conformal maps were applied to two examples: the first was an [...] Read more.
An analytical treatment for two-dimensional point group 10 mm decagonal quasicrystals with defects was suggested based on the complex potential method. On the basis of the assumption of linear elasticity, two new conformal maps were applied to two examples: the first was an arc with an elliptic notch inner surface in a decagonal quasicrystal, where the complex potentials could be exactly obtained; and the second was concerned with a decagonal point group 10 mm quasicrystalline strip weakened by a Griffith crack, which was subjected to a pair of uniform static pressures. Using the basic idea underlying crack theory, the extent of the stress intensity factors was analytically estimated. If the height was allowed to approach infinity, these results can be turned into the known results of an “ordinary” crystal with only phonon elastic parameters when the phason and phonon-phason elastic constants are eliminated. Full article
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Open AccessArticle
Atomic Structure of Decagonal Al-Cu-Rh Quasicrystal–Revisited: New Correction for Phonons
Crystals 2019, 9(2), 78; https://doi.org/10.3390/cryst9020078 - 01 Feb 2019
Cited by 3
Abstract
The standard approach applies the Gaussian distribution function to estimate atomic displacements due to thermal vibrations in periodic and aperiodic systems, which is used in a form of the Debye–Waller factor during the structure refinement. Acoustic phonons provide the largest contribution to the [...] Read more.
The standard approach applies the Gaussian distribution function to estimate atomic displacements due to thermal vibrations in periodic and aperiodic systems, which is used in a form of the Debye–Waller factor during the structure refinement. Acoustic phonons provide the largest contribution to the Gaussian correction although the character of other phonon modes remains relatively unclear. In this paper, we provide an alternative description of localized and dispersionless phonons based on an assumption of the harmonic displacement distribution function, which was recently proposed for model quasicrystals, and apply this approach for a decagonal Al-Cu-Rh quasicrystal that was previously studied by Kuczera et al. in 2012. We used the same X-ray diffraction data and the statistical method of structural analysis of the aperiodic systems. The correction function for phonons takes the form of a Bessel function instead of a conventional (Gaussian) Debye–Waller factor. This allowed us to achieve R-factor of 7.2% compared to 7.9% reported in the original paper. A significant improvement of the calculated atomic composition towards experimentally obtained and minor positional changes is also reported compared to the original paper. The results show the usefulness of investigating different corrective terms for diffraction data during a structure refinement. Full article
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2018

Jump to: 2019, 2017

Open AccessArticle
Non-Local Game of Life in 2D Quasicrystals
Crystals 2018, 8(11), 416; https://doi.org/10.3390/cryst8110416 - 06 Nov 2018
Abstract
On a two-dimensional quasicrystal, a Penrose tiling, we simulate for the first time a game of life dynamics governed by non-local rules. Quasicrystals have inherently non-local order since any local patch, the emperor, forces the existence of a large number of tiles at [...] Read more.
On a two-dimensional quasicrystal, a Penrose tiling, we simulate for the first time a game of life dynamics governed by non-local rules. Quasicrystals have inherently non-local order since any local patch, the emperor, forces the existence of a large number of tiles at all distances, the empires. Considering the emperor and its local patch as a quasiparticle, in this case a glider, its empire represents its field and the interaction between quasiparticles can be modeled as the interaction between their empires. Following a set of rules, we model the walk of life in different setups and we present examples of self-interaction and two-particle interactions in several scenarios. This dynamic is influenced by both higher dimensional representations and local choice of hinge variables. We discuss our results in the broader context of particle physics and quantum field theory, as a first step in building a geometrical model that bridges together higher dimensional representations, quasicrystals and fundamental particles interactions. Full article
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Open AccessArticle
Dynamic Fracture Mechanism of Quasicrystal-Containing Al–Cr–Fe Consolidated Using Spark Plasma Sintering
Crystals 2018, 8(10), 385; https://doi.org/10.3390/cryst8100385 - 10 Oct 2018
Cited by 1
Abstract
The potential applications of quasicrystals (QCs) in automotive and aerospace industries requires the investigation of their fracture and failure mechanisms under dynamic loading conditions. In this study, Al–Cr–Fe powders were consolidated into pellets using spark plasma sintering at 800 °C for 30 min. [...] Read more.
The potential applications of quasicrystals (QCs) in automotive and aerospace industries requires the investigation of their fracture and failure mechanisms under dynamic loading conditions. In this study, Al–Cr–Fe powders were consolidated into pellets using spark plasma sintering at 800 °C for 30 min. The microhardness and dynamic failure properties of the samples were determined using nanoindentation and split-Hopkinson pressure bar technique, respectively. Scanning electron microscopy and transmission electron microscopy were employed to analyze fracture particles. The dynamic failure strength obtained from the tests is 653 ± 40 MPa. The dynamic failure process is dominated by transgranular fracture mechanisms. The difficulty in the metadislocation motion in the dynamic loading leads to the high brittleness of the spark plasma sintered (SPSed) Al–Cr–Fe materials. Full article
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Open AccessArticle
Quasicrystal Tilings in Three Dimensions and Their Empires
Crystals 2018, 8(10), 370; https://doi.org/10.3390/cryst8100370 - 20 Sep 2018
Cited by 1
Abstract
The projection method for constructing quasiperiodic tilings from a higher dimensional lattice provides a useful context for computing a quasicrystal’s vertex configurations, frequencies, and empires (forced tiles). We review the projection method within the framework of the dual relationship between the Delaunay and [...] Read more.
The projection method for constructing quasiperiodic tilings from a higher dimensional lattice provides a useful context for computing a quasicrystal’s vertex configurations, frequencies, and empires (forced tiles). We review the projection method within the framework of the dual relationship between the Delaunay and Voronoi cell complexes of the lattice being projected. We describe a new method for calculating empires (forced tiles) which also borrows from the dualisation formalism and which generalizes to tilings generated projections of non-cubic lattices. These techniques were used to compute the vertex configurations, frequencies and empires of icosahedral quasicrystals obtained as a projections of the D 6 and Z 6 lattices to R 3 and we present our analyses. We discuss the implications of this new generalization. Full article
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2017

Jump to: 2019, 2018

Open AccessArticle
Lempel-Ziv Complexity of Photonic Quasicrystals
Crystals 2017, 7(7), 183; https://doi.org/10.3390/cryst7070183 - 23 Jun 2017
Abstract
The properties of one-dimensional photonic quasicrystals ultimately rely on their nontrivial long-range order, a hallmark that can be quantified in many ways depending on the specific aspects to be studied. Here, we assess the quasicrystal structural features in terms of the Lempel-Ziv complexity. [...] Read more.
The properties of one-dimensional photonic quasicrystals ultimately rely on their nontrivial long-range order, a hallmark that can be quantified in many ways depending on the specific aspects to be studied. Here, we assess the quasicrystal structural features in terms of the Lempel-Ziv complexity. This is an easily calculable quantity that has proven to be useful for describing patterns in a variety of systems. One feature of great practical relevance is that it provides a reliable measure of how hard it is to create the structure. Using the generalized Fibonacci quasicrystals as our thread, we give analytical fitting formulas for the dependence of the optical response with the complexity. Full article
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