Topical Collection "Structure and Properties of Quasicrystals"

Editor

Collection Editor
Prof. Dr. Enrique Maciá Barber

Dept. Física de Materiales, Facultad Ciencias Fisicas, Universidad Complutense de Madrid, E-28040 Madrid, Spain
Website | E-Mail
Interests: quasicrystals; complex metallic alloys; bulk thermoelectric materials; quasiperiodic heterostructures; photonic and phononic quasicrystals; electronic and thermal transport in DNA molecules

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

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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 (5 papers)

2019

Jump to: 2018, 2017

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
Received: 22 January 2019 / Revised: 28 January 2019 / Accepted: 30 January 2019 / Published: 1 February 2019
Cited by 1 | PDF Full-text (1245 KB) | HTML Full-text | XML Full-text | Supplementary Files
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
Received: 25 September 2018 / Revised: 25 October 2018 / Accepted: 31 October 2018 / Published: 6 November 2018
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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
Received: 15 August 2018 / Revised: 28 September 2018 / Accepted: 8 October 2018 / Published: 10 October 2018
PDF Full-text (15696 KB) | HTML Full-text | XML Full-text
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
Received: 20 August 2018 / Revised: 15 September 2018 / Accepted: 19 September 2018 / Published: 20 September 2018
PDF Full-text (29266 KB) | HTML Full-text | XML Full-text
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
Received: 27 April 2017 / Revised: 20 June 2017 / Accepted: 21 June 2017 / Published: 23 June 2017
PDF Full-text (498 KB) | HTML Full-text | XML Full-text
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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