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Structure and Properties of Quasicrystals 2016

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A special issue of Crystals (ISSN 2073-4352). This special issue belongs to the section "Inorganic Crystalline Materials".

Deadline for manuscript submissions: closed (30 September 2016) | Viewed by 77640

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Prof. Dr. Enrique Maciá Barber

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Departamento de 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
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Special Issue Information

Dear Colleagues,

This Special Issue 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.

The Special Issue on “Structure and Properties of Quasicrystals” is intended to provide a unique international forum aimed at critically review the possible role of quasiperiodic order in the physical and chemical properties of quasicrystals. 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.

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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

Structure and Properties of Quasicrystals in Crystals (8 articles)

Published Papers (12 papers)

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Editorial

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229 KiB

Open AccessEditorial

Quo Vadis Quasicrystals?

by Enrique Maciá Barber

Crystals 2017, 7(3), 64; https://doi.org/10.3390/cryst7030064 - 24 Feb 2017

Cited by 3 | Viewed by 4260

Abstract

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. Full article

(This article belongs to the Special Issue Structure and Properties of Quasicrystals 2016)

Research

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2943 KiB

Open AccessArticle

Structural and Spectral Properties of Deterministic Aperiodic Optical Structures

by Luca Dal Negro, Ren Wang and Felipe A. Pinheiro

Crystals 2016, 6(12), 161; https://doi.org/10.3390/cryst6120161 - 09 Dec 2016

Cited by 28 | Viewed by 7696

Abstract

In this comprehensive paper we have addressed structure-property relationships in a number of representative systems with periodic, random, quasi-periodic and deterministic aperiodic geometry using the interdisciplinary methods of spatial point pattern analysis and spectral graph theory as well as the rigorous Green’s matrix method, which provides access to the electromagnetic scattering behavior and spectral fluctuations (distributions of complex eigenvalues as well as of their level spacing) of deterministic aperiodic optical media for the first time. Full article

(This article belongs to the Special Issue Structure and Properties of Quasicrystals 2016)

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5742 KiB

Open AccessArticle

Symmetry-Induced Light Confinement in a Photonic Quasicrystal-Based Mirrorless Cavity

by Gianluigi Zito, Giulia Rusciano, Antonio Sasso and Sergio De Nicola

Crystals 2016, 6(9), 111; https://doi.org/10.3390/cryst6090111 - 08 Sep 2016

Cited by 4 | Viewed by 4066

Abstract

We numerically investigate the electromagnetic field localization in a two-dimensional photonic quasicrystal generated with a holographic tiling. We demonstrate that light confinement can be induced into an air mirrorless cavity by the inherent symmetry of the spatial distribution of the dielectric scatterers forming the side walls of the open cavity. Furthermore, the propagation direction can be controlled by suitable designs of the structure. This opens up new avenues for designing photonic materials and devices. Full article

(This article belongs to the Special Issue Structure and Properties of Quasicrystals 2016)

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2150 KiB

Open AccessArticle

Elastodynamic Analysis of a Hollow Cylinder with Decagonal Quasicrystal Properties: Meshless Implementation of Local Integral Equations

by Seyed Mahmoud Hosseini, Jan Sladek and Vladimir Sladek

Crystals 2016, 6(8), 94; https://doi.org/10.3390/cryst6080094 - 17 Aug 2016

Cited by 5 | Viewed by 4251

Abstract

A meshless approximation and local integral equation (LIE) formulation are proposed for elastodynamic analysis of a hollow cylinder made of quasicrystal materials with decagonal quasicrystal properties. The cylinder is assumed to be under shock loading. Therefore, the general transient elastodynamic problem is considered for coupled phonon and phason displacements and stresses. The equations of motion in the theory of compatible elastodynamics of wave type for phonons and wave-telegraph type for phasons are employed and can be easily modified to the elasto-hydro dynamic equations for quasicrystals (QCs). The angular dependence of the tensor of phonon–phason coupling coefficients handicaps utilization of polar coordinates, when the governing equations would be given by partial differential equations with variable coefficients. Despite the symmetry of the geometrical shape, the local weak formulation and meshless approximation are developed in the Cartesian coordinate system. The response of the cylinder in terms of both phonon and phason stress fields is obtained and studied in detail. Full article

(This article belongs to the Special Issue Structure and Properties of Quasicrystals 2016)

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7214 KiB

Open AccessArticle

An Exact Method to Determine the Photonic Resonances of Quasicrystals Based on Discrete Fourier Harmonics of Higher-Dimensional Atomic Surfaces

by Farhad A. Namin and Douglas H. Werner

Crystals 2016, 6(8), 93; https://doi.org/10.3390/cryst6080093 - 10 Aug 2016

Cited by 3 | Viewed by 5066

Abstract

A rigorous method for obtaining the diffraction patterns of quasicrystals is presented. Diffraction patterns are an essential analytical tool in the study of quasicrystals, since they can be used to determine their photonic resonances. Previous methods for approximating the diffraction patterns of quasicrystals have relied on evaluating the Fourier transform of finite-sized super-lattices. Our approach, on the other hand, is exact in the sense that it is based on a technique that embeds quasicrystals into higher dimensional periodic hyper-lattices, thereby completely capturing the properties of the infinite structure. The periodicity of the unit cell in the higher dimensional space can be exploited to obtain the Fourier series expansion in closed-form of the corresponding atomic surfaces. The utility of the method is demonstrated by applying it to one-dimensional Fibonacci and two-dimensional Penrose quasicrystals. The results are verified by comparing them to those obtained by using the conventional super-lattice method. It is shown that the conventional super-cell approach can lead to inaccurate results due to the continuous nature of the Fourier transform, since quasicrystals have a discrete spectrum, whereas the approach introduced in this paper generates discrete Fourier harmonics. Furthermore, the conventional approach requires very large super-cells and high-resolution sampling of the reciprocal space in order to produce accurate results leading to a very large computational burden, whereas the proposed method generates accurate results with a relatively small number of terms. Finally, we propose how this approach can be generalized from the vertex model, which assumes identical particles at all vertices, to a more realistic case where the quasicrystal is composed of different atoms. Full article

(This article belongs to the Special Issue Structure and Properties of Quasicrystals 2016)

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Review

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60834 KiB

Open AccessReview

The Physics of the Hume-Rothery Electron Concentration Rule

by Uichiro Mizutani and Hirokazu Sato

Crystals 2017, 7(1), 9; https://doi.org/10.3390/cryst7010009 - 06 Jan 2017

Cited by 57 | Viewed by 11640

Abstract

For a long time we have shared the belief that the physics of the Hume-Rothery electron concentration rule can be deepened only through thorough investigation of the interference phenomenon of itinerant electrons with a particular set of lattice planes, regardless of whether d-states are involved near the Fermi level or not. For this purpose, we have developed the FLAPW-Fourier theory (Full potential Linearized Augmented Plane Wave), which is capable of determining the square of the Fermi diameter,

{(2 k_{F})}^{2}

, and the number of itinerant electrons per atom, e/a, as well as the set of lattice planes participating in the interference phenomenon. By determining these key parameters, we could test the interference condition and clarify how it contributes to the formation of a pseudogap at the Fermi level. Further significant progress has been made to allow us to equally handle transition metal (TM) elements and their compounds. A method of taking the center of gravity energy for energy distribution of electrons with a given electronic state has enabled us to eliminate the d-band anomaly and to determine effective

{(2 k_{F})}^{2}

, and e/a, even for systems involving the d-band or an energy gap across the Fermi level. The e/a values for 54 elements covering from Group 1 up to Group 16 in the Periodic Table, including 3d-, 4d- and 5d-elements, were determined in a self-consistent manner. The FLAPW-Fourier theory faces its limit only for elements in Group 17 like insulating solids Cl and their compounds, although the value of e/a can be determined without difficulty when Br becomes metallic under high pressures. The origin of a pseudogap at the Fermi level for a large number of compounds has been successfully interpreted in terms of the interference condition, regardless of the bond-types involved in the van Arkel-Ketelaar triangle map. Full article

(This article belongs to the Special Issue Structure and Properties of Quasicrystals 2016)

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6466 KiB

Open AccessReview

Elasto-Dynamics of Quasicrystals

by Wu Li and Tianyou Fan

Crystals 2016, 6(11), 152; https://doi.org/10.3390/cryst6110152 - 23 Nov 2016

Cited by 3 | Viewed by 3947

Abstract

A review on elasto-dynamics of quasicrystals (QCs) and their applications based on mathematical elasticity is given. In this study, recent studies on elasto-dynamics of QCs are reviewed, in which the focus of the problem lies in the role of phason variables and the coupling effect between phonons and phasons in the dynamic deformation process. On summarizing and describing the development of the elastic dynamics of QCs, this review mainly presents theelasto-dynamics of QCs and their application in a variety of research areas, ranging from problems with different QCs, including one-, two-, and three-dimensional QCs to various coupling problems. The plane elasticity and anti-plane elasticity of quasicrystals are included in this review. Full article

(This article belongs to the Special Issue Structure and Properties of Quasicrystals 2016)

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5926 KiB

Open AccessReview

Quasicrystals and Other Aperiodic Structures in Mineralogy

by Carlos M. Pina and Victoria López-Acevedo

Crystals 2016, 6(11), 137; https://doi.org/10.3390/cryst6110137 - 27 Oct 2016

Cited by 4 | Viewed by 10937

Abstract

In this article, we first present and discuss eighteenth-century descriptions of minerals that contributed decisively to the development of crystallography. Remarkably, these old crystallographic descriptions included morphologies with symmetries incompatible with an internal periodic order of atoms, which, however, have been recognised to be characteristics of quasicrystals. Moreover, we also review a number of studies of minerals with aperiodic crystal structures, including recently reported natural quasicrystals of extra-terrestrial origin. Finally, we discuss the current investigations addressing the search for new quasicrystalline minerals in nature. Full article

(This article belongs to the Special Issue Structure and Properties of Quasicrystals 2016)

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4956 KiB

Open AccessReview

Quantum Simulation of a 2D Quasicrystal with Cold Atoms

by Nicolas Macé, Anuradha Jagannathan and Michel Duneau

Crystals 2016, 6(10), 124; https://doi.org/10.3390/cryst6100124 - 23 Sep 2016

Cited by 15 | Viewed by 5468

Abstract

We describe a way to obtain a two-dimensional quasiperiodic tiling with eight-fold symmetry using cold atoms. One can obtain a series of such optical tilings, related by scale transformations, for a series of specific values of the chemical potential of the atoms. A theoretical model for the optical system is described and compared with that of the well-known cut-and-project method for the Ammann–Beenker tiling. The relation between the two tilings is discussed. This type of cold atom structure should allow the simulation of several important lattice models for interacting quantum particles and spins in quasicrystals. Full article

(This article belongs to the Special Issue Structure and Properties of Quasicrystals 2016)

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4002 KiB

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A Review of Transmission Electron Microscopy of Quasicrystals—How Are Atoms Arranged?

by Ruitao Li, Zhong Li, Zhili Dong and Khiam Aik Khor

Crystals 2016, 6(9), 105; https://doi.org/10.3390/cryst6090105 - 26 Aug 2016

Cited by 17 | Viewed by 10195

Abstract

Quasicrystals (QCs) possess rotational symmetries forbidden in the conventional crystallography and lack translational symmetries. Their atoms are arranged in an ordered but non-periodic way. Transmission electron microscopy (TEM) was the right tool to discover such exotic materials and has always been a main technique in their studies since then. It provides the morphological and crystallographic information and images of real atomic arrangements of QCs. In this review, we summarized the achievements of the study of QCs using TEM, providing intriguing structural details of QCs unveiled by TEM analyses. The main findings on the symmetry, local atomic arrangement and chemical order of QCs are illustrated. Full article

(This article belongs to the Special Issue Structure and Properties of Quasicrystals 2016)

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3198 KiB

Open AccessReview

Statistical Approach to Diffraction of Periodic and Non-Periodic Crystals—Review

by Radoslaw Strzalka, Ireneusz Buganski and Janusz Wolny

Crystals 2016, 6(9), 104; https://doi.org/10.3390/cryst6090104 - 26 Aug 2016

Cited by 14 | Viewed by 4805

Abstract

In this paper, we show the fundamentals of statistical method of structure analysis. Basic concept of a method is the average unit cell, which is a probability distribution of atomic positions with respect to some reference lattices. The distribution carries complete structural information required for structure determination via diffraction experiment regardless of the inner symmetry of diffracting medium. The shape of envelope function that connects all diffraction maxima can be derived as the Fourier transform of a distribution function. Moreover, distributions are sensitive to any disorder introduced to ideal structure—phonons and phasons. The latter are particularly important in case of quasicrystals. The statistical method deals very well with phason flips and may be used to redefine phasonic Debye-Waller correction factor. The statistical approach can be also successfully applied to the peak’s profile interpretation. It will be shown that the average unit cell can be equally well applied to a description of Bragg peaks as well as other components of diffraction pattern, namely continuous and singular continuous components. Calculations performed within statistical method are equivalent to the ones from multidimensional analysis. The atomic surface, also called occupation domain, which is the basic concept behind multidimensional models, acquires physical interpretation if compared to average unit cell. The statistical method applied to diffraction analysis is now a complete theory, which deals equally well with periodic and non-periodic crystals, including quasicrystals. The method easily meets also any structural disorder. Full article

(This article belongs to the Special Issue Structure and Properties of Quasicrystals 2016)

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Other

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1993 KiB

Open AccessConcept Paper

Two-Level Electron Excitations and Distinctive Physical Properties of Al-Cu-Fe Quasicrystals

by Alexandre Prekul and Natalya Shchegolikhina

Crystals 2016, 6(9), 119; https://doi.org/10.3390/cryst6090119 - 19 Sep 2016

Cited by 7 | Viewed by 4355

Abstract

This article is not a review in the conventional sense. Rather, it is a monographic study of the implications of detection in Al-Cu-Fe quasicrystals of the electronic heat capacity contributions associated with the two-level electron excitations. Our aim was to reveal correlations between these contributions, on the one hand, and specific features of electron transport, magnetic susceptibility, Hall-effect, tunnelling and optical spectra, on the other hand. It is shown that the full range of these features can be understood in the framework of the unified conceptual scheme based on two-level electron excitations. Full article

(This article belongs to the Special Issue Structure and Properties of Quasicrystals 2016)

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