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Crystals
Special Issues
Structures, Properties and Applications of Quasicrystals
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Structures, Properties and Applications of Quasicrystals

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

Deadline for manuscript submissions: closed (15 March 2024) | Viewed by 8026

Special Issue Editors

Dr. Peidong Li

E-Mail Website
Guest Editor
Department of Mechanics, School of Architecture and Environment, Sichuan University, Chengdu 610065, China
Interests: multi-field coupling; fracture mechanics; damage mechanics; phase field modeling; quasicrystal; porous media; functionally graded materials
Prof. Dr. Yang Gao

E-Mail Website
Guest Editor
Department of Applied Mechanics, China Agricultural University, Beijing 100083, China
Interests: elasticity and defects concerning mechanical/physical behavior of heterogeneous materials and quasicrystalline materials
Dr. Yuan Li

E-Mail Website
Guest Editor
Henan Academy of Big Data, Zhengzhou University, Zhengzhou 450001, China
Interests: multi-field coupling; fracture mechanics; displacement discontinuity method; boundary element method; data-driven method; piezoelectric quasicrystals
Dr. Ruifeng Zheng

E-Mail Website
Guest Editor
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, China
Interests: fracture mechanics; multiferroic composite materials; multi-physics coupling; mechanics of quasicrystals

Special Issue Information

Dear Colleagues,

Quasicrystals, as a new kind of material between crystals and non-crystals, do not have spatial translational symmetry, but they have a long-range orientational order with a 5-fold or greater than 6-fold symmetry axis that is disallowed by the law of crystallography. This special structural form was first discovered in 1982 by Danielle Shechtman, who was awarded the Nobel Prize of Chemistry 2011. This important discovery changed the traditional concept of classifying solids into two classes, crystals and non-crystals, and has pushed material science into a new era. Today, the study of the macro and micro properties of quasicrystals has become an important research field. Furthermore, the special atomic arrangement of quasicrystals leads to many interesting properties different from those of traditional crystals, such as low friction, low adhesion, high wear resistance, high corrosion resistance, and special optical properties. These desirable properties lend quasicrystals great potential in various engineering practices, including energy storage, aerospace, medical equipment, optical engineering, etc. Studies on the microstructures, macro and micro properties, and applications of quasicrystals are welcome for submission to the present Special Issue, “Recent Advances on Quasicrystals”. This Special Issue may become a status reports summarizing the progress achieved in recent years.

Dr. Peidong Li
Prof. Dr. Yang Gao
Dr. Yuan Li
Dr. Ruifeng Zheng
Guest Editors

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. 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 2100 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
  • microstructures of quasicrystals
  • physical properties of quasicrystals
  • chemical properties of quasicrystals
  • mechanical properties of quasicrystals
  • engineering application of quasicrystals
  • mechanics of quasicrystal structures
  • quasicrystal composites
  • fracture mechanics of quasicrystals
  • contact mechanics of quasicrystals
  • quasicrystal inclusion problems

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Published Papers (5 papers)

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Research

22 pages, 5833 KiB  
Article
Three-Dimensional Axisymmetric Analysis of Annular One-Dimensional Hexagonal Piezoelectric Quasicrystal Actuator/Sensor with Different Configurations
by Yang Li and Yang Gao
Crystals 2024, 14(11), 964; https://doi.org/10.3390/cryst14110964 - 6 Nov 2024
Cited by 2 | Viewed by 700
Abstract
The presented article is about the axisymmetric deformation of an annular one-dimensional hexagonal piezoelectric quasicrystal actuator/sensor with different configurations, analyzed by the three-dimensional theory of piezoelectricity coupled with phonon and phason fields. The state space method is utilized to recast the basic equations [...] Read more.
The presented article is about the axisymmetric deformation of an annular one-dimensional hexagonal piezoelectric quasicrystal actuator/sensor with different configurations, analyzed by the three-dimensional theory of piezoelectricity coupled with phonon and phason fields. The state space method is utilized to recast the basic equations of one-dimensional hexagonal piezoelectric quasicrystals into the transfer matrix form, and the state space equations of a laminated annular piezoelectric quasicrystal actuator/sensor are obtained. By virtue of the finite Hankel transform, the ordinary differential equations with constant coefficients for an annular quasicrystal actuator/sensor with a generalized elastic simple support boundary condition are derived. Subsequently, the propagator matrix method and inverse Hankel transform are used together to achieve the exact axisymmetric solution for the annular one-dimensional hexagonal piezoelectric quasicrystal actuator/sensor. Numerical illustrations are presented to investigate the influences of the thickness-to-span ratio on a single-layer annular piezoelectric quasicrystal actuator/sensor subjected to different top surface loads, and the effect of material parameters is also presented. Afterward, the present model is applied to compare the performance of different piezoelectric quasicrystal actuator/sensor configurations: the quasicrystal multilayer, quasicrystal unimorph, and quasicrystal bimorph. Full article
(This article belongs to the Special Issue Structures, Properties and Applications of Quasicrystals)
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16 pages, 323 KiB  
Article
Three-Dimensional and Two-Dimensional Green Tensors of Piezoelectric Quasicrystals
by Markus Lazar and Eleni Agiasofitou
Crystals 2024, 14(10), 835; https://doi.org/10.3390/cryst14100835 - 26 Sep 2024
Cited by 2 | Viewed by 1307
Abstract
In this work, within the framework of the linear piezoelectricity theory of quasicrystals, the three-dimensional and two-dimensional Green tensors for arbitrary piezoelectric quasicrystals are derived. In the piezoelectricity of quasicrystals, where phonon, phason and electric fields exist, we introduce the corresponding multifields by [...] Read more.
In this work, within the framework of the linear piezoelectricity theory of quasicrystals, the three-dimensional and two-dimensional Green tensors for arbitrary piezoelectric quasicrystals are derived. In the piezoelectricity of quasicrystals, where phonon, phason and electric fields exist, we introduce the corresponding multifields by developing a hyperspace notation for piezoelectric quasicrystals. Using Fourier transform and the multifield formalism, the three-dimensional Green tensor for piezoelectric quasicrystals as well as its spatial gradient necessary for applications, are derived. The solutions for the “displacement”, “distortion” and “stress” multifields in the presence of a “force” multifield in a piezoelectric quasicrystal as well as the solution of the generalised Kelvin problem, are given. In addition, the two-dimensional Green tensors of piezoelectric quasicrystals as well as of quasicrystals, are determined. Full article
(This article belongs to the Special Issue Structures, Properties and Applications of Quasicrystals)
15 pages, 748 KiB  
Article
A Closed-Form Solution to the Mechanism of Interface Crack Formation with One Contact Area in Decagonal Quasicrystal Bi-Materials
by Zhiguo Zhang, Baowen Zhang, Xing Li and Shenghu Ding
Crystals 2024, 14(4), 316; https://doi.org/10.3390/cryst14040316 - 28 Mar 2024
Cited by 2 | Viewed by 2307
Abstract
Cracks and crack-like defects in engineering structures have greatly reduced the structural strength. An interface crack with one contact area in a combined tension–shear field of decagonal quasicrystal bi-material is investigated. Based on the deformation compatibility equation and displacement potential function, the complex [...] Read more.
Cracks and crack-like defects in engineering structures have greatly reduced the structural strength. An interface crack with one contact area in a combined tension–shear field of decagonal quasicrystal bi-material is investigated. Based on the deformation compatibility equation and displacement potential function, the complex representation of stress and displacement is given. Using the mixed boundary conditions, the closed-form expressions for the stresses and the displacement jumps in the phonon field and phason field on the material interface are obtained. The results show that the stress intensity factor at the crack tip is zero for the phason field. The variation in the stress intensity factor and the length of the contact zone in the phonon field is given, and the result is consistent with the properties of the crystal. The design of safe engineering structures and the formulation of reasonable quality acceptance standards may benefit from the theoretical research carried out here. Full article
(This article belongs to the Special Issue Structures, Properties and Applications of Quasicrystals)
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13 pages, 5232 KiB  
Article
From the Fibonacci Icosagrid to E8 (Part I): The Fibonacci Icosagrid, an H3 Quasicrystal
by Fang Fang and Klee Irwin
Crystals 2024, 14(2), 152; https://doi.org/10.3390/cryst14020152 - 31 Jan 2024
Cited by 1 | Viewed by 1465
Abstract
This paper introduces a new kind of quasicrystal by Fibonacci-spacing a multigrid of a certain symmetry, like H2, H3, T3, etc. Multigrids of a certain symmetry can be used to generate quasicrystals, but multigrid vertices are not [...] Read more.
This paper introduces a new kind of quasicrystal by Fibonacci-spacing a multigrid of a certain symmetry, like H2, H3, T3, etc. Multigrids of a certain symmetry can be used to generate quasicrystals, but multigrid vertices are not a quasicrystal due to arbitrary closeness. By Fibonacci-spacing the grids, the structure transit into an aperiodic order becomes a quasicrystal itself. Unlike the quasicrystal generated by the dual-grid method, this kind of quasicrystal does not live in the dual space of the grid space. It is the grid space itself and possesses quasicrystal properties, except that its total number of vertex types are not finite and fixed for the infinite size of the quasicrystal but bounded by a slowly logarithmic growing number. A 2D example, the Fibonacci pentagrid, is given. A 3D example, the Fibonacci icosagrid (FIG), is also introduced, as well as its subsets, the Fibonacci tetragrid (FTG). The FIG can be thought of as a golden composition of five sets of FTGs. The golden composition procedure is another way to transit a random structure into aperiodic order, and the associated rotational angle is the same as the angle that resolves the geometric frustration for the H3 tetrahedral clusters. The FIG resembles another quasicrystal that is the same golden composition of five quasicrystals that are cut and projected and sliced from the E8 lattice. This leads to further exploration in mapping the FIG to the E8 lattice, and the results will be published following this paper. Full article
(This article belongs to the Special Issue Structures, Properties and Applications of Quasicrystals)
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25 pages, 1009 KiB  
Article
Analytical Solution of the Interference between Elliptical Inclusion and Screw Dislocation in One-Dimensional Hexagonal Piezoelectric Quasicrystal
by Zhiguo Zhang, Xing Li and Shenghu Ding
Crystals 2023, 13(10), 1419; https://doi.org/10.3390/cryst13101419 - 24 Sep 2023
Cited by 4 | Viewed by 1136
Abstract
This study examines the interference problem between screw dislocation and elliptical inclusion in one-dimensional hexagonal piezoelectric quasicrystals. The general solutions are obtained using the complex variable function method and the conformal transformation technique. When the screw dislocation is located outside or inside the [...] Read more.
This study examines the interference problem between screw dislocation and elliptical inclusion in one-dimensional hexagonal piezoelectric quasicrystals. The general solutions are obtained using the complex variable function method and the conformal transformation technique. When the screw dislocation is located outside or inside the elliptical inclusion, the perturbation method and Laurent series expansion are employed to derive explicit analytical expressions for the complex potentials in the elliptical inclusion and the matrix, respectively. Considering four types of far-field force and electric loading conditions, analytical solutions for various specific cases are obtained by using matrix operations. Expressions for the phonon field stress, phason field stress, and electric displacement are given for special cases, including the absence of a dislocation, the presence of an elliptical hole, and the interference between a screw dislocation and circular inclusion, as well as the case of a circular hole. The design and analysis of quasicrystal inclusion structures can benefit from the results of this work. Full article
(This article belongs to the Special Issue Structures, Properties and Applications of Quasicrystals)
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