Properties Of Quasicrystals Research Articles

Application of quasicrystals to data processing

Abstract We propose a data processing method based on properties of quasicrystals and apply it to bitmap images. The method uses the mapping between the physical and internal spaces of a quasi-crystal to uniformly distribute the part of data that is lost in the transmitting or storing processes. At the same time, it is possible to unambiguously restore the rest of the data. The main advantages are strict aperiodicity of discrete sets and everywhere discontinuous property of the mapping as well as the speed of computation, simplicity of implementation and a straightforward possibility of extending the method to encryption of higher dimensional data. Several examples of construction of quasicrystals and examples of image processing are given.

Topological superconductivity in Fibonacci quasicrystals

We investigate the properties of a Fibonacci quasicrystal (QC) arrangement of a one-dimensional topological superconductor, such as a magnetic atom chain deposited on a superconducting surface. We uncover a general mutually exclusive competition between the QC properties and the topological superconducting phase with Majorana bound states (MBS): there are no MBS inside the QC gaps and the MBS never behave as QC subgap states and, likewise, no critical or winding QC subgap states exist inside the topological superconducting gaps. Surprisingly, despite this competition, we find that the QC is still highly beneficial for realizing topological superconductivity with MBS. It both leads to additional large nontrivial regions with MBS in parameter space, that are topologically trivial in crystalline systems, and increases the topological gap protecting the MBS. We also find that shorter approximants of the Fibonacci QC display the largest benefits. As a consequence, our results promote QCs, and especially their short approximants, as an appealing platform for improved experimental possibilities to realize MBS as well as generally highlight the fundamental interplay between different topologies. Published by the American Physical Society 2024

Quasicrystal structure and growth models: discussion of the status quo and the still open questions

Where are we now in quasicrystal (QC) research more than three decades after Dan Shechtman’s discovery? Do we fully understand the origin of quasiperiodicity, the formation, growth, thermodynamic stability, structure and properties of quasicrystals? First, I will shortly present the status quo, then I will address the still open questions, and identify potential focus areas for future research. Because of the limited space, I will focus on decagonal quasicrystals (DQCs); the status quo for research on icosahedral quasicrystals (IQCs) is comparable.

Emergent quasicrystals in strongly correlated systems

Commensurability is of paramount importance in numerous strongly interacting electronic systems. In the Fractional Quantum Hall effect, a rich cascade of increasingly narrow plateaux appear at larger denominator filling fractions. Rich commensurate structures also emerge, at certain filling fractions, in high temperature superconductors and other electronic systems. A natural question concerns the character of these and other electronic systems at irrational filling fractions. Here we demonstrate that quasicrystalline structures naturally emerge in these situations, and trigger behaviors not typically expected of periodic systems. We first show that irrationally filled quantum Hall systems cross over into quasiperiodically ordered configuration in the thin-torus limit. Using known properties of quasicrystals, we argue that these states are unstable against the effects of disorder, in agreement with the existence of quantum Hall plateaux. We then study analogous physical situations in a system of cold Rydberg atoms placed on an optical lattice. Such an experimental setup is generally disorder free, and can therefore be used to detect the emergent quasicrystals we predict. We discuss similar situations in the Falicov-Kimball model, where known exact results can be used to establish quasicrystalline structures in one and two dimensions. We briefly speculate on possible relations between our theoretical findings and the existence of glassy dynamics and other features of strongly correlated electronic systems.

Surfaces of quasicrystals

The remarkable surface properties of quasicrystals have motivated extensive investigations of their intrinsic atomic and electronic structures. In this article, we summarize some of the main conclusions obtained so far. We also describe adsorption experiments where quasiperiodic surfaces are used as templates to grow thin films with novel structures. Finally we discuss some of their useful properties of current interest.

Indentation on one-dimensional hexagonal quasicrystals: general theory and complete exact solutions

This paper presents a general account of the indentation responses of a one-dimensional hexagonal quasicrystal half-space pressed by an axisymmetric rigid punch. Based on Green's functions of the half-space subjected to point sources on the surface, the mixed boundary value problem is transformed to integral equations and solved exactly using the results of the potential theory method. Explicit expressions for the generalised pressures and indentation forces are derived for three common indenters (cylinder, cone and approximate sphere) in a systematic manner. For conical and spherical indenters, relations between the contact radius and indentation loads are determined. The coupling phonon–phason fields in the half-space under indentation are accurately expressed in terms of elementary functions. Numerical calculations are performed and discussions on related physical phenomena are given. The present exact solutions can serve as benchmarks for approximate or numerical analyses and can guide the experimental characterisation of material properties of quasicrystals.

Discovery of stable icosahedral quasicrystals: progress in understanding structure and properties

The geometrical concept and structural framework of quasicrystals (QCs) were established shortly after the discovery of QCs. Specifically, the static and dynamic properties of the atoms and the electronic structures of quasiperiodic lattices were theoretically developed. Experimental studies lagged behind theoretical progress due to the lack of suitable samples. This situation changed with the discovery of several highly ordered stable QCs. Studies of these new QCs have provided new insights into the structure and properties of QCs. This article chronologically reviews the discoveries of various stable icosahedral QCs and subsequent studies that determined their structures, properties, and stabilization mechanisms.

Study of the Elasticity Module through Indentation Instrumented Technical of AlCuFeB Quasicrystalline Alloy

Quasicrystalline materials have unique properties such as high hardness, excellent surface properties, good resistance to oxidation and corrosion and low electrical and thermal conductivities. These materials can be obtained by conventional methods of metallurgy. However, quasicrystals are quite weak and this characteristic complicates their use in the form of billets for the manufacture of mechanical components. For this reason, the evaluation of mechanical properties of quasicrystalline materials using conventional methods, such as tension, compression, fatigue, among others, is not feasible. One method to evaluate the mechanical properties of quasicrystals is through instrumented indentation, once it is a very efficient tool for the calculation of properties such as hardness, fracture toughness and modulus of elasticity. The latter was the property studied in this work and that it is an important design criterion for the manufacturing of quasicrystalline alloys for their use in industry.

DNA, dichotomic classes and frame synchronization: a quasi-crystal framework

In this article, we show how a new mathematical model of the genetic code can be exploited for investigating the almost periodic properties of DNA and mRNA protein-coding sequences. We present the main mathematical features of the model and highlight its connections with both number theory and group theory. The group theoretic framework presents interesting analogies with the theory of crystals. Moreover, we exploit the information provided by dichotomic classes, binary variables naturally derived from the mathematical model, in order to build statistical classifiers for retrieving and predicting the normal reading frame used by the ribosome in protein synthesis. The results show that coding sequences possess a local informational structure that can be related to frame synchronization processes. The information for retrieving the normal reading frame, which implies the existence of short-range correlations and almost periodic structures related to the organization of codons, offers an interesting analogy with the properties of quasi-crystals. From a theoretical point of view, our results might contribute to clarifying the relation between biological information and shape in nucleic acids and proteins. Also, from the point of view of applications, we present new promising tools for designing efficient algorithms for frame synchronization, which plays a crucial role in faithful synthesis of proteins.

Study of the structure and physical properties of quasicrystals using large scale facilities

Abstract Quasicrystals have been puzzling scientists since their discovery. In this article we review some of the recent advances in this field and show how the use of large scale facilities has brought in decisive information for the understanding of their structure and physical properties.

Quasi-Hamilton Principle of Quasi-Crystals Beam.

Quasi-crystals is not only a new structure of solids but also a new class of functional and structural materials. With the research and development of quasi-crystals, the mechanical properties of quasi-crystals get more and more attention. In the paper, quasi-Hamilton principle of quasi-crystals beam is established in non-conservative systems. And applying the quasi-Hamilton principle, all the equations of non-conservative quasi-crystals beam problem are obtained in the phonon field and the phason field respectively.

Structural Stability and Kinetics of Hydrogen in TiZrNi Quasicrystals

When hydrogen atoms slowly diffuse into a metastable structure, a coherence length of thin TiZrNi quasicrystal metallic ribbons is increased. Improved atomic order with addition of hydrogen is an uncommon phenomenon in metals, and may reflect the unordinary structural property of quasicrystals. Metastable TiZrNi quasicrystals prepared by rapid quenching of molten ingots were hydrogenated in a low pressure of hydrogen (lower than 1000 Torr) at high temperature. After completion of the pressure-composition-temperature measurements between 200 to 300 degrees C, X-ray diffraction data revealed that the full width at half maximum values of the diffraction peaks were decreased suggesting that the quasicrystal phase may stabilized by hydrogen inclusion. Annealing of the same sample at 200 degrees C without hydrogen yields no change of the relative intensity of diffraction peaks.

ChemInform Abstract: Magnetism in Quasicrystals

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

The Role of Ni for Magnetism in Ti-Zr-Ni Quasicrystals

The interesting structural property of quasicrystals is characterized by exhibition of a five-fold symmetry which is forbidden in crystal. Most of the quasicrystals are discovered in Al- and Ti-based alloys made with rapid quenching indicating that they are metastable. Ti-based quasicrystals are still interesting in terms of structural stability and magnetic state when a sample contains Ni. We prepared metastable Ti55-xZr33Ni12+x (x = 0 , 3, 5, 7, 9) metallic ribbons of quasicrystals by rapid quenching method. A pure quasicrystal phase was obtained in a range of 5 les x les 9. The magnetization and magnetic hysteresis were measured by using a vibrating sample magnetometer (VSM). Interestingly, quasicrystal samples made with x = 7 and 9 showed magnetic hysteresis at room temperature, while no evidence for the hysteresis was noted from the samples made with x = 5. This suggests that a magnetic state of quasicrystal is strongly influenced by the Ni concentration. The magnetization values measured at zero-field-cooled (ZFC) and field-cooled (FC) conditions demonstrated little hint of significant difference suggesting that no rapid change in magnetization value is expected.

X-ray photoelectron diffraction on the 6-fold (001) μ-Al4Mn approximant surface

In theoretical investigations, the study of the properties of quasicrystals via analysis of periodic approximant structures has proven to be very successful. We performed experimental surface structure studies on the μ-Al4Mn approximant, exhibiting a large unit cell of 563 atoms, to get on to the origin of the unusual physical properties of complex quasicrystalline systems. The 6-fold (001) μ-Al4Mn surface was investigated by surface-sensitive low energy electron diffraction and X-ray photoelectron diffraction. Detailed analysis of the experimental data using single scattering cluster calculations revealed a pure bulk truncated surface, which is cut at the z = c/2 and 3c/4 layers of the unit cell, with a slight preference for the z = 3c/4 termination. The possibility of preparing well ordered, bulk terminated surfaces of such a complex, yet periodic, crystal structure in the Al–Mn system allows the application of a wealth of surface analytical tool to obtain a greater understanding of the physical properties of complex metallic alloys in relation to quasicrystals.

Comparative dynamics

Comparison of the vibrations of a quasicrystal with those of a conventional crystal opens the way to a better understanding of the consequences of aperiodicity on the properties of quasicrystals.

Growth of single crystals of quasicrystalline phases

To study the mechanical and physical properties of quasicrystals, single-crystal samples of large size (several centimeters) are necessary. However, obtainment of such single crystals meets a number of difficulties related to the peritectic character of melting of quasicrystalline compounds, high volatility and oxidizability of the initial components, low growth rate in aperiodic directions, and metastability of the most quasicrystalline structures. In this study, criteria for stable growth of quasicrystalline phases have been determined. The growth mechanisms of icosahedral and decahedral single crystals are described and experimental techniques of single-crystal growth are reviewed.

Aperiodic Intermetallics: The Example of Quasicrystals

This article presents an overview about the properties of quasicrystals. The atomic structure of icosahedral and decagonal compounds is described within the framework of high-dimensional crystallography and emphasis is put on phase diagrams. Attention is also paid to the electronic structure of these intermetallics. Several physical properties in connection with possible applications are briefly presented.

Acoustical analogs of condensed-matter problems

As a result of advances in experimental and theoretical physics, many interesting problems have arisen in condensed-matter physics, typically as a result of the quantum-mechanical nature of a system. Areas of interest include Anderson localization, universal conductance fluctuations, normal electron persistent currents, and the properties of quasicrystals. Understanding such systems is challenging because of complications arising from the large number of particles involved, intractable symmetries, the presence of time-dependent or nonlinear terms in the Schr\odinger equation, etc. Some progress has been made by studying large scale classical analog experiments which may accurately model the salient quantum-mechanical features of a condensed-matter system. This paper describes research with a number of acoustical systems which have addressed contemporary problems in condensed-matter physics.

Phonons in the icosahedral quasicrystal i-AlPdMn studied by coherent inelastic scattering of synchrotron radiation

The thermal and vibrational properties of quasicrystals have remained difficult to understand. It has been noted that specific heat measurements do not agree with the experimental sound velocity and vibrational density of states (DOS). To explain these discrepancies, non-acoustic localized states have been postulated but never directly observed. We have studied the pho-non dispersion curves of the icosahedral i-AlPdMn using a new method: coherent inelastic scattering of synchrotron radiation at the ID28 beamline of ESRF on a single grain i-AlP-dMn. We have studied both the longitudinal (LA) parallel to and the transverse acoustic (TA) modes perpendicular to the 2-fold axis up to a reduced scattering vector q = Q-G = 5 nm−1. Both TA and LA branches agree well in the q → 0 limit given by the sound velocity. Both branches deviate from linearity even at very low q: at ca. 2 (LA) to 3 (TA) nm−1, as has been found from inelastic neutron scattering. Some evidence was found for non-acoustic, probably dispersionless, modes around the LA and TA branches. One advantage of this new method is the necessity for only small single grain samples.