Quasicrystalline Materials Research Articles

Surface and interfacial waves in anisotropic elastic quasicrystals

We present the Stroh formalism for two-dimensional subsonic steady-state motion of anisotropic quasicrystals. Using this new formalism and a series of identities and properties which follow, we investigate subsonic surface and interfacial waves in anisotropic quasicrystals. Our results suggest that there exist at most three subsonic surface wave speeds. This interesting observation is quite different from the unique surface wave speed known for anisotropic crystals. The degenerate case of decagonal quasicrystalline materials is discussed in detail.

Mathematical Theory and Methods of Mechanics of Quasicrystalline Materials

The review is devoted to introduce the recent development of the study in mathematical theory and methods of mechanics of quasicrystals, respectively. The mechanics of quasicrystalline materials includes elasticity, plasticity, defects, dynamics, fracture etc. In the article some relevant measured data are collected for some important quasicrystal systems, which are necessary for understanding physics and applications of the materials. It is very interesting that the mathe-matical theory and solving methods of the mechanics of quasicrystals have developed rapidly in recent years, which is strongly supported by the experiments and applications. The theoretical development strongly enhances the understanding in-depth the physics including mechanics of the materials. The mathematical theory and computational methods provide a basis to the applications of quasicrystals as functional and structural materials in practice as well. More recently the quasicrystals in soft matter are observed, which challenge the study of based on the quasicrystals of binary and ternary alloys and greatly enlarge the scope of the materials and have aroused a great deal attention of researchers, an introduction about this new phase and its mathematical theory is also given in the review.

Complex Analysis of Plane Problem of Two-Dimensional Quasicrystals

The fracture behavior of materials and structures are always caused by stress concentration near the defects in materials. This article describes the complex potential method for solving plane problems of quasicrystalline materials with defects. In order to prove effectiveness and success of the method, an example is given, and the results have very important significance in studying two-dimensional quasicrystals.

GROUPING MODEL IN FERMI SURFACE APPLIED TO QUASICRYSTALS

Studies performed on energy levels in Fermi surface in groupings showed that crystals have plans periodically gathered. On the contrary, quasicrystals have their plans reunited non periodically. This paper shows the development of a mathematical model comprising not only the symmetries of AlMnPd alloys but also the physical stability of groupings versus AlCoNi geometry by considering Fermi energy in its surface. The model also discusses electron conductivity, quantum interfaces in quasicrystals, its physical formation and chemical properties. The model allows a better understanding of interactions between atoms in the quasicrystals formation, functioning of energy bonds and of gaps and pseudogaps in the electronic structures of quasicrystalline materials.

Mechanical Milling: a Top Down Approach for the Synthesis of Nanomaterials and Nanocomposites

Synthesis of nanomaterials by a simple, low cost and in high yield has been a great challenge since the very early development of nanoscience. Various bottom and top down approaches have been developed so far, for the commercial production of nanomaterials. Among all top down approaches, high energy ball milling, has been widely exploited for the synthesis of various nanomaterials, nanograins, nanoalloy, nanocomposites and nano -quasicrystalline materials. Mechanical alloying techniques have been utilized to produce amorphous and nanocrystalline alloys as well as metal/non-metal nano- composite materials by milling and post annealing, of elemental or compound powders in an inert atmosphere. Mechanical alloying is a non-equilibrium processing technique in which different elemental powders are milled in an inert atmosphere to create one mixed powder with the same composition as the constituents. In high-energy ball milling, plastic deformation, cold-welding and fracture are predominant factors, in which the deformation leads to a change in particle shape, cold-welding leads to an increase in particle size and fracture leads to decrease in particle size resulting in the formation of fine dispersed alloying particles in the grain-refined soft matrix. By utilizing mechanical milling various kind of aluminium/ nickel/ mag- nesium/ copper based nanoalloys, wear resistant spray coatings, oxide and carbide strengthened aluminium alloys, and many other nanocomposites have been synthesized in very high yield. The mechanical milling has been utilized for the synthesis of nanomaterials either by milling and post annealing or by mechanical activation and then applying some other process on these activated materials. This review is a systematic view of the basic concept of mechanical milling, historical view and appli- cations of mechanical milling in the synthesis of various nanomaterials, nanosomposites, nnaocarbons and nano quasicrys- talline materials.

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.

Effect of the Milling Time and Addition of a Grinding Agent of Quasicrystalline Powder Based on AlCuFeB Alloys

Quasicrystalline (QC) materials represent a new class of alloys differing from amorphous and crystalline materials due to quasicrystalline periodicity and therefore unusual properties. Applications of quasicrystals range from surface coatings, thin films to reinforcements of ductile matrix composites such aluminum and, more recently, polymers. Quasicrystalline alloys show fundamentally different behavior compared to crystalline alloys even when their compositions are very similar, including low friction coefficient, high hardness and high brittleness. Due to this brittle behavior there are some limitations with respect to what methods can be used to process QC materials restricting their applications to powder form. One of the techniques for particle size reduction is mechanical milling which, however may lead to destabilization of the icosahedral phase. Therefore, there is a need to study the stability of quasicrystalline alloys during this comminution process. In the present study, AlCuFeB alloys were milled with the aid of a grinding agent that helps reduce overheating and thus controlling the QC powder stability. It was found that QC phase was destabilized after 10 h while the addition of a grinding agent led to milling times of 20 h without destabilizing the QC phase.

Adhesion Tests Using Epoxy Quasicrystal Composites

Quasicrystals (QC) are usually complex metal alloys with atypical structures. Due to their physical, mechanical and surface properties, quasicrystals have been widely studied. Although methods to manufacture quasicrystalline materials are well known, much effort has been expended in obtaining suitable quasicrystalline materials for use in industry. As quasicrystalline materials are very brittle, they are usually used in powder form as a reinforcement for additives in composites as well as in coating technology. In this work, Al–Cu–Fe quasicrystalline powder was used as a reinforcement in epoxy resin and the influence of the quasicrystal particles incorporation on the adhesive properties of the epoxy was investigated. Single lap joints (SLJ) adhesion tests were performed in order to assess the shear mode bond strength. Results show that the effect of QC reinforcement is not linear with respect to the adherence of the composites.

Theory of linear, nonlinear and dynamic fracture for quasicrystals

In this paper, fracture theory of quasicrystalline material is presented, concerning with linear, nonlinear and dynamic fracture problems for different quasicrystal systems observed to date. Main attention is however paid to three-dimensional icosahedral quasicrystals and two-dimensional decagonal quasicrystals, which play the central role in the new kind of materials. Relevant experimental results are also discussed.

Problems and recent advances in melt crystal growth technology

The present review deals with the novel developments in melt growth techniques which have arisen mostly within recent five-ten years and focuses on recent progress in growing bulk crystals of dielectrics, however, many developments could be easily applied to the semiconductor growth technology. The scaling of size and yield of crystals grown from the melt, and various ways and tricks to improve crystal perfection via homogenization of melt composition and governing the heat and mass transfer are under consideration. Particular developments such as low-thermal gradient and low-melt level growth techniques, governing by heat field rotation and applying of low-frequency vibration, as well as the use of double crucibles and submerged baffles are considering. The paper also discusses the current problems of bulk crystal growth due to the competition with arisen alternative technologies of manufacture the bulk crystalline or quasi-crystalline materials including transparent ceramics and glass-ceramics as well as the solid-state single crystal growth technology.

Quasicrystals in Soft Matter

AbstractTwo decades after the first publication on quasicrystals in aluminum manganese alloys by Shechtman et al., a “soft quasicrystal” was found in nature. Since then a number of materials successively joined the family of soft quasicrystals, including liquid crystals, polymers, nanoparticles, colloids, mesoporous silica, and even water and silicon. In this article, important experimental advances are reviewed to introduce readers to the emerging research front of soft quasicrystalline materials. The world of quasicrystals opened by Daniel Shechtman extends its reach into the twenty‐first century chemistry.

Plastic analysis of the crack problem in two-dimensional decagonal Al-Ni-Co quasicrystalline materials of point group **Project supported by the National Natural Science Foundation of China (Grant No. 10672022).

The fundamental plastic nature of the quasicrystalline materials remains an open problem due to its essential complicacy. By developing the proposed generalized cohesive force model, the plastic deformation of crack in point group decagonal quasicrystals is analysed strictly and systematically. The crack tip opening displacement (CTOD) and the size of the plastic zone around the crack tip are determined exactly. The quantity of the crack tip opening displacement can be used as a parameter of nonlinear fracture mechanics of quasicrystalline material. In addition, the present work may provide a way for the plastic analysis of quasicrystals.

Study of the electronic structure of the quasicrystalline Ti—Zr—Ni system

Photoelectron spectra and optical absorption spectra for clean surfaces of quasicrystalline samples of the Ti—Zr—Ni system are measured. The resonant photoelectron spectra are also measured in the range of photon energies corresponding to Ni 2p and Zr 3d absorption thresholds. The change in the intensities of the spectrum of the valence band near the Zr 3d threshold is insignificant. The emission of Auger electrons increases near the Ni 2p threshold in a resonance way. Our studies make it possible to reveal certain specific features of the electronic structure of quasicrystals, which can be used to construct models of actual electronic structures of quasi-crystalline materials.

Twenty years of fun with resonant ultrasound.

Resonant ultrasound (RUS) is an elegant method for determining the elastic and anelastic properties of materials. The development of computational methods, robust computer codes, and sensitive instrumentation by a few key players has resulted in a simple, yet powerful, tool. The speaker was introduced to RUS 20 years ago. During the past two decades he, along with numerous students and in collaboration with many colleagues, has used this technique to study various problems: phase transitions, texture in alloys, and the elastic and anelastic properties of several materials—hydrogen absorbing compounds and alloys, nanocrystalline materials, and quasicrystalline materials—over an extended temperature range. All of these problems would have been difficult, if not impossible, to address with conventional ultrasonic methods. A few examples—phase transitions and internal friction due to hydrogen hopping, in particular—will be used to illustrate the power of RUS.

Quasicrystalline phase formation during heat treatment in mechanically alloyed Al65Cu20Fe15 alloy

Quasicrystalline phase formation during heat treatment in the mechanically alloyed Al65Cu20Fe15 powders was studied by X-ray diffraction (XRD) and differential scanning calorimeter (DSC). The mechanical alloying was performed at speed of 300 rev min–1 for times up to 70 h. It was found that mechanical alloying of the Al65Cu20Fe15 powders did not result in the quasicrystalline (QC) icosahedral phase (i-phase) formation. The long time milling resulted in the formation of a cubic Al (Cu,Fe) solid solution phase (β-phase). The cubic Al (Cu,Fe) solid solution identified as β-phase was observed to be present as one of the major phases in the Al65Cu20Fe15 alloy. The formation of the quasicrystalline icosahedral phase (i-phase) was only observed for short time milled powders after additional annealing at temperature above 500°C. The present investigation also showed that a tetragonal Al2Cu phase (θ-phase) forms with short time milling. The tetragonal Al7Cu2Fe1 phase (w-phase) was observed after heat treatment of the short time milled and unmilled powders. The present investigation indicated that an effective process to prepare the quasicrystalline materials was using a combination of short time milling and subsequent annealing.

Geometry and Topology of Structure in Amorphous Solids

The geometrical concept of an ideal solid and a method for its construction are presented as novel contributions to the understanding of atomic arrangements in amorphous solids. This ideal amorphous structure serves as a base-line model for atomic arrangements and as a universal reference from which any changes in atomic arrangement can be measured. The model is intended to represent the ideal structure of amorphous solids and not the way a real glass is formed. This provides for amorphous materials the same kind of base-line reference as an ideal crystal does for real crystalline materials, or tiling patterns for quasi-crystalline materials. Characteristic properties are described, including Debye X-ray scattering to show how relevant information can be derived about the presence of vacancies and compositional changes.

The strict theory of complex variable function method for sextuple harmonic equation and applications

The strict theory of the complex variable function method for the sextuple harmonic equation is given in detail, which is a development of the work on the quadruple harmonic equation of the authors. Both of the above mentioned works develop the well-known Muskhelishvili complex variable function method for solving the biharmonic equation used in the classical theory of elasticity. Meanwhile, some applications to the elasticity, plasticity, and fracture theories of quasicrystalline materials have shown that the theory and method are successful and effective.

Plastic analysis of crack problems in three-dimensional icosahedral quasicrystalline material

Due to their complexity, the basic plastic properties of all quasicrystalline materials are essentially unknown [M. Feuerbacher, C. Thomas, K. Urban, Plastic behaviour of quasicrystalline materials, in Quasicrystals: Structure and Physical Properties, H.R. Trebin, ed., Wiley/VCH, Berlin, 2003]. Plastic deformation of cracks in icosahedral quasicrystals have been analyzed in a strict and systematic form and the crack tip opening displacement (CTOD) and size of the plastic zone around the crack tip was determined exactly. CTOD is suggested as a parameter of plastic fracture for quasicrystalline materials. The present work may also provide a novel methodology for plastic analysis of quasicrystals.

Linear-scaling first-principles study of a quasicrystalline molecular material

Quasicrystals exhibit long-range order without translational periodicity by siting their constituent atoms on the nodes of a quasiperiodic tiling. Zhou and Harris [Z. Zhou, K.D.M. Harris, ChemPhysChem 7 (2006) 1649] have proposed engineering a 2D molecular quasicrystal where each node of a Penrose tiling is occupied by a discrete molecule, the 10,5-coronene. First-principles quantum-mechanical calculations have been performed on the stability and energetics of this molecule using the linear-scaling density-functional theory package onetep. The suitability of the 10,5-coronene as a molecular building block is confirmed and different design strategies are compared.

Natural Quasicrystals

Quasicrystals are solids whose atomic arrangements have symmetries that are forbidden for periodic crystals, including configurations with fivefold symmetry. All examples identified to date have been synthesized in the laboratory under controlled conditions. Here we present evidence of a naturally occurring icosahedral quasicrystal that includes six distinct fivefold symmetry axes. The mineral, an alloy of aluminum, copper, and iron, occurs as micrometer-sized grains associated with crystalline khatyrkite and cupalite in samples reported to have come from the Koryak Mountains in Russia. The results suggest that quasicrystals can form and remain stable under geologic conditions, although there remain open questions as to how this mineral formed naturally.