Structure Of Icosahedral Quasicrystals Research Articles

Effect of Cu on the Precipitation of α-Al(Mn,Cr)Si Dispersoids in an Al-Mg-Si-Mn-Cr Alloy

Nanoscale dispersoids will retard or inhibit recrystallization of aluminum alloys during thermomechanical processes. In the present study, the influence of an addition of 0.6 wt. % Cu on the precipitation behavior of dispersoids in an Al-Mg-Si-Mn-Cr alloy had been investigated. Large amounts of dispersoids with different shapes, e.g. cubic, rod-like and plate-like, were achieved in the experimental alloys after homogenization. Compared with the Cu-free alloy, Cu-added alloy exhibits a higher proportion of cubic shape dispersoid. HRTEM results indicated that the cubic shape dispersoid has an icosahedral quasicrystal structure, while the rod-like or plate-like shape dispersoids show a simple cubic crystal structure. Due to the presence of a high number density of quasicrystalline dispersoids, the Cu-added alloy exhibits a higher recrystallization resistance during hot compression. This study presents a new insight that besides the precipitation strengthening, the Cu alloying in an Al-Mg-Si-Mn-Cr alloy can also contributes to the precipitation of dispersoids.

A group of ductile metallic glasses prepared by modifying local structure of icosahedral quasicrystals

Inspired by research into the association between icosahedral local orders and the plasticity of metallic glasses (MGs), beryllium (Be) is added to the icosahedral quasi-crystal forming alloy Zr40Ti40Ni20. In this way, bulk metallic glasses (BMGs) with favorable compressive plasticity are fabricated. Therein, the icosahedral quasi-crystalline phase is the main competing phase of amorphous phases and icosahedral local orders are the main local atomic motifs in amorphous phases. The alloys of (Zr40Ti40Ni20)76Be24 and (Zr40Ti40Ni20)72Be28 with their greater plastic strain capacity show similar characteristics to highly plastic amorphous systems: The serrated flow of compression curves always follows a near-exponential distribution. The primary and secondary shear bands intersect each other, bifurcate, and bend. Typical vein patterns are densely distributed on the fracture surfaces. The relaxation enthalpy of four MGs is linearly correlated with the plastic strain, that is, the greater the relaxation enthalpy, the larger the plastic strain.

Icosahedral quasicrystal structure of the Mg40Zn55Nd5 phase and its thermodynamic stability

Icosahedral quasicrystal structure of the Mg40Zn55Nd5 phase and its thermodynamic stability

Structure of icosahedral quasicrystals within the multiple-cell approach

The multiple-cell approach is discussed as an alternative to the higher-dimensional crystallographic description of icosahedral quasicrystals. Four types of quasi-unit cells fill the space without gaps and overlappings. Every cell in the whole tiling is decorated by specific atoms in a particular way and is associated with a triad: type, position, and orientation. The key features of the proposed approach are the subgroup/coset decomposition of icosahedral symmetry groups in accordance with the orbit-stabilizer theorem, a strict mathematical formalization of the substitution rules for all types of quasi-unit cells in the Socolar-Steinhardt tiling, formalization of the recursive inflation/deflation rules, and the eigenvalue-eigenvector analysis of corresponding substitution matrices. The similar approach can be applied to almost all types of quasicrystals.

Preparation of bulk metallic glasses by modifying local structure of icosahedral quasicrystals

An attempt is carried out to design metallic glasses by modifying the local structure of icosahedral quasicrystals. A series of metallic glasses are prepared by introducing beryllium to the quasicrystal former, Zr40Ti40Ni20, and the maximum diameter of the glasses reaches 20 mm. A phase transformation diagram is constructed for the alloys of (Zr40Ti40Ni20)100-xBex, revealing the transition from stable crystal to quasicrystal and then to metallic glasses with the increased Be content. This study shows a connection between the formation of metallic glasses and the specific thermodynamics of the initially precipitated quasicrystals. Interestingly, both improvements in the forming ability for glasses and quasicrystals are observed over a wide composition range. Ab initio molecular dynamic simulations show the evolution of the structural features of the metallic melts for the optimised glass forming region, which guarantee the primary precipitation of quasicrystal.

Digital Alchemy for Materials Design: Colloids and Beyond.

Starting with the early alchemists, a holy grail of science has been to make desired materials by modifying the attributes of basic building blocks. Building blocks that show promise for assembling new complex materials can be synthesized at the nanoscale with attributes that would astonish the ancient alchemists in their versatility. However, this versatility means that making a direct connection between building-block attributes and bulk structure is both necessary for rationally engineering materials and difficult because building block attributes can be altered in many ways. Here we show how to exploit the malleability of the valence of colloidal nanoparticle "elements" to directly and quantitatively link building-block attributes to bulk structure through a statistical thermodynamic framework we term "digital alchemy". We use this framework to optimize building blocks for a given target structure and to determine which building-block attributes are most important to control for self-assembly, through a set of novel thermodynamic response functions, moduli, and susceptibilities. We thereby establish direct links between the attributes of colloidal building blocks and the bulk structures they form. Moreover, our results give concrete solutions to the more general conceptual challenge of optimizing emergent behaviors in nature and can be applied to other types of matter. As examples, we apply digital alchemy to systems of truncated tetrahedra, rhombic dodecahedra, and isotropically interacting spheres that self-assemble diamond, fcc, and icosahedral quasicrystal structures, respectively. Although our focus is on colloidal systems, our methods generalize to any building blocks with adjustable interactions.

Structure factor for an icosahedral quasicrystal within a statistical approach.

This paper describes a detailed derivation of a structural model for an icosahedral quasicrystal based on a primitive icosahedral tiling (three-dimensional Penrose tiling) within a statistical approach. The average unit cell concept, where all calculations are performed in three-dimensional physical space, is used as an alternative to higher-dimensional analysis. Comprehensive analytical derivation of the structure factor for a primitive icosahedral lattice with monoatomic decoration (atoms placed in the nodes of the lattice only) presents in detail the idea of the statistical approach to icosahedral quasicrystal structure modelling and confirms its full agreement with the higher-dimensional description. The arbitrary decoration scheme is also discussed. The complete structure-factor formula for arbitrarily decorated icosahedral tiling is derived and its correctness is proved. This paper shows in detail the concept of a statistical approach applied to the problem of icosahedral quasicrystal modelling.

Atomic structure of icosahedral quasicrystals: stacking multiple quasi-unit cells

An effective tiling approach is proposed for the structural description of icosahedral quasicrystals based on the original substitution algorithm.

The Structure of Icosahedral Quasicrystals and Seven Blunders in Quasicrystallography

This structural study of quasicrystals is based on extremely dense icosahedral unit cells that are systematically and consistently measured for the first time. The structure and pattern indexation are 3-dimensional. A formula is given for scattering from atoms in hierarchic arrangement and geometric series. The Quasi-Bragg law is a new law in physics, with possible applications beyond crystallography. The structure is compared with previous, unsuccessful, and contradictory, attempts at analysis.

About the atomic structures of icosahedral quasicrystals

Abstract This paper is a survey of the crystallographic methods that have been developed these last twenty five years to decipher the atomic structures of the icosahedral stable quasicrystals since their discovery in 1982 by D. Shechtman. After a brief recall of the notion of quasiperiodicity and the natural description of Z -modules in 3-dim as projection of regular lattices in N > 3 -dim spaces, we give the basic geometrical ingredients useful to describe icosahedral quasicrystals as irrational 3-dim cuts of ordinary crystals in 6-dim space. Atoms are described by atomic surfaces (ASs) that are bounded volumes in the internal (or perpendicular) 3-dim space and the intersections of which with the physical space are the actual atomic positions. The main part of the paper is devoted to finding the major properties of quasicrystalline icosahedral structures. As experimentally demonstrated, they can be described with a surprisingly few high symmetry ASs located at high symmetry special points in 6-dim space. The atomic structures are best described by aggregations and intersections of high symmetry compact interpenetrating atomic clusters. We show here that the experimentally relevant clusters are derived from one generic cluster made of two concentric triacontahedra scaled by τ and an external icosidodecahedron. Depending on which ones of the orbits of this cluster are eventually occupied by atoms, the actual atomic clusters are of type Bergman, Mackay, Tsai and others….

Dislocations and mechanical properties of icosahedral quasicrystals

Abstract In this article we interpret the mechanical properties of icosahedral quasicrystals with the dislocation theory. After having defined the concept of dislocation in a periodic crystal, we extend this notion to quasicrystals in the 6-dimensional space. We show that perfect dislocations and imperfect dislocations trailing a phason fault can be defined and observed in transmission electron microscopy (TEM). In-situ straining TEM experiments at high temperature show that dislocations move solely by climb, a non-conservative motion-requiring diffusion. This behavior at variance with that of crystals which deform mainly by glide is explained by the atypical nature of the atomic structure of icosahedral quasicrystals.

Short-range order and singularities of the electronic structure of icosahedral quasicrystals

For icosahedral phases of the Al-Cu-Fe system, components of the electrical conductivity, magnetic susceptibility, Hall effect, and heat capacity associated with thermally induced charge carriers for the first time have been considered jointly over a wide temperature range. It has been shown that the full range of thermal effects can be understood in the framework of the unified concept, which is based on an inhomogeneous system of two-level electronic excitations. A model of the inhomogeneous electronic state and the mechanism of its formation with the dominant role of short-range order have been proposed.

Mechanical properties of the icosahedral phase reinforced duplex Mg–Li alloy both at room and elevated temperatures

Through investigating tensile properties of the duplex Mg–Li alloys with and without I-phase (Mg3Zn6Y, icosahedral quasicrystal structure) tested both at ambient and elevated temperatures, it demonstrates that I-phase can not only improve the tensile strength at room temperature, but also be beneficial for the mechanical improvement at elevated temperatures. Based on the microstructural observations of the sample surfaces before and after tests, the I-phase particles can effectively suppress the plastic flow of β phase at 220 °C, resulting in the I-phase reinforced duplex Mg–Li alloy having higher mechanical properties at elevated temperatures.

ChemInform Abstract: Atomic Structure of Quasicrystals

AbstractReview: 50 refs.

Structures of icosahedral quasicrystals and approximants

Structure determination of quasicrystals (QCs) has been one of the most challenging tasks since their discovery by Shechtman et al.[1] In this work we will assess the present state of the art conce ...

Atomic structure of quasicrystals

The 2011 Nobel Prize in chemistry has been awarded to Dan Shechtman for his discovery of quasicrystals. The discovery has indeed been a breakthrough in crystallography and solid state physics and chemistry. After a brief introduction to the subject, we review some of the recent advances in the understanding of the atomic structure of icosahedral quasicrystals and in particular for the binary Cd–Yb type quasicrystal. Thanks to a combined analysis of periodic approximant, high quality synchrotron data, and the superspace approach, a detailed insight in the crystal chemistry of this binary quasicrystal has been achieved.

Three-dimensional reconstruction of the atomic arrangement of icosahedral quasicrystals by binary discrete tomography

A three-dimensional reconstruction of the structure of icosahedral quasicrystals from high-resolution transmission electron microscope images observed along high-symmetry zone-axis projections is studied. As in discrete tomography, the quasicrystalline structure is treated as a discrete set of atoms arranged on the icosahedral lattice, including atom flip sites, which is a structural disorder originating from the degrees of freedom in the internal space. The occupancy of the atoms on each site of the lattice is determined using only the zone-axis projection images without any knowledge of the image intensity. Simulation studies using icosahedral model lattices composed of several thousands of atoms were carried out to test the present reconstruction method. In the case of the ideal icosahedral lattice, a reconstruction rate of 90% is achieved from 10 projection images and a reconstruction rate of 99% is achieved from 18 projections. The reconstruction rate degrades when the projection images are misaligned. Reconstruction of the three-dimensional distribution of the atom flips is discussed.

Similarity of Deuterium Absorption at Room Temperature for Different Ti-Zr-Ni Quasicrystals

Ti-Zr-Ni icosahedral quasicrystals (IQCs) have been regarding as potential hydrogen storage materials due to their high hydrogen ability. Nevertheless, their hydrogen capacities are largely different as reported by different researchers, which is toughly understood.We investigated in this paper deuterium absorption at room temperature for quasicrystalline alloys Ti45Zr38Ni17, Ti41.5Zr41.5Ni17, Ti40Zr40Ni20 with corresponding phase structures of IQC+β(Ti,Zr), IQC+C14(TiZrNi), IQC. The results indicated the same solid solution state for the deuterium in these alloys, whose deuterium concentration was 12~13mmol/g. Given that all these alloys are in a single IQC phase, we believe very similar deuterium capacities for them, which surely needs more strict experimental evidence.

Discrete tomography of icosahedral model sets

The discrete tomography of mathematical quasicrystals with icosahedral symmetry is investigated, placing emphasis on reconstruction and uniqueness problems. The work is motivated by the requirement in materials science for the unique reconstruction of the structures of icosahedral quasicrystals from a small number of images produced by quantitative high-resolution transmission electron microscopy.

The strengthening effect of icosahedral phase on as-extruded Mg–Li alloys

Through investigating the mechanical properties of three kinds of Mg–Li–Zn–Y alloys, a strengthening method, i.e. introducing I-phase (Mg3Zn6Y, icosahedral quasicrystal structure) in the matrix of Mg–Li alloys, for as-extruded Mg–Li alloys has been demonstrated. The tensile results indicate that I-phase can effectively strengthen the alloys. The substantial enhancement of strength has been explained by microstructure changes.