Crystal chemistry and chemical order in ternary quasicrystals and approximants

In this work we review our current understanding of structure, stability and formation of icosahedral quasicrystals and approximants. The work has special emphasis on Cd–Yb type phases, but several concepts are generalized to other families of icosahedral quasicrystals and approximants. The paper handles topics such as chemical order and site preference at the cluster level for ternary phases, valence electron concentration and its influence on formation and composition, fundamental building blocks and cluster linkages, and the similarities and differences between different families of icosahedral quasicrystals and approximants.     

Localized diffuse scattering from icosahedral Ti-Mn

In diffraction from some icosahedral quasicrystals, diffuse scattering is concentrated on arcs in TEM diffraction patterns. The new Ti-Mn icosahedral phase produces much more intense arcs than previously observed in quasicrystals, allowing a significantly deeper study of them.     

Decagonal quasicrystals

Following the discovery of two dimensional quasicrystals in rapidly solidified Al-Mn alloys by us and L. Bendersky in 1985, a number of fascinating studies has been conducted to unravel the atomic configuration of quasicrystals with decagonal symmetry. A comprehensive mapping of the reciprocal space of decagonal quasicrystals is now available. The interpretation of the diffraction patterns brings out the comparative advantages of various indexing schemes. In addition, the nature of the variable periodicity can be addressed as a form of polytypism. The relation between decagonal quasicrystals and their crystalline homologues will be explored with emphasis on Al₆₀Mn₁₁Ni₄ and ‘Al₃Mn’. It will also be shown that decagonal quasicrystals are closely related to icosahedral quasicrystals, icosahedral twins and vacancy ordered phases.     

Isotropic and anisotropic physical properties of quasicrystals

Since quasicrystals have positional and orientational long-range order, they are essentially anisotropic. However, the researches show that some physical properties of quasicrystals are isotropic. On the other hand, quasicrystals have additional phason degrees of freedom which can influence on their physical behaviours. To reveal the quasicrystal anisotropy, we investigate the quasicrystal elasticity and other physical properties, such as thermal expansion, piezoelectric and piezoresistance, for which one must consider the contributions of the phason field. The results indicate that: for the elastic properties, within linear phonon domain all quasicrystals are isotropic, and within nonlinear phonon domain the planar quasicrystals are still isotropic but the icosahedral quasicrystals are anisotropic. Moreover, the nonlinear elastic properties due to the coupling between phonons and phasons may reveal the anisotropic structure of QCs. For the other physical properties all quasicrystals behave like isotropic media except for piezoresistance properties of icosahedral quasicrystals due to the phason field.     

Icosahedral quasicrystals solids with an elliptic hole under uniform heat flow

The complex variable method for solving the two-dimensional thermal stress problem of icosahedral quasicrystals is stated. The closed-form solutions for icosahedral quasicrystals containing an elliptical hole subjected to a remote uniform heat flow are obtained. When the hole degenerates into a crack, the explicit solutions for the stress intensity factors is presented.     

Correlation functions and the dynamical structure factor of quasicrystals

The icosahedral or decagonal symmetry of quasicrystals is well described by a periodic structure in higher dimensions. One consequence is the existence of dynamic phason modes in addition to the phonon modes. In an atomistic model phasons show up as correlated atomic jumps. We detect the phasons by the calculation of correlation functions and the dynamical structure factor in molecular dynamics simulations similar to the procedure used for phonons. In the simulations it is also possible to observe atomic jump processes directly. The models studied here represent icosahedral AlCuLi and decagonal AlCuCo quasicrystals. Ring processes are observed in the icosahedral case, and flips in the decagonal model. Received 17 March 2000 and Received in final form 8 June 2000     

Dislocations and mechanical properties of icosahedral quasicrystals

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.     

Basics of NMR line shape in quasicrystals

The measurement and analysis of broad nuclear magnetic resonance (NMR) spectra of quasicrystals require experimental methods and theoretical interpretations different from NMR investigations of regular periodic crystals. Frequency- and field-sweep methods for recording quasicrystalline NMR spectra are described and compared with the measurement of²⁷Al NMR spectra of icosahedral AlPdMn and decagonal AlNiCo quasicrystals. The nuclear spin interactions that determine the NMR line shape are the same for both types of the above Al-based quasicrystals, where the electric quadrupolar interaction with the broad distribution of its electric field gradient parameters predominantly determines the shape of the broad satellite “background” intensity. The essential observations are an almost isotropic²⁷Al NMR spectrum of the icosahedral quasicrystals and a strong angular dependence of the spectrum of decagonal quasicrystals.     

Quasicrystals

After some introductory remarks about quasicrystals, ME spectra of icosahedral AlMnFe-, AlCuFe- and TiNiFeSi-alloys are summarised. The results are interpreted in terms of the current understanding of the structure of quasicrystals. Further a ME-application to the stability criteria of quasicrystals is discussed. A dominant factor is the band splitting factor or the Hume-Rothery rule.     

Section method for projected structures of icosahedral quasicrystals and its application to electron-microscopy-image and surface analyses

A section method for projected structures of icosahedral quasicrystals (IQCs) is given. A structure projected along a specified direction can be calculated directly from a six-dimensional periodic structure by this method. The method concludes that all peaks in high-resolution transmission electron-microscopy images of an IQC have different projected atom densities in general and leads to different chemical compositions and densities for all atom layers, suggesting that all surfaces of an IQC are different. Its application to icosahedral Al-Pd-Mn quasicrystals is shown.     

Phonon-spectrum of an F-type icosahedral quasicrystal

We present calculations for the vibrational properties of F-type icosahedral quasicrystals. Two different approaches are compared, a cluster with complete icosahedral symmetry, and periodic approximants. Though no gaps in the spectra are observed, the well-known rescaling symmetry of ID systems is rediscovered in a generalized way.     

Defocus convergent beam electron diffraction determination of Burgers vectors of dislocations in quasicrystals

Principles, method and some application examples of determining Burgers vectors of dislocations in crystals and quasicrystals by means of defocus convergent-beam electron diffraction (CBED) technique are described and reviewed and compared with contrast experiment techniques. By using defocus CBED technique, dislocation reactions during high-temperature plastic deformation of face-centered icosahedral quasicrystals have been studied. These studies lead to a preliminary understanding to the micromechanism of high-temperature plastic deformation of quasicrystals.     

A basis for the synthesis of quasicrystals

It has been established that quasicrystals with icosahedral point group symmetry occur in a rapidly solidified Mg₃₂ (Al, Zn)₄₉ alloy chosen on the basis of its equilibrium crystal structure. This alloy has a natural tendency to form icosahedral atomic clusters stabilised by size difference amongst constituent atoms. Results highlight the relationship between equilibrium crystal structure and the tendency to form quasicrystals.     

Continuous transformation from quasicrystals to approximants in Al–Cu–Fe alloys

Continuous transformation of icosahedral quasicrystals as observed in Al-Cu-Fe alloys proceeds through intermediate modulated structures towards rational approximants with a rhombohedral structure. Corresponding to the diffuse scattering in the electron diffraction during the transformation, a tweed contrast emerges throughout the icosahedral phase matrix. High-resolution electron microscopy reveals a complex modulated structure which tends to evolve into rhombohedral microdomains. The observed distortion of the reciprocal quasilattice due to the structural modulation has been simulated on a computer by introducing linear phason strains into the quasicrystals.     

Sign reversals of the carriers and the volume change in Al-Cu-Fe quasicrystalline alloys

New results of dilatometric experiments with rapidly quenched Al-Cu-Fe quasicrystalline alloys in the course of their thermal annealing are presented. It is established that the icosahedral (I) phases with different types of carriers exhibit different signs of volume changes with ordering. The observed effect is a direct experimental proof of the fact that structural defects in icosahedral quasicrystals are electrically active centers.     

Experimental evaluation of phonon–phason coupling in icosahedral quasicrystals

By measuring phonon strain introduced in crystal approximants, the sign and magnitude of the phonon–phason coupling constant have been evaluated for icosahedral quasicrystals of Mg–Ga–Al–Zn and Al–Cu–Fe systems. The evaluated coupling constants are approximately ?0.04μ and 0.004μ (μ?=?shear modulus) for the former and the latter, respectively. They are in good agreement with the results of a previously reported theoretical calculation. Possible effects of phonon–phason coupling on the onset of phasonic elastic instability in icosahedral quasicrystals are discussed.     

Ferromagnetism in quasicrystals: Symmetry aspects

Magnetic-group analysis of the symmetries typical of quasicrystals shows that ferromagnetism is incompatible with the icosahedral symmetry. Depending on the magnetic field direction, the icosahedral symmetry in the magnetic field is reduced to pentagonal, trigonal or rhombic symmetries.     

How do quasicrystals grow?

Using molecular simulations, we show that the aperiodic growth of quasicrystals is controlled by the ability of the growing quasicrystal nucleus to incorporate kinetically trapped atoms into the solid phase with minimal rearrangement. In the system under investigation, which forms a dodecagonal quasicrystal, we show that this process occurs through the assimilation of stable icosahedral clusters by the growing quasicrystal. Our results demonstrate how local atomic interactions give rise to the long-range aperiodicity of quasicrystals.