Elastic and anelastic behaviour of icosahedral quasicrystals (original) (raw)

Elastic theory of icosahedral quasicrystals - application to straight dislocations

The European Physical Journal B, 2001

In quasicrystals, there are not only conventional, but also phason displacement fields and associated Burgers vectors. We have calculated approximate solutions for the elastic fields induced by two-, three-and fivefold straight screw-and edge-dislocations in infinite icosahedral quasicrystals by means of a generalized perturbation method. Starting from the solution for elastic isotropy in phonon and phason spaces, corrections of higher order reflect the two-, three-and fivefold symmetry of the elastic fields surrounding screw dislocations. The fields of special edge dislocations display characteristic symmetries also, which can be seen from the contributions of all orders.

Elastic Green's function of icosahedral quasicrystals

The European Physical Journal B, 1998

The elastic theory of quasicrystals considers, in addition to the "normal" displacement field, three "phason" degrees of freedom. We present an approximative solution for the elastic Green's function of icosahedral quasicrystals, assuming that the coupling between the phonons and phasons is small.

Dislocation climb in icosahedral quasicrystals

Scripta Materialia, 2003

We discuss here some arguments in favor of climb being the dominant mode of dislocation motion responsible for the plastic deformation of icosahedral quasicrystals.

On the Anisotropy of Quasicrystal Structures

Acta Crystallographica Section A, 1996

Textures of melt-spun icosahedral and decagonal quasicrystals have been analysed via texture simulation by a sum of limited fibre components. The model has been extended to include the axial textures with an anisotropic spread of the texture axis. An orientation distribution function of the textured icosahedral quasicrystal has been calculated. It is shown that textured decagonal structures may exhibit an anisotropy of physical properties even in the ribbon plane. may calculate half of the series-expansion coefficients for cubic crystalline symmetry (only even coefficients), only 30% of the coefficients may be obtained for hexagonal crystals (Bunge, 1987). The ghost phenomena of ODF reproduction may be bypassed by the direct ODF approximation in an analytical form. This paper deals with the investigation and simulation of textures (both pole figures and ODFs) of the quasicrystal phases with icosahedral and decagonal symmetries.

Numerical simulation of dislocation motion in three-dimensional icosahedral quasicrystals

Philosophical Magazine A, 2000

In a large number of experiments it has been shown that plastic deformation of quasicrystals can occur by a dislocation mechanism. By molecular dynamics simulations close to zero temperature we have investigated the application of shear stress to a three-dimensional model quasicrystal consisting of Lennard± Jones particles and containing an edge dislocation of the Peierls± Nabarro type. Various visualization methods have been used to trace the dislocation line. To determine suitable Burgers vectors we have calculated the gamma surface, that is the mis® t energy obtained by a rigid shift of two probe halves along a glide plane. Glide motion of the dislocation on di erent glide planes was observed. In its wake a plane of phasonic defects was detected.

Dynamic fracture of icosahedral model quasicrystals: A molecular dynamics study

Physical Review B, 2005

] have fractured icosahedral Al-Mn-Pd single crystals in ultrahigh vacuum and have investigated the cleavage planes in-situ by scanning tunneling microscopy (STM). Globular patterns in the STM-images were interpreted as clusters of atoms. These are significant structural units of quasicrystals. The experiments of Ebert et al. imply that they are also stable physical entities, a property controversially discussed currently. For a clarification we performed the first large scale fracture simulations on three-dimensional complex binary systems. We studied the propagation of mode I cracks in an icosahedral model quasicrystal by molecular dynamics techniques at low temperature. In particular we examined how the shape of the cleavage plane is influenced by the clusters inherent in the model and how it depends on the plane structure. Brittle fracture with no indication of dislocation activity is observed. The crack surfaces are rough on the scale of the clusters, but exhibit constant average heights for orientations perpendicular to high symmetry axes. From detailed analyses of the fractured samples we conclude that both, the plane structure and the clusters, strongly influence dynamic fracture in quasicrystals and that the clusters therefore have to be regarded as physical entities.

Bravais Quasilattices of Icosahedral Quasicrystals

Physical Review Letters, 2004

A classification of icosahedral quasicrystals based the mutual-local-derivability (MLD) concept is performed. There are eighteen MLD classes within the reservation that the faces of the hyperatoms (windows) are perpendicular to the two-, three-, or fivefold axes. Each MLD class has a representative member to be called the Bravais quasilattice from which the structure of each member of the class is derived by decorating it according to a local rule depending on the member.

New group of stable icosahedral quasicrystals: structural properties and formation conditions

Journal of Non-Crystalline Solids, 2004

Structural studies on the icosahedral quasicrystals in Zn-Mg-Sc, Cu-Ga-Mg-Sc, and Zn-Mg-Ti alloys as well as their corresponding 1/1 cubic approximants, have revealed that these quasicrystals belong to a new structural group similar to Cd-based quasicrystals. This group is characterized by a triple-shell icosahedral cluster different from both Mackay-and Bergman-types. The presence of the atomic cluster has been deduced from the structure model of the approximant crystal, Zn 17 Sc 3 , in which the clusters are embedded in a periodic network of so-called 'glue atoms'. Density measurement suggested the presence of at least 2.7 Zn atoms in the first shell of the cluster in this approximant. The substitutional relationship in these three quasicrystals indicates the important role of Hume-Rothery rule for the formation of this type of quasicrystal. The occurrence of a P-type icosahedral quasicrystal in Zn-Mg-Yb alloy is also reported. PACS: 61.44.Br, 61.66.Dk 1. Introduction After the discovery of the Al-Mn quasicrystal by Shechtman et al. [1], many icosahedral quasicrystals were found in various alloy systems, including thermodynamically stable phases, such as Al-Cu-Fe, Al-Pd-Mn, Zn-Mg-L (L: lanthanoid elements), etc. In particular, in the past two years, new icosahedral quasicrystals have been discovered in Cd-based [2,3,4], Mg-based [5], Zn-based [6,7], Ag-In based [8] and Cu-based [9] alloys. All quasicrystals known so far are classified into several groups from metallurgical and structural points of view. Classification with respect to the local atomic configurations (or atomic clusters) is useful to understand the local structural features of an icosahedral quasicrystal. Two famous atomic clusters are the so-called Mackay and Bergman clusters [10], in which the atoms are arranged to satisfy the icosahedral symmetry. Usually, Al-based quasicrystals such as Al-Cu-Fe and Al-Pd-Mn are classified as Mackay-type, and Zn-based quasicrystals such as Zn-Mg-L as Bergman-type. The existence of approximant crystals including these two types of clusters [10], in which the clusters are arranged in periodic manner, may support this classification. However, recent studies on the approximants suggested that the classification by only two clusters is too simple [11]. Moreover, the Cd-based quasicrystals were expected to have an atomic cluster which is different from the Mackay and Bergman types [4]; this was deduced from the structures of their approximants.