Geometry of dislocations in icosahedral quasicrystals (original) (raw)

Dislocations and mechanical properties of icosahedral quasicrystals

Comptes Rendus Physique, 2014

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.

The Equivalence Between Unit-Cell Twinning and Tiling in Icosahedral Quasicrystals

Scientific Reports

It is shown that tiling in icosahedral quasicrystals can also be properly described by cyclic twinning at the unit cell level. The twinning operation is applied on the primitive prolate golden rhombohedra, which can be considered a result of a distorted face-centered cubic parent structure. The shape of the rhombohedra is determined by an exact space filling, resembling the forbidden five-fold rotational symmetry. Stacking of clusters, formed around multiply twinned rhombic hexecontahedra, keeps the rhombohedra of adjacent clusters in discrete relationships. Thus periodicities, interrelated as members of a Fibonacci series, are formed. The intergrown twins form no obvious twin boundaries and fill the space in combination with the oblate golden rhombohedra, formed between clusters in contact. Simulated diffraction patterns of the multiply twinned rhombohedra and the Fourier transform of an extended model structure are in full accord with the experimental diffraction patterns and can be indexed by means of three-dimensional crystallography. The alternative approach is fully compatible to the rather complicated descriptions in a hyper-space. Ever since quasicrystals (QCs) were first reported 1 they attracted great interest, because they apparently contradicted some basic concepts of crystallography 2-4. Contrary to fully disordered solids and perfectly grown single crystals, characterized by their rotational and translational symmetries, QCs with their forbidden five-fold rotational symmetry and with the apparently lost translational order represented something in between the two categories. However, some of their properties contradict this distinction. Their shapes can be well developed and the corresponding diffraction patterns (DPs) show exceptionally sharp reflections, without any diffuse scattering, characteristic of short-range order, modulation, or any other deviation from an ideal crystalline structure. Pauling was convinced that none of the existing crystallographic rules was violated in the newly discovered materials 5-10. He believed these crystals were composed of twinned cubic domains with huge unit cells, whose basic building elements were composed of one Mn atom linked to twelve Al atoms. Although the existing experiments seemingly supported his model, he after all run into problems. Another major problem with Pauling's approach was, that no twin boundaries were ever detected in QCs 11. Contrary to Pauling, a number of researchers 12-18 considered QCs an exception to the known solid state structures, which required a novel approach. Their explanation was based on the so-called Amman tiling 19 , the three-dimensional equivalent of the two-dimensional Penrose tiling. Likewise to two Penrose rhombic tiles filling a plane, their three-dimensional equivalents, the prolate and the oblate golden rhombohedra, will fill the space and form the QC structure. It is shown in the present work that tiling in the icosahedral QC structure can also be properly explained by cyclic unit cell twinning 20,21 , applied on primitive golden rhombohedra, forming thus intergrown twins without explicit twin-boundaries. Results Procedure. Instead of describing a QC structure in a hyper-space, the present description is based on twinning of the basic building units. Dependent on the sizes and the composition of the constituent atoms a hypothetical parent face-centered cubic structure of an alloy may collapse into a primitive rhombohedral one along four equivalent directions. If the resulting rhombohedral angle is close to 63.43°, i.e. the angle of a prolate golden rhombohedron, it will lock

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.

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.

The Curled Up Dimension in Quasicrystals

MDPI Crystals, 2021

Most quasicrystals can be generated by the cut-and-project method from higher dimensional parent lattices. In doing so they lose the periodic order their parent lattice possess, replaced with aperiodic order, due to the irrationality of the projection. However, perfect periodic order is discovered in the perpendicular space when gluing the cut window boundaries together to form a curved loop. In the case of a 1D quasicrystal projected from a 2D lattice, the irrationally sloped cut region is bounded by two parallel lines. When it is extrinsically curved into a cylinder, a line defect is found on the cylinder. Resolving this geometrical frustration removes the line defect to preserve helical paths on the cylinder. The degree of frustration is determined by the thickness of the cut window or the selected pitch of the helical paths. The frustration can be resolved by applying a shear strain to the cut-region before curving into a cylinder. This demonstrates that resolving the geometrical frustration of a topological change to a cut window can lead to preserved periodic order.

Structural transformations in quasicrystals induced by higher dimensional lattice transitions

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012

We study the structural transformations induced, via the cut-and-project method, in quasicrystals and tilings by lattice transitions in higher dimensions, with a focus on transition paths preserving at least some symmetry in intermediate lattices. We discuss the effect of such transformations on planar aperiodic Penrose tilings, and on three-dimensional aperiodic Ammann tilings with icosahedral symmetry. We find that locally the transformations in the aperiodic structures occur through the mechanisms of tile splitting, tile flipping and tile merger, and we investigate the origin of these local transformation mechanisms within the projection framework.

Simulation of Dislocations in Icosahedral Quasicrystals with IMD

High Performance Computing in Science and Engineering ’01, 2002

We report on recent investigations performed with IMD (ITAP Molecular Dynamics), a general purpose program for classical molecular dynamics simulations on workstations and massively parallel supercomputers. Especially the simulations of dislocations in icosahedral quasicrystals are described. The quasiperiodic structure leads to new interesting properties. The visualization of a dislocation is much more complicated than in periodic crystals and is presented in detail. An overview of the software used is also provided.

Cleavage Planes of Icosahedral Quasicrystals: A Molecular Dynamics Study

MRS Proceedings, 2003

ABSTRACTThe propagation of mode I cracks in a three-dimensional icosahedral model quasicrystal has been studied by molecular dynamics techniques. In particular, the dependence on the plane structure and the influence of clusters have been investigated. Crack propagation was simulated in planes perpendicular to five-, two- and pseudo-twofold axes of the binary icosahedral model.Brittle fracture without any crack tip plasticity is observed. The fracture surfaces turn out to be rough on the scale of the clusters. These are not strictly circumvented, but to some extent cut by the dynamic crack. However, compared to the flat seed cracks the clusters are intersected less frequently. Thus the roughness of the crack surfaces can be attributed to the clusters, whereas the constant average heights of the fracture surfaces reflect the plane structure of the quasicrystal. Furthermore a distinct anisotropy with respect to the in-plane propagation direction is found.