Geometry of dislocations in icosahedral quasicrystals

Abstract

Quasicrystals are complex metallic alloys that are ductile at high temperatures close to their melting point. It has been early recognized that their plasticity is due to a flux of moving linear defects in all respects similar to dislocations in ordinary crystals. The present paper is an attempt to propose in a short didactic review a simple synthetic analysis of the basic underlying geometry of quasicrystalline dislocations exemplified with experimental and calculated images of electron microscopy in icosahedral phases.

Notes

†This does not imply lies in this 2D-subspace: in fact is in a rational 2D-plane with respect to Λ that is oblique with respect to E_‖. It is the irrationality of this oblique orientation that makes the relation between the lattice nodes of this rational plane and their projections in E_‖ a one-to-one correspondence.

‡There are a priori no basic physical reasons for choosing this particular law except that it can be reasonably assumed that the phason field spreads out isotropically around the dislocation line.