Phasons and the Plastic Deformation of Quasicrystals
  The plastic deformation of a quasicrystal (QC) is ruled by singularities of its 'phonon' strain field and of its 'phason' strain field. In the framework of the topological theory of defects, and the QC being defined as an irrational subset of a high dimensional crystal, both types of defects appear as distinct components of the same entity, a 'disvection'. Each of them can also be described in classical terms, within a detailed analysis of the Volterra process:(a)- the 'phonon' singularity breaks some symmetry of translation, represented by a Burgers vector projected from the high dimensional crystal onto the physical space; it is akin to an ordinary perfect dislocation, (b)- the 'phason' singularities are dislocation dipoles whose Burgers vectors are of a special type; they break not only a particular symmetry of translation but also, in the QCs' jargon, the 'class of local isomorphism' of the QC. In fact, such dipoles, if they open up into loops, bound stacking faults; a phason singularity is thus an imperfect dislocation. It is suggested that the interplay of perfect and imperfect dislocations is at the origin of the peculiar characters of the plastic deformation of QCs, namely the brittle-ductile transition followed by a stage of work softening; in particular the brittle-ductile transition could be related to a cooperative transition of the Kosterlitz-Thouless type which affects the dipoles and turn them into (imperfect) dislocation loops. 
Maurice Kleman