  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.
