  The approximants xi, xi' and xi'_n of the quasicrystal Al-Mn-Pd display most
interesting plastic properties as for example phason-induced deformation
processes (Klein, H., Audier, M., Boudard, M., de Boissieu, M., Beraha, L., and
Duneau, M., 1996, Phil. Mag. A, 73, 309.) or metadislocations (Klein, H.,
Feuerbacher, M., Schall, P., and Urban, K., 1999, Phys. Rev. Lett., 82, 3468.).
Here we demonstrate that the phases and their deformed or defected states can
be described by a simple projection formalism in three-dimensional space - not
as usual in four to six dimensions. With the method we can interpret
microstructures observed with electron microscopy as phasonic phase boundaries.
Furthermore we determine the metadislocations of lowest energy and relate them
uniquely to experimentally observed ones. Since moving metadislocations in the
xi'-phase can create new phason-planes, we suggest a dislocation induced phase
transition from xi' to xi'_n. The methods developed in this paper can as well
be used for various other complex metallic alloys.
