It was noted that approximants of the Al–Mn–Pd quasi-crystal exhibited interesting plastic properties such as phason-induced deformation processes and meta-dislocations. It was demonstrated that the phases, and their deformed or defect states, could be described by using a simple projection formalism in 3-dimensional space rather than in 4 to 6 dimensions. By using this method, it was possible to interpret the microstructures, observed using electron microscopy, as being phasonic phase boundaries. The meta-dislocations of lowest energy were determined and were uniquely related to experimentally observed ones. Because moving meta-dislocations in one of the phases could create new phason planes, a dislocation-induced phase transition from one phase to the other was posited.

A Unified Projection Formalism for the Al–Pd–Mn Quasi-Crystal Ξ-Approximants and their Metadislocations. M.Engel, H.R.Trebin: Philosophical Magazine, 2005, 85[20], 2227-47