A unified projection formalism for the Al–Pd–Mn quasi-crystal Ξ-approximants and their metadislocations

Abstract

The approximants ξ, ξ′ and

of the Al–Mn–Pd quasi-crystal display interesting plastic properties, such as, for example, phason-induced deformation processes and metadislocations. Here we demonstrate that the phases and their deformed or defect states can be described by a simple projection formalism in three-dimensional space—not, as usual, in four to six dimensions. Using this method we can interpret the 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 ξ′ phase can create new phason planes, we suggest a dislocation-induced phase transition from ξ′ to

. The methods developed in this paper can also be applied for various other complex metallic alloys.