Theoretical models of double twinning in magnesium

Satisfactory theoretical treatment of double twin growth has thus far not been achieved. Phenomenological theories of double twinning are based on the assumption that a double twin embryo grows on an invariant plane of the double twin transformation by means of a simple shear mechanism. We demonstrate the equivalence of A. G. Crocker's approach, which aims to identify the double twin invariant planes, and of later models of nonclassical twinning, which entail the use of correspondence matrices. These treatments, however, do not account for features of double twin growth observed in experiment, namely that this is a two-step process, where a primary twin forms fully before secondary twinning occurs internally. To resolve this conundrum, we introduce topological models of double twinning, which focus on the motion of twinning disconnections as the actors of twin growth. We first treat the case of secondary twinning disconnections interacting with a primary twin interface and calculate the magnitude of the resulting rotation of the habit plane; secondly, we model the interaction of secondary twinning disconnections with an array of primary twinning disconnections in the primary twin interface. We show that the latter model produces similar predictions for the double twin habit plane as those of the phenomenological theories, and we discuss validation of the topological models by experiment.