The candidacy of shuffle and shear during compound twinning in hexagonal close-packed structures

This paper proposes a systematic generalized formulation for calculating both atomic shuffling and shear candidates for a given compound twinning mode in hexagonal closed-packed metals. Although shuffles play an important role in the mobility of twinning dislocations in non-symmorphic crystals, their analytical expressions have not been previously derived. The method is illustrated for both flat planes and corrugated planes which are exemplified by image and image twinning modes, respectively. The method distinguishes between shuffle displacements and net shuffles. While shuffle displacements correspond to movements between ideal atom positions in the parent and twin lattices, net shuffles comprise contributions from shear on overlying planes which can operate along opposite directions to those of shuffle displacements. Thus, net shuffles in the twinning direction can vanish in a limiting case, as is interestingly the case for those needed in the second plane by the b4 dislocation candidate in image twinning. It is found that while shuffle displacement vectors can be irrational when K1 is corrugated, net shuffle vectors are always rational.