Shear and shuffle in twinning in titanium

Abstract

In classical twinning theory, the K 2 plane of 11 22 f gAE11 2 3ae twinning mode was predicted to be 11 2 4 f g, with a twinning shear of ;0.22 which was experimentally "confirmed". However, these twinning elements cannot be reproduced or verified in atomistic simulations. The K 2 plane in the simulations is always (0001), but this K 2 plane would lead to a nominal twining shear of 1.26 which is unrealistically large. In this work, atomistic simulations were performed to investigate the migration of 11 22 f g twin boundary in titanium (Ti). Shear and atomic shuffles for three different, reported K 2 planes were analyzed in great detail, for the first time. The analyses show that K 2 ¼ f11 2 4g leads to very complex shuffles despite the small twinning shear and is unfavorable. If K 2 ¼ f11 2 2g, only half of the parent atoms are involved in the shuffling, but the twinning shear is very large (0.96) and is also unfavorable. When K 2 5 (0001), the parent atoms are carried to twin positions partly by shear and partly by a simple shuffle. Because shuffling makes no contribution to the twinning shear, the actual twinning shear is 0.66, instead of 1.26. Thus, K 2 5 (0001) is the most favorable and the conflict between the simulation results and the classical twinning theory can be reconciled.