Shear and shuffle in $\left\{{11\bar 22} \right\}\left\langle {11\bar 2\bar 3} \right\rangle$ twinning in titanium

Abstract

In classical twinning theory, the K₂ plane of $\left\{{11\bar 22} \right\}\left\langle {11\bar 2\bar 3} \right\rangle$ twinning mode was predicted to be $\left\{{11\bar 2\bar 4} \right\}$, with a twinning shear of ∼0.22 which was experimentally “confirmed”. However, these twinning elements cannot be reproduced or verified in atomistic simulations. The K₂ plane in the simulations is always (0001), but this K₂ 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 $\left\{{11\bar 22} \right\}$ twin boundary in titanium (Ti). Shear and atomic shuffles for three different, reported K₂ planes were analyzed in great detail, for the first time. The analyses show that ${K_2} = \left\{{11\bar 2\bar 4} \right\}$ leads to very complex shuffles despite the small twinning shear and is unfavorable. If ${K_2} = \left\{{11\bar 2\bar 2} \right\}$, 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 K₂ = (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, K₂ = (0001) is the most favorable and the conflict between the simulation results and the classical twinning theory can be reconciled.