Shear and shuffle in $\left\{{11\bar 22} \right\}\left\langle {11\bar 2\bar 3} \right\rangle$
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gÆ1123æ twinning mode was predicted to be In classical twinning theory, the K2 plane of f1122 2 4g, with a twinning shear of ;0.22 which was experimentally “confirmed”. However, these f11 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 f1122g 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 K2 ¼ f1124g leads to very complex shuffles despite the small twinning shear and is unfavorable. If K2 ¼ f1122g, 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 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, K2 5 (0001) is the most favorable and the conflict between the simulation results and the classical twinning theory can be reconciled. I. INTRODUCTION
Contrary to metals with high symmetry crystal structures in which the dislocation slip plays a dominant role in plastic deformation, for metals with low symmetry hexagonal close-packed (hcp) structures, deformation twinning strongly influences their mechanical properties.1–5 In hcp metals, except for the pyramidal slip systems, the basal and the prismatic slip systems are unable to accommodate the strain along the c-axis. Thus, all the twinning modes in hcp which provide a strain component along the c-axis are crucially important for strain accommodation. A significant difference between the twinning modes in hcp and those twinning modes in cubic metals is that, the magnitude of the Burgers vectors of the elementary twinning dislocations (bT) is usually only a small fraction of the Burgers vector of matrix dislocations.6 Twin growth is mediated by zonal dislocations6–10 that involve at least two twinning planes simultaneously, in contrast to twinning in cubic metals where twin growth is mediated by a partial dislocation on each twinning plane.11,12 But the configurations of the zonal twinning dislocations are quite complex and their structures are not fully understood. In face-centered-cubic metals, twinning can be accomplished by a homogeneous shear mediated by the glide of
Contributing Editor: Susan B. Sinnott a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2015.371 J. Mater. Res., Vol. 30, No. 24, Dec 28, 2015
Shockley partials, without the need for any extra atomic movements. The parent atoms can be directly carried to the twin positions by the homogeneous shear. In sharp contrast, in hcp metals a homogeneous shear alone is unable to complete the twinning process and atomic shuffling is required to achi
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