Plasticity of hexagonal systems: Split slip modes and inverse Peierls relation in $\alpha$-Ti

The plasticity of hexagonal titanium is reexamined based on the split slip modes phenomenon, revealing the existence of subslip modes in prismatic and pyramidal hcp slip systems. The energetics of dislocation emission and motions were described using all-dimension relaxed atomic models of crystal slip, calculated with density functional theory. The proposed computational methodology is based on the generalized stacking fault energy concept and respects all elastic effects arising within dislocation nucleation. As a result, improved accuracy has been obtained with regard to ductility prediction and a breach has been discovered in the fundamental Peierls-Nabarro rule. This approach is essential for the Rice and Peierls-Nabarro models and can be used as an effective tool for ductility predictions when designing new hexagonal alloys.

Figure 1

(a) Slip modes in fcc, bcc, and hcp single unit cells. The Burgers vectors and glide planes are labeled as red vectors and planes, respectively. (b) The interplanar spacing $d_{\left\{X\right\}}$ is shown in the side view (parallel to the glide planes) of the $2\times 2\times 2$ unit cells. (c) The slab supercells used in $\gamma$ curve calculations; arrows marked I and II describe split slip modes with different interplanar distance, while A,B,C,D denote the stacking sequence of atomic planes (colored spheres).

Figure 2

(a) Results of the rigid (direct) and NEB $\gamma$ curve calculations for seven $\alpha$-Ti slip modes, slip traces (solid colored lines), and movements of atoms [colored circle stacking is similar to Fig. 1] located below the glide planes: (b) view perpendicular to Burgers vector and parallel to glide plane, and (c) view perpendicular to Burgers vector and glide plane. The half black points represent equilibrium positions, and “S” and “F” symbols indicate start and finish of the slip paths, respectively.

Figure 3

The $\langle a\rangle$ pyramidal slip modes with marked different interplanar spacing (dashed lines). The arrows denote Burgers vector and the pairs of red and yellow spheres [the colors are not equivalent to those used in Fig. 1] indicate the position of the atomic planes above and below the glide plane in the middle of the slip. The presented structures were calculated with NEB.