Nucleation and stability of twins in hcp metals

We propose a three-dimensional model for twin nucleation in hcp materials based on the nonplanar dissociation of the leading dislocation in a pile-up of < a > slip dislocations. Continuum linear elastic dislocation theory is used to calculate the change in free energy with extension of the dissociated configuration, consisting of a stair rod and glissile twinning dislocation loops. The model is applied to Mg, which deforms primarily by basal slip, and to Zr, which deforms primarily by prismatic slip. It is found that dissociations from an isolated < a > slip dislocation are energetically unable to produce a stable twin fault loop, at least larger than 2r(0), the core width of the initial < a > slip dislocation. For some reactions, dissociations of the lead dislocation in a basal or prismatic dislocation pile-up can, however, lead to a stable and sizable twin loop. In these, the loop size is found to increase with decreasing twin boundary energy and increasing number of dislocations in the pile-up.