Analysis of dissociation of < c > and < c+a > dislocations to nucleate (1 0 -1 2) twins in Mg

A mechanism for (1 0 (1) over bar 2) twin nucleation in Mg is studied in which edge < c > and mixed < c + a > lattice dislocations dissociate into a stable twin, having at least the minimum 6-layer thickness formed by three glissile twinning dislocations, plus a residual stair rod dislocation. Continuum dislocation theory is used to compute the energy of the initial and final states of the proposed dissociation process, using the twin boundary energy computed by density functional theory. For the < c > dislocation, the proposed dissociation is energetically favorable. An alternative dissociation path into partials on two {1 0 (1) over bar 1}-type pyramidal planes is possible, as seen in an atomistic analysis, and the continuum analysis predicts this alternative path to be more favorable than the twin process. For the < c + a > dislocation, the continuum model also predicts that dissociation into the twinned structure is energetically favorable for 6-layer and thicker twins. In both < c > and < c + a > cases, the equilibrium twin length is predicted to increase with increasing applied resolved shear stress and grow unstably beyond a critical stress. Atomistic simulations of these processes are then performed. For < c >, a twinned structure is stable under zero loading but with higher energy than the alternative dissociation on two {1 0 (1) over bar 1} planes. Under a positive applied strain of 4%, resolved on the twin plane, the twinning structure grows while under a negative applied strain of -3%, it reverts back to the alternative low-energy dissociated configuration on the pyramidal planes. For the mixed < c + a > dislocation, the atomistic models predict that the dissociation into twinning dislocations does not occur spontaneously at zero applied strain but there is a stable twinned region at finite applied loads. These results demonstrate that dislocation-assisted mechanisms for twinning in Mg, initiating from lattice dislocations with large Burgers vectors, are physically feasible, and therefore twin nucleation from grain boundaries is not necessarily the dominant mechanism of twinning in Mg.