Analysis of double cross-slip of pyramidal I ⟨c+a⟩ screw dislocations and implications for ductility in Mg alloys

Solute accelerated cross-slip of pyramidal ⟨c+a⟩ screw dislocations has recently been recognized as a crucial mechanism in enhancing the ductility of solid-solution Mg alloys. In pure Mg, cross-slip is ineffective owing to the energy difference between the high energy pyramidal I and low energy pyramidal II ⟨c+a⟩ screw dislocations. A small addition of solutes, especially rare earth (RE) elements, can reduce this energy difference and accelerate cross-slip, thus enabling enhanced ductility. With increasing solute concentrations, the pyramidal I dislocation can become energetically favorable, which switches the primary ⟨c+a⟩ slip plane and alters the cross-slip process. Here, the transition path and energetics for double cross-slip of pyramidal I ⟨c+a⟩ dislocations are analysed in the regime where the pyramidal I dislocation is energetically more favorable than the pyramidal II. This is achieved using nudged elastic band simulations on a proxy MEAM potential for Mg designed to favor the pyramidal I over pyramidal II. The minimum energy transition path for pyramidal I double cross-slip is found to initiate with cross-slip onto a pyramidal II plane followed by cross-slip onto a pyramidal I plane parallel to the original pyramidal I plane. A previous mechanistic model for ductility is then extended to higher solute concentrations where pyramidal I is favorable. The model predicts an upper limit of solute concentrations beyond which ductility again becomes poor in Mg alloys. The model predictions are consistent with limited experiments of Mg-RE alloys at high concentrations and motivate further experimental studies in the high concentration regime.