Solute/Stacking Fault Energies in Mg and Implications for Ductility

Mg is the lightest structural metal but pure Mg has low ductility due to strong plastic anisotropy and to a transition of <c+a> pyramidal dislocations to a sessile basal-oriented structure [1]. Alloying generally improves ductility, but the mechanisms of the enhancement are not yet known. Mg-3 wt% RE (RE = Y, Tb, Dy, Ho, Er) show high ductility [2], as compared to most commercial Mg–Al–Zn alloys at similar grain size. To investigate possible proposed mechanisms of ductility in alloys, and differences between Al, Zn, and Y solutes, first-principles density functional theory (DFT) calculations are used to compute all relevant stacking fault (SF) energies as a function of solute type (Y, Al, Zn) and concentration in the dilute limit. 
In DFT calculations, we compute the solute-SF interaction energy E_int (d_i ) versus solute-SF distance d_i Accurate energies requires the use of large supercells. For the pyramidal II plane, a single solute may induce migration of the SF. Constraints, and corrections for the constraints, are thus needed. In the random alloy, every atom site has a probability c (in at.) to be occupied by a solute atom. The value of the SF energy of the alloy, at small c, is then γ^A = γ^Mg + c/A₀ Σ_i E_int (d_i ) 
The stacking fault energies for basal and pyramidal faults versus concentration are shown in Fig. 1 for the solutes Y, Al and Zn. From these results, we can draw some conclusions regarding ductility in Mg alloys. First, the proposed role of the I₁ basal SF in ductility enhancement in Mg–Y [2] is not supported. The effects of Y can be achieved at twice the concentration using Al. However, neither Mg–Al or Mg–Zn alloys show significantly enhanced ductility. Second, using the I₁ and pyr. II SFs for Y, elasticity calculations show that Y does not appear to significantly alter the energetics of the detrimental pyramidal-to-basal orientation transformation. Third, the only unique property of Y, compared to Al and Zn, is the much larger reduction of the pyramidal I SF energy. This suggests new mechanisms for enhanced ductility that will be discussed and supported by further results on other solutes.