# Impact of Alloying on Stacking Fault Energies in \(\gamma\)-TiAl
## 3 Results and Discussion
### Impact of Alloying Elements  
In order to tune various application-related properties, alloying elements are introduced to \(\gamma\)-TiAl-based alloys. This section thus presents predictions of the impact of early transition metals (TMs, group IVB-VIB elements) on SFs of \(\gamma\)-TiAl. Experimentally, the most relevant are Ti-rich  
Figure 2: Energy profile along the dissociation path according to (**a**) Equation (2) and (**b**) Equation (3). The right panels show the dissociation path overlayed on the calculated \(\{111\}\) GSFE surface of the \(\gamma\)-TiAl lattice.  
compositions [1; 3; 25]. Moreover, the early TMs preferably occupy the Ti sublattice in \(\gamma\)-TiAl [26; 27]. Therefore, a scenario with a Ti anti-site (Ti atom on the Al sublattice) and a TM substitutional atom on the Ti sublattice was considered. The supercells consisted of six \(\{111\}\) planes, each containing eight atoms (a \(2\times 2\) supercell laterally), and the calculations were performed using the tilted \(\vec{a}_{3}\) geometry (Figure 1). Both the alloying element (having a concentration \(1/48\approx 0.02\)) and the Ti anti-site were put in the fault plane. The results are summarized in Figure 3.  
The SFEs are predicted to significantly decrease by 20-40% as a result of the alloying (see Figure 3a; atomic positions were relaxed only in the direction perpendicular to the fault plane). Regarding the SISF, the biggest impact has Ti simply leading to a bigger Ti/Al non-stoichiometry (\(\mathrm{Al}/(\mathrm{Ti}+\mathrm{Al})=47.9\)) in comparison with the ternary systems (\(\mathrm{Al}/(\mathrm{Ti}+\mathrm{Al})=48.9\)). From the ternary additions, the most pronounced effect has Mo (\(\gamma_{\mathrm{SISF}}\) drops by 36%) closely followed by Ta. The largest reduction of the CSF energy is caused by Cr, V and W, while the APB energy is most significantly decreased by Mo and W. The relative reduction of SFEs is even more pronounced when the full atomic relaxation is performed (Figure 3b).  
The SFEs presented in (Figure 3 contained the alloying element directly in the fault plane. In order to see how localized the alloying impact is, we calculated the SFEs for the off-stoichiometric TiAl, i.e., 52 Ti-48 Al, as a function of the distance of the substitutional Ti atom from the fault plane. It turns out that the huge SFE reduction happens only in the case when Ti is directly in the SF (\(N=0\) in  
Figure 3: Impact of alloying on \(\gamma\)-TiAl with a composition Ti-48 Al-2X (X = transition metal element): (**a**) SFs fixed to their geometrically-dictated configurations and relaxed only in the perpendicular direction and (**b**) atomic positions fully relaxed.  
Figure 4). When positioned in the neighboring layer (\(N=1\)), SFE is still decreased with respect to the stoichiometric value (most significantly in the SISF case). For \(N\geq 2\), the SFEs stay practically constant, though slightly lower than in the stoichiometric case.  
Alloying does not only influence the SFE, but the whole GSFE surface including its topology. Figure 5 gives an example of the GSFE profiles along the two dissociation paths, Equations (2) and (3), for \(\gamma\)-TiAl + Nb. When compared with analogous profiles in Figure 2, two observations can be made. Firstly, in addition to lower values of the local minima, also the local maxima (transformation barriers) are lower, leading to an overall easier creation of SFs. Secondly, while the APB was predicted to be unstable for stoichiometric \(\gamma\)-TiAl, a shallow local minimum is developed in the case of TiAl + Nb, suggesting that Nb stabilizes this fault geometry. A similar effect was predicted also for the V and Ti off-stoichiometry (52 Ti-48 Al).  
Figure 4: Dependence of SFEs on the location of the substitutional atom (here, Ti). \(N\) labels the layer number away from the fault plane (located at \(N=0\)), and the dashed line represents a reference value for the stoichiometric TiAl (Table 1).