# Impact of Alloying on Stacking Fault Energies in \(\gamma\)-TiAl
## 3 Results and Discussion
### Comparison with Experiment  
A critical point for validating theoretical predictions is a comparison with available experimental data. The reported values for SISF energies decrease with Ti content from \(\approx\)140 mJ/m\({}^{2}\) for Ti-54 Al [6; 7] to \(\approx\)97 mJ/m\({}^{2}\) for Ti-49.6 Al [8] to 67 mJ/m\({}^{2}\) for Ti-48 Al [8]. While these values are lower than those predicted by the ab initio methods (which, however, are all mutually consistent, cf. Table 1), the theory and the experiment agree on ordering the SFE as \(\gamma_{\rm{APB}}>\gamma_{\rm{CSF}}>\gamma_{\rm{SISF}}\) ([6; 7] and Table 1), as well as on the decreasing value of SISF energy with increasing Ti content ([8] and Figures 3 and 4). Seemingly better agreement is obtained between experiment and semi-empirical atomistic simulations yielding SISF energies in the range from 3 to 250 mJ/m\({}^{2}\) (see [7; 10] and the references therein). This is, however, not surprising since SFEs are often contained in the set of data used for fitting the interatomic potentials. Moreover, our own molecular dynamics calculations yielded an apparent disagreement between the SFEs' hierarchy using two embedded-atom method potentials [28]: while the one parametrized by [PERSON] and [PERSON] [29] yields \(\gamma_{\rm{CSF}}>\gamma_{\rm{APB}}>\gamma_{\rm{SISF}}\), the one by [PERSON] and [PERSON] [30] results in the same ordering as the ab initio calculations.  
SISF energies for Nb-containing \(\gamma\)-TiAl were experimentally measured to be 63 mJ/m\({}^{2}\) for Ti-48 Al-1 Nb [9] and 66 mJ/m\({}^{2}\) for Ti-45 Al-10 Nb [8]. Using the value of \(\gamma_{\rm{SISF}}=97\) mJ/m\({}^{2}\) reported for almost stoichiometric TiAl [8], Nb causes \(\gamma_{\rm{SISF}}\) to drop by \(\approx\)30%, a value in an excellent agreement with our predictions (cf. Figure 3). It is worth noting that since we estimated that Nb impacts SFE only when present directly in the fault plane (or a plane next to it) and since each of the \(\{111\}\) planes in our supercells contained eight atoms, we predict a drop by \(\approx\)30% effectively for Ti-50 Al-12.5 Nb.  
Consequently, we conclude that the ab initio predicted SFE values agree only semi-quantitatively with the experimental observations, but are expected to be representative of the prevailing trend: early TMs (group IVB-VIB elements) decrease SFE in Ti-rich \(\gamma\)-TiAl alloys. They increase valence electron concentration, which according to [PERSON]'s semi-empirical observation, leads to a decrease of the SFE [31]. Therefore, alloying these elements in \(\gamma\)-TiAl is expected to lead to various effects, which can be utilized for advanced alloy design. For example, a decreased SFE is accompanied by a dissociation of dislocations and, hence, decreasing their mobility (climb rate) at elevated temperatures. On the other hand, a lower SFE enhances the propensity for mechanical twinning, thus increasing the ductility at temperatures below the brittle-to-ductile transition temperature. However, it should be noted that an alloying element, before being eventually selected, must fulfil also other criteria, e.g., influence on oxidation behavior, etc.