# Impact of Alloying on Stacking Fault Energies in \(\gamma\)-TiAl
## 1 Introduction  
Titanium aluminides are intermetallic compounds and alloys with a wide reach for high-temperature applications. These range from low-pressure turbine blades in the aircraft industry to turbocharger turbine wheels and valves in the automotive industry [1; 2; 3]. Their outstanding properties include low mass density, high specific strength and stiffness and good creep properties up to 750 \({}^{\circ}\)C. They outperform titanium alloys by their good oxidation behavior and burn resistance [2]. In contrast to ceramic materials, titanium aluminides also exhibit the ability to plastically deform at room temperature [4].  
Current state-of-the-art TiAl alloys consist of a close to face-centered cubic (fcc) \(\gamma\)-TiAl phase, a hexagonal \(\alpha_{2}\)-Ti\({}_{3}\)Al phase, a body-centered cubic (bcc) \(\beta_{0}\)-TiAl phase, and, occasionally, additional minor phases [1]. However, the main constituent is the \(\gamma\)-TiAl phase, which fundamentally influences the alloy properties during processing, e.g., hot-forging and application.  
The \(\gamma\)-TiAl phase has an \(\mathrm{L}1_{0}\) structure which is a tetragonally strained fcc lattice with \((001)\) planes occupied alternatively by Ti and Al atoms. Therefore, stacking faults (SFs) become a topic of a great importance, similar to fcc metals, in which a stacking fault is a deviation from the normal stacking sequence \(\ldots ABCABC\ldots\) of the \((111)\) planes. The stacking fault energy (SFE), \(\gamma\), an energy stored by the stacking fault defect, has a huge impact on a plastic deformation behavior of fcc metals. It determines the spreading of dissociated partial dislocations and, therefore, influences the cross-slip properties of screw dislocations. It is observed that metals with smaller stacking fault energiesexhibit more mechanical twinning whereby they possess an additional deformation mechanism [5]. Especially, this effect was utilized in the development of novel high-strength \(\gamma\)-TiAl-based alloys exhibiting a certain ductility at room temperature. Here, the reader is referred to [1; 2] and the papers cited therein.  
Measuring the stacking fault energies experimentally is, nevertheless, non-trivial. Most commonly, they are measured indirectly using transmission electron microscopy (TEM) from the separation of partial dislocations. Such an experimental procedure is, however, time consuming and deals with all the difficulties related to a multi-phase complex alloy (non-homogeneous concentrations, stresses, sample preparation, to name a few). Consequently, experimental works dealing with this topic in \(\gamma\)-TiAl are scarce [6; 7; 8; 9]. Hence, theoretical studies of stacking fault energies comprise a welcome alternative to examine stacking faults. These included both ab initio methods [10; 11; 12; 13; 14], as well as empirical atomistic modeling [15; 16; 17].  
Nonetheless, the \"real\" alloys go beyond the simple binary Ti-Al system [1; 2; 4]. It is therefore of immense interest to know what impact alloying has on the SFEs and, consequently, on the expected deformation mechanisms. A rare example of such modeling effort is the study of [PERSON] and [PERSON] [18], who used the coherent potential approximation (CPA) to investigate the impact of Nb and Cr on SFEs in \(\gamma\)-TiAl. This formalism, however, does not allow for any relaxations of the local atomic environments. Moreover, information on other alloying elements, namely the group IVB, VB, and VIB transition metal (TM) elements, commonly used experimentally, is still missing. The aim of the present study is to fill this gap by investigating the impact of ternary alloying elements on planar faults in \(\gamma\)-TiAl using ab initio techniques.