Fig. 1. Crystal structure of multi-doped D022-TiAl3 (a) 2×2×1 and (b) 3×3×1 supercell with designated atomic locations of Ti (blue sphere), Al (yellow sphere), W (red sphere), M (green sphere), and mono vacancy position V1 and V2 (grey sphere) labelled with red arrow.

Fig. 2. Representative (002) planar view of 2d_system with defect dopants in 2×2×1 supercell without vacancy (a) and with vacancy V1 (b) and V2 (c). The dashed arrow represents the positional transition of group IV M atom as its atomic size increases. In (a), M-atom is found constrained due to the inter-atomic repulsion of neighboring Al atoms. In (b), a [11¯0] transitional behavior for M atom toward V1 position is observed when its atomic size increases. The relative positions of Si, Ge, Sn are marked by red ‘X’ in order of increasing atomic size from C toward Pb. The nearest Al atom to M atom in the same plane are labelled Al1 and Al2 and their purposes are described in text. In (c), while C shifts in [1¯00] direction and occupies an interstitial position, the bigger M-atoms shift in [110] direction and occupy vacancy V2 position.

Fig. 3. Representative 2a_system with alloying dopants in 2×2×1 supercell with vacancy V1 only. The transitional behavior of dopants in systems without vacancy and with vacancy V2 behaved similarly to their counterparts shown in Fig. 2, and therefore not shown here. The dashed arrow represents the positional transition of group IV M atom as its atomic size increases. Unlike its counterpart in Fig. 2 (b), Pb atom did not position itself at V1 location after full relaxation of crystal. The relative positions of Si, Ge, Sn are marked by red ‘X’ in order of increasing atomic size from C toward Pb. The nearest Al atom to M atom in the same plane are labelled Al1 and Al2 and their purposes are described in text.

Fig. 4. Representative 3a_system with alloying components in 3×3×1 supercell without vacancy (a) and with vacancy V1 (b) and V2 (c). The modes of transition of various alloy systems are identical to that with defect components in 2×2×1 supercell shown in Fig. 2. The dashed arrow represents the positional transition of group IV M atom as its atomic size increases. The nearest Al atom to M atom in the same plane are labelled Al1 and Al2 and their purposes are described in text.

Fig. 5. (a) Formation enthalpy (ΔH) with dopants concentration for TiAl3WM (top), TiAl3WMV1 (middle) and TiAl3WMV2 (bottom). Linearity can be assumed within this concentration range and converged to -0.391 eV/atom, which is ΔH of D022-TiAl3. Thermodynamic stability for all alloy system is illustrated by their negative value of ΔH. (b) Corresponding vacancy formation energy EV (eV) of TiAl3WMV1 and TiAl3WMV2 for different dopant concentrations.

Fig. 6. Pugh’s ratio for various multi-doped system with defect and alloying dopants treatment and different doping concentration. The ratio for pristine D022- and L12-TiAl3 are indicated with solid black arrows. The chart displays the Pugh’s ratio for TiAl3W, TiAl3WM and TiAl3WMV1/2 systems, where solid and dashed lines denote vacancy V1 and V2 systems.

Fig. 7. Bulk Young’s modulus sensitivity towards strain modulus ratio εc/εa.

Fig. 8. A replot of Fig. 7 to replace ΔE-axis with (ΔE/εa)-axis. Linear relation for TiAl3WM, TiAl3WMV1 and TiAl3WMV2 are shown with good regression. TiAl3WCV1, TiAl3PbV1 and TiAl3WCV2 (boxed) are not included in the trending as they are considered outliners due to their different transition behavior.

Fig. 9. Electron charge difference density maps of (a) pristine D022-TiAl3 and (b) mono-doped TiAl3W alloy systems. (c), (e) and (g) represent 2d_, 2a_ and 3a_TiAl3WC, respectively. (d), (f) and (h) represent 2d_, 2a_ and 3a_TiAl3WPb, respectively. Regions colored cyan (magenta) represent a net gain (loss) in electron charge.

Fig. 10. Partial density of states of W and M atoms in multi-doped (a) TiAl3WC and (b) TiAl3WPb for 2d_, 2a_ and 3a_system in order.