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Preferential site occupancy of alloying elements in TiAl-based phases

First principles calculations are used to study the preferential occupation of ternary alloying additions into the binary Ti-Al phases, namely $γ$-TiAl, $α_2$-Ti$_3$Al, $β_{\mathrm{o}}$-TiAl, and B19-TiAl. While the early transition metals (TMs, group IVB, VB , and VIB elements) prefer to substitute for Ti atoms in the $γ$-, $α_2$-, and B19-phases, they preferentially occupy Al sites in the $β_{\mathrm{o}}$-TiAl. Si is in this context an anomaly, as it prefers to sit on the Al sublattice for all four phases. B and C are shown to prefer octahedral Ti-rich interstitial positions instead of substitutional incorporation. The site preference energy is linked with the alloying-induced changes of energy of formation, hence alloying-related (de)stabilisation of the phases. We further show that the phase-stabilisation effect of early TMs on $β_{\mathrm{o}}$-phase has a different origin depending on their valency. Finally, an extensive comparison of our predictions with available theoretical and experimental data (which is, however, limited mostly to the $γ$-phase) shows a consistent picture.