Atomistic modelling of TiAl I. Bond-order potentials with environmental dependence

Bond-order potentials (BOPs) for L1₀ TiAl have been developed and constructed within a tight-binding framework. In addition to the usual attractive bond-energy contribution arising from the formation of covalent bonds and pairwise contribution describing the overlap repulsion and electrostatic interaction, we have included an environmentally dependent term to represent the strong repulsion experienced by the valence sp electrons in transition metals and their alloys. The latter contribution is crucial for reproducing the negative Cauchy pressures of TiAl and other transition-metal-based intermetallic compounds. The constructed BOPs have been tested in the following ways: firstly, examination of the mechanical stability of the tetragonal L1₀ lattice with respect to large deformations and other crystal structures with the same stoichiometry; secondly, calculation of the γ surface for {111} and related evaluation of the energies of stacking-fault-type defects; thirdly, calculation of energies of the γ-γ interfaces that are present in the lamellar TiAl and energies associated with the formations of point defects in TiAl. The results of all these calculations show very good agreement with various ab-initio calculations. Importantly, we find that this potential is transferable to the different bonding environment in the hexagonal D0₁₉ Ti₃Al. Hence these BOPs are suitable for atomistic study of dislocations and other extended defects not only in L1₀ TiAl but also in Ti₃Al and possibly structures with other titanium-rich stoichiometries.