Formation of $\mathrm{L}1_2$-ordered $\gamma'$-$\mathrm{Ni}_3\mathrm{Al}$ precipitates in ternary Cu-Ni-Al alloys modelled using an ab initio concentration wave theory and atomistic simulations
Precipitation-strengthened Cu-Ni-Al alloys are of interest for technological applications because coherent, $\mathrm{L}1_2$-ordered $\gamma'$-$\mathrm{Ni}_3\mathrm{Al}$ precipitates can confer high mechanical strength while allowing the material to retain many of the good transport properties characteristic of elemental Cu. In this work, we study the thermodynamics and phase stability of the pseudobinary $\textrm{Cu}_x (\textrm{Ni}_{3/4} \textrm{Al}_{1/4})_{1-x}$ system, $0 \leq x \leq 1$. We use a computational modelling framework combining first-principles electronic structure calculations with a concentration wave analysis from which atom-atom effective pair interactions are extracted for use in atomistic Monte Carlo simulations. Our modelling reveals three distinct, composition-dependent regimes of phase behaviour, in qualitative agreement with the experimentally determined phase diagram. At low Cu content, Cu is soluble in the $\mathrm{L}1_2$-ordered $\mathrm{Ni}_3\mathrm{Al}$ phase, with a single identifiable phase transition corresponding to chemical ordering between Ni and Al. At intermediate compositions, this high-temperature ordering is followed at lower temperatures by phase separation of Cu and $\mathrm{L}1_2$-ordered $\mathrm{Ni}_3\mathrm{Al}$. Finally, at high Cu content, $\mathrm{L}1_2$-ordered $\mathrm{Ni}_3\mathrm{Al}$ precipitates directly from the solid solution, with no clearly identifiable secondary transition. We relate these phase transformations to features of the underlying electronic structures of the considered alloys. Overall, this work demonstrates a computationally efficient workflow capturing both chemical ordering and coherent precipitation in multicomponent substitutional alloys, with relevance to the study of phenomena such as precipitation strengthening.