First-principles study of the (Cu x Ni1 − x )3Sn precipitations with different structures in Cu–Ni–Sn alloys

The structural parameters, the formation energies, and the elastic and thermodynamic properties of the (Cu x Ni 1 − x ) 3 Sn phase with different structures are studied by the virtual crystal approximation (VCA) and super-cell (SC) methods. The lattice constants, formation energies, and elastic constants obtained by SC and VCA are generally consistent with each other. It can be inferred that the VCA method is suitable for (Cu x Ni 1 − x ) 3 Sn ordered phase calculation. The calculated results show that the equilibrium structures of Cu 3 Sn and Ni 3 Sn are D0 a and D0 19 respectively. (Cu x Ni 1 − x ) 3 Sn_D0 3 with various components are the metastable phase at temperature of 0 K, just as D0 22 and L1 2 . With the temperature increase, the free energy of the D0 3 is lower than those of D0 22 and L1 2 , and D0 22 and L1 2 eventually turn into D0 3 in the aging process. The (Cu x Ni 1 − x ) 3 Sn_D0 22 is first precipitated in a solid solution because its structure and cell volume are most similar to those of a solid solution matrix. The L1 2 and the D0 22 possess better mechanical stability than the D0 3 . Also, they may play a more important role in the strengthening of Cu–Ni–Sn alloys. This study is valuable for further research on Cu–Ni–Sn alloys.