First-principles study of the (CuxNi1 − x)3Sn precipitations with different structures in Cu–Ni–Sn alloys**Project supported by the National Key Research and Development Program of China (Grant No. 2016YFB0301402), the Project of Innovation-Driven Plan in Central South University, and the State Key Laboratory of Powder Metallurgy, Central South University, Changsha, China.

Abstract

The structural parameters, the formation energies, and the elastic and thermodynamic properties of the (CuxNi1 − x)3Sn 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 (CuxNi1 − x)3Sn ordered phase calculation. The calculated results show that the equilibrium structures of Cu3Sn and Ni3Sn are D0a and D019 respectively. (CuxNi1 − x)3Sn_D03 with various components are the metastable phase at temperature of 0 K, just as D022 and L12. With the temperature increase, the free energy of the D03 is lower than those of D022 and L12, and D022 and L12 eventually turn into D03 in the aging process. The (CuxNi1 − x)3Sn_D022 is first precipitated in a solid solution because its structure and cell volume are most similar to those of a solid solution matrix. The L12 and the D022 possess better mechanical stability than the D03. 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.