First-principles calculations of elastic properties of Cu-Sn crystalline phases

Elastic properties of a solid are closely related to many fundamental solid-state properties. Theoretical calculations on elastic constants are well motivated by the advance in computational technologies, especially when mechanical testing on submicron components is extremely difficult. Elastic constants of a number of anisotropic lattice systems have been calculated based on the density functional theory, and good agreements between computational and experimental results have been found. In this study, we report elastic properties of the Cu-Sn crystalline phases, the ε-Cu
3
Sn and η-Cu
6
Sn
5
, using first-principles calculations. The polycrystalline moduli obtained using the Voigt-Reuss scheme are 134.16 GPa for Cu
3
Sn and 125.98 GPa for Cu
6
Sn
5
. The calculation results show these Cu-Sn crystalline phases have the greatest stiffness along the c direction. In particular, the results reveal the unique anisotropic feature along a and b directions within the Cu
3
Sn superstructure, which cannot be resolved from experiments. Our results also suggest that the least stiffness in the long-period direction is associated with the lattice modulation within the Cu
3
Sn superstructure.