First principles calculation of elastic and lattice constants of orthorhombic Cu3Sn crystal

Phase-field study of IMC growth in Sn–Cu/Cu solder joints including elastoplastic effects

“…2. For Cu 3 Sn, the values are similar to those of [59] and there is a large difference with the other calculated values from literature, even though An et al [58] have used the same structure as that used in this work. Since there are no experimentally measured values for the stiffness of Cu 3 Sn, we cannot comment further on the accuracy of the calculated values.…”

“…There are some measurements of Young's modulus using compression tests [56] and micro-and nano-indentation [49], but since none of these phases is isotropic, we need measurements of the full stiffness tensor. Ab initio calculations have been performed [57,58,59,60,61] for Cu 3 Sn and Cu 6 Sn 5 , however there is a large spread on the reported data and it is difficult to conclude on which values are most accurate. Therefore, we have performed extra ab initio calculations for the 4 phases, with convergence criteria that are more severe than in any of the previous studies, to guide our selection of appropriate stiffness coefficients for the phase-field simulations.…”

Crystal size and direction dependence of the elastic properties of Cu3Sn through molecular dynamics simulation and nanoindentation testing

“…The calculated polycrystalline Young's modulus is further compared with the published data obtained from nanoindentation testing [12,14], whereas the calculated polycrystalline Poisson's ratio is compared with those measured by the microindentation technique [11] and the pulse-echo technique [13]. Besides, these polycrystalline Young's moduli are also compared with the published theoretical data using first-principles calculations [16,19]. The comparisons are made in Figs.…”

“…For example, Chen et al [16] performed density functional theory (DFT) calculations within the generalized-gradient approximation (GGA) [17] using the Vienna Ab-initio Simulation Package (VASP) [18] to assess the elastic properties of Cu 3 Sn monocrystal. Pang et al [19] carried out first-principles calculations based on the plane wave pseudo-potential method of DFT, combining with GGA, as implemented in the DACAPO™ package [20] to investigate the elastic properties of single crystal Cu 3 Sn. Unfortunately, first-principles calculations are restricted to picoseconds and relatively small system (a few hundred atoms) because of limited computer capacities such as computer speed and memory.…”

Weakening of the Cu/Cu3Sn(100) Interface by Bi Impurities

“…The lattice constants of Cu 3 Sn were also calculated and are presented in Table I; the results of the calculation are 2% larger than the experimental data. [19][20][21] The bulk modulus of Cu 3 Sn was calculated to be 1.087 Mbar, which is approximately 4.6% lower than the experimental data of 1.138 Mbar. 22 Overall, our calculated results for both Cu and Cu 3 Sn are in good agreement with experimental data, which is a prerequisite for applying the methodology and the bulk properties to study the interfacial segregations.…”