Selection of additive elements for lead-free solders by use of a Kriging-based method for efficiently searching materials

A Kriging-based method for efficiently searching materials was used to select additive elements in lead-free solders that are effective for suppressing the grain-boundary diffusion, which is the cause of smaller breaking elongation than lead-contained solders. By using the idea of the L9-orthogonal-array design methodology, we selected nine combinations of additive elements, and investigated the dependence of diffusion coefficients on four parameters (the atomic radius of the 1st additive, the cohesive energy of the 1st additive, the atomic radius of the 2nd additive, and the cohesive energy of the 2nd additive). The diffusion coefficients were calculated by using molecular-dynamics simulations. The calculation results showed that the diffusion can be suppressed when the atomic radii of the 1st and 2nd additives are close to that of tin (Sn), and when the cohesive energies of the 1st and 2nd additives are smaller than that of tin. According to these conditions, we found that two additives selected from silver (Ag), indium (In), and bismuth (Bi) are effective for suppressing the diffusion and for increasing the breaking elongation. Because these results were confirmed by tensile deformation test, the Kriging-based method is considered to be practical for effectively searching materials.