A study of the coarsening in tin/lead solders

This paper presents a model, which is capable to simulate the coarsening process observed during thermo-mechanical treatment of binary tin–lead solders. Fourier transforms and spectral theory are used for the numerical treatment of the thermo-elastic as well as of the diffusion problem encountered during phase separation in these alloys. More specifically, the analysis is based exclusively on continuum theory and, first, relies on the numerical computation of the local stresses and strains in a representative volume element. Second, this information is used in an extended diffusion equation to predict the local concentrations of the constituents of the solder. Besides the classical driving forces for phase separation, as introduced by Fick and Cahn–Hilliard, this equation contains an additional term which links the mechanical to the thermodynamical problem. It connects internal and external stresses, strains, temperature, as well as concentrations and allows for a comprehensive study of the coarsening and aging process