Computer modeling of the coarsening process in tin–lead solders

Abstract

The temporal progress of phase separation and coarsening observed in eutectic tin/lead (SnPb) solders was investigated using computer modeling. The modeling framework is based on an extended diffusion equation of the phase-field model type that includes classical Fickean diffusion, effects of surface tensions according to the Cahn–Hilliard formalism, as well as diffusive morphology changes due to local thermo-mechanical stresses and strains. The numerical solution of the extended diffusion equation for a eutectic tin/lead microstructure is performed by means of discrete Fourier transforms (DFTs). In particular, a one-dimensional computer modeling procedure will be presented in detail. The phase separation and the coarsening process are discussed, and it is investigated how these depend on different initial conditions and on different temperature levels. The results are in fair agreement with experimental observation. Moreover, the weight and volume fractions of the α- and β-phase, as well as an average “α-particle size” are determined numerically and their temporal development is studied.