A Higher Gradient Theory of Multiphase Solid Mixtures and its Application to Lead-Free Solder Micro-Morphology

In order to analyze the micro-morphology evolution in today's (lead-free) solders we present a theory of multi- component heterogeneous solid mixtures based on fundamental thermodynamic principles. We derive an extended diffusion equation, which allows to predict the diffusion-induced phase separation and coarsening process within solids under the presence of local (thermo-)mechanical strains on a theoretical basis. As an example we specialize to the lead-free binary case study alloy Ag-Cu and simulate the spinodal decomposition and coarsening process. We end with a model for the formation and growth of pores within the solder material, which is particularly driven by the so-called Kirkendall effect in the different phases of the composite material.