Thermomigration in SnPb solders: Material model

In this work we provide an extended Cahn-Hilliard equation describing separation processes in binary alloys affected by temperature gradients coupled with a heat equation. The three important material parameters used in the model, namely the Gibbs' configurational free energy density, the mobility of atoms and their heats of transport, are modelled as sufficiently smooth function in mole fraction and absolute temperature for Sn-Pb alloys. The model consists of two nonlinear fourth order partial differential equations. Consequently, the variational formulation of the problem mandates approximation functions which are at least C1-continuous. In order to fulfil this requirement, a NURBS based finite element (FE) scheme is employed. Here we provide only a brief overview of the used discretization techniques. Details on the numerical treatment of the model, in particular on the implementation of essential boundary conditions within NURBS spaces, can be found in our work. Concluding computational studies of two- and three dimensional thermomigration events within Sn-Pb alloys will demonstrate the quality of our model.