Multiphase field modelling of alloy solidification

We present an approach to alloy solidification modelling that incorporates binary interface energies in a manner that correctly reproduces the associated theoretical angles at triple junctions in eutectic solidification. We find that simply applying the principle that the correct binary junction behaviour is recovered when only two phases are present is insufficient. Previous research (Toth \cite{Toth2016}) recommends a modification of the surface energy by adding an energy barrier at the triple junction, and we explore alternative models that would benefit from this approach. The main approach we recommend here, though, is to extend the minimal model of Folch and Plapp \cite{folch2003,FolchPlapp2005}, which, without modification, is limited to $120^\circ$ junction angles. This is achieved by a linear transformation of this formulation, and facilitated by an analytical multiphase solution presented here for the first time.