Phase-field simulations of non-isothermal binary alloy solidification

A phase-field method for two-dimensional simulations of binary alloy solidification is studied. Phase-field equations that involve both temperature and solute redistribution are formulated. The equations are solved using the finite element method with triangular elements on unstructured meshes, which are adapted to the solution. Dendritic growth into a supersaturated melt is simulated for two temperature regimes: (a) the temperature is prescribed on the boundary of the computational domain; and (b) the heat is extracted through the domain boundary at a constant rate. In the former regime the solute redistribution is compared with the one given by an isothermal model. In the latter case the influence of the size of the computational domain and of the heat extraction rate on dendritic structure is investigated. It is shown that at high cooling rates the supersaturation is replaced by thermal undercooling as the driving force for growth.