The phase-field method: Simulation of alloy dendritic solidification during recalescence

An overview of the phase-field method for modeling solidification is given and results for nonisothermal alloy dendritic growth are presented. By defining a ''phase-field'' variable and a corresponding governing equation to describe the state (solid or liquid) in a material as a function of position and time, the diffusion equations for heat and solute can be solved without tracking the liquid-solid interface. The interfacial regions between liquid and solid involve smooth, but highly localized variations of the phase-field variable and the composition. Simple finite-difference techniques on a uniform mesh can be used to treat the evolution of complex growth patterns. However, large-scale computations are required. The method has been applied to a variety of problems, including thermally driven dendritic growth in pure materials, solute-driven isothermal dendritic growth in alloys, eutectic growth (all at high supercoolings or supersaturations), solute trapping at high velocity, and coarsening of liquid-solid mixtures. To include thermal effects in solute-driven dendritic growth in alloys, a simplified approach is presented here that neglects the spatial variation of temperature in the computational domain but provides for changes with time and thus includes recalescence. Growth morphologies and solute patterns in the liquid and solid obtained for several values of an imposed heat flux are compared to results for isothermal growth.