Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method

A comprehensive model is developed for solving the heat and solute diffusion equations during solidification that avoids tracking the liquid—solid interface. The bulk liquid and solid phases are treated as regular solutions and an order parameter (the phase field) is introduced to describe the interfacial region between them. Two-dimensional computations are performed for ideal solutions and for dendritic growth into an isothermal and highly supersaturated liquid phase. The dependence upon various material and computational parameters, including the approach to conventional sharp interface theories, is investigated. Realistic growth patterns are obtained that include the development, coarsening, and coalescence of secondary and tertiary dendrite arms. Microsegregation patterns are examined and compared for different values of the solid diffusion coefficient.