Growth of solutal dendrites: A cellular automaton model and its quantitative capabilities

Abstract

A model based on the cellular automaton (CA) technique for the simulation of dendritic growth controlled by solutal effects in the low Peclet number regime was developed. The model does not use an analytical solution to determine the velocity of the solid-liquid (SL) interface as is common in other models, but solves the solute conservation equation subjected to the boundary conditions at the interface. Using this approach, the model does not need to use the concept of marginal stability and stability parameter to uniquely define the steady-state velocity and radius of the dendrite tip. The model indeed contains an expression for the stability parameter, but the process determines its value. The model proposes a solution for the artificial anisotropy in growth kinetics valid at zero and 45° introduced in calculations by the square cells and trapping rules used in previous CA formulations. It also introduces a solution for the calculation of local curvature, which eliminates mesh dependency of calculations. The model is able to reproduce qualitatively most of the dendritic features observed experimentally, such as secondary and tertiary branching, parabolic tip, arms generation, selection and coarsening, etc. Computation results are validated in two ways. First, the simulated secondary dendrite arm spacing (SDAS) is compared with literature values. Then, the predictions of the classic Lipton-Glicksman-Kurz (LGK) theory for steady-state tip velocity are compared with simulated values as a function of melt undercooling. Both comparisons are found to be in very good agreement.