A numerical study on pattern selection in crystal growth by using anisotropic lattice Boltzmann-phase field method

Pattern selection during crystal growth is studied by using the anisotropic lattice Boltzmann-phase field model. In the model, the phase transition, melt flows, and heat transfer are coupled and mathematically described by using the lattice Boltzmann (LB) scheme. The anisotropic streaming-relaxation operation fitting into the LB framework is implemented to model interface advancing with various preferred orientations. Crystal pattern evolutions are then numerically investigated in the conditions of with and without melt flows. It is found that melt flows can significantly influence heat transfer, crystal growth behavior, and phase distributions. The crystal morphological transition from dendrite, seaweed to cauliflower-like patterns occurs with the increase of undercoolings. The interface normal angles and curvature distributions are proposed to quantitatively characterize crystal patterns. The results demonstrate that the distributions are corresponding to crystal morphological features, and they can be therefore used to describe the evolution of crystal patterns in a quantitative way.