Orientation selection of equiaxed dendritic growth by three-dimensional cellular automaton model

A three-dimensional (3-D) adaptive mesh refinement (AMR) cellular automata (CA) model is developed to simulate the equiaxed dendritic growth of pure substance. In order to reduce the mesh induced anisotropy by CA capture rules, a limited neighbor solid fraction (LNSF) method is presented. It is shown that the LNSF method reduced the mesh induced anisotropy based on the simulated morphologies for isotropic interface free energy. An expansion description using two interface free energy anisotropy parameters (ε ₁, ε ₂) is used in the present 3-D CA model. It is illustrated by present 3-D CA model that the positive ε ₁ favors the dendritic growth with the 〈100〉 preferred directions, and negative ε ₂ favors dendritic growth with the 〈110〉 preferred directions, which has a good agreement with the prediction of the spherical plot of the inverse of the interfacial stiffness. The dendritic growths with the orientation selection between 〈100〉 and 〈110〉 are also discussed using the different ε ₁ with ε ₂=-0.02. It is found that the simulated morphologies by present CA model are as expected from the minimum stiffness criterion.