Effects of physical parameters on the cell-to-dendrite transition in directional solidification

A quantitative cellular automaton model is used to study the cell-to-dendrite transition (CDT) in directional solidification. We give a detailed description of the CDT by carefully examining the influence of the physical parameters, including: the Gibbs–Thomson coefficient Γ, the solute diffusivity D_l, the solute partition coefficient k₀, and the liquidus slope m_l. It is found that most of the parameters agree with the Kurz and Fisher (KF) criterion, except for k₀. The intrinsic relations among the critical velocity V_cd, the cellular primary spacing λ_{c, max}, and the critical spacing λ_cd are investigated.