Time-dependent interface stability during directional solidification of a single phase alloy (I) Theoretical

The initial transient solute redistribution during directional solidification is systematically investigated by carefully comparing the current theoretical models with experimental results. It is shown that at the transient front solute redistribution generally meets an exponential profile no matter whether there exists liquid convection or pure diffusion in front of the liquid/solid interface. The profile can be described by a unified formula. Based on this, a general time-dependent linear dynamic analysis of the morphological instability of a solidifying planar interface during directional solidification is carried out. It is found that the time-dependent instability solution has the same form as the steady-state solution described by Mullins and Sekerka, but the time-dependent concentration gradient G_C^t, interface velocity V_i and diffusion length l should replace the corresponding steady-state concentration gradient G_C, interface velocity V_i, diffusion length D_L/V in Mullins and Sekerka solution.