Nonlinear Theory on Dynamic Controlling interface Patterns During Solidification of a Dilute Binary Alloy

In non-equilibrium nonlinear region, the nonlinear equations of time dependence of perturbation amplitude at the solid/liquid interface during solidification of a dilute binary alloy are established on the base of assuming that there is local equilibrium at the solid/liquid interface and considering that curvature, temperature and composition at the solid/liquid interface which are related to the perturbation amplitude are nonlinear. As a result, patterns at the solid/liquid interface during solidification process, which is from nonsteady state to steady state can be controlled by these nonlinear equations.