The morphological linear stability and non-linear stability of solid-liquid interface of Al-Zn dilute binary alloy were investigated by thermodynamics method. Different stable regions between linear-stability and nonlinear stability of solid-liquid interface were approached

which was calculated by the thermo-dynamic method and the linear binary parameter method

respectively. Interface morphology evolution after solid-liquid interface instability was analyzed

and sub-critical bifurcation range of solid-liquid interface was presented. The results reveal that the calculated results by coupling with thermo-dynamics method are more well in agreement with the experimental ones. Instable region calculated by the method is more than that by linear binary parameters

especially under linear-stability.