Influence of interface kinetics parameters on the overall fluctuation instability of the interface morphology of deep cell crystal

Abstract

The effect of interface kinetics on the stability of deep cell morphology in directional solidification is studied. By using the multiple variable method and the matching asymptotic methodandby finding the mode solution of the system,the dispersion relation satisfied by the change rate of the disturbance amplitude of the cell-crystal interface is derived , and the quantization condition of the interface morphology is obtained. The results show that there are two global instability mechanisms in the directional solidification system with considering the growth of deep cell crystal with interfacial dynamic parameters : global oscillation instability mechanism and low-frequency instability. The stability analysis shows that the interface stability parameter <inline-formula><tex-math id="M4">\begin{document}$\mathrm{\varepsilon }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20220322_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20220322_M4.png"/></alternatives></inline-formula>is related to the cell relative parameter <inline-formula><tex-math id="M5">\begin{document}$ {\mathrm{\lambda }}_{0} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20220322_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20220322_M5.png"/></alternatives></inline-formula>, and thatthe larger the interface dynamic parameter <inline-formula><tex-math id="M6">\begin{document}$ {M}_{\text{*}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20220322_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20220322_M6.png"/></alternatives></inline-formula>, the larger the stable region of the overall fluctuation instability of the dendrite structure in the overall oscillation modeis.