过冷纯熔体中晶体生长扰动解的可解性条件

Solvability condition of the perturbed solution for crystal growth in undercooled pure melts

在晶体液固界面上考虑动力过冷,对凝固系统控制方程的扰动解进行渐近展开,分别求其零级、一级近似解。推出判别液固平界面稳定性的色散关系,该关系式适合于任意的扰动波长。结果表明,过冷纯熔体中非快速凝固晶体生长的液固界面是不稳定的。

This paper considers kinetic undercooling of the crystal growth on the liquid-solid interface, and makes the asymptotic expansion for the perturbed solution of the governing equations. The zerothorder and the first-order approximation solutions are given. The dispersion relation, which is the stability criterion of the planar interface for all the wavelength of perturbations, is obtained to modify the M-S dispersion relation. It is concluded that the liquid-solid planar interface is not stable for non-rapid solidification in undercooled melts.