过冷纯熔体中晶体生长平界面的稳定性分析

Stability analysis of the planar interface for crystal growth in undercooled pure melts

具有匀速运动平直界面的一维凝固系统,一经扰动其界面将不再为平面。Mullins-Sekerka在假定扰动波长远远小于热扩散长度与液固界面满足局部平衡条件的基础上,推出了M-S色散关系。在界面上也存在着动力学的作用,即界面的稳定性也依赖于动力过冷。文章在界面上考虑动力学影响,应用渐近分析理论继续分析过冷纯熔体液固界面的稳定性。结果表明,非快速凝固系统的液固界面不会绝对稳定。

The kinetic effect of crystal growth on the liquid-solid interface is considered. By using the asymptotic analysis method, the stability of the liquid-solid planar interface in unsteady solidification is studied. It is showed that, if the crystal growth velocity is not too fast, the liquid-solid planar interface can not be absolutely stable. A planar interface which is moving with a constant velocity in solidification is not the planar by imposing an infinitesimal perturbation. Mullins and Sekerka gave an M-S dispersion relation based on that the wavelength of perturbations was much smaller than the thermal diffusion length and the liquid-solid interface met the local equilibrium condition. There is the kinetic effect on the interface whose stability also relies on the kinetic undercooling. This paper investigates the stability of the interface in undercooled pure melts. It is concluded that the liquid-solid planar interface can not be absolutely stable for non-rapid solidification.