Directional Growth of a Faceted Smectic B Plastic Crystal
Directional solidification of metals, alloys and organic materials (including plastic crystals and liquid crystals) has been intensively studied over the past several years. Most of the experiments have been performed on non-faceting materials, for which the “solid-liquid” interface is atomically rough. It is well known that the front is unstable above a critical growth velocity and that the cellular bifurcation is either subcritical or supercritical depending upon the material. This instability results from a competition between the destabilizing effect of the diffusion field and the stabilizing effects of both the temperature gradient and the surface tension. The linear stability analysis of this problem was first carried out by Mullins and Sekerka1 in 1964. This calculation is the fundamental key of our understanding of this instability. Later, Woolkind and Segel2 and Caroli et al 3 did a weakly non-linear bifurcation analysis. They showed that the nature of the bifurcation depends on the value of the solute partition coefficient. This prediction has been well verified experimentally4. The current problem is to understand the non-linear evolution of deep-cell arrays and their dynamics. So far, there is no unified theory describing the wavelength selection as well as the cell to dendrite transition.
KeywordsHopf Bifurcation Critical Velocity Directional Solidification Linear Stability Analysis Equilibrium Shape
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