Crystallization stability during capillary shaping: I. General theory of capillary and thermal stability

When shaped crystals are grown from the melt, their cross section is determined by the shape of the melt column. The crystal radius and the height of the crystallization front may vary independently, i.e. we deal with a system of two degrees of freedom. The stability of this system is investigated by Liapunov's method. The concepts of capillary and thermal stabilities are introduced. The stability of the system depends on the shape of the pulled crystal, the boundary conditions for the melt column, and the thermal conditions during pulling.