Diffusion and convection in vapor crystal growth

Abstract

The dynamics of diffusion-limited vapor growth are analyzed for three cases: growth of microscopic crystallites immediately following nucleation, growth of crystals when vapor transport from the source is due entirely to diffusion, and growth of crystals when vapor transport is increased by natural or forced convection. In the convection case the rate-determining step is the diffusion of the vapor through a boundary layer in the gas phase adjacent to the growth interface. Forced convection decreases the thickness of this boundary layer and leads to rapid growth. It is shown that in this case the growth rate is proportional to the first power of the concentration difference between the source and the interface, and to the square root of carrier gas velocity. The growth rate expression contains one adjustable constant which depends on the geometry of the system. The stability of the growth interface is analyzed in terms of constitutional supercooling. It is shown that a heat source must be introduced between the source and the growth interface in order for a plane interface to be stable. The use of forced convection permits the introduction of a virtual heat source at the outer edges of the boundary layer. Crystals of iodine and camphor have been grown in a system in which forced convection makes it possible to control both carrier gas velocity and the temperature gradient at the interface. The observed growth rates exhibit the calculated dependence on concentration difference and gas velocity, provided that the interface gradient is suitably adjusted for smooth growth. A maximum smooth growth rate of 4 mm/hr was achieved for iodine and camphor, a value approaching rates of growth from the melt.