FREE-CONVECTION AND SURFACE KINETICS IN CRYSTAL-GROWTH FROM SOLUTION

As a crystal grows from solution, there is ordinarily a boundary layer depleted in solute, which forms at the crystal-solution interface. Wh en the normal to the growing crystal surface is oriented in any direct ion other than parallel to gravity, the boundary layer is set into mot ion by the force of buoyancy. Using a similarity transformation and a boundary layer approximation, we have solved the Navier-Stokes equatio n and the equation for convective diffusion for a crystal in the form of a flat plate growing with normal perpendicular to gravity. Paramete rs in the theory include solute concentration, c(0), and diffusion coe fficient, D; solution shear viscosity, mu, mass density, rho, and loga rithmic density derivative with respect to concentration, alpha; cryst al solubility, c(s), height, h, and linear growth rate, k(G); the spec ific rate, k (sticking coefficient), of the reaction which transfers m olecules from the solution to the crystal and the kinetic order, n, of this reaction; and the acceleration due to gravity, g. We find these parameters to be related by the equation log[1-Sh/a (Sc) (1/4)(Gr) (1/ 4)phi(s)(1/4)]= (1/n) log[a(5/4) (n)(D/hkc (n-1)(0))(Sc) (1/4)(Gr) (1/ 4)] + [(5/4-n)/n]log phi(s), where a=0.9, Sh=k(G)h/D, Sc=mu/rho D, Gr= g alpha h(3)rho(2)/4 mu(2), and phi(s)=(c(0)-c(s))/c(0). Given a knowl edge of the solution physical properties, if Sh is measured as a funct ion of phi(s) and the results plotted in accord with the above equatio n, both n and k can be determined. (C) 1998 American Institute of Phys ics.