Journal of Crystal Growth 84 (1987) 509—514 509 North-Holland, Amsterdam MASS TRANSFER PROCESSES IN KDP CRYSTAL GROWTH FROM SOLUTIONS * V.1. BREDIKHIN, V.P. ERSHOV, V.V. KOROLIKHIN, V.N. LIZYAKINA, S.Yu. POTAPENKO and N.y. KHLYUNEV Institute of Applied Physics, Academy of Sciences of the USSR, Gorky, USSR Received 2 October 1986; manuscript received in final form 27 March 1987 The kinetics of KDP crystal growth from aqueous solutions at free convection have been investigated experimentally using a laser interference-polarization technique. Growth at free convection is compared with growth at forced convection. The effect of Al 3 ± and Fe3 + impurities on the crystal growth rate and singular points of kinetic curves was studied. Supersaturations at which the crystal grows in the diffusion or in the kinetic regime are defined. The energy of impurity adsorption is estimated. 1. Introduction concentration at the saturation point. Combining (1) and (2), we obtain the well-known expression Mass transfer from a bulk solution to a grow- for the growth rate: ing surface and incorporation of atoms into the crystal lattice are the basic processes which define R = C 00 — C0 (3) 1/b + p6/D the kinetics of crystal growth from solutions. If the boundary condition for salt concentra- With free convection, the thickness ~ of the tion C~on the crystal surface is linear (for exam- diffusion layer in (1) depends on the growth rate. ple, C~ = constant or j = — D 0C5/8n = contant), Analysis of the orders of magnitude of the terms then mass transfer processes in the absence of in the Navier—Stokes and diffusion equations for natural convection are described as follows [1]: the case of layer-by-layer growth of vertical faces R = —~-(c~~ — C5), shows that 3 depends on R and x: ~2/3D7/3x\’/ 5 g 8po (la) where R is the normal growth rate of the crystal ~ (x) ( ypR ) ‘ ~ = face, D is the diffusion coefficient, C 5 and C00 are the concentrations of solution on the crystal where v is the kinematic viscosity, p0 is the solu- surface and in the bulk solution, respectively, ~ is tion density, g is the acceleration due to gravity the crystal density, and ~ is the effective thickness and x is the vertical coordinate along the face. of the diffusion layer independent of growth rate. In any case, even with a more complicated Incorporation processes can be written for sim- relation between R and (C5 — C0), the depen- plicity as dence of R on zlC in (2) is smooth. However, such smooth dependences are far from being always R = b(C~ — C0), (2) observed. The largest deviations from the type (3) relation have been observed for the growth of a where b is the kinetic coefficient and C0 is the prismatic (100) face of a KDP crystal, with R(~C) depending on the impurity concentration in the * The results of this work were presented at the Eighth Inter- solution. We find it interesting to study physical national Conference on Crystal Growth (ICCG-8), York, mechanisms involved in kinetic dependences in UK, July 1986. the presence of impurities in the solution. 0022-0248/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)