FACET MORPHOLOGY RESPONSE TO NONUNIFORMITIES IN NUTRIENT AND IMPURITYSUPPLY .2. NUMERICAL SIMULATIONS

A model for the evolution of facet morphologies in growth from solutio ns is presented. The numerical model links, for the first time, bulk t ransport of solute and impurities in a solution growth cell with micro scopic interfacial kinetics processes. The macroscopic transport is de alt with as in the 2D model [H. Lin, F. Rosenberger, J.I.D. Alexander and A, Nadarajah, J. Crystal Growth 151 (1995) 153] of a crystallizati on cell used for lysozyme in our laboratory. The microscopic kinetics is incorporated through a meso-scale continuum model of growth step mo tion in response to the interfacial concentration distributions. Local growth step velocities are linearly interpolated from the values obta ined at the grid points of the bulk transport simulation. Experimental ly determined kinetics and transport coefficients are employed. We fin d that the facets remain macroscopically nat, in spite of the lower nu trient and impurity concentrations in the facet center regions. This s tabilization is achieved through the formation of a microscopic depres sion in the facet, with nonuniform vicinal slope (step density). If th e step density in the facet center exceeds a certain value, no further stabilization results on further steepening, and the facet loses its macroscopic morphological stability. This loss of morphological stabil ity depends sensitively on the value of the steps' kinetic coefficient . For pure lysozyme-precipitant solutions, we obtain microscopic depre ssions with a higher slope at the facet center than at the edge. Howev er, with an impurity that impedes step kinetics and is preferentially incorporated into the crystal, the simulations produce microscopic fac et depressions with higher slope at the edge. Impurity depletion at th e interface, due to low initial concentration and/or slow diffusion le ads to mixed shapes, and eventually to shapes typical of growth from p ure solution. Quantitative agreement with facet morphologies observed on lysozyme crystals [P.G. Vekilov and F. Rosenberger 158 (1996) 540] is obtained, assuming overlap of the steps' diffusion fields.