NONLINEAR RESPONSE OF LAYER GROWTH DYNAMICS IN THE MIXED KINETICS-BULK-TRANSPORT REGIME

In situ high-resolution interferometry on horizontal facets of the pro tein lysozyme reveal that the local growth rate R, vicinal slope p, an d tangential (step) velocity v fluctuate by up to 80% of their average values. The time scale of these fluctuations, which occur under stead y bulk transport conditions through the formation and decay of step bu nches (macrosteps), is of the order of IO min. The fluctuation amplitu de of R increases with grow th rate (supersaturation) and crystal size , while the amplitude of the v and p fluctuations changes relatively l ittle. Based on a stability analysis for equidistant step trains in th e mixed transport-interface-kinetics regime, we argue that the fluctua tions originate from the coupling of hulk transport with nonlinear int erface kinetics. Furthermore, step bunches moving across the interface in the direction of or opposite to the buoyancy-driven convective flo w increase or decrease in height, respectively. This is in agreement w ith analytical treatments of the interaction of moving steps with solu tion flow. Major excursions in growth rate are associated with the for mation of lattice defects (striations). We show that, in general, the system-dependent kinetic Peclet number, Pe(k), i.e., the relative weig ht of bulk transport and interface kinetics in the control of the grow th process, governs the step bunching dynamics. Since Pe(k) can be mod ified by either forced solution flow or suppression of buoyancy-driven convection under reduced gravity, this model provides a rationale for the choice of specific transport conditions to minimize the formation of compositional inhomogeneities under steady bulk nutrient crystalli zation conditions.