Nonlinear response of layer growth dynamics in the mixed kinetics-bulk-transport regime

Abstract

In situ high-resolution interferometry on horizontal facets of the protein lysozyme reveal that the local growth rate $R$, vicinal slope $p$, and tangential (step) velocity $\nu$ fluctuate by up to 80% of their average values. The time scale of these fluctuations, which occur under steady bulk transport conditions through the formation and decay of step bunches (macrosteps), is of the order of 10 min. The fluctuation amplitude of $R$ increases with growth rate (supersaturation) and crystal size, while the amplitude of the $\nu$ and $p$ fluctuations changes relatively little. Based on a stability analysis for equidistant step trains in the mixed transport-interface-kinetics regime, we argue that the fluctuations originate from the coupling of bulk transport with nonlinear interface kinetics. Furthermore, step bunches moving across the interface in the direction of or opposite to the buoyancy-driven convective flow increase or decrease in height, respectively. This is in agreement with analytical treatments of the interaction of moving steps with solution flow. Major excursions in growth rate are associated with the formation of lattice defects (striations). We show that, in general, the system-dependent kinetic Peclet number, ${\mathrm{Pe}}_k$, i.e., the relative weight of bulk transport and interface kinetics in the control of the growth process, governs the step bunching dynamics. Since ${\mathrm{Pe}}_k$ can be modified 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 crystallization conditions.