Pg. Vekilov et al., NONLINEAR RESPONSE OF LAYER GROWTH DYNAMICS IN THE MIXED KINETICS-BULK-TRANSPORT REGIME, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 54(6), 1996, pp. 6650-6660
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.