TY - JOUR
T1 - Steps behaving badly
T2 - Nonlinear dynamics and a terrace-loading instability during solution growth of lysozyme crystals
AU - Kwon, Yong Il
AU - Dai, Bing
AU - Derby, Jeffrey J.
N1 - Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/11/1
Y1 - 2022/11/1
N2 - A detailed finite-element model for step motion during solution crystal growth is applied to analyze the nonlinear growth dynamics of lysozyme. Insights from this model are applied to develop a much simpler, lumped-parameter model to describe step motion for this growth system. Bifurcation analysis applied to the lumped-parameter model demonstrates a critical bulk supersaturation at which an equidistant step train loses stability, via a supercritical Hopf bifurcation, to a stable, time-periodic system that exhibits a single step bunch. As supersaturation is further increased, additional bifurcations lead to more complicated behaviors, such as quasi-periodic patterns, multiple step bunches, and period doubling. The initial instability of the step train arises from the dynamics of terrace loading due to slow adsorption and step incorporation kinetics under high bulk supersaturation. These effects cause a time lag in the surface supersaturation level with respect to changes in terrace width, producing a phase shift of the surface supersaturation field in the direction of step motion and driving the formation of step bunches.
AB - A detailed finite-element model for step motion during solution crystal growth is applied to analyze the nonlinear growth dynamics of lysozyme. Insights from this model are applied to develop a much simpler, lumped-parameter model to describe step motion for this growth system. Bifurcation analysis applied to the lumped-parameter model demonstrates a critical bulk supersaturation at which an equidistant step train loses stability, via a supercritical Hopf bifurcation, to a stable, time-periodic system that exhibits a single step bunch. As supersaturation is further increased, additional bifurcations lead to more complicated behaviors, such as quasi-periodic patterns, multiple step bunches, and period doubling. The initial instability of the step train arises from the dynamics of terrace loading due to slow adsorption and step incorporation kinetics under high bulk supersaturation. These effects cause a time lag in the surface supersaturation level with respect to changes in terrace width, producing a phase shift of the surface supersaturation field in the direction of step motion and driving the formation of step bunches.
KW - A.1 Mass transfer
KW - A1. Growth models
KW - A1. Interfaces
KW - A1. Morphological stability
KW - A2. Growth from solutions
KW - B1. Lysozyme
UR - http://www.scopus.com/inward/record.url?scp=85137677519&partnerID=8YFLogxK
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U2 - 10.1016/j.jcrysgro.2022.126852
DO - 10.1016/j.jcrysgro.2022.126852
M3 - Article
AN - SCOPUS:85137677519
SN - 0022-0248
VL - 597
JO - Journal of Crystal Growth
JF - Journal of Crystal Growth
M1 - 126852
ER -