Steps behaving badly: Nonlinear dynamics and a terrace-loading instability during solution growth of lysozyme crystals

Yong Il Kwon, Bing Dai, Jeffrey J. Derby

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Article number126852
JournalJournal of Crystal Growth
StatePublished - Nov 1 2022
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported in part by the National Science Foundation, USA grant CTS-0121467 and the University of Minnesota Supercomputing Institute. The authors would like to thank the editors of this Special Issue for the invitation to contribute and M.F. Doherty, whose close reading and many suggestions improved the manuscript. JJD would like to express sincere appreciation to his co-authors for their hard work, insight, innovation, and patience in the long road to publishing these results.

Publisher Copyright:
© 2022 Elsevier B.V.


  • A.1 Mass transfer
  • A1. Growth models
  • A1. Interfaces
  • A1. Morphological stability
  • A2. Growth from solutions
  • B1. Lysozyme


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