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Center for Nonlinear Studies |
The dynamics of crystal surfaces at low temperatures is dominated by the motion of steps, which move by the attachment or detachment of adatoms at the step edge. The associated change in free energy given by a small step displacement defines a local step chemical potential and many features of surface dynamics can be understood as arising from gradients in these step chemical potentials. We extend this general perspective to describe the dramatic effects of impurities in solution growth of crystals. Impurities that impede the motion of surface steps typically produce step-bunching instabilities during vapor growth, and reduce the growth rate. However Land, et. al [1] showed that during solution growth of KDP crystals impurities can induce very different behavior. In particular, under appropriate conditions, while single steps are blocked by impurities, large coherent bunches of steps emerge that can move much faster than single individual steps. These "supersteps" dominate the subsequent crystal growth. We introduce a new and general model of impurity effects during crystal growth that describes both steps and impurities using effective chemical potentials. Essential features of model account for the effective impurity strength, the different mechanisms of mass transport during vapor or solution growth, and the effect of step repulsions. The latter can produce an increased driving force on the first step in the bunch and lead to superstep motion. Good agreement with many features of the experiments is found. [1] T. N. Thomas,T. A. Land, W. H. Casey,and J. J. DeYoreo, Phys. Rev. Lett. 92, 216103/1-4 (2004)
Host: Joshua Coe (T-14) / Lawrence Pratt (T-12)