[M-IS13] Interface- and nano-phenomena on crystal growth and dissolution

[MIS13-10] A numerical simulation of crystal growth inhibition by mobile impurities adsorbed on crystal surface

*Yudai Kimura¹, Hitoshi Miura¹ (1.Nagoya City University)

Keywords:crystal growth, impurity, crystal growth inhibition, numerical simulation, phase-field model

It is important to understand the effect of the impurities on crystal growth because small amounts of impurities affect crystal growth significantly. One of the effects of impurities is a pinning effect [1]. The crystal surface has steps with a thickness equivalent to a molecule, which is called “step”, and crystals grow one layer at a time as the step takes in molecules and moves forward. When a particle different from the molecules that make up the crystal (so-called impurity) is adsorbed on the crystal surface, the adsorbed impurity obstructs step passage at the location adsorbed. Most conventional theoretical studies on the pinning mechanism assumed that adsorbed impurities do not move along the crystal surface (immobile impurity). However, in fact, the adsorbed impurities are possible to diffuse along the crystal surface (mobile impurity). Voronkov and Rashkovich [2] theoretically showed that the surface diffusion of the adsorbed impurities can affect the crystal growth inhibition. They discussed the attenuation of the growth inhibition due to the migration of adsorbed impurities pushed by the moving step and the formation of impurity clusters due to the aggregation of the adsorbed impurities in “pockets” of the curved step. However, few numerical studies have been reported on the relationship between the mobility of the adsorbed impurities and the growth inhibition, and on the aggregation process of impurities due to the moving steps.
We have performed numerical calculations of step dynamics considering the surface diffusion of the adsorbed impurities to clarify the effect of their mobility on crystal growth. The numerical model in this study is based on the phase-field model that considers the pinning effect of randomly adsorbing and desorbing impurities on the crystal surface [3]. We considered anisotropy in the surface diffusivity of impurities caused by the interaction with the step. As a result of numerical simulations, we reproduced the process of the impurity clusters formation, in which impurities adsorbed on the crystal surface are pushed by the moving step and swept into the pockets. We showed that the size distribution of the impurity clusters varies greatly with the degree of supersaturation, and that the impurity clusters consisting of several dozen impurities are formed on the crystal surface. Furthermore, we found that the mobility of impurities weakens the growth inhibitory effect at low supersaturation but conversely strengthens it at high supersaturation. This result indicates that the mobility of the adsorbed impurities affects the crystal growth inhibition depending on the degree of supersaturation.

References:
[1] N. Cabrera and D. A. Vermilyea, Proceedings of the International Conference Cooperstown, NY; Wiley (1958) 393 - 410.
[2] V. V. Voronkov and L. N. Rashkovich, Journal of Crystal Growth 144 (1994) 107 -115.
[3] H. Miura, Crystal Growth & Design 16 (2016) 2033 - 2039.