[M-IS18] Interface- and nano-phenomena on crystal growth and dissolution

[MIS18-P04] A numerical simulation of crystal growth inhibition by mobile impurity adsorbed on crystal surface

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

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

Small amounts of impurities affect crystal growth significantly. The impurity-induced growth inhibition is believed to be caused by impurity particles adsorbed on the crystal surface that inhibit the advancement of steps. As a typical mechanism of inhibition to step advancement, a pinning mechanism was proposed [1]. In the pinning mechanism, the adsorbed impurity obstructs step passage at the location adsorbed. This leads that impurity inflects step edge and reduces the step velocity. It has been shown that some experimental data on crystal growth inhibition by impurities can be interpreted by the pinning mechanism [2-4]. Most of conventional theoretical studies on the pinning mechanism assumed that adsorbed impurities do not move until they desorb from there (immobile impurity). However, in fact, the adsorbed impurities are possible to diffuse along the crystal surface (mobile impurity). Voronkov and Rashkovich theoretically suggested that the surface diffusion of adsorbed impurities has an influence on the crystal growth inhibition [5]. They considered that the adsorbed impurities are piled up in front of the moving step and the piled up impurities reinforce the growth inhibition. They also considered that the piled up impurities are accumulated into "pocket" of curved steps to form cluster of impurities. However, they did not reproduce the progress of the impurity clustering, so it is still unknown how the impurity cluster has an impact on the crystal growth inhibition.
This study aims to elucidate the impact of the mobile impurity on the growing crystal by numerically reproducing the step pinning caused by mobile impurities. The numerical model in this study is based on the phase-field model for step dynamics [6,7]. We set up the behavior of adsorbed impurity as follows. The impurity adsorbed on terrace diffuses isotropically. On the other hand, the impurity adsorbed on neighborhood of step, diffuses preferentially in the direction away from the moving step. The free energy of the crystal surface when an impurity is adsorbed near the step was calculated to determine the migration probability for each direction. The surface diffusion of adsorbed impurities was numerically calculated by Monte Carlo method. As a result of numerical simulations, we reproduced moving step while pushing the adsorbed impurities away. We also confirmed that steps were bent by adsorbed impurities, the impurities gathered at "pocket", which is dent of the curved step, and impurity clusters are formed.
In this talk, we will present the effect of the piled up impurities on crystal growth inhibition.

[1] N. Cabrera and D. A. Vermilyea, New York (1958) 393.
[2] S. Choudhury and R. Jayaganthan, Materials Chemistry and Physics 109 325–333.
[3] J. P. Lee-Thorp, A. G. Shtukenberg, and R. V. Kohn, Crystal Growth & Design 20 (2020) 1940–1950.
[4] J. F. Lutsko et al., Crystal Growth & Design 14 (2014) 6129–6134.
[5] V. V. Voronkov and L. N. Rashkovich, Journal of Crystal Growth 144 (1994) 107–115.
[6] H. Miura, Crystal Growth & Design 16 (2016) 2033–2039.
[7] H. Miura, Crystal Growth & Design 15 (2015) 4142–4148.