Theory of Impurity Induced Step Pinning and Recovery in Crystal Growth from Solutions

Ranganathan, Madhav; Weeks, John D.

doi:10.1103/physrevlett.110.055503

Cited by 18 publications

(17 citation statements)

References 16 publications

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“…Step bunches we observe in our simulations consist of single steps that have size of one unit cell, but also of macrosteps with size of multiple unit cells. Such formations are seen in experiments [24] and their time evolution remains subject of studies [25,26]. Macrosteps are created during the surface evolution process because there is no step-step repulsion incorporated into the model.…”

Section: Introductionmentioning

confidence: 96%

Step bunching and macrostep formation in 1D atomistic scale model of unstable vicinal crystal growth

Krzyżewski

Załuska‐Kotur

Krasteva

et al. 2017

Journal of Crystal Growth

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Abstract. We devise a new 1D atomistic scale model of vicinal growth based on Cellular Automaton. In it the step motion is realized by executing the automaton rule prescribing how adatoms incorporate into the vicinal crystal. Time increases after each rule execution and then n DS diffusional updates of the adatoms are performed. The increase of n DS switches between the diffusion-limited (DL, n DS =1) and kinetics-limited (KL, n DS >> 1) regimes of growth. We study the unstable step motion by employing two alternative sources of instability -biased diffusion and infinite inverse Ehrlich-Schwoebel barrier (iiSE). The resulting step bunches consist of steps but also of macrosteps since there is no step-step repulsion incorporated explicitly into the model. This complex pattern formation is quantified by studying the time evolution of the bunch size N and macrostep size N m in order to find the proper parameter combinations that rescale the time and thus to obtain the full time-scaling relations including the pre-factors. For the case of biased diffusion the time-scaling exponent β of N is 1/2 while for the case of iiSE it is 1/3. In both cases the time-scaling exponent β m of N m is ~3β/4 in the DL regime and 3β/5 in the KL one.

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Section: Introductionmentioning

confidence: 96%

Step bunching and macrostep formation in 1D atomistic scale model of unstable vicinal crystal growth

Krzyżewski

Załuska‐Kotur

Krasteva

et al. 2017

Journal of Crystal Growth

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“…In reality, steps do not display the smooth curvatures as assumed in their simplified model, but rather are discrete, atomistic objects subject to fluctuations. This was already realized by Frank [12] and explored further by van Enckevort and van den Berg [9] and more recently by Ranganathan and Weeks who developed a coarse grained terrace-step-kink model to study impurity induced step bunching [10,11].…”

mentioning

confidence: 94%

“…Such a dead zone occurs for a specific class of impurities, namely, those that are firmly adsorbed onto the surface with (near-) infinite residence times (Dynamic residues with finite residence times can in extreme cases lead to kinetic arrest, but only at very high concentrations.) The moments leading up to this growth cessation event have been the subject of intense study [4][5][6][7][8][9][10][11] and are thought to be well understood. The first theoretical description was developed as early as 1958 by Cabrera and Vermilyea (CV) [3], whose core views on the subject still persist today.…”

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confidence: 99%

Mesoscopic Impurities Expose a Nucleation-Limited Regime of Crystal Growth

et al. 2015

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Nanoscale self-assembly is naturally subject to impediments at the nanoscale. The recently developed ability to follow processes at the molecular level forces us to resolve older, coarse-grained concepts in terms of their molecular mechanisms. In this Letter, we highlight one such example. We present evidence based on experimental and simulation data that one of the cornerstones of crystal growth theory, the Cabrera-Vermilyea model of step advancement in the presence of impurities, is based on incomplete physics. We demonstrate that the piercing of an impurity fence by elementary steps is not solely determined by the Gibbs-Thomson effect, as assumed by Cabrera-Vermilyea. Our data show that for conditions leading up to growth cessation, step retardation is dominated by the formation of critically sized fluctuations. The growth recovery of steps is counter to what is typically assumed, not instantaneous. Our observations on mesoscopic impurities for lysozyme expose a nucleation-dominated regime of growth that has not been hitherto considered, where the system alternates between zero and near-pure velocity. The time spent by the system in arrest is the nucleation induction time required for the step to amass a supercritical fluctuation that pierces the impurity fence.

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“…From Monte Carlo simulations, Weeks and co-workers [5,8,9] were able to study twodimensional step motion and showed that mesh-like step bunch patterns are formed by step bunching. In their model, the effect of impurities is taken into account as a reduction in the probability of step advancing.…”

Section: Introductionmentioning

confidence: 99%

Effect of the Surface Diffusion and Evaporation of Impurities on Step Bunching Induced by Impurities

Sato

2019

J. Phys. Soc. Jpn.

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We consider a vicinal face, where atoms and impurities impinge and evaporate to a vapor phase, to study how the surface diffusion and evaporation of impurities affect step bunching induced by impurities. When the lifetime of impurities on the vicinal face τ imp is long and the surface diffusion of impurities is neglected, the step bunches induced by impurities are tight. When τ imp decreases, the size of the step bunches, which means the number of steps in the bunches, decreases but the separation of single steps from bunches does not occur. When we take into account fast surface diffusion of impurities, the separation and collision between single steps and step bunches occur repeatedly.

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Theory of Impurity Induced Step Pinning and Recovery in Crystal Growth from Solutions

Cited by 18 publications

References 16 publications

Step bunching and macrostep formation in 1D atomistic scale model of unstable vicinal crystal growth

Step bunching and macrostep formation in 1D atomistic scale model of unstable vicinal crystal growth

Mesoscopic Impurities Expose a Nucleation-Limited Regime of Crystal Growth

Effect of the Surface Diffusion and Evaporation of Impurities on Step Bunching Induced by Impurities

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