Traveling waves of step density and solution supersaturation in the assigned diffusion layer thickness model of step bunching

Bredikhin, V. I.; Malshakova, O. A.; Yunakovsky, A. D.

doi:10.1016/j.jcrysgro.2009.12.015

Cited by 5 publications

(8 citation statements)

References 18 publications

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“…From numerical simulations of the nonlinear equation, a quasi-regular array of high step density appears. The form of the array is similar to that of bunches observed in the experiments [6][7][8].…”

Section: Introductionsupporting

confidence: 67%

“…By using their model, we probably find the effect of the bulk diffusion filed, which is not rigorously taken into account in our simplified model. In previous studies [6,7], the step bunching occurs without flow. In their model, however, effect of the velocity of the step motion to the diffusion equation is taken into account.…”

Section: Discussionmentioning

confidence: 96%

“…From the linear stability analyses and numerical studies [3][4][5], a growing vicinal face is unstable for a long-wavelength fluctuation owing to the step-down flow. Bredikhin and coworkers [6,7] derived the nonlinear evolution equation of step density and studied the behavior of the unstable vicinal face. From numerical simulations of the nonlinear equation, a quasi-regular array of high step density appears.…”

Section: Introductionmentioning

confidence: 99%

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Step bunching induced by flow in solution

Sato

2011

Journal of Crystal Growth

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By carrying out Monte Carlo simulations, we study step bunching induced by flow in solution during dissolving. For simplicity, we assume that steps are straight and express an array of steps as dots on one-dimensional vicinal face. We consider a two square lattice to represent the diffusion field in a solution. The diffusion of atoms in a solution is expressed as the hopping of atoms on lattice sites. During dissolving, the step bunching occurs in the case of step-up flow. In an early stage, the width of the fluctuation of step distance, w, increases with time as t α . The exponent α is equal to 1/2 in the initial stage. Then, α decreases and is approximately given by 1/4. In a late stage, the width w is saturated. The saturated value of w increases with the strength of flow.

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Section: Introductionsupporting

confidence: 67%

Section: Discussionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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Step bunching induced by flow in solution

Sato

2011

Journal of Crystal Growth

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“…[1][2][3][4] Chernov and coworkers theoretically studied the stability of a vicinal face. [5][6][7] When a flow in a solution is in the step-down direction, the vicinal face growing from a solution is unstable.…”

Section: Introductionmentioning

confidence: 99%

“…Bredikhin and co-workers studied the time evolution of the vicinal face, and numerically showed the formation of an equidistant train of bunches. 3,4) In previous studies, 3, 5-7) the step distance was assumed to be so high that the vicinal face was treated as the linear sink of atoms. The motion of each steps during step bunching was not investigated.…”

Section: Introductionmentioning

confidence: 99%

Effect of Flow in Solution on Motion of Steps during Solution Growth

Inaba

Sato

2011

J. Phys. Soc. Jpn.

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We study step bunching on a vicinal face in solution growth. Assuming that steps are straight, we consider a two-dimensional diffusion filed to represent a solution and a onedimensional vicinal face. The steps are expressed as dots in the vicinal face. Taking account of a flow in a solution, we numerically solve the diffusion equation and the Navier-Stokes equation in the solution, and determine step velocities. If a flow in a solution is absent or is in the step-up direction, a vicinal face is stable. When the flow is in the step-down direction, the vicinal face is unstable and step bunching occurs. In the initial stage, small bunches are formed. Then, owing to the coalescence of small bunches, large bunches are formed.

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2D mesoscale colloidal crystal patterns on polymer substrates

Bredikhin

Bityurin

2018

Mater. Res. Express

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Traveling waves of step density and solution supersaturation in the assigned diffusion layer thickness model of step bunching

Cited by 5 publications

References 18 publications

Step bunching induced by flow in solution

Step bunching induced by flow in solution

Effect of Flow in Solution on Motion of Steps during Solution Growth

2D mesoscale colloidal crystal patterns on polymer substrates

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