Emergence of step flow from an atomistic scheme of epitaxial growth in 1+1 dimensions.

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2015-03

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Lu, Jianfeng
Liu, Jian-Guo
Margetis, Dionisios

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Abstract

The Burton-Cabrera-Frank (BCF) model for the flow of line defects (steps) on crystal surfaces has offered useful insights into nanostructure evolution. This model has rested on phenomenological grounds. Our goal is to show via scaling arguments the emergence of the BCF theory for noninteracting steps from a stochastic atomistic scheme of a kinetic restricted solid-on-solid model in one spatial dimension. Our main assumptions are: adsorbed atoms (adatoms) form a dilute system, and elastic effects of the crystal lattice are absent. The step edge is treated as a front that propagates via probabilistic rules for atom attachment and detachment at the step. We formally derive a quasistatic step flow description by averaging out the stochastic scheme when terrace diffusion, adatom desorption, and deposition from above are present.

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10.1103/PhysRevE.91.032403

Publication Info

Lu, Jianfeng, Jian-Guo Liu and Dionisios Margetis (2015). Emergence of step flow from an atomistic scheme of epitaxial growth in 1+1 dimensions. Phys Rev E Stat Nonlin Soft Matter Phys, 91(3). p. 032403. 10.1103/PhysRevE.91.032403 Retrieved from https://hdl.handle.net/10161/14096.

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Scholars@Duke

Lu

Jianfeng Lu

Professor of Mathematics

Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science, machine learning, and other related fields.

More specifically, his current research focuses include:
High dimensional PDEs; generative models and sampling methods; control and reinforcement learning; electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis.

Liu

Jian-Guo Liu

Professor of Physics

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