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Diffusion-controlled growth rate of stepped interfaces.

P Saidi1, J J Hoyt1

  • 1Department of Materials Science and Engineering, McMaster University, Hamilton, Ontario, Canada.

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Summary
This summary is machine-generated.

This study numerically models crystal growth rates on stepped surfaces using the boundary element method (BEM). It reveals how step spacing and fluid diffusion influence growth and identifies conditions for step bunching instability.

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Area of Science:

  • Materials Science
  • Surface Science
  • Computational Physics

Background:

  • Crystalline surfaces and interfaces often feature mobile steps and immobile terraces.
  • A complete theoretical understanding of growth rates for such step-terraced structures remains elusive.

Purpose of the Study:

  • To numerically compute concentration profiles and growth rates for step-terraced interfaces.
  • To investigate the phenomenon of step bunching instability during crystal growth.

Main Methods:

  • Boundary Element Method (BEM) for numerical computation of fluid phase concentration profiles.
  • Analysis of step motion controlled by diffusion through a fluid boundary layer.
  • Matched asymptotic expansion for analytic solutions in stagnant liquid scenarios.

Main Results:

  • BEM calculations provide growth rates for varying step spacing, supersaturation, and boundary layer widths.
  • Step bunching instability is predicted for sufficiently large perturbations in step position (without elastic strain).

Conclusions:

  • The study offers a theoretical framework for understanding growth kinetics on stepped surfaces.
  • Numerical and analytical methods elucidate the mechanisms governing crystal growth and step bunching.