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Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model

Publication ,  Journal Article
Liu, JG; Lu, J; Margetis, D; Marzuola, JL
Published in: Physica D: Nonlinear Phenomena
June 1, 2019

In the absence of external material deposition, crystal surfaces usually relax to become flat by decreasing their free energy. We study analytically an asymmetry in the relaxation of macroscopic plateaus, facets, of a periodic surface corrugation in 1+1 dimensions via a continuum model below the roughening transition temperature. The model invokes a continuum evolution law expressed by a highly degenerate parabolic partial differential equation (PDE) for surface diffusion, which is related to the nonlinear gradient flow of a convex, singular surface free energy with a certain exponential mobility in homoepitaxy. This evolution law is motivated both by an atomistic broken-bond model and a mesoscale model for crystal steps. By constructing an explicit solution to this PDE, we demonstrate the lack of symmetry in the evolution of top and bottom facets in periodic surface profiles. Our explicit, analytical solution is compared to numerical simulations of the continuum law via a regularized surface free energy.

Duke Scholars

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

June 1, 2019

Volume

393

Start / End Page

54 / 67

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Liu, J. G., Lu, J., Margetis, D., & Marzuola, J. L. (2019). Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model. Physica D: Nonlinear Phenomena, 393, 54–67. https://doi.org/10.1016/j.physd.2019.01.004
Liu, J. G., J. Lu, D. Margetis, and J. L. Marzuola. “Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model.” Physica D: Nonlinear Phenomena 393 (June 1, 2019): 54–67. https://doi.org/10.1016/j.physd.2019.01.004.
Liu JG, Lu J, Margetis D, Marzuola JL. Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model. Physica D: Nonlinear Phenomena. 2019 Jun 1;393:54–67.
Liu, J. G., et al. “Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model.” Physica D: Nonlinear Phenomena, vol. 393, June 2019, pp. 54–67. Scopus, doi:10.1016/j.physd.2019.01.004.
Liu JG, Lu J, Margetis D, Marzuola JL. Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model. Physica D: Nonlinear Phenomena. 2019 Jun 1;393:54–67.
Journal cover image

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

June 1, 2019

Volume

393

Start / End Page

54 / 67

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics