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Homogenization of reconstructed crystal surfaces: Fick’s law of diffusion

Dionisios Margetis

  • Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA

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Phys. Rev. E 79, 052601 – Published 14 May, 2009

DOI: https://doi.org/10.1103/PhysRevE.79.052601

Abstract

Fick’s law for the diffusion of adsorbed atoms (adatoms) on crystal surfaces below roughening is generalized to account for surface reconstruction. In this case, material parameters vary spatially at the microscale, and the coarse graining for crystal steps via Taylor expansions is not strictly applicable. By invoking elements of the theory of composites in one independent space dimension, we homogenize the microscale description to derive the macroscopic adatom flux from step kinetics. This approach relies on a multiscale expansion for the adatom density. The effective surface diffusivity is determined through appropriate discrete averages of microscale kinetic parameters.

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Phys. Rev. E 79, 052601– Published 14 May, 2009
  • Received 22 January 2009

© 2009 American Physical Society

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