The elastic field of a surface step: The Marchenko-Parshin formula in the linear case

Document Type

Article

Publication Date

11-15-2006

Abstract

Strain has significance for both the growth characteristics and material properties of thin epitaxial films. In this work, the method of lattice statics is applied to an epitaxial system with cubic symmetry, using harmonic potentials. The energy density and force balance equations are written using a finite difference formalism that clearly shows their consistency with continuum elasticity. For simplicity, the atomic interactions are assumed to be maximally localized. For a layered material system with a material/vacuum interface and with surface steps, force balance equations are derived, and intrinsic surface stress at the material/vacuum interface is included by treating the atoms at the surface as having different elastic properties. By defining the strain relative to an appropriately chosen nonequilibrium lattice, as in the method of eigenstrains, analytic formulas in terms of microscopic parameters are found for the local force field near a step and for the macroscopic monopole and dipole moment forces due to a step. These results provide an atomistic validation of the Marchenko-Parshin formula for the dipole moment in terms of the elastic surface stress. © 2005 Elsevier B.V. All rights reserved.

Identifier

33746267067 (Scopus)

Publication Title

Journal of Computational and Applied Mathematics

External Full Text Location

https://doi.org/10.1016/j.cam.2005.08.020

ISSN

03770427

First Page

368

Last Page

386

Issue

2

Volume

196

Grant

19-02-1-0336

Fund Ref

Army Research Office

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