### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 368-386 |

Number of pages | 19 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 196 |

Issue number | 2 |

DOIs | |

State | Published - Nov 15 2006 |

### Fingerprint

### Keywords

- Elasticity
- Epitaxial growth
- Marchenko-Parshin formula

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics

### Cite this

*Journal of Computational and Applied Mathematics*,

*196*(2), 368-386. https://doi.org/10.1016/j.cam.2005.08.020

**The elastic field of a surface step : The Marchenko-Parshin formula in the linear case.** / Connell, Cameron R.; Caflisch, Russel; Luo, Erding; Simms, Geoff.

Research output: Contribution to journal › Article

*Journal of Computational and Applied Mathematics*, vol. 196, no. 2, pp. 368-386. https://doi.org/10.1016/j.cam.2005.08.020

}

TY - JOUR

T1 - The elastic field of a surface step

T2 - The Marchenko-Parshin formula in the linear case

AU - Connell, Cameron R.

AU - Caflisch, Russel

AU - Luo, Erding

AU - Simms, Geoff

PY - 2006/11/15

Y1 - 2006/11/15

N2 - 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.

AB - 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.

KW - Elasticity

KW - Epitaxial growth

KW - Marchenko-Parshin formula

UR - http://www.scopus.com/inward/record.url?scp=33746267067&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746267067&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2005.08.020

DO - 10.1016/j.cam.2005.08.020

M3 - Article

AN - SCOPUS:33746267067

VL - 196

SP - 368

EP - 386

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 2

ER -