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

Cameron R. Connell, Russel Caflisch, Erding Luo, Geoff Simms

Research output: Contribution to journalArticle

### 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) 368-386 19 Journal of Computational and Applied Mathematics 196 2 https://doi.org/10.1016/j.cam.2005.08.020 Published - Nov 15 2006

### Fingerprint

Balance Equations
Dipole moment
Dipole
Vacuum
Eigenstrain
Moment
Harmonic Potential
Epitaxial films
Elastic Properties
Force Field
Monopole
Local Field
Energy Density
Material Properties
Non-equilibrium
Elasticity
Simplicity
Materials properties
Finite Difference
Continuum

### Keywords

• Elasticity
• Epitaxial growth
• Marchenko-Parshin formula

### ASJC Scopus subject areas

• Computational Mathematics
• Applied Mathematics

### Cite this

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

In: Journal of Computational and Applied Mathematics, Vol. 196, No. 2, 15.11.2006, p. 368-386.

Research output: Contribution to journalArticle

Connell, Cameron R. ; Caflisch, Russel ; Luo, Erding ; Simms, Geoff. / The elastic field of a surface step : The Marchenko-Parshin formula in the linear case. In: Journal of Computational and Applied Mathematics. 2006 ; Vol. 196, No. 2. pp. 368-386.
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