### Abstract

A flat surface of stressed solid is unstable to small perturbations. This morphological instability is called Asaro-Tiller-Grinfield instability. Nonlinear evolution of this instability will result in the formation of cusp singularities. This instability can be described by a continuum model with surface diffusion driven by a stress-dependent chemical potential. The stress and strain in the solid are coupled with surface morphology and an elasticity problem must be solved numerically. We derive a nonlinear approximation equation governing the evolution of this instability in which the stress-dependent chemical potential is expressed explicitly as a function of the surface morphology. Linear instability analysis using our equation shows the same results as the well-known Asaro-Tiller-Grinfeld instability result. Compared with the exact solution of the elasticity problem for cycloid surface obtained by Chiu and Gao, our nonlinear approximation has a much wider range of applicability than linear approximation. Numerical simulation using our nonlinear evolution equation shows that the surface evolves towards a cusplike morphology from small perturbations, which agrees very well with results obtained by solving the full elasticity problem.

Original language | English (US) |
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Pages (from-to) | 9414-9422 |

Number of pages | 9 |

Journal | Journal of Applied Physics |

Volume | 91 |

Issue number | 11 |

DOIs | |

State | Published - Jun 1 2002 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

*Journal of Applied Physics*,

*91*(11), 9414-9422. https://doi.org/10.1063/1.1477259