We present a diffuse interface (DI) model for capturing microstructure formed during the coarsening of a two dimensional, elastically stressed binary alloy. The DI model is based on a generalized Cahn-Hilliard free energy; evolution occurs to lower the free energy. Using a matched asymptotic expansion, we show that the DI model converges to a well-studied sharp interface system as the thickness of the diffuse interface approaches zero. Numerical simulations confirm this equivalence. We develop pseudo-spectral numerical methods to solve the DI system and we carefully investigate the dependence of results on numerical parameters. The DI model is used to follow microstructural evolution through topological transitions such as particle merging and vanishing. We show that in isotropic media, elastic inhomogeneity may lead to interesting topology changes such as a reversal of the roles of the precipitate and matrix phases.
Bibliographical noteFunding Information:
We wish to thank R. V. Kohn, Q. Nie, M. J. Shelley and P. Voorhees for interesting discussions concerning this work. We gratefully acknowledge the support of the Minnesota Supercomputer Institute. In addition, this work is partially supported by National Science Foundation grants CMS-9503393 (PHL) and DMS-940310 (JSL), and the Sloan foundation (JSL).