The microstructural evolution and long-time coarsening behavior of a thin film attached to a compliant substrate is investigated for a spinodally decomposing, binary, two-phase alloy using a Cahn-Hilliard type equation. Elastic fields arise because of composition dependence of the lattice parameter (compositional self-strain) as well as an average misfit between the film and substrate. This leads to a local mass flux within the film that depends on the global composition field as well as the thickness and elastic properties of the substrate. Three distinct coarsening regimes are observed: a rapid initial stage of spinodal decomposition into alternating phases, a transition region where internal interfaces grow and coalesce, and a final coarsening regime where the outermost layers grow with little change in the internal structure. An asymptotic expression for the long-time coarsening rate is derived as a function of the compositional self-strain, the average misfit strain, the film thickness and the total (film plus substrate) thickness. The analytic predictions are in good agreement with numerical simulations for a variety of film and substrate thicknesses and compositional and average film misfit strains.
Bibliographical noteFunding Information:
The authors gratefully acknowledge the financial support of the Division of Materials Science at the Department of Energy through Grants Nos DE-FG02-99ER45770 (PHL) and DE-FG02-99ER45771 (WCJ).
- Phase transformations (nucleation, growth)
- Theory & modeling
- Thin films