| A generalized Cahn-Hilliard model is used to investigate diffusional phase transformations in elastically stressed solid films. The elastic field arises due to the dependence of lattice parameter on the composition. Both a free-standing film and film-substrate system are considered, for materials with isotropic and cubic symmetry. Both two and three-dimensional geometries are considered. The elastic fields are solved analytically using a Laplace transform. Saint Venant solutions are obtained for all cases, and an exact closed form solution is derived for the two-dimensional free-standing film by using a finite Laplace transform.; The elastic solution is used in numerical simulations of the generalized Cahn-Hilliard system in both two and three dimensions. Simulations are first performed to study the kinetics and the metastable configurations for a system with constant mobility. System parameters such as elastic strength, interfacial energy, epitaxial misfit, anisotropy, thickness ratio, and external mechanical loading, are systematically investigated. In the film-substrate system, the epitaxial misfit strain is the most important factor controlling system behavior. Phenomena such as forming of columnar and layered structures, and alignment in soft elastic directions are observed. The results also show that a multilayer system generally is not stable and tends to degrade to a bilayer or columnar structure.; In addition to the constant mobility case, a model is developed to account for non-uniform mobility owing to grain boundaries. In particular, a connection is established between the high diffusivity of the grain boundary and the mobility in the Cahn-Hilliard model. Both fixed and migrating grain boundaries are considered. Numerical simulations are performed in both two and three dimensions for different initial conditions. Simulation results show that the grain boundary structure acts as an amplifier for the various driving forces in the evolution system and greatly alters the kinetics of phase separation and coarsening. The roles of the grain boundary and its triple junctions are discussed. |
