Surface-directed spinodal decomposition in a stressed, two-dimensional, thin film

Two-dimensional simulations of the spinodal decomposition of self-stressed, binary thin films using a Cahn-Hilliard model are presented. Two different sets of mechanical boundary conditions are considered, and compositional strains for a cubic-anisotropic system under plane strain are treated. A composition-dependent interaction energy is assumed at the free surface. Numerical solution of the coupled Cahn-Hilliard and elastic equilibrium equations are obtained using an efficient nonlinear multigrid method. Results of simulations show that, for large enough compositional strain, surface-directed decomposition occurs at the traction-free surface, even when there is negligible surface interaction energy initially attracting one of the components. This decomposition is controlled by elasticity, and results in a local alignment of phases perpendicular to the free surface, in contrast to the parallel alignment produced by surface energy in stress-free systems.