A class of strongly coupled elasticity and diffusion problems in thin metal films

When surface diffusion is neglected, the constrained grain boundary diffusion in polycrystalline thin metal films on substrates is studied based on the elasticity and grain boundary diffusion equations in which no sliding and no diffusion are allowed at the film/substrate interface. The solution of the problem is obtained by an analysis of the diffusional eigenmodes. Each eigenmode is governed by an integro-differential equation which is transformed into a standard Cauchy type singular integral equation before numerical methods are applied to calculate the solution. It is shown that the higher eigenmodes decay much faster in comparison with the first eigenmode and the overall process is dominated by the first eigenmode. Such a diffusion process leads to the formation of crack-like grain boundary wedges which cause the normal traction along the grain boundary to decay exponentially with time.; The coupled grain boundary and surface diffusion is simulated by a simplified one-dimensional model which treats surface diffusion as a matter source or sink when the grain boundary diffusion is analyzed, and vice versa. The grain boundary diffusion and surface diffusion are coupled at the junction by the requirements of continuity of the chemical potential and mass conservation.; The experiments of Al-Cu thin films show that the contrast of interface dislocations disappears in the electron beam of transmission electron microscopy. This phenomenon is modeled by assuming that the contrast dissolution is due to the spreading of the dislocation core at the crystalline/amorphous interface. The radiation induced diffusion at the interface is assumed to be controlled by the viscous rule under which slip occurs only if the shear stress is larger than the interface strength. An implicit finite difference method with Gaussian-Chebyshev quadrature scheme is developed to solve the derived integro-differential equations. By taking into account the effect of dislocation core spreading, the thin film strength is investigated according to Nix's model. It is found that for weak interfaces, the thin film strength is strongly decreased by the dislocation core spreading.