Nonlinear diffusion

We have demonstrated that perturbation methods and five point central difference numerical scheme can be successfully employed to solve the non-linear diffusion equation particularly in the case of up-hill diffusion (spinodal decomposition) and metallic or semiconductor super-lattices. On the practical side, these solutions provide an excellent method of studying and predicting the properties of spinodal alloys as their superior properties depend on the microstructure which in turn is developed through the non-linear diffusion process. Experimental results in a number of systems have verified the current theories of kinetics at later stages of decomposition. On the other hand, the nonlinear diffusion behavior of metallic, amorphous and semiconductor superlattices have shown excellent agreement with theoretical predictions. The theoretical predictions can be used to provide valuable information about the interdiffusion in the layers, the sharpness of the interfaces and also to calculate certain important structural and thermodynamic parameters upon which several intriguing properties of this new class of materials depend.