An efficient semi-implicit Fourier spectral method is implemented to solve the Cahn-Hilliard equation with a variable mobility. The method is orders of magnitude more efficient than the conventional forward Euler finite-difference method, thus allowing us to simulate large systems for longer times. We studied the coarsening kinetics of interconnected two-phase mixtures using a Cahn-Hilliard equation with its mobility depending on local compositions. In particular, we compared the kinetics of bulk-diffusion-dominated and interface-diffusion-dominated coarsening in two-phase systems. Results are compared with existing theories and previous computer simulations.

An integrated approach, combining the continuum theory of sintering with a kinetic Monte-Carlo (KMC) model-based mesostructure evolution simulation is reviewed. The effective sintering stress and the normalized bulk viscosity are derived from mesoscale simulations. A KMC model is presented to simulate microstructural evolution during sintering of complex microstructures taking into consideration grain growth, pore migration, and densification. The results of these simulations are used to generate sintering stress and normalized bulk viscosity for use in continuum level simulation of sintering. The advantage of these simulations is that they can be employed to generate more accurate constitutive parameters based on most general assumptions regarding mesostructure geometry and transport mechanisms of sintering. These constitutive parameters are used as input data for the continuum simulation of the sintering of powder bilayers. Two types of bilayered structures are considered: layers of the same particle material but with different initial porosity, and layers of two different materials. The simulation results are verified by comparing them with shrinkage and warping during the sintering of bilayer ZnO powder compacts.

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