Discontinuous Galerkin solution of a phase-field model in isothermal chemical vapor infiltration of SiC

The microstructure evolution of the isothermal chemical vapor infiltration (ICVI) of silicon carbide (SiC) from methyltrichlorosilane (MTS) is simulated by a phase-field model which is implemented numerically using the discontinuous Galerkin method. The model consists of a phase-field equation describing the diffusive interface kinetics and a species transport equation describing the mass balance. For the diffusive interface kinetics, a new form of the free energy density related to the ICVI process is adopted to ensure two stable states of gas phase and solid phase, and the Gibbs free energy changing between these two phases is taken as driving force. For the mass balance, two process intensities depending on the phase-field parameter are introduced to account for the homogeneous gas reaction and the heterogeneous surface reaction including the influence of the by-product hydrogen chloride (HCl). Finally, a discontinuous Galerkin formulation is derived for the nonlinear phase-field model and a priori error analysis is used for the semi-discontinuous formulations based on the proof of the uniqueness of the solution of the discontinuous approximation. Two numerical examples are presented to demonstrate the validity of the discontinuous Galerkin method and to investigate the effect of geometric parameters on microstructure evolution.