Phase-field study on the growth of magnesium silicide occasioned by reactive diffusion on the surface of Si-foams

Magnesium silicide has been widely exploited in thermoelectric and photovoltaic devices. In contrast to the fabrication of the magnesium silicide phase on flat Si-substrates in literature, we here concentrate on the growth of the Mg₂Si phase on the surface of Si-foams by solid-state phase transformation. Based on the reactive diffusion mechanism, which is responsible for the growth of magnesium silicide, we adopt a grand-potential-based phase-field model to investigate the microstructural evolution during the solid-state phase transformation. The presently developed phase-field concept is capable to model the solid-state phase transformation between three stoichiometric phases, Mg₂Si, diamond, and Mg-hcp phases. The simulated microstructures are scrutinized via a skeleton algorithm. The simulation results reveal that the thickness distribution of the Mg₂Si phase follows the one of the foam-ligaments and that the average thickness of the magnesium silicide phase strongly depends upon the surface-volume ratio of the Si-foam rather than the porosity. In addition, it has been found that for a constant porosity, the mean value for the thickness of the magnesium silicide is different when the thickness distribution of the foam-strut is different. The relationship between the local thickness of the magnesium silicide phase and the foam-strut is analyzed based on the skeleton of the microstructure.