Morphology of Silicon Nitride Grown from a Liquid Phase

To explain the recent experimental observation of liquid-grown silicon nitride (Si₃N₄) crystals with a concave depression in the center of the (0001) end face, we propose a new growth mechanism and develop an analytical solution for the steady state. The model allows for atoms that diffuse via the liquid to the side surface but demands that the majority of these atoms be transported to the end caps to feed axial growth. The analysis shows that, for a large radius crystal, the redistribution of atoms by surface diffusion on the end caps requires a long relaxation time; hence, a nonequilibrium shape results. For an isolated Si₃N₄ crystal growing in a liquid environment, the shape of the end cap is largely determined by the ratio of the supersaturation to the equilibrium surface potential, which is inversely proportional to the crystal radius. A large shape distortion is predicted to occur during the growth stage for large-radius crystals and during the coarsening stage for a population of crystals with a large size distribution. This mechanism ceases to operate when the liquid flux to the side surface is blocked, as in silicon nitride ceramics, but is otherwise insensitive to factors such as radial growth kinetics and liquid diffusivity.