Formation of nick instabilities due to particle clustering along crystal interfaces

The kinetic growth of crystal grains is simulated on a square lattice in the presence of mobile particles. The model is based on the Eden and the dynamic epidemic models. Trapping of the particles by the advancing front and a short-range repulsion of the particles by the front are both allowed. The grain boundary morphology is studied through the kink density concept and the spatial distribution of particles is discussed. Indeed, the clustering of particles along the crystal edges is found to induce the formation of so-called nick instabilities at the liquid-solid interface. The particles, when trapped near such instabilities, occur as oblique filamentary structures in the crystal matrix, just like river networks. These findings agree with recent experimental observations. The numerical laws are also explained by theoretical arguments based on different characteristic lengths.