Theoretical and computer models of three-dimensional grain boundary migration with mobile particles

In this work, the migration of a three-dimensional (3D) spherical crystal in the presence of mobile particles using a Monte Carlo algorithm was studied. Different concentrations of particles (f) and different particle mobilities (M_p) were used. It was found that the grain size reaches a critical radius (R_c), which depends exclusively on f. This dependence can be written as R_c ∝ f^1/3. The dynamic equation of grain size evolution and its analytical solution were also found. The proposed analytical solution successfully fits the simulation results. The particle fraction in the grain boundary was also found analytically and it fits the computational data. (author)