Grain boundary migration and grooving in thin 3-D systems

We employ numerical simulations and experimental methods to study grain boundary migration in idealized 3-D systems of three grains in a thin film, focusing on hole formation and annihilation of small grains. The initial structure is taken to be columnar, and isotropy is assumed for simplicity. The grain boundaries and the external surfaces of the three-grain system are assumed to be governed by mean curvature motion and surface diffusion, respectively. Along the thermal grooves, where the grain boundaries and the exterior surfaces couple, balance of mechanical forces, continuity of the surface chemical potential, and balance of mass flux dictate the boundary conditions. Using a parametric description for the evolving surfaces yields partial differential algebraic equations which are solved with finite-difference schemes on staggered grids. The evolution of the three-grain system results in hole formation or annihilation of the smallest grain, depending on the relative size of the smallest grain. Shortly prior to annihilation, the exterior surface of the smallest grains may invert, partially losing its convexity, with annihilation being accompanied by accelerated pitting rates. Similar features were observed experimentally.