Finite element analysis of shape instabilities for plate-like grains

Based on classical theory of surface diffusion and evaporation-condensation, a finite element program is developed to simulate the unstable shape evolution of plate-like grains. The results show that the plate-like grains will evolve into cylinders when the thermal grooving angle θ = 0(without internal boundary). When internal boundary exists, there is a critical thermal grooving angle θ_min. If θ > θ_min, the plate will split along the internal boundary of the plate-like grains. An approximate formulation of θ_min as a function of β is given, i.e., θ_min=4.836+42.94e^{[-(β-1.61)/1.478]}+61.90e ^{[-(β-1.61)/9.734]}. The initial termination shape of the plate has a weak effect on the evolution process. When β > 10, its effect can be neglected. Both the mobility M^→→ and surface energy γ_s only influence the rate of the evolution.