A generalized vertex dynamics model for grain growth in three dimensions

A generalized three-dimensional (3D) vertex dynamics model for simulating grain growth is presented. In this approach, grain boundaries (GB) are triangulated and the microstructural evolution is driven by the minimization of the GB energy. The generalized model includes misorientation and inclination dependent GB energies and mobilities. The model systems considered are SrTiO3 ceramics. The paper describes the derivation of the equations for the dynamics and the algorithm for handling topological changes in the GB network in detail. For isotropic grain growth, the numerical results for the volume change rate of embedded grains are in excellent agreement with the MacPherson-Srolovitz relation which can be interpreted as the 3D analogue of the von Neumann Mullins law. The inclination dependent GB energy yields a torque contribution on the GB shape. This is illustrated by means of 2D cross-sections of structures modelled with and without inclination dependence showing rather flat GBs for the energetically favourable GB inclinations.