Non-self-similar grain growth by zero-temperature Potts model

Abstract

Self-similar coarsening, a well-researched aspect of normal grain growth, is a key component of grain growth theories and visible in mesoscopic simulations of ideal grain growth. One particular simulation algorithm is the Potts model, which can be used to perform a thorough investigation of the temporal evolution of polycrystalline microstructures. Used with carefully selected parameters, the Potts model recreates normal grain growth quite accurately. One specific feature necessary to reach this goal is the simulation temperature, i.e. simulation thermal energy. It prevents grain boundaries from aligning along the underlying simulation lattice. Nevertheless, there are still today many researchers who implement classical zero-temperature Potts model simulations—often for reasons of simplification and/or modeling speed. In the current study, we show in detail the negative effect of setting the simulation temperature to zero. As a result, a unique type of non-self-similar coarsening is observed, where, e.g., the von Neumann-Mullins-relation shows unexpected time-dependent behavior. Hence, this study can be understood as a blueprint on why not to use a zero-temperature Potts model.

Effect of boundary grooving on grain growth by Potts model simulations

“…The underlying lattice must not affect the simulated growth kinetics. For this, the simulation temperature is of great importance, since it influences the grain boundary roughness as well as the angles between boundaries in triple junctions therewith ultimately affecting the growth kinetics as shown in [19,20]. While the simulation temperature is solely a technical parameter, (only) two real material parameters are relevant in the simulations, namely the grain boundary mobility and the grain boundary energy .…”