Quantitative analysis of grain boundary properties in a generalized phase field model for grain growth in anisotropic systems

A good choice of model formulation and model parameters is one of the most important and difficult aspects in mesoscale modeling and requires a systematic and quantitative analysis. In this paper, it is studied how the model parameters of a generalized phase field model affect the landscape of the free-energy density functional, the phase field profiles at the grain boundaries, and the corresponding trajectory along the free-energy landscape. The analysis results in quantitative relations between the model parameters, on one hand, and grain boundary energy and mobility, on the other hand. Based on these findings, a procedure is derived that generates a suitable set of model parameters that reproduces accurately a material's grain boundary energy and mobility for arbitrary misorientation and inclination dependence. The misorientation and inclination dependence are formulated so that the diffuse interface width is constant, resulting in uniform stability and accuracy conditions for the numerical solution. The proposed model formulation and parameter choice allow us to perform quantitative simulations with excellent controllability of the numerical accuracy and therefore of the material behavior.