The grain boundary stiffness and its impact on equilibrium shapes and boundary migration: Analysis of the Σ 5, 7, 9, and 11 boundaries in Ni

Grain boundaries (GBs) play a critical role in the formation of microstructure during materials processing and its subsequent evolution under service conditions. While GB misorientation is commonly used to describe the boundary’s properties, a more complete description should also account for the GB plane normal, in which the GB stiffness is the relevant property controlling many GB dynamical processes. Herein, we leverage published atomistic simulation data to construct the full GB energy–plane normal diagrams for Σ 5, 7, 9, and 11 GBs in Ni. The functional fits are used to obtain a complete mapping of the GB stiffness as a function of the plane normal, construct the equilibrium shapes, and determine the driving force for GB migration. It is shown that the GB stiffness can be larger in magnitude and more anisotropic than the energy itself. Further, many boundary inclinations are found to exhibit negative stiffness, indicating propensity for faceting. Results from our GB stiffness analysis are shown to be in qualitative agreement with experimental GB plane normal distributions in polycrystalline Ni. In broad terms, our results provide future avenues to account for the plane normal dependency of GB properties in mesoscale treatments of GB migration and microstructural evolution.