Analysis of the Correlation Between the Energy and Crystallographic Orientation of Grain Boundaries in Fe Based on Atomistic Simulations

The grain boundary (GB) energy is one of the fundamental structure-dependent proper-ties of GB and plays a crucial role in the GB-related behaviors and properties of polycrystalline materials. An in-depth understanding of GB energy will help to explore the corresponding mechanisms and provide significant guidance for tailoring material properties based on GB engineering. The crystallographic orien-tation of GB strongly dominates the GB energy. However, a relatively comprehensive understanding of the orientation dependence of the GB energy is still lacking, especially for bcc materials. In this study, the energies of 1568 tilt GBs in bcc Fe, which covers the misorientation angle (theta) of 0 degrees-180 degrees and 40 distinct misorientation axes (O), were computed using the cutoff sphere bicrystal molecular dynamics model. The energy dataset was used to statistically analyze the correlation between GB energy (gamma) and GB crystallo-graphic orientation, thereby revealing the underlying mechanisms. The results show that the tendencies of gamma-theta correlationcan be considerably different in the high-angle range for GBs with distinct O. Statistical-ly, GB energies increase with theta and disorientation angle in the low-angle range and then level off for high-er angles. The energies for noncoincident site lattice (non-CSL) GBs are not necessarily higher than those of CSL GBs and follow the same trend in the low-theta range as CSL GBs. The energies of the tilt GBs decrease with the variation of O from the central regions to the edge and then the corners of the stereo-graphic triangle due to the increasing tendency of the symmetry of the boundary structure. Therefore, the lowest energies are observed for GBs with O close to <111>. Relatively low energies are not observed for GBs terminated by low-index or dense planes. The GB energy shows an overall increasing trend with the surface energy of the boundary plane until a plateau in the GB energy is reached. No distinct correlation is observed between the GB energy and coincidence index (Sigma) value. However, the cusp in the gamma(theta) curve for GBs with a common O is found to be generally located at the GB with a much lower Sigma than its neigh-boring GBs. Additionally, the potential correlations and laws concerning GB energy and its crystallograph-ic orientation for bcc metals are observed to be partially similar or consistent with those of fcc meta.