Ab initio perspective of the ⟨110⟩ symmetrical tilt grain boundaries in bcc Fe: application of local energy and local stress

The mechanical properties of polycrystalline metals are strongly dependent on the microscopic structure, stability, and elastic properties of grain boundaries (GBs). By using ab initio local energy, local stress, and local Young's modulus, we attempt to provide a comprehensive view on the stability and structural properties of a series of < 110 > symmetrical tilt GBs (STGBs) in bcc Fe. We deal with four representative STGBs, the Sigma 3 (112), Sigma 3 (111), Sigma 11 (332), and Sigma 9 (221) GBs with the rotation angles ranging from 109.47A degrees to 38.94A degrees. The Sigma 3 (112) GB shows special stability due to stable structural units of four-membered rings with negligible bond-length changes except for substantial bond-direction changes, like stacking faults or twins. The other GBs are constructed by periodic arrangement of 5-3 and bulk structural units as usual coincidence GBs, while the 5-3 unit in the Sigma 9 (221) GB has an aspect of an edge-dislocation array in a small-angle tilt GB such as alternate compressive and tensile stresses at both the edges and relatively wide spread of local energy and local stress on both sides. In the GBs other than the Sigma 3 (112) GB, there exist commonly two kinds of interface atoms; atoms with larger atomic volumes reveal higher local energies, tensile stresses, and enhanced magnetic moments, while the other kind of atoms forming compressed bonds reveal lower local energies, compressed stresses, and reduced magnetic moments. For the four GBs, the local Young's modulus averaged in the structural units ranges from 60 to 90 % of the bulk Young's modulus in accordance with the degree of structural disorder or GB energies. There exists clear correlation among the local Young's modulus, local energy, local stress, local magnetic moment, and local bonding nature at the structural units in the Fe GBs.