First-principles-based mesoscale modeling of the solute-induced stabilization of 〈1 0 0〉 tilt grain boundaries in an Al–Pb alloy

A first-principles disclination structural units (DSUM) model was used to calculate the energies of 12 〈0 0 1〉 symmetric tilt grain boundaries in Al for a pure system and a system in which Pb atoms substitute for Al at one-half of the lattices sites along the interfacial plane. The grain boundaries are modeled as disclination dipole walls with energies given as a weighted sum of individual disclination energies determined from special low-sigma structures, elastic terms and disclination core energies. Predictions of the DSUM using the bulk Al shear modulus and Poisson’s ratio in the elastic and core energy terms are found to be comparable to energies for fully atomistic simulations calculated using a modified embedded-atom method (MEAM) potential. No relation between grain boundary energies in pure Al and the degree of stabilization due to Pb doping was found. The DSUM parameterized to density functional theory calculations predicts a ∼50% reduction in the energy anisotropy with respect to angle due to doping compared to the pure system, while MEAM calculations yield no appreciable reduction in the energy anisotropy.