Theoretical and experimental investigations of structures and energies of Σ = 3, [112] tilt grain boundaries in copper

Abstract

Using atomistic computer simulations, symmetric and asymmetric Σ = 3 <112> tilt grain boundaries in Cu were investigated. Equilibrium energies and structures were calculated by static and dynamic energy minimization. A semi-empirical N-body potential served as a model of the interatomic forces in Cu. The atomistic structure of the grain boundary inclined at about 84° to the {111} twin boundary was investigated by high-resolution transmission electron microscopy (HRTEM). Plotted against the inclination angle Φ₁₁₂ of the boundary plane, the calculated grain boundary energies increase monotonically up to Φ₁₁₂ ≈ 73°. At larger inclination angles the data indicate an energy minimum at about 80°. The computer simulations predic that boundaries equilibrated at temperatures near T = 0K are planar for inclination angles σ₁₁₂ < 73°, but consist of a three-dimensional layer of predominantly body-centred-cubic (bcc) Cu for inclination angles greater than 73°. In all three-dimensional boundaries by bcc layer is about 1 nm wide in the direction perpendicular to the boundary plane. By analysing the microfaceting of these boundaries and its influence on the misfit strain of the bcc layer, we explain the observation of a local energy minimum close to 80°. For the boundary inclined at about 84°, the calculated atomistic structure and the HRTEM images display striking similarities, suggesting that the bcc crystal structure is the equilibrium structure within this grain boundary at low temperatures.