The influence of grain boundary inclination on the structure and energy of σ = 3 grain boundaries in copper

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Abstract
In a combined theoretical and experimental study, the energies and structures of σ = 3, [011] tilt boundaries in Cu were investigated. Equilibrium atomistic structures and grain-boundary energies were calculated by static energy minimization using an embedded-atom potential. Cu bicrystals of the same boundary orientations were fabricated by welding of Cu single crystals. Grain-boundary energies were measured by the thermal grooving technique. The atomistic structure of the {211} twin boundary was investigated by high-resolution transmission electron microscopy (HRTEM). The calculated grain-boundary energies γb plotted against the inclination of the boundary plane show a minimum for the {111} twin boundary and a second minimum at an inclination of about 82° to the {111} boundary. The calculated dependence of γb on inclination is confirmed by the measured energies over the entire range. Common to all calculated boundary structures is a microfaceting into {111} and {211} twin facets. The structures calculated for grain boundaries around the second energy minimum show significant atomic rearrangements extending over several planes normal to the boundary together with large translations. A striking feature of these structures is a bending of the {111} planes that run continuously through the boundary. This is confirmed by HRTEM. The structures are explained in terms of a rhombohedral 9R phase of Cu forming a thin (1–2 nm) layer at the boundary.