The Influence of Grain Boundary Inclination on the Structure and Energy of Σ3 Twin Boundaries in Copper

Abstract

In a combined theoretical and experimental study, the energies and structures of Σ3 [011] twin boundaries in Cu were investigated. The atomic structures and the grain boundary energies were calculated using the Embedded Atom Method (EAM). Grain boundary energies of welded Cu bicrystals of the same boundary orientations were also obtained by the thermal grooving technique. The atomic structure of the symmetric {211} incoherent twin boundary (SITB) was investigated by High Resolution Transmission Electron Microscopy (HRTEM). Calculated grain boundary energies γ_b plotted against the inclination angle Φ of the boundary plane relative to the {111} coherent twin boundary (CTB) plane show a mininmm for the CTB (Φ = 0°) and a second minimum at Φ = 82°. This dependence on the inclination is also confirmed by the measured energies. Common to all calculated boundary structures is a microface 11 ing into CTB and SITB segments with a symmetric orientation of the adjacent crystals. Additionally, strong relaxations occur for the grain boundaries near the second energy minimum. This relaxation can be interpreted as a sequence of stacking faults located almost perpendicular to the mean boundary plane. They are terminated by partial dislocations which form a small angle boundary. The most apparent feature of these structures is a bending of the {111} planes running across the boundary. The structural properties were confirmed by HRTEM.