The energy and structure of (0 0 1) twist grain boundary in noble metals

The relaxed energy and structure of (0 0 1) twist grain boundary (GB) in noble metals Au, Ag and Cu are simulated by the MAEAM. In-boundary translation between two adjacent grains results in a periodic energy variation and the period is a square with the side length L_Σ/Σ. The lowest energy appears when the two grains are translated relatively to either corner or center of the periodic square. The relaxed GB energy increases smoothly for low-angle boundaries and levels off for larger-angle boundaries except a cusp appeared at θ = 36.87° (Σ = 5). After relaxation, the symmetry of the GB structure is not changed but the displacement of the atoms parallel to the GB plane decreases with increasing the distance of the atoms from the GB plane.