Co-energy of surface and grain boundary in Ag film

A model is proposed for calculating the co-energy of surface and grain boundary (GB) by the modified analytical embedded atom method (MAEAM). As example, the energy densities E_d of the two adjacent grains are obtained when their (0 0 1) twist GB meets the free surface (h₁ k₁ 0)/(h₂ k₂ 0) of Ag film. The period along the boundary line on the surface is found and the energy density is calculated for the situations either with or without periodicity. The results show that, the energy value achieved via this model can be stable even for most grains with boundary line smaller than 100 nm. Among the grains with (h k 0) surface, (1 0 0) grains should be favored and grow fastest when they meet (1 1 0) grains.