Anisotropy analysis of the surface stress and surface energy in Cu surfaces with the modified embedded atom method

Taking Cu as an example, the surface stress and surface energy in three low index surfaces and two families of representative surfaces ( h k 0 ) and ( h h l ) belong to [0 0 1]- and [ 1 ¯ 1 0 ] -rotating axis respectively, have been calculated using MEAM. For the three low index surfaces, the decrease in the surface energy is small after relaxation, while the surface stresses in the surface planes τ x x and τ y y show opposite changes (decreasing and increasing) for inward and outward relaxations. The resulting relaxation direction is related to the normal stress τ z z before relaxation. For the surfaces of the ( h k 0 ) and ( h h l ) families, with the increasing angle α (between the ( h k 0 ) and (1 0 0) planes, and between ( h h l ) and (0 0 1) planes, respectively), the surface stress and surface energy go through an oscillatory change. The surface stress and surface energy are symmetric about the planes (1 0 0), (1 1 0) and (0 1 0) at α = 0 ∘ , 45∘ and 90∘, and about the planes (0 0 1) and (1 1 0) at α = 0 ∘ and 90∘ respectively, due to crystal symmetry.