Calculations for surface energies and displacements using empirical interatomic forces

Calculations have been carried out for the surface energy and surface relaxation over the full spherical triangle for W and α-Fe using empirically determined short-ranged two-body central interactions and volume-dependent energy terms. The minimum surface energy is sensitive to parameter variations and may be either γ₁₀₀ or γ₁₁₀, while γ₁₁₁ is always considerably greater. The results of the present model are γ₁₀₀=2552, γ₁₁₀=2646, γ₁₁₁=3157, and γ₁₁₂=2942 erg/cm² for W and γ₁₀₀=1273, γ₁₁₀=1206, γ₁₁₁=1458, and γ₁₁₂=1347 erg/cm² for α-Fe. For both W and α-Fe, the first plane relaxes outward and the second inward for {100}; there is no relaxation for {110}; the first plane relaxes slightly outward, the second inward, and the third outward for {111}, and there is negligible normal relaxation but considerable tangential relaxation for {112}. The present model is discussed relative to other surface calculations. It is concluded that models based on short-ranged potentials with volume-dependent terms yield a satisfactory approximation for surface-energy calculations for transition and noble metals. Corrections due to electron redistribution may play an important role for surface relaxations and should be necessary for adatom binding and migration energies.