Calculations for surface energies and displacements using empirical interatomic forces

Abstract

Calculations have been carried out for the surface energy and surface relaxation over the full spherical triangle for W and $\alpha -\mathrm{Fe}$ 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 ${\gamma }_{100}$ or ${\gamma }_{110}$, while ${\gamma }_{111}$ is always considerably greater. The results of the present model are ${\gamma }_{100}=2552\mathrm{}$, ${\gamma }_{110}=2646\mathrm{}$, ${\gamma }_{111}=3157\mathrm{}$, and ${\gamma }_{112}=2942\mathrm{}$ erg/${\mathrm{cm}}^2$ for W and ${\gamma }_{100}=1273\mathrm{}$, ${\gamma }_{110}=1206\mathrm{}$, ${\gamma }_{111}=1458\mathrm{}$, and ${\gamma }_{112}=1347\mathrm{}$ erg/${\mathrm{cm}}^2$ for $\alpha -\mathrm{Fe}$. For both W and $\alpha -\mathrm{Fe}$, 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.