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 $\ensuremath{\alpha}\ensuremath{-}\mathrm{Fe}$ 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 ${\ensuremath{\gamma}}_{100}$ or ${\ensuremath{\gamma}}_{110}$, while ${\ensuremath{\gamma}}_{111}$ is always considerably greater. The results of the present model are ${\ensuremath{\gamma}}_{100}=2552$, ${\ensuremath{\gamma}}_{110}=2646$, ${\ensuremath{\gamma}}_{111}=3157$, and ${\ensuremath{\gamma}}_{112}=2942$ erg/${\mathrm{cm}}^{2}$ for W and ${\ensuremath{\gamma}}_{100}=1273$, ${\ensuremath{\gamma}}_{110}=1206$, ${\ensuremath{\gamma}}_{111}=1458$, and ${\ensuremath{\gamma}}_{112}=1347$ erg/${\mathrm{cm}}^{2}$ for $\ensuremath{\alpha}\ensuremath{-}\mathrm{Fe}$. For both W and $\ensuremath{\alpha}\ensuremath{-}\mathrm{Fe}$, 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.