The multilayer-relaxation geometry of a tungsten (111) surface has been calculated using both a first-principles approach within the local-density approximation and an empirical approach using an embedded-atom-type potential with angular forces. Both calculations predict the same relaxation pattern of a triplet of W layers moving toward each other and an expansion of the layer spacing between each triplet. The first-principles calculations were carried out for three-, five-, and seven-layer thin films using mixed-basis pseudopotential techniques and including scalar-relativistic interactions. Within these approximations, the electronic structure of the W(111) surface is characterized by a surface resonance near the Fermi level and near the point of the surface Brillouin zone, which is insensitive to surface relaxation. The empirical calculations were carried out for 3- to 15-layer thin films. The relaxation geometries calculated for the three-, five-, and seven-layer films are consistent with the first-principles results; geometries calculated for the larger films indicate that the main relaxation effects occur in the first four layers near the surface, although measurable relaxations occur far from the surface.
ASJC Scopus subject areas
- Condensed Matter Physics