Multilayer-relaxation geometry and electronic structure of a W(111) surface

Abstract

The multilayer-relaxation geometry of a tungsten (111)surface has been calculated using both a firstprinciples 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 I point of the surface Brillouin zone, which is insensitive to surface relaxation. The empirical calculations were carried out for 3to 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.

Quantum modeling (DFT) and experimental investigation of beryllium–tungsten alloy formation

“…However, the W(111) surface undergoes a larger relaxation than the W(100): the two first interlayer distances are contracted by -20 and -16 %, whereas the third one is dilated by +12 %. The multilayer-relaxation geometry of the W(111) surface depends strongly on the method and the number of layers used, nevertheless most of the calculations predict the same relaxation pattern of a triplet of W layers moving towards each other and an expansion of the next layer spacing [17]. Our results are in good general agreement with the other quantum calculations [17,13,18].…”

“…These considerations, and also the contraction of the three upper layers that increases the electron density near the surface [17], implicate that the respective action of each of these "superficial layers" towards the beryllium will be cumulative and the resulting reactivity towards Be enhanced in the positive as well as in the negative direction (minimums in energy or energy barriers).…”

Growth morphology, structure, and magnetism of ultrathin Co films on W(111)

“…Strong relaxation of the ͑111͒ orientation has also been noted in previous local density functional and empirical potential calculations for clean W͑111͒. 36,37 IV. DISCUSSION…”

Surface atomic structure and energetics of tantalum

“…1) the contraction and expansion of the second and third interlayer distance are still very large (P15%). The above relaxation pattern, which fully develops at the slab thickness increased to 15 layers and shows the formation of the contracted triplets of layers, seems to be a generic feature of bcc(1 1 1) since similar variations were reported for the DFT calculations performed within local density approximation (LDA) for the Mo(1 1 1) [18] and W(1 1 1) surfaces [22,23]. Such pattern was also reported previously for the empirical potential calculations of W(1 1 1) ( [22] and references therein).…”