Structure and energetics of the elbows in the Au(111) herringbone reconstruction

Abstract

We study the structure of the threading edge dislocations, or ``elbows,'' which are an essential component of the well-known herringbone reconstruction of the (111) surface of Au. Previous work had shown that these dislocations can be stabilized by long-range elastic relaxations into the bulk. However, the validity of the harmonic spring model that had been used to estimate the energies of the dislocations is uncertain. To enable a more refined model of the dislocation energetics, we have imaged the atomic structure of these dislocations using scanning tunneling microscopy. We find that the harmonic spring model does not adequately reproduce the observed structure. We are able to reproduce the structure, however, with a two-dimensional Frenkel-Kontorova (FK) model that uses a pairwise Morse potential to describe the interactions between the top layer Au atoms on a rigid substrate. The parameters of the potential were obtained by fitting the energy of uniaxially compressed phases, or ``stripes'', computed with density functional theory, as a function of surface Au density. Within this model, the formation of the threading dislocations remains unfavorable. However, the large forces on the substrate atoms near the threading-dislocation cores, render the assumption of a completely rigid substrate questionable. Indeed, if the FK parameters are modified to account for the relaxation of just one more atomic layer, threading dislocations can, in principle, become favorable, even without bulk elastic relaxations. Additional evidence for a small elbow energy is that our computed change in the Au(111) surface stress tensor caused by the $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}22)$ reconstruction is considerably smaller than previous estimates.