Reconstruction of charged surfaces: General trends and a case study of Pt(110) and Au(110)

Abstract

The stability of missing-row reconstructions of (110) surfaces with respect to surface charging has been investigated using ab initio theory, taking Pt and Au as representative systems. A thermodynamic formulation is derived to compare the relative stability of charged surfaces either in constant-potential or constant-charge mode. By generalizing Koopmans' theorem to charged metallic surfaces, we obtain an expression for the surface (excess) energy as a function of charge (or potential) in terms of the neutral surface energy, work function, and the position of the image plane. A surface is shown to reconstruct in constant-charge mode if and only if it reconstructs in constant-potential mode. We next address the question of whether a positive (negative) surface charge can lift (induce) the reconstruction, as suggested in the literature. This turns out not to be the case. Instead the following consistent picture arises: at small surface charges, the effect of the charge follows the difference of the work functions; i.e., positive charge favors a surface having a smaller work function and vice versa. Larger charges, either positive or negative, tend to stabilize the reconstructed surface or, more generally, the $1\ifmmode\times\else\texttimes\fi{}r$ reconstruction with larger r. The latter essentially results in that the $1\ifmmode\times\else\texttimes\fi{}2$ reconstruction in either Pt or Au is never lifted in our study, although the $1\ifmmode\times\else\texttimes\fi{}3$ surface in Au eventually becomes more stable.