Adsorbate-substrate and adsorbate-adsorbate interactions of Na and K adlayers on Al(111)

We present total-energy, force, and electronic-structure calculations for Na and K adsorbed in various geometries on an Al(111) surface. The calculations apply density-functional theory together with the local-density approximation and the ab initio pseudopotential formalism. Two adsorbate meshes, namely, (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )R30\ifmmode^\circ\else\textdegree\fi{} and (2\ifmmode\times\else\texttimes\fi{}2), are considered and for each of them the geometry of the adlayer relative to the substrate is varied over a wide range of possibilities. By total-energy minimization we determine stable and metastable geometries. For Na we find for both adsorbate meshes that the ordering of the calculated binding energies per adatom is such that the substitutional geometry, where each Na atom replaces a surface Al atom, is most favorable and the on-top position is most unfavorable. The (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )R30\ifmmode^\circ\else\textdegree\fi{} structure has a lower energy than the (2\ifmmode\times\else\texttimes\fi{}2) structure. This is shown to be a substrate effect and not an effect of the adsorbate-adsorbate interaction. In contrast to the results for Na, we find for the (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )R30\ifmmode^\circ\else\textdegree\fi{} K adsorption that the calculated adsorption energies for the on-top, threefold hollow, and substitutional sites are equal within the accuracy of our calculation, which is \ifmmode\pm\else\textpm\fi{}0.03 eV. The similarity of the energies of the on-surface adsorption sites is explained as a consequence of the bigger size of K which implies that the adatom experiences a rather small substrate electron-density corrugation. Therefore for potassium the on-top and hollow sites are close in energy already for the unrelaxed Al(111) substrate. Because the relaxation energy of the on-top site is larger than that of the threefold hollow site both sites receive practically the same adsorption energy. The unexpected possibility of surface-substitutional sites is explained as a consequence of the ionic nature of the bonding which, at higher coverages, can develop strongest when the adatom can dive into the substrate as deep as possible. The interesting result of the studied systems is that the difference in bond strengths between the ``normal'' and substitutional geometries is sufficiently large to kick out a surface Al atom.