Ab initiostudy of quasiperiodic monolayers on a fivefoldi−AlPdMnsurface

Abstract

We present a structural model for quasiperiodic monolayers formed on the fivefold surface of an icosahedral AlPdMn quasicrystal, based on ab initio density functional calculations. As a starting point we have investigated the relative stability of unsupported triangular, square, and quasiperiodic monolayers. The unsupported quasiperiodic monolayers are shown to be unstable upon relaxation by interatomic forces. This result indicates the important role of the adsorbate/substrate interaction for the stabilization of a quasiperiodic layer. The structural model of a monolayer adsorbed on the fivefold surface has been constructed on the basis of a mapping of the potential-energy landscape of an isolated adatom on the $i\text{\ensuremath{-}}\mathrm{Al}\mathrm{Pd}\mathrm{Mn}$ substrate. The structure of a clean fivefold $i\text{\ensuremath{-}}\mathrm{Al}\mathrm{Pd}\mathrm{Mn}$ surface is well described by a $P1$ tiling, with the vertices of the tiling located in the centers of $B$ (Bergman) clusters and occupied by Pd atoms. The potential-energy mapping emphasizes the important role of the $P1$ skeleton for the stabilization of a quasiperiodic adlayer: adsorption at the vertices of the $P1$ tiling leads to high binding energies of $\ensuremath{\simeq}4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\text{atom}$. The midedge positions of the $P1$ tiling and Mn atoms exposed at the surface are identified as further favorable adsorption sites. Altogether this leads to a structural model of the quasiperiodic adlayer with atoms at the vertices and midedge positions of the $P1$ tiling, centered pentagonal motifs decorating the pentagonal tiles, and one additional atom in the center of the pentagonal star and of the boat tile. For this structure we calculate a surface coverage of $\ensuremath{\simeq}0.09\phantom{\rule{0.3em}{0ex}}\text{atoms}∕{\mathrm{\AA{}}}^{2}$ in perfect agreement with experiment. The diffraction pattern of the adlayer exhibits (pseudo)decagonal symmetry. The structural stability of a $2∕1$ approximant to this model has been tested for Sn, Bi, and Sb monolayers via relaxation by the Hellmann-Feynman forces from ab initio density function theory calculations. The skeleton of adsorbed monolayers based on the $P1$ tiling was found to be stable, although the atomic decoration inside the tiles is partially distorted, albeit without violating the overall symmetry.