Structure and morphology of the tenfold surface of decagonalAl71.8Ni14.8Co13.4in its low-temperature random tiling type-I modification

Abstract

We have investigated the structure and morphology of the tenfold surface of decagonal ${\mathrm{Al}}_{71.8}{\mathrm{Ni}}_{14.8}{\mathrm{Co}}_{13.4}$ by highly surface sensitive He atom scattering (HAS), high resolution low energy electron diffraction(SPA-LEED), and low temperature scanning tunneling microscopy (STM). The SPA-LEED patterns reveal more than 500 individual diffraction spots in the $\mathbf{k}$-vector range of $\ensuremath{\mid}{\mathbf{k}}_{\ensuremath{\Vert}}\ensuremath{\mid}l3\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}1}$. The positions of all observed diffraction spots agree with the surface projections of the reciprocal lattice structure of the type-I bulk phase. HAS shows identical spot positions as SPA-LEED, thus demonstrating a top surface layer with long range quasicrystalline order and a reciprocal lattice structure consistent with that of a bulk truncated surface. SPA-LEED peak widths are found to vary between different diffraction orders. Based on an analysis of a randomized Fibonacci sequence, this is linked to the random nature of the tiling of the type-I structure. STM measurements reveal a surface morphology characterized by rough single-height steps separating terraces with widths on the order of $100\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$. Two different surface terminations are observed, a coarse and a fine one, frequently coexisting on single terraces. The fine structure termination directly reflects the atomic structure of a bulk truncated surface, allowing a random rhombic tiling to be identified. In order to compare diffraction, real-space data, and atomic structure models, the Patterson function and autocorrelation of the surface structure, respectively, are studied. This allows an understanding of the coarse structure termination as consisting of subunits of a few atoms each arranged statistically on sites defined by the atomic tiling of the bulk tenfold planes.