Bulk termination of the quasicrystalline fivefold surface ofAl70Pd21Mn9

Abstract

The structure of the ${\mathrm{Al}}_{70}{\mathrm{Pd}}_{21}{\mathrm{Mn}}_{9}$ surface has been investigated using high-resolution scanning tunneling microscopy. From two large fivefold terraces on the surface in a short decorated Fibonacci sequence, atomically resolved surface images have been obtained. One of these terraces carries a rare local configuration in the form of a ring. The location of the corresponding sequence of terminations in the bulk model $\mathcal{M}$ of icosahedral i-AlPdMn based on the three-dimensional tiling ${\mathcal{T}}^{*(2F)}$ of an F phase has been estimated using this ring configuration and the requirement from low-energy electron diffraction work of Gierer et al. that the average atomic density of the terminations is 0.136 atoms per ${\mathrm{\AA{}}}^{2}.$ A termination contains two atomic plane layers separated by a vertical distance of 0.48 \AA{}. The position of the bulk terminations is fixed within the layers of Bergman polytopes in the model $\mathcal{M}:$ they are 4.08 \AA{} in the direction of the bulk from a surface of the most dense Bergman layers. From the coding windows of the top planes in terminations in $\mathcal{M}$ we conclude that a Penrose (P1) tiling is possible on almost all fivefold terraces. The shortest edge of the tiling P1 is either 4.8 or 7.8 \AA{}. The experimentally derived tiling of the surface with the ring configuration has an edge length of $8.0\ifmmode\pm\else\textpm\fi{}0.3\mathrm{\AA{}}$ and hence matches the minimal edge length expected from the model.