Decagonal Sn clathrate on d -Al-Ni-Co

Decagonal quasiperiodic ordering of Sn thin films on $d$-Al-Ni-Co is shown based on scanning tunneling microscopy (STM), low-energy electron diffraction, and density functional theory (DFT). Interestingly, the decagonal structural correlations are partially retained even up to a large film thickness of 10 nm grown at $165\ifmmode\pm\else\textpm\fi{}10\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. The nucleation centers called ``Sn white flowers'' identified by STM at submonolayer thickness are recognized as valid patches of the decagonal clathrate structure with low adsorption energies of these motifs. Due to the excellent lattice matching (to within 1%) between columns of Sn dodecahedra in the clathrate structure and pentagonal motifs at the $d$-Al-Ni-Co surface, the interfacial energy favors clathrate over the competing Sn crystalline forms. DFT study of the Sn/Al-Ni-Co composite model shows good mechanical stability, as shown by the work of separation of Sn from Al-Ni-Co slab that is comparable to the clathrate self-separation energy. The relaxed surface terminations of the ${\mathrm{R}}₂{\mathrm{T}}₄$ clathrate approximant are in self-similarity correspondence with the motifs observed in the STM images from monolayer to the thickest Sn film.