  Decagonal quasiperiodic ordering of Sn thin film 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 up to a large film thickness of 10 nm grown
at a 165$\pm$10 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. 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 clathrate self-separation energy. The relaxed surface terminations of the
R$_2$T$_4$ clathrate approximant are in self-similarity correspondence with the
motifs observed in the STM images from monolayer to thickest Sn film.
