Quasicrystal approximants in the two-dimensional Ba-Ti-O system on Pd(111): A LEED, XPS, and STM study

Long-range aperiodically ordered dodecagonal oxide quasicrystals (OQCs) have been observed on Pt(111), together with a variety of related approximants. All structures contain barium, titanium, and oxygen atoms in ${\mathrm{Ti}}_n{\mathrm{O}}_n$ ring structures with rings of $n$ = 4, 7, and 10. Barium decorates the larger rings and forms a dodecagonal square-triangle-rhombus tiling. In contrast to these studies on Pt(111), we report here on Ba-Ti-O layers on Pd(111), which has a 1% smaller lattice constant than Pt(111). We find a series of quasicrystal approximants with unit cells consisting of up to 60 triangles, 22 squares, and eight rhombuses. The latter resembles the largest quasicrystal approximant reported to date. The basis for these structures are local patches of the $\ensuremath{\sigma}$-phase square-triangle approximant, into which rhombuses are incorporated due to the formation of ordered antiphase domain boundaries in two orthogonal directions. A structural phase diagram of all quasicrystal approximants on Pd(111) system is presented.