Fig. 4: Stone–Wales transformation converting honeycomb structure into square-triangle tiling and rhombus formation by incorporation of additional oxygen.
From: 2D honeycomb transformation into dodecagonal quasicrystals driven by electrostatic forces
a Transition from a honeycomb lattice by subsequent Stone–Wales (S–W) transformations into a structure of four- and seven-member rings. b Comparison of the DFT relaxed structures of the Ba-decorated Ti2O3 honeycomb structure and c the Ba-Ti-O sigma-phase approximant on Pt(111). The DFT calculations were performed for these commensurate Ba8Ti24O36 supercells ontop of three layers of Pt(111) (Pt not shown). The lowest energy phase is the sigma-phase approximant. d The addition of one oxygen atom to a Ti-O-Ti edge of two adjoining hexagons leads upon relaxation to the n = 10 ring of the oxide QC (compare central n = 10 ring with those in Fig. 2).
