A four-dimensional model for the Ba–Ti–O dodecagonal quasicrystal

Abstract

A four-dimensional (4D) model is presented of the first oxide dodecagonal quasicrystal found in a Ba–Ti–O ultra-thin film on a Pt(111) single-crystal substrate. The 4D model, with a 4D dodecagonal lattice constant a d  = 8.39 Å, was derived by considering a tile decoration model of dodecagonal Niizeki–Gähler tiling composed of squares, triangles and 30° rhombuses. The model consists of four kinds of occupation domain, and 4D positional vectors defining the shape of each occupation domain are given. Moreover, the atomic arrangement of two Ba–Ti–O periodic approximants, the sigma-phase approximant and a 25.6 Å approximant were derived from the 4D model by the introduction of linear phason strains.