The atomically resolved real-space structure of a long-range-ordered dodecagonal quasicrystal is determined based on scanning tunnelling microscopy. For the BaTiO3-derived oxide quasicrystal which spontaneously forms on a Pt(111) surface, 8100 atomic positions have been determined and are compared with an ideal Niizeki–Gähler tiling. Although the Niizeki–Gähler tiling has a complex three-element structure, the abundance of the triangle, square and rhomb tiling elements in the experimental data closely resembles the ideal frequencies. Similarly, the frequencies of all possible next-neighbour tiling combinations are, within the experimental uncertainty, identical to the ideal tiling. The angular and orientational distributions of all individual tiling elements show the characteristics of the dodecagonal quasicrystal. In contrast, the analysis of the orientation of characteristic and more complex tiling combinations indicates the partial decomposition of the quasicrystal into small patches with locally reduced symmetry. These, however, preserve the long-range quasicrystal coherence. The symmetry reduction from dodecagonal to sixfold is assigned to local interaction with the threefold substrate. It leads to atomic flips which preserve the number of quasicrystal tiling elements.

中文翻译：

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十二角准晶体的全实空间分析


基于扫描隧道显微镜确定了长程有序十二角准晶体的原子分辨实空间结构。对于在 Pt(111) 表面自发形成的 BaTiO3 衍生氧化物准晶，已确定了 8100 个原子位置，并与理想的 Niizeki-Gähler 平铺进行了比较。尽管 Niizeki-Gähler 平铺具有复杂的三元素结构，但实验数据中三角形、正方形和菱形平铺元素的丰富度与理想频率非常相似。类似地，在实验不确定性范围内，所有可能的相邻平铺组合的频率与理想平铺相同。所有单个平铺元件的角度和方向分布显示了十二角准晶体的特征。相反，对特征和更复杂的平铺组合的方向的分析表明准晶体部分分解成具有局部对称性降低的小斑块。然而，这些保留了长程准晶体相干性。对称性从十二角形减少到六角形归因于与三重底物的局部相互作用。它导致原子翻转，从而保留准晶体平铺元素的数量。