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Packing Sierpiński Triangles into Two-Dimensional Crystals.

Fractals are of fundamental importance in science and technology. Theoretical simulations indicate that Sierpiński triangles (STs) possess specific optical and electronic properties. To study their properties and uncover their potential applications, it is necessary to pack STs into large-scale two-dimensional crystalline structures. Here, a series of ordered structures consisting of ST units are successfully constructed on gold surfaces through coordination between 1,3-bis(4-pyridyl) benzene molecules and Fe atoms. Crystals of STs are characterized by scanning tunneling microscopy. K-map analysis explains the structural formation mechanism, which is further verified by density functional theory calculations. The molecular free diffusion and nice structure matching between STs and gold surfaces play important roles in the formation of crystals of STs.