Extended Data Fig. 10: The oxygen-oxygen radial distribution function (RDF) of two superstructures and the ideal 1 × 1 surfaces.

a, The RDF graph containing both experimental and theoretical data. g_OO(r) defines the probability of finding an O atom at a distance r from another O atom within the upper part of the topmost bilayer. The green curve is statistically derived from the AFM image of superstructures, with binomial smoothing. The black, red and blue curves are obtained by averaging all surface structures with different S_OH in simulation (64 structures for both ideal 1×1 phase and \(\sqrt{19}\times \sqrt{19}\) phase, 29 structures for \(2\sqrt{19}\times \sqrt{19}\) phase), using a bin size of 0.2 Å. The simulation results have good agreement with the experiment values. The calculated truncation distance of 5.5 Å effectively distinguishes the first nearest neighbors of the undercoordinated water molecules within the upper part of the topmost bilayer, consistent with the definition of S_OH. b, The top view of schematic \(\sqrt{19}\times \sqrt{19}\) phase. In the superstructures, the nearest-neighbor peak (ranging from 3.8 to 5.4 Å) exhibits significant broadening compared to that of the ideal surface (ranging from 3.9 to 4.5 Å). Such a difference arises from the nearest-neighbor water molecules within the five, seven and eight-membered rings at the defective boundaries, indicated by black (average distance: 4.1 Å) and green (average distance: 4.9 Å) lines in b. Compared to the ideal surface, the next nearest-neighbor peak is also broader and gets closer to the nearest-neighbor peak in superstructures, typically resulting from the next nearest-neighbor water pairs (average distance: 6.55 Å) crossing the defective boundaries, indicated by purple lines in b.