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. 2025 Dec 9;17:672. doi: 10.1038/s41467-025-67318-y

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© The Author(s) 2025

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Fig. 4 — Partial radial distribution function, g(r), with the bulk amorphous a aRuO₂, b aRuO_1.75, and c aRuO_1.50 structures, where the highest peak for the Ru–O, O–O, and Ru–Ru bond pairs is denoted by black, red, and blue dotted lines. d Stability of amorphous surfaces under oxygen-rich condition. e Top view of amorphous RuO_x surfaces. Calculated Gibbs free energy diagrams of aRuO_2.08 surface for f AEM and g LOM. In a, b, c, e, f, g, Ru, O, H atoms are denoted by violet, yellow, and white spheres, respectively. Darker RuO_x polyhedra denote highly undercoordinated Ru atoms.