Fig. 4. Establishment of the thermodynamic equilibrium model.

a Representative HRTEM image of Au-3 nm-H400. b Schematic of encapsulation of Au particle (in a spherical segment) by TiO₂ support. r (black arrow) represents the radius of Au particle, and γ_Au (orange arrow), ${\gamma }_{{\mathrm{TiO}}_{2-x}}$ (red arrow), and γ_int (blue arrow) are the surface tensions of the Au particle, TiO₂ support, and the interface between them. The thick and thin dashed red line in (b) indicate the outline of the encapsulation layer and the outline of the original TiO₂ support, respectively.