Lattice Monte Carlo Simulation of Atomic Ordering in Gold-Silver Nanocages

We present a two-stage lattice Monte Carlo method for predicting atomic ordering, surface segregation, and cavity healing in hollow Au–Ag nanocages. Starting from face-centered cubic (fcc) and icosahedral templates (4500 sites), we construct 3000-atom cages with Au:Ag ratios of 1:1, 1:3, and 3:1. We propose a modification to the Warren–Cowley short-range order parameter, in which atomic concentrations are calculated locally, taking into account atomic coordination numbers. This makes it applicable to nanoparticles with pronounced surface segregation. Our results indicate that Ag preferentially enriches outer layers and vertices, while Au tends to occupy subsurface sites, lowering energy by 5–10 meV/atom relative to random alloys. In systems with a high Au:Ag ratio, the inner layers are nearly free of Ag, while systems with a low Au:Ag ratio have the maximum number of mixed Ag–Au bonds and a more uniform local order. Our computational pipeline—capable of performing millions of Monte Carlo moves per minute—can be extended to multicomponent systems and off-lattice potentials for rapid nanocage design.