Understanding AuPd Alloy Nanoparticle Structure under Vacuum Using DFT and Monte Carlo Methods

AuPd is a miscible metal alloy that is often used in catalysis. Supported AuPd catalysts, at high Au/Pd ratios, form single-atom alloys (SAAs) that have been shown to enhance rates and/or selectivities for many catalytic reactions, including (de)hydrogenations, hydrogenolysis, and C–C and C–O coupling reactions. While many computational studies have examined the stability of AuPd structures (the arrangement of atoms within the miscible alloy), most focused on generic alloys rather than SAAs and those that have closely investigated SAAs focused on single crystal surfaces. In this work, we use density functional theory (DFT) to calculate exchange energies (swapping an Au atom with a Pd atom) in a 201-atom truncated octahedral nanoparticle model with a focus on particles with high Au/Pd ratios. We calculate these exchange energies as a function of Pd location within the nanoparticle, the number of Pd atoms neighboring and near those exchange sites, and the total Pd content in the nanoparticle. These DFT-calculated exchange energies are also used to inform simple physics-based models (in contrast to cluster expansion or neural network models) that show good agreement with DFT-calculated values with relatively few regressed parameters. These models are then implemented into Monte Carlo (MC) simulations to predict the nanoparticle structure as a function of composition and temperature. The results show that Pd prefers to be in the subsurface of nanoparticles and that Pd prefers to be isolated from itself within Au. Both observations agree well with prior experimental and computational studies of single-crystal systems. We also show that the overall composition of the nanoparticle influences exchange energies by changing the electronic properties (e.g., Fermi level) of the system, which is relevant as Pd has one fewer valence electron than Au. MC simulations show that, in a vacuum, Pd begins to populate the surface of these ∼2 nm nanoparticles at around 20 mol % Pd (at 298 K) and that the number of Pd surface monomers, desired for SAA applications, goes through a maximum near 40 mol % Pd. As the temperature increases, Pd is more prevalent at the surface, but the influence of temperature is relatively muted. While AuPd structures are known to change in the presence of reactive gases (e.g., CO or O₂), these studies characterize the baseline thermodynamic arrangements that can be used to understand surface restructuring during catalyst characterization and reaction studies.