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.