Accelerated Approach toward Predicting Coverage-Dependent Surface Free Energies on Transition-Metal Surfaces

Equilibrium morphologies of promoted nanoparticles are determined by Wulff constructions, which require surface free energies of promoter-decorated crystal planes as inputs. Computing these surface free energies with density functional theory (DFT) is challenging because of the large configurational space of adsorbed promoters. We present a physics-based surrogate model for determining surface free energies that is inspired by ab initio thermodynamics formalisms. This model estimates the surface free energies (Ω) of arbitrary (hkl) planes decorated with promoters, on-the-fly, with accuracies of ∼0.005 eV/Ų compared to DFT. Using this surrogate model, we determine Ω using a brute-force enumeration of different coverages of sulfur on the Pt(hkl) facets. The Ω values are then used to construct ab initio phase diagrams. These phase diagrams reveal that the equilibrium sulfur coverages for the (111) facets are between 0.25 and 0.5 monolayers, for the (100) facet is 0.5 monolayers, while for the (211) edge-sites between 0.5 and 0.83 monolayers of sulfur at a temperature of 730 K, and for ratios of the H₂S/H₂ partial pressures ranging from 10^–12 to 10¹². These Ω values are input into Wulff constructions to understand how the adsorption of sulfur alters nanoparticle morphologies. Sulfur transforms the shape of Pt nanoparticles by enhancing the proportion of the (111) and (100) facets while reducing the fraction of the (211) facet. This structural transformation results in a greater number of terrace sites compared to edgesites. Our easily trainable surrogate model for surface free energies not only provides insights into the morphological changes of nanoparticles at equilibrium but can also identify equilibrium structures for the most abundant reaction intermediates. In future, our approach can be harnessed to develop more realistic surface structures for constructing microkinetic models.