(696e) Accelerated Phase Diagrams for Metal Carbide Catalysts Under Reaction Conditions Using a Graph-Based Approach

Metal carbide catalysts evolve into oxy-carbide phases during the hydrodeoxygenation of biomass, dry reforming of methane, and ethanol dehydration. Prior studies indicate that oxy-carbide formation is dictated by the chemical potentials of the reductant (e.g., CH₄) and oxidizing gases (e.g., CO₂). The atomic structure of such oxy-carbide phases has however not yet been determined. We present a graph-based approach that determines the equilibrium coverage of oxy-carbide surfaces as a function of the chemical potential of the environment (CH₄:CO₂ ratio) on (100), (111), and (110) surfaces of early transition metal carbides (VC and TiC). Co-adsorbate interactions between oxygen atoms on the surface are partitioned as pair-wise interactions. The pair-wise interactions are in turn, determined using a distance-dependent quadratic function, whose form is inspired by generalized additive models in machine learning. The functions are constructed based of three observations: (a) co-adsorbate interactions rapidly decay with distance, (b) co-adsorbate interactions are confined to within three nearest neighbours of the active site, and (c) co-adsorbate interactions have weak structure sensitivity. The quadratic functions are trained on density functional theory calculations of O* adsorbed across top, bridge, and hollow sites having coverages ranging from 1/8 to 1 monolayer. The functions yield surface energies under reaction conditions with errors of 4 meV/Ų. These errors are comparable with more sophisticated yet less interpretable neural networks. Upon training the model, we then determine surface energies of 4000+ crystal planes on low index surfaces of TiC, essentially on-the-fly. We down select the most stable surfaces under a given reaction environment and validate their energies with explicit DFT calculations. We employ this tool to determine the most stable (100), (111), and (110) surfaces of VC, as the CH₄:CO₂ ratio is varied. These surface energies are inputted into Wulff constructions, thus revealing how the formation of oxy-carbides alters the carbide morphology.