Size-Dependent Thermodynamic Analyses for Transition Metal Carbides and Supported Oxides

Transition metal carbides (TMCs) and supported metal oxides are key catalysts in various industrial processes due to their versatile properties. TMCs have applications in fuel cells, batteries, and biomass conversion, while supported metal oxide catalysts are used in chemical processing, pollution control, and petroleum refining. However, synthesis of these catalysts face challenges such as size dependency and complex phase behavior. Here, we employ Density Functional Theory (DFT) calculations to analyze the phase stability of molybdenum and tungsten carbides (TMCs) and titania and silica supported tungsten oxide clusters under varying synthesis conditions and sizes. Our modified phase diagrams consider factors such as particle size integrated with synthesis/reaction conditions, which is used to reveal metastable landscapes that change with these parameters. For TMCs, we focus on nanoparticles (>2 nm) generated in vacuum, while for supported tungsten oxide catalysts, we examine sub-nanometer clusters (monomers, dimers, and trimers) on the two supports. The size dependency for TMC nanoparticles was studied using particle-size dependent phase diagrams. For the supported tungsten oxide catalysts, we used both separate phase diagrams for each domain size, and diagrams that combine all domain sizes for a given support. The thermodynamic analysis in this work advances our understanding of catalyst stability and performance and increases our fundamental understanding of the relationships between material properties, reaction conditions, and catalytic behavior.