When size determines crystal structure: crossover between cubic and hexagonal structures of molybdenum carbide...

Molybdenum carbide (MoC) nanoparticles (NPs) have attracted extensive interest due to their superior catalytic performance, yet studying the properties of realistic, experimental-scale models by means of first principles-based methods remains computationally unfeasible. Here, an efficient on-the-fly machine learning force field (MLFF) workflow was employed to overcome this difficulty. By sampling bulks, slabs, and clusters at the cost of thousands of DFT single-point calculations only, the present approach reliably predicts the properties of large-scale NPs. Our results revealed that subnanometric cubic δ-MoC clusters are energetically stable, whereas metastable hexagonal α-MoC clusters exhibit greater structural flexibility. Furthermore, a phase transition crossover diameter at ∼4.3 nm was identified, beyond which bulk-like α-MoC NPs replace δ-MoC ones as the most stable morphology. This rationalizes prior experimental observations that cubic δ-MoC phases are prevalent at small sizes while hexagonal α-MoC phases dominate the large particle size regime. The present study not only provides an efficient workflow to build reliable MLFFs for realistic transition metal carbide NPs but also provides critical insights into the size-dependent morphology to guide the rational design of MoC-based nanocatalysts and related materials.