Nanoparticle Size Effects on Phase Stability for Molybdenum and Tungsten Carbides

Transition-metal carbides (TMCs) are important materials for a variety of applications and industrial processes, in part because of their variable crystal structures and surfaces. However, the synthesis of TMCs often proceeds through metastable phases during particle growth, the appearance of which cannot be described by traditional phase diagrams. Here, we use density functional theory calculations and thermodynamic analyses to construct particle size-dependent phase diagrams for Mo and W carbides and reveal the relationships between phase stability and TMC nanoparticle size. We compute size-dependent phase diagrams for a wide range of Mo carbide and W carbide phases, determine predicted crystallization pathways during synthesis, and compare model results with experimental data. We provide insights for the influence of nanoparticle size on TMC nucleation and growth during synthesis and provide a computationally guided road map for navigating the synthesis of target TMC surfaces and phases.