Rational Synthesis of Iron Carbide Nanocatalysts for Fischer–Tropsch Synthesis: The Role of Carbon Chemical Potential

Understanding nanoparticle phase behavior under reactive conditions is critical for rational catalyst design in sustainable energy technologies. Yet, the phase transformations of multielement catalytic solids remain poorly understood, particularly when accompanied by compositional changes in reactive environments. Using iron carbide (Fe_<i>x</i>C_<i>y</i>) as a model system, we investigate size-dependent phase stability and transformation kinetics across various chemical environments relevant to Fischer-Tropsch synthesis. By integrating nanoscale thermodynamics and kinetics into a unified theoretical framework, we construct comprehensive phase diagrams that explain the anomalous predominance of the <i>χ</i>-Fe₅C₂ phase and the rarity of the Fe₇C₃ phase─a longstanding puzzle in heterogeneous catalysis. Located at the intersection of all other phase stability regions across a broad range of carbon chemical potentials and particle sizes, <i>χ</i>-Fe₅C₂ functions as a central hub, facilitating transitions among various iron carbide phases, and has relatively low formation kinetic barriers from neighboring phases. In contrast, Fe₇C₃ is thermodynamically stable and kinetically favorable only within a very narrow range (approximately 0.03 eV) of carbon chemical potential at relatively large particle sizes. Our theoretical predictions, rigorously validated through precisely designed phase transformation experiments, reveal how nanoscale effects fundamentally govern phase selectivity and transformation pathways in iron carbides. This integrated approach provides mechanistic insights into the <i>in situ</i> formation and interconversion of catalytically active phases and establishes a general framework for predicting and manipulating phase behavior in complex multielement nanocatalysts for carbon-neutral fuel production and environmental applications.