Synthesizability, hardness, and stacking order in multicomponent transition metal carbides from machine-learned potentials

Abstract Multicomponent transition metal carbides are promising for extreme-environment applications, but identifying compositions that are both synthesizable and hard remains challenging. We fine-tune the MACE machine-learned interatomic potential on approximately 28,000 density functional theory calculations spanning the composition space of groups 4–6 transition metals and carbon to predict the thermodynamic stability and elastic properties of multicomponent carbides. The fine-tuned model achieves formation energy errors of ~10 meV/atom for thermodynamically relevant structures with only 20% of the training data. We screen over 1500 equiatomic compositions across rocksalt, hexagonal, and hcp prototypes, combining free energy models with elasticity-based hardness surrogates. Synthesizability predictions at 1500 °C agree well with experimental reports for both single-phase and multiphase carbides. The group number of the constituent metals governs both stability and hardness. Short-range order contributes only a few meV/atom to the free energy, so the disordered phase can be treated as a random solid solution when screening rocksalt carbides at high temperature. For compositions mixing group 4/5 and group 6 metals, we identify a new family of stacking-ordered phases with formation energies well below those of disordered rocksalt or hexagonal structures. DFT calculations corroborate these predictions and suggest that stacking-ordered phases should be experimentally accessible in multicomponent carbides. This study provides a framework for screening synthesizable multicomponent materials with target properties, identifies promising carbide compositions across the full nine-component space, and reveals a new class of stacking-ordered carbides accessible only in multicomponent compositions.