fig1

Figure 1. Cluster-glue-atom model in MC-type carbides. (A) Atomic structure of ZrC structure, showing that the CN6 cluster polyhedron is centered by a C atom (green sphere) and surrounded by six metal atoms (blue spheres); (B) Vacancy-ordered structure extracted from a 3 × 3 × 3 supercell of MC, showing the vacancy channels along the [211] direction; (C and D) Derived cluster units for M₆C₅ and M₆C₄, illustrating the arrangement of vacancies within the channel framework; (E and F) Three-dimensional periodic supercells of M₆C₅ and M₆C₄, constructed by the stacking of cluster units shown in (C and D). The cluster models were generated using the Visualization for Electronic and Structural Analysis (VESTA) software.