Defect formation and migration in zirconium carbide under charge variation: A first-principles study

Abstract

Zirconium carbide (ZrC), a high-performance refractory ceramic, exhibits complex defect dynamics that critically influence its behavior in extreme environments. In this work, we employ density functional theory (DFT) simulations to determine the formation energies and migration barriers of four defect types—isolated carbon vacancies, divacancies, Frenkel pairs, and Schottky pairs—across various charge states. The calculated formation energies reveal that isolated carbon vacancies are the most energetically favorable (1.13 eV), followed by Frenkel pairs (3.29 eV), while divacancies (6.86 eV) and Schottky pairs (8.29 eV) require higher formation energies, indicating their lower intrinsic concentrations. Isolated carbon vacancies exhibit the highest migration barrier (4.11 eV) in ZrC, with a modest increase to 4.13 eV upon adding one electron to 64-atom supercell and a decrease to 4.06 eV with two electrons/64-atom supercell—reflecting charge redistribution that stabilizes the local environment and weakens nearby Zr–C bonds. In contrast, Frenkel and Schottky pairs show barrier increases with electron doping and decreases with holes (ranging from 3.26 to 3.44 eV and 3.37 to 3.73 eV, respectively), while divacancies display increases (carbon vacancies: 2.69 to 2.93 eV; zirconium vacancies: 3.60 to 3.69 eV) upon electron addition. These results reveal the defect-specific impact of charge carriers on mobility in ZrC, offering key insights for optimizing its performance in extreme environments.