Self-assembly of Carbon Vacancies in Sub-stoichiometric ZrC(1−x)

Sub-stoichiometric interstitial compounds, including binary transition metal carbides (MC(1−x)), maintain structural stability even if they accommodate abundant anion vacancies. This unique character endows them with variable-composition, diverse-configuration and controllable-performance through composition and structure design. Herein, the evolution of carbon vacancy (V(C)) configuration in sub-stoichiometric ZrC(1−x) is investigated by combining the cluster expansion method and first-principles calculations. We report the interesting self-assembly of V(C)s and the fingerprint V(C) configuration (V(C) triplet constructed by 3(rd) nearest neighboring vacancies) in all the low energy structures of ZrC(1−x). When V(C) concentration is higher than the critical value of 0.5 (x > 0.5), the 2(nd) nearest neighboring V(C) configurations with strongly repulsive interaction inevitably appear, and meanwhile, the system energy (or formation enthalpy) of ZrC(1−x) increases sharply which suggests the material may lose phase stability. The present results clarify why ZrC(1−x) bears a huge amount of V(C)s, tends towards V(C) ordering, and retains stability up to a stoichiometry of x = 0.5.